Coding for reliable satellite communications

NASA Technical Reports Server (NTRS)

Gaarder, N. T.; Lin, S.

1986-01-01

This research project was set up to study various kinds of coding techniques for error control in satellite and space communications for NASA Goddard Space Flight Center. During the project period, researchers investigated the following areas: (1) decoding of Reed-Solomon codes in terms of dual basis; (2) concatenated and cascaded error control coding schemes for satellite and space communications; (3) use of hybrid coding schemes (error correction and detection incorporated with retransmission) to improve system reliability and throughput in satellite communications; (4) good codes for simultaneous error correction and error detection, and (5) error control techniques for ring and star networks.

Joint Schemes for Physical Layer Security and Error Correction

ERIC Educational Resources Information Center

Adamo, Oluwayomi

2011-01-01

The major challenges facing resource constraint wireless devices are error resilience, security and speed. Three joint schemes are presented in this research which could be broadly divided into error correction based and cipher based. The error correction based ciphers take advantage of the properties of LDPC codes and Nordstrom Robinson code. A…

Error correcting coding-theory for structured light illumination systems

NASA Astrophysics Data System (ADS)

Porras-Aguilar, Rosario; Falaggis, Konstantinos; Ramos-Garcia, Ruben

2017-06-01

Intensity discrete structured light illumination systems project a series of projection patterns for the estimation of the absolute fringe order using only the temporal grey-level sequence at each pixel. This work proposes the use of error-correcting codes for pixel-wise correction of measurement errors. The use of an error correcting code is advantageous in many ways: it allows reducing the effect of random intensity noise, it corrects outliners near the border of the fringe commonly present when using intensity discrete patterns, and it provides a robustness in case of severe measurement errors (even for burst errors where whole frames are lost). The latter aspect is particular interesting in environments with varying ambient light as well as in critical safety applications as e.g. monitoring of deformations of components in nuclear power plants, where a high reliability is ensured even in case of short measurement disruptions. A special form of burst errors is the so-called salt and pepper noise, which can largely be removed with error correcting codes using only the information of a given pixel. The performance of this technique is evaluated using both simulations and experiments.

Performance analysis of a cascaded coding scheme with interleaved outer code

NASA Technical Reports Server (NTRS)

Lin, S.

1986-01-01

A cascaded coding scheme for a random error channel with a bit-error rate is analyzed. In this scheme, the inner code C sub 1 is an (n sub 1, m sub 1l) binary linear block code which is designed for simultaneous error correction and detection. The outer code C sub 2 is a linear block code with symbols from the Galois field GF (2 sup l) which is designed for correcting both symbol errors and erasures, and is interleaved with a degree m sub 1. A procedure for computing the probability of a correct decoding is presented and an upper bound on the probability of a decoding error is derived. The bound provides much better results than the previous bound for a cascaded coding scheme with an interleaved outer code. Example schemes with inner codes ranging from high rates to very low rates are evaluated. Several schemes provide extremely high reliability even for very high bit-error rates say 10 to the -1 to 10 to the -2 power.

Correcting quantum errors with entanglement.

PubMed

Brun, Todd; Devetak, Igor; Hsieh, Min-Hsiu

2006-10-20

We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error-correcting codes, thus allowing us to "quantize" all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement enables quantum communication.

Asymmetric Memory Circuit Would Resist Soft Errors

NASA Technical Reports Server (NTRS)

Buehler, Martin G.; Perlman, Marvin

1990-01-01

Some nonlinear error-correcting codes more efficient in presence of asymmetry. Combination of circuit-design and coding concepts expected to make integrated-circuit random-access memories more resistant to "soft" errors (temporary bit errors, also called "single-event upsets" due to ionizing radiation). Integrated circuit of new type made deliberately more susceptible to one kind of bit error than to other, and associated error-correcting code adapted to exploit this asymmetry in error probabilities.

Is a Genome a Codeword of an Error-Correcting Code?

PubMed Central

Kleinschmidt, João H.; Silva-Filho, Márcio C.; Bim, Edson; Herai, Roberto H.; Yamagishi, Michel E. B.; Palazzo, Reginaldo

2012-01-01

Since a genome is a discrete sequence, the elements of which belong to a set of four letters, the question as to whether or not there is an error-correcting code underlying DNA sequences is unavoidable. The most common approach to answering this question is to propose a methodology to verify the existence of such a code. However, none of the methodologies proposed so far, although quite clever, has achieved that goal. In a recent work, we showed that DNA sequences can be identified as codewords in a class of cyclic error-correcting codes known as Hamming codes. In this paper, we show that a complete intron-exon gene, and even a plasmid genome, can be identified as a Hamming code codeword as well. Although this does not constitute a definitive proof that there is an error-correcting code underlying DNA sequences, it is the first evidence in this direction. PMID:22649495

Spatially coupled low-density parity-check error correction for holographic data storage

NASA Astrophysics Data System (ADS)

Ishii, Norihiko; Katano, Yutaro; Muroi, Tetsuhiko; Kinoshita, Nobuhiro

2017-09-01

The spatially coupled low-density parity-check (SC-LDPC) was considered for holographic data storage. The superiority of SC-LDPC was studied by simulation. The simulations show that the performance of SC-LDPC depends on the lifting number, and when the lifting number is over 100, SC-LDPC shows better error correctability compared with irregular LDPC. SC-LDPC is applied to the 5:9 modulation code, which is one of the differential codes. The error-free point is near 2.8 dB and over 10-1 can be corrected in simulation. From these simulation results, this error correction code can be applied to actual holographic data storage test equipment. Results showed that 8 × 10-2 can be corrected, furthermore it works effectively and shows good error correctability.

Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guth, Larry, E-mail: lguth@math.mit.edu; Lubotzky, Alexander, E-mail: alex.lubotzky@mail.huji.ac.il

2014-08-15

Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are low density parity check codes with linear rate and distance n{sup ε}. Their rate is evaluated via Euler characteristic arguments and their distance using Z{sub 2}-systolic geometry. This construction answers a question of Zémor [“On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction,” in Proceedings of Second International Workshop on Coding and Cryptology (IWCC), Lecture Notes in Computer Science Vol. 5557 (2009), pp. 259–273], who asked whether homological codes with such parameters could exist at all.

Coherent errors in quantum error correction

NASA Astrophysics Data System (ADS)

Greenbaum, Daniel; Dutton, Zachary

Analysis of quantum error correcting (QEC) codes is typically done using a stochastic, Pauli channel error model for describing the noise on physical qubits. However, it was recently found that coherent errors (systematic rotations) on physical data qubits result in both physical and logical error rates that differ significantly from those predicted by a Pauli model. We present analytic results for the logical error as a function of concatenation level and code distance for coherent errors under the repetition code. For data-only coherent errors, we find that the logical error is partially coherent and therefore non-Pauli. However, the coherent part of the error is negligible after two or more concatenation levels or at fewer than ɛ - (d - 1) error correction cycles. Here ɛ << 1 is the rotation angle error per cycle for a single physical qubit and d is the code distance. These results support the validity of modeling coherent errors using a Pauli channel under some minimum requirements for code distance and/or concatenation. We discuss extensions to imperfect syndrome extraction and implications for general QEC.

Reed-Solomon error-correction as a software patch mechanism.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pendley, Kevin D.

This report explores how error-correction data generated by a Reed-Solomon code may be used as a mechanism to apply changes to an existing installed codebase. Using the Reed-Solomon code to generate error-correction data for a changed or updated codebase will allow the error-correction data to be applied to an existing codebase to both validate and introduce changes or updates from some upstream source to the existing installed codebase.

Demonstration of a quantum error detection code using a square lattice of four superconducting qubits

PubMed Central

Córcoles, A.D.; Magesan, Easwar; Srinivasan, Srikanth J.; Cross, Andrew W.; Steffen, M.; Gambetta, Jay M.; Chow, Jerry M.

2015-01-01

The ability to detect and deal with errors when manipulating quantum systems is a fundamental requirement for fault-tolerant quantum computing. Unlike classical bits that are subject to only digital bit-flip errors, quantum bits are susceptible to a much larger spectrum of errors, for which any complete quantum error-correcting code must account. Whilst classical bit-flip detection can be realized via a linear array of qubits, a general fault-tolerant quantum error-correcting code requires extending into a higher-dimensional lattice. Here we present a quantum error detection protocol on a two-by-two planar lattice of superconducting qubits. The protocol detects an arbitrary quantum error on an encoded two-qubit entangled state via quantum non-demolition parity measurements on another pair of error syndrome qubits. This result represents a building block towards larger lattices amenable to fault-tolerant quantum error correction architectures such as the surface code. PMID:25923200

Demonstration of a quantum error detection code using a square lattice of four superconducting qubits.

PubMed

Córcoles, A D; Magesan, Easwar; Srinivasan, Srikanth J; Cross, Andrew W; Steffen, M; Gambetta, Jay M; Chow, Jerry M

2015-04-29

The ability to detect and deal with errors when manipulating quantum systems is a fundamental requirement for fault-tolerant quantum computing. Unlike classical bits that are subject to only digital bit-flip errors, quantum bits are susceptible to a much larger spectrum of errors, for which any complete quantum error-correcting code must account. Whilst classical bit-flip detection can be realized via a linear array of qubits, a general fault-tolerant quantum error-correcting code requires extending into a higher-dimensional lattice. Here we present a quantum error detection protocol on a two-by-two planar lattice of superconducting qubits. The protocol detects an arbitrary quantum error on an encoded two-qubit entangled state via quantum non-demolition parity measurements on another pair of error syndrome qubits. This result represents a building block towards larger lattices amenable to fault-tolerant quantum error correction architectures such as the surface code.

Modeling coherent errors in quantum error correction

NASA Astrophysics Data System (ADS)

Greenbaum, Daniel; Dutton, Zachary

2018-01-01

Analysis of quantum error correcting codes is typically done using a stochastic, Pauli channel error model for describing the noise on physical qubits. However, it was recently found that coherent errors (systematic rotations) on physical data qubits result in both physical and logical error rates that differ significantly from those predicted by a Pauli model. Here we examine the accuracy of the Pauli approximation for noise containing coherent errors (characterized by a rotation angle ɛ) under the repetition code. We derive an analytic expression for the logical error channel as a function of arbitrary code distance d and concatenation level n, in the small error limit. We find that coherent physical errors result in logical errors that are partially coherent and therefore non-Pauli. However, the coherent part of the logical error is negligible at fewer than {ε }-({dn-1)} error correction cycles when the decoder is optimized for independent Pauli errors, thus providing a regime of validity for the Pauli approximation. Above this number of correction cycles, the persistent coherent logical error will cause logical failure more quickly than the Pauli model would predict, and this may need to be combated with coherent suppression methods at the physical level or larger codes.

NP-hardness of decoding quantum error-correction codes

NASA Astrophysics Data System (ADS)

Hsieh, Min-Hsiu; Le Gall, François

2011-05-01

Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expects degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or nondegenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.

Biometrics encryption combining palmprint with two-layer error correction codes

NASA Astrophysics Data System (ADS)

Li, Hengjian; Qiu, Jian; Dong, Jiwen; Feng, Guang

2017-07-01

To bridge the gap between the fuzziness of biometrics and the exactitude of cryptography, based on combining palmprint with two-layer error correction codes, a novel biometrics encryption method is proposed. Firstly, the randomly generated original keys are encoded by convolutional and cyclic two-layer coding. The first layer uses a convolution code to correct burst errors. The second layer uses cyclic code to correct random errors. Then, the palmprint features are extracted from the palmprint images. Next, they are fused together by XORing operation. The information is stored in a smart card. Finally, the original keys extraction process is the information in the smart card XOR the user's palmprint features and then decoded with convolutional and cyclic two-layer code. The experimental results and security analysis show that it can recover the original keys completely. The proposed method is more secure than a single password factor, and has higher accuracy than a single biometric factor.

Fast decoding techniques for extended single-and-double-error-correcting Reed Solomon codes

NASA Technical Reports Server (NTRS)

Costello, D. J., Jr.; Deng, H.; Lin, S.

1984-01-01

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. For example, some 256K-bit dynamic random access memories are organized as 32K x 8 bit-bytes. Byte-oriented codes such as Reed Solomon (RS) codes provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special high speed decoding techniques for extended single and double error correcting RS codes. These techniques are designed to find the error locations and the error values directly from the syndrome without having to form the error locator polynomial and solve for its roots.

HyDEn: A Hybrid Steganocryptographic Approach for Data Encryption Using Randomized Error-Correcting DNA Codes

PubMed Central

Regoui, Chaouki; Durand, Guillaume; Belliveau, Luc; Léger, Serge

2013-01-01

This paper presents a novel hybrid DNA encryption (HyDEn) approach that uses randomized assignments of unique error-correcting DNA Hamming code words for single characters in the extended ASCII set. HyDEn relies on custom-built quaternary codes and a private key used in the randomized assignment of code words and the cyclic permutations applied on the encoded message. Along with its ability to detect and correct errors, HyDEn equals or outperforms existing cryptographic methods and represents a promising in silico DNA steganographic approach. PMID:23984392

A (72, 36; 15) box code

NASA Technical Reports Server (NTRS)

Solomon, G.

1993-01-01

A (72,36;15) box code is constructed as a 9 x 8 matrix whose columns add to form an extended BCH-Hamming (8,4;4) code and whose rows sum to odd or even parity. The newly constructed code, due to its matrix form, is easily decodable for all seven-error and many eight-error patterns. The code comes from a slight modification in the parity (eighth) dimension of the Reed-Solomon (8,4;5) code over GF(512). Error correction uses the row sum parity information to detect errors, which then become erasures in a Reed-Solomon correction algorithm.

Noise Estimation and Adaptive Encoding for Asymmetric Quantum Error Correcting Codes

NASA Astrophysics Data System (ADS)

Florjanczyk, Jan; Brun, Todd; CenterQuantum Information Science; Technology Team

We present a technique that improves the performance of asymmetric quantum error correcting codes in the presence of biased qubit noise channels. Our study is motivated by considering what useful information can be learned from the statistics of syndrome measurements in stabilizer quantum error correcting codes (QECC). We consider the case of a qubit dephasing channel where the dephasing axis is unknown and time-varying. We are able to estimate the dephasing angle from the statistics of the standard syndrome measurements used in stabilizer QECC's. We use this estimate to rotate the computational basis of the code in such a way that the most likely type of error is covered by the highest distance of the asymmetric code. In particular, we use the [ [ 15 , 1 , 3 ] ] shortened Reed-Muller code which can correct one phase-flip error but up to three bit-flip errors. In our simulations, we tune the computational basis to match the estimated dephasing axis which in turn leads to a decrease in the probability of a phase-flip error. With a sufficiently accurate estimate of the dephasing axis, our memory's effective error is dominated by the much lower probability of four bit-flips. Aro MURI Grant No. W911NF-11-1-0268.

Quantum error-correcting codes from algebraic geometry codes of Castle type

NASA Astrophysics Data System (ADS)

Munuera, Carlos; Tenório, Wanderson; Torres, Fernando

2016-10-01

We study algebraic geometry codes producing quantum error-correcting codes by the CSS construction. We pay particular attention to the family of Castle codes. We show that many of the examples known in the literature in fact belong to this family of codes. We systematize these constructions by showing the common theory that underlies all of them.

Quantum error-correction failure distributions: Comparison of coherent and stochastic error models

NASA Astrophysics Data System (ADS)

Barnes, Jeff P.; Trout, Colin J.; Lucarelli, Dennis; Clader, B. D.

2017-06-01

We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault-tolerant quantum error correcting circuit for a d =3 Steane and surface code. We find that the output distributions are markedly different for the two error models, showing that no simple mapping between the two error models exists. Coherent errors create very broad and heavy-tailed failure distributions. This suggests that they are susceptible to outlier events and that mean statistics, such as pseudothreshold estimates, may not provide the key figure of merit. This provides further statistical insight into why coherent errors can be so harmful for quantum error correction. These output probability distributions may also provide a useful metric that can be utilized when optimizing quantum error correcting codes and decoding procedures for purely coherent errors.

Error-correction coding

NASA Technical Reports Server (NTRS)

Hinds, Erold W. (Principal Investigator)

1996-01-01

This report describes the progress made towards the completion of a specific task on error-correcting coding. The proposed research consisted of investigating the use of modulation block codes as the inner code of a concatenated coding system in order to improve the overall space link communications performance. The study proposed to identify and analyze candidate codes that will complement the performance of the overall coding system which uses the interleaved RS (255,223) code as the outer code.

Decoding of DBEC-TBED Reed-Solomon codes. [Double-Byte-Error-Correcting, Triple-Byte-Error-Detecting

NASA Technical Reports Server (NTRS)

Deng, Robert H.; Costello, Daniel J., Jr.

1987-01-01

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256 K bit DRAM's are organized in 32 K x 8 bit-bytes. Byte-oriented codes such as Reed-Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. The paper presents a special decoding technique for double-byte-error-correcting, triple-byte-error-detecting RS codes which is capable of high-speed operation. This technique is designed to find the error locations and the error values directly from the syndrome without having to use the iterative algorithm to find the error locator polynomial.

Observations on Polar Coding with CRC-Aided List Decoding

DTIC Science & Technology

2016-09-01

9 v 1. INTRODUCTION Polar codes are a new type of forward error correction (FEC) codes, introduced by Arikan in [1], in which he...error correction (FEC) currently used and planned for use in Navy wireless communication systems. The project’s results from FY14 and FY15 are...good error- correction per- formance. We used the Tal/Vardy method of [5]. The polar encoder uses a row vector u of length N . Let uA be the subvector

A simplified procedure for correcting both errors and erasures of a Reed-Solomon code using the Euclidean algorithm

NASA Technical Reports Server (NTRS)

Truong, T. K.; Hsu, I. S.; Eastman, W. L.; Reed, I. S.

1987-01-01

It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial and the error evaluator polynomial in Berlekamp's key equation needed to decode a Reed-Solomon (RS) code. A simplified procedure is developed and proved to correct erasures as well as errors by replacing the initial condition of the Euclidean algorithm by the erasure locator polynomial and the Forney syndrome polynomial. By this means, the errata locator polynomial and the errata evaluator polynomial can be obtained, simultaneously and simply, by the Euclidean algorithm only. With this improved technique the complexity of time domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches. As a consequence, decoders for correcting both errors and erasures of RS codes can be made more modular, regular, simple, and naturally suitable for both VLSI and software implementation. An example illustrating this modified decoding procedure is given for a (15, 9) RS code.

Error coding simulations in C

NASA Technical Reports Server (NTRS)

Noble, Viveca K.

1994-01-01

When data is transmitted through a noisy channel, errors are produced within the data rendering it indecipherable. Through the use of error control coding techniques, the bit error rate can be reduced to any desired level without sacrificing the transmission data rate. The Astrionics Laboratory at Marshall Space Flight Center has decided to use a modular, end-to-end telemetry data simulator to simulate the transmission of data from flight to ground and various methods of error control. The simulator includes modules for random data generation, data compression, Consultative Committee for Space Data Systems (CCSDS) transfer frame formation, error correction/detection, error generation and error statistics. The simulator utilizes a concatenated coding scheme which includes CCSDS standard (255,223) Reed-Solomon (RS) code over GF(2(exp 8)) with interleave depth of 5 as the outermost code, (7, 1/2) convolutional code as an inner code and CCSDS recommended (n, n-16) cyclic redundancy check (CRC) code as the innermost code, where n is the number of information bits plus 16 parity bits. The received signal-to-noise for a desired bit error rate is greatly reduced through the use of forward error correction techniques. Even greater coding gain is provided through the use of a concatenated coding scheme. Interleaving/deinterleaving is necessary to randomize burst errors which may appear at the input of the RS decoder. The burst correction capability length is increased in proportion to the interleave depth. The modular nature of the simulator allows for inclusion or exclusion of modules as needed. This paper describes the development and operation of the simulator, the verification of a C-language Reed-Solomon code, and the possibility of using Comdisco SPW(tm) as a tool for determining optimal error control schemes.

DNA Barcoding through Quaternary LDPC Codes

PubMed Central

Tapia, Elizabeth; Spetale, Flavio; Krsticevic, Flavia; Angelone, Laura; Bulacio, Pilar

2015-01-01

For many parallel applications of Next-Generation Sequencing (NGS) technologies short barcodes able to accurately multiplex a large number of samples are demanded. To address these competitive requirements, the use of error-correcting codes is advised. Current barcoding systems are mostly built from short random error-correcting codes, a feature that strongly limits their multiplexing accuracy and experimental scalability. To overcome these problems on sequencing systems impaired by mismatch errors, the alternative use of binary BCH and pseudo-quaternary Hamming codes has been proposed. However, these codes either fail to provide a fine-scale with regard to size of barcodes (BCH) or have intrinsic poor error correcting abilities (Hamming). Here, the design of barcodes from shortened binary BCH codes and quaternary Low Density Parity Check (LDPC) codes is introduced. Simulation results show that although accurate barcoding systems of high multiplexing capacity can be obtained with any of these codes, using quaternary LDPC codes may be particularly advantageous due to the lower rates of read losses and undetected sample misidentification errors. Even at mismatch error rates of 10−2 per base, 24-nt LDPC barcodes can be used to multiplex roughly 2000 samples with a sample misidentification error rate in the order of 10−9 at the expense of a rate of read losses just in the order of 10−6. PMID:26492348

DNA Barcoding through Quaternary LDPC Codes.

PubMed

Tapia, Elizabeth; Spetale, Flavio; Krsticevic, Flavia; Angelone, Laura; Bulacio, Pilar

2015-01-01

For many parallel applications of Next-Generation Sequencing (NGS) technologies short barcodes able to accurately multiplex a large number of samples are demanded. To address these competitive requirements, the use of error-correcting codes is advised. Current barcoding systems are mostly built from short random error-correcting codes, a feature that strongly limits their multiplexing accuracy and experimental scalability. To overcome these problems on sequencing systems impaired by mismatch errors, the alternative use of binary BCH and pseudo-quaternary Hamming codes has been proposed. However, these codes either fail to provide a fine-scale with regard to size of barcodes (BCH) or have intrinsic poor error correcting abilities (Hamming). Here, the design of barcodes from shortened binary BCH codes and quaternary Low Density Parity Check (LDPC) codes is introduced. Simulation results show that although accurate barcoding systems of high multiplexing capacity can be obtained with any of these codes, using quaternary LDPC codes may be particularly advantageous due to the lower rates of read losses and undetected sample misidentification errors. Even at mismatch error rates of 10(-2) per base, 24-nt LDPC barcodes can be used to multiplex roughly 2000 samples with a sample misidentification error rate in the order of 10(-9) at the expense of a rate of read losses just in the order of 10(-6).

Error-correcting pairs for a public-key cryptosystem

NASA Astrophysics Data System (ADS)

Pellikaan, Ruud; Márquez-Corbella, Irene

2017-06-01

Code-based Cryptography (CBC) is a powerful and promising alternative for quantum resistant cryptography. Indeed, together with lattice-based cryptography, multivariate cryptography and hash-based cryptography are the principal available techniques for post-quantum cryptography. CBC was first introduced by McEliece where he designed one of the most efficient Public-Key encryption schemes with exceptionally strong security guarantees and other desirable properties that still resist to attacks based on Quantum Fourier Transform and Amplitude Amplification. The original proposal, which remains unbroken, was based on binary Goppa codes. Later, several families of codes have been proposed in order to reduce the key size. Some of these alternatives have already been broken. One of the main requirements of a code-based cryptosystem is having high performance t-bounded decoding algorithms which is achieved in the case the code has a t-error-correcting pair (ECP). Indeed, those McEliece schemes that use GRS codes, BCH, Goppa and algebraic geometry codes are in fact using an error-correcting pair as a secret key. That is, the security of these Public-Key Cryptosystems is not only based on the inherent intractability of bounded distance decoding but also on the assumption that it is difficult to retrieve efficiently an error-correcting pair. In this paper, the class of codes with a t-ECP is proposed for the McEliece cryptosystem. Moreover, we study the hardness of distinguishing arbitrary codes from those having a t-error correcting pair.

Permanence analysis of a concatenated coding scheme for error control

NASA Technical Reports Server (NTRS)

Costello, D. J., Jr.; Lin, S.; Kasami, T.

1983-01-01

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however, the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for the planetary program, is analyzed.

Probability of undetected error after decoding for a concatenated coding scheme

NASA Technical Reports Server (NTRS)

Costello, D. J., Jr.; Lin, S.

1984-01-01

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, the inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for NASA telecommand system is analyzed.

Error coding simulations

NASA Technical Reports Server (NTRS)

Noble, Viveca K.

1993-01-01

There are various elements such as radio frequency interference (RFI) which may induce errors in data being transmitted via a satellite communication link. When a transmission is affected by interference or other error-causing elements, the transmitted data becomes indecipherable. It becomes necessary to implement techniques to recover from these disturbances. The objective of this research is to develop software which simulates error control circuits and evaluate the performance of these modules in various bit error rate environments. The results of the evaluation provide the engineer with information which helps determine the optimal error control scheme. The Consultative Committee for Space Data Systems (CCSDS) recommends the use of Reed-Solomon (RS) and convolutional encoders and Viterbi and RS decoders for error correction. The use of forward error correction techniques greatly reduces the received signal to noise needed for a certain desired bit error rate. The use of concatenated coding, e.g. inner convolutional code and outer RS code, provides even greater coding gain. The 16-bit cyclic redundancy check (CRC) code is recommended by CCSDS for error detection.

Asymmetric soft-error resistant memory

NASA Technical Reports Server (NTRS)

Buehler, Martin G. (Inventor); Perlman, Marvin (Inventor)

1991-01-01

A memory system is provided, of the type that includes an error-correcting circuit that detects and corrects, that more efficiently utilizes the capacity of a memory formed of groups of binary cells whose states can be inadvertently switched by ionizing radiation. Each memory cell has an asymmetric geometry, so that ionizing radiation causes a significantly greater probability of errors in one state than in the opposite state (e.g., an erroneous switch from '1' to '0' is far more likely than a switch from '0' to'1'. An asymmetric error correcting coding circuit can be used with the asymmetric memory cells, which requires fewer bits than an efficient symmetric error correcting code.

Measurement-free implementations of small-scale surface codes for quantum-dot qubits

NASA Astrophysics Data System (ADS)

Ercan, H. Ekmel; Ghosh, Joydip; Crow, Daniel; Premakumar, Vickram N.; Joynt, Robert; Friesen, Mark; Coppersmith, S. N.

2018-01-01

The performance of quantum-error-correction schemes depends sensitively on the physical realizations of the qubits and the implementations of various operations. For example, in quantum-dot spin qubits, readout is typically much slower than gate operations, and conventional surface-code implementations that rely heavily on syndrome measurements could therefore be challenging. However, fast and accurate reset of quantum-dot qubits, without readout, can be achieved via tunneling to a reservoir. Here we propose small-scale surface-code implementations for which syndrome measurements are replaced by a combination of Toffoli gates and qubit reset. For quantum-dot qubits, this enables much faster error correction than measurement-based schemes, but requires additional ancilla qubits and non-nearest-neighbor interactions. We have performed numerical simulations of two different coding schemes, obtaining error thresholds on the orders of 10-2 for a one-dimensional architecture that only corrects bit-flip errors and 10-4 for a two-dimensional architecture that corrects bit- and phase-flip errors.

Error Correcting Codes I. Applications of Elementary Algebra to Information Theory. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 346.

ERIC Educational Resources Information Center

Rice, Bart F.; Wilde, Carroll O.

It is noted that with the prominence of computers in today's technological society, digital communication systems have become widely used in a variety of applications. Some of the problems that arise in digital communications systems are described. This unit presents the problem of correcting errors in such systems. Error correcting codes are…

Reed-Solomon Codes and the Deep Hole Problem

NASA Astrophysics Data System (ADS)

Keti, Matt

In many types of modern communication, a message is transmitted over a noisy medium. When this is done, there is a chance that the message will be corrupted. An error-correcting code adds redundant information to the message which allows the receiver to detect and correct errors accrued during the transmission. We will study the famous Reed-Solomon code (found in QR codes, compact discs, deep space probes,ldots) and investigate the limits of its error-correcting capacity. It can be shown that understanding this is related to understanding the "deep hole" problem, which is a question of determining when a received message has, in a sense, incurred the worst possible corruption. We partially resolve this in its traditional context, when the code is based on the finite field F q or Fq*, as well as new contexts, when it is based on a subgroup of F q* or the image of a Dickson polynomial. This is a new and important problem that could give insight on the true error-correcting potential of the Reed-Solomon code.

Performance of concatenated Reed-Solomon trellis-coded modulation over Rician fading channels

NASA Technical Reports Server (NTRS)

Moher, Michael L.; Lodge, John H.

1990-01-01

A concatenated coding scheme for providing very reliable data over mobile-satellite channels at power levels similar to those used for vocoded speech is described. The outer code is a shorter Reed-Solomon code which provides error detection as well as error correction capabilities. The inner code is a 1-D 8-state trellis code applied independently to both the inphase and quadrature channels. To achieve the full error correction potential of this inner code, the code symbols are multiplexed with a pilot sequence which is used to provide dynamic channel estimation and coherent detection. The implementation structure of this scheme is discussed and its performance is estimated.

A Very Low Cost BCH Decoder for High Immunity of On-Chip Memories

NASA Astrophysics Data System (ADS)

Seo, Haejun; Han, Sehwan; Heo, Yoonseok; Cho, Taewon

BCH(Bose-Chaudhuri-Hoquenbhem) code, a type of block codes-cyclic codes, has very strong error-correcting ability which is vital for performing the error protection on the memory system. BCH code has many kinds of dual algorithms, PGZ(Pererson-Gorenstein-Zierler) algorithm out of them is advantageous in view of correcting the errors through the simple calculation in t value. However, this is problematic when this becomes 0 (divided by zero) in case ν ≠ t. In this paper, the circuit would be simplified by suggesting the multi-mode hardware architecture in preparation that v were 0~3. First, production cost would be less thanks to the smaller number of gates. Second, lessening power consumption could lengthen the recharging period. The very low cost and simple datapath make our design a good choice in small-footprint SoC(System on Chip) as ECC(Error Correction Code/Circuit) in memory system.

Syndrome-source-coding and its universal generalization. [error correcting codes for data compression

NASA Technical Reports Server (NTRS)

Ancheta, T. C., Jr.

1976-01-01

A method of using error-correcting codes to obtain data compression, called syndrome-source-coding, is described in which the source sequence is treated as an error pattern whose syndrome forms the compressed data. It is shown that syndrome-source-coding can achieve arbitrarily small distortion with the number of compressed digits per source digit arbitrarily close to the entropy of a binary memoryless source. A 'universal' generalization of syndrome-source-coding is formulated which provides robustly effective distortionless coding of source ensembles. Two examples are given, comparing the performance of noiseless universal syndrome-source-coding to (1) run-length coding and (2) Lynch-Davisson-Schalkwijk-Cover universal coding for an ensemble of binary memoryless sources.

Superdense coding interleaved with forward error correction

DOE PAGES

Humble, Travis S.; Sadlier, Ronald J.

2016-05-12

Superdense coding promises increased classical capacity and communication security but this advantage may be undermined by noise in the quantum channel. We present a numerical study of how forward error correction (FEC) applied to the encoded classical message can be used to mitigate against quantum channel noise. By studying the bit error rate under different FEC codes, we identify the unique role that burst errors play in superdense coding, and we show how these can be mitigated against by interleaving the FEC codewords prior to transmission. As a result, we conclude that classical FEC with interleaving is a useful methodmore » to improve the performance in near-term demonstrations of superdense coding.« less

Ciliates learn to diagnose and correct classical error syndromes in mating strategies

PubMed Central

Clark, Kevin B.

2013-01-01

Preconjugal ciliates learn classical repetition error-correction codes to safeguard mating messages and replies from corruption by “rivals” and local ambient noise. Because individual cells behave as memory channels with Szilárd engine attributes, these coding schemes also might be used to limit, diagnose, and correct mating-signal errors due to noisy intracellular information processing. The present study, therefore, assessed whether heterotrich ciliates effect fault-tolerant signal planning and execution by modifying engine performance, and consequently entropy content of codes, during mock cell–cell communication. Socially meaningful serial vibrations emitted from an ambiguous artificial source initiated ciliate behavioral signaling performances known to advertise mating fitness with varying courtship strategies. Microbes, employing calcium-dependent Hebbian-like decision making, learned to diagnose then correct error syndromes by recursively matching Boltzmann entropies between signal planning and execution stages via “power” or “refrigeration” cycles. All eight serial contraction and reversal strategies incurred errors in entropy magnitude by the execution stage of processing. Absolute errors, however, subtended expected threshold values for single bit-flip errors in three-bit replies, indicating coding schemes protected information content throughout signal production. Ciliate preparedness for vibrations selectively and significantly affected the magnitude and valence of Szilárd engine performance during modal and non-modal strategy corrective cycles. But entropy fidelity for all replies mainly improved across learning trials as refinements in engine efficiency. Fidelity neared maximum levels for only modal signals coded in resilient three-bit repetition error-correction sequences. Together, these findings demonstrate microbes can elevate survival/reproductive success by learning to implement classical fault-tolerant information processing in social contexts. PMID:23966987

Analysis of error-correction constraints in an optical disk.

PubMed

Roberts, J D; Ryley, A; Jones, D M; Burke, D

1996-07-10

The compact disk read-only memory (CD-ROM) is a mature storage medium with complex error control. It comprises four levels of Reed Solomon codes allied to a sequence of sophisticated interleaving strategies and 8:14 modulation coding. New storage media are being developed and introduced that place still further demands on signal processing for error correction. It is therefore appropriate to explore thoroughly the limit of existing strategies to assess future requirements. We describe a simulation of all stages of the CD-ROM coding, modulation, and decoding. The results of decoding the burst error of a prescribed number of modulation bits are discussed in detail. Measures of residual uncorrected error within a sector are displayed by C1, C2, P, and Q error counts and by the status of the final cyclic redundancy check (CRC). Where each data sector is encoded separately, it is shown that error-correction performance against burst errors depends critically on the position of the burst within a sector. The C1 error measures the burst length, whereas C2 errors reflect the burst position. The performance of Reed Solomon product codes is shown by the P and Q statistics. It is shown that synchronization loss is critical near the limits of error correction. An example is given of miscorrection that is identified by the CRC check.

Analysis of error-correction constraints in an optical disk

NASA Astrophysics Data System (ADS)

Roberts, Jonathan D.; Ryley, Alan; Jones, David M.; Burke, David

1996-07-01

The compact disk read-only memory (CD-ROM) is a mature storage medium with complex error control. It comprises four levels of Reed Solomon codes allied to a sequence of sophisticated interleaving strategies and 8:14 modulation coding. New storage media are being developed and introduced that place still further demands on signal processing for error correction. It is therefore appropriate to explore thoroughly the limit of existing strategies to assess future requirements. We describe a simulation of all stages of the CD-ROM coding, modulation, and decoding. The results of decoding the burst error of a prescribed number of modulation bits are discussed in detail. Measures of residual uncorrected error within a sector are displayed by C1, C2, P, and Q error counts and by the status of the final cyclic redundancy check (CRC). Where each data sector is encoded separately, it is shown that error-correction performance against burst errors depends critically on the position of the burst within a sector. The C1 error measures the burst length, whereas C2 errors reflect the burst position. The performance of Reed Solomon product codes is shown by the P and Q statistics. It is shown that synchronization loss is critical near the limits of error correction. An example is given of miscorrection that is identified by the CRC check.

Hard decoding algorithm for optimizing thresholds under general Markovian noise

NASA Astrophysics Data System (ADS)

Chamberland, Christopher; Wallman, Joel; Beale, Stefanie; Laflamme, Raymond

2017-04-01

Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of error-correcting codes have been obtained. However, realistic quantum systems can undergo noise processes that differ significantly from Pauli noise. In this paper, we present an efficient hard decoding algorithm for optimizing thresholds and lowering failure rates of an error-correcting code under general completely positive and trace-preserving (i.e., Markovian) noise. We use our hard decoding algorithm to study the performance of several error-correcting codes under various non-Pauli noise models by computing threshold values and failure rates for these codes. We compare the performance of our hard decoding algorithm to decoders optimized for depolarizing noise and show improvements in thresholds and reductions in failure rates by several orders of magnitude. Our hard decoding algorithm can also be adapted to take advantage of a code's non-Pauli transversal gates to further suppress noise. For example, we show that using the transversal gates of the 5-qubit code allows arbitrary rotations around certain axes to be perfectly corrected. Furthermore, we show that Pauli twirling can increase or decrease the threshold depending upon the code properties. Lastly, we show that even if the physical noise model differs slightly from the hypothesized noise model used to determine an optimized decoder, failure rates can still be reduced by applying our hard decoding algorithm.

Entanglement renormalization, quantum error correction, and bulk causality

NASA Astrophysics Data System (ADS)

Kim, Isaac H.; Kastoryano, Michael J.

2017-04-01

Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progres-sively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.

Continuous quantum error correction for non-Markovian decoherence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oreshkov, Ognyan; Brun, Todd A.; Communication Sciences Institute, University of Southern California, Los Angeles, California 90089

2007-08-15

We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximatelymore » follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics.« less

A concatenated coding scheme for error control

NASA Technical Reports Server (NTRS)

Lin, S.

1985-01-01

A concatenated coding scheme for error contol in data communications was analyzed. The inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if either the inner code decoder fails to make a successful decoding or the outer code decoder detects the presence of errors after the inner code decoding. Probability of undetected error of the proposed scheme is derived. An efficient method for computing this probability is presented. Throughout efficiency of the proposed error control scheme incorporated with a selective repeat ARQ retransmission strategy is analyzed.

"ON ALGEBRAIC DECODING OF Q-ARY REED-MULLER AND PRODUCT REED-SOLOMON CODES"

DOE Office of Scientific and Technical Information (OSTI.GOV)

SANTHI, NANDAKISHORE

We consider a list decoding algorithm recently proposed by Pellikaan-Wu for q-ary Reed-Muller codes RM{sub q}({ell}, m, n) of length n {le} q{sup m} when {ell} {le} q. A simple and easily accessible correctness proof is given which shows that this algorithm achieves a relative error-correction radius of {tau} {le} (1-{radical}{ell}q{sup m-1}/n). This is an improvement over the proof using one-point Algebraic-Geometric decoding method given in. The described algorithm can be adapted to decode product Reed-Solomon codes. We then propose a new low complexity recursive aJgebraic decoding algorithm for product Reed-Solomon codes and Reed-Muller codes. This algorithm achieves a relativemore » error correction radius of {tau} {le} {Pi}{sub i=1}{sup m} (1 - {radical}k{sub i}/q). This algorithm is then proved to outperform the Pellikaan-Wu algorithm in both complexity and error correction radius over a wide range of code rates.« less

Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes

NASA Astrophysics Data System (ADS)

Harrington, James William

Quantum information theory is concerned with identifying how quantum mechanical resources (such as entangled quantum states) can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g. , factoring large numbers, securely communicating over a public channel, and simulating quantum mechanical systems) that appear to be very difficult with just classical resources. In addition to identifying the separation between classical and quantum computational power, much of the theoretical focus in this field over the last decade has been concerned with finding novel ways of encoding quantum information that are robust against errors, which is an important step toward building practical quantum information processing devices. In this thesis I present some results on the quantum error-correcting properties of oscillator codes (also described as symplectic lattice codes) and toric codes. Any harmonic oscillator system (such as a mode of light) can be encoded with quantum information via symplectic lattice codes that are robust against shifts in the system's continuous quantum variables. I show the existence of lattice codes whose achievable rates match the one-shot coherent information over the Gaussian quantum channel. Also, I construct a family of symplectic self-dual lattices and search for optimal encodings of quantum information distributed between several oscillators. Toric codes provide encodings of quantum information into two-dimensional spin lattices that are robust against local clusters of errors and which require only local quantum operations for error correction. Numerical simulations of this system under various error models provide a calculation of the accuracy threshold for quantum memory using toric codes, which can be related to phase transitions in certain condensed matter models. I also present a local classical processing scheme for correcting errors on toric codes, which demonstrates that quantum information can be maintained in two dimensions by purely local (quantum and classical) resources.

Error-correcting codes in computer arithmetic.

NASA Technical Reports Server (NTRS)

Massey, J. L.; Garcia, O. N.

1972-01-01

Summary of the most important results so far obtained in the theory of coding for the correction and detection of errors in computer arithmetic. Attempts to satisfy the stringent reliability demands upon the arithmetic unit are considered, and special attention is given to attempts to incorporate redundancy into the numbers themselves which are being processed so that erroneous results can be detected and corrected.

Cooperative MIMO communication at wireless sensor network: an error correcting code approach.

PubMed

Islam, Mohammad Rakibul; Han, Young Shin

2011-01-01

Cooperative communication in wireless sensor network (WSN) explores the energy efficient wireless communication schemes between multiple sensors and data gathering node (DGN) by exploiting multiple input multiple output (MIMO) and multiple input single output (MISO) configurations. In this paper, an energy efficient cooperative MIMO (C-MIMO) technique is proposed where low density parity check (LDPC) code is used as an error correcting code. The rate of LDPC code is varied by varying the length of message and parity bits. Simulation results show that the cooperative communication scheme outperforms SISO scheme in the presence of LDPC code. LDPC codes with different code rates are compared using bit error rate (BER) analysis. BER is also analyzed under different Nakagami fading scenario. Energy efficiencies are compared for different targeted probability of bit error p(b). It is observed that C-MIMO performs more efficiently when the targeted p(b) is smaller. Also the lower encoding rate for LDPC code offers better error characteristics.

Cooperative MIMO Communication at Wireless Sensor Network: An Error Correcting Code Approach

PubMed Central

Islam, Mohammad Rakibul; Han, Young Shin

2011-01-01

Cooperative communication in wireless sensor network (WSN) explores the energy efficient wireless communication schemes between multiple sensors and data gathering node (DGN) by exploiting multiple input multiple output (MIMO) and multiple input single output (MISO) configurations. In this paper, an energy efficient cooperative MIMO (C-MIMO) technique is proposed where low density parity check (LDPC) code is used as an error correcting code. The rate of LDPC code is varied by varying the length of message and parity bits. Simulation results show that the cooperative communication scheme outperforms SISO scheme in the presence of LDPC code. LDPC codes with different code rates are compared using bit error rate (BER) analysis. BER is also analyzed under different Nakagami fading scenario. Energy efficiencies are compared for different targeted probability of bit error pb. It is observed that C-MIMO performs more efficiently when the targeted pb is smaller. Also the lower encoding rate for LDPC code offers better error characteristics. PMID:22163732

A Parallel Decoding Algorithm for Short Polar Codes Based on Error Checking and Correcting

PubMed Central

Pan, Xiaofei; Pan, Kegang; Ye, Zhan; Gong, Chao

2014-01-01

We propose a parallel decoding algorithm based on error checking and correcting to improve the performance of the short polar codes. In order to enhance the error-correcting capacity of the decoding algorithm, we first derive the error-checking equations generated on the basis of the frozen nodes, and then we introduce the method to check the errors in the input nodes of the decoder by the solutions of these equations. In order to further correct those checked errors, we adopt the method of modifying the probability messages of the error nodes with constant values according to the maximization principle. Due to the existence of multiple solutions of the error-checking equations, we formulate a CRC-aided optimization problem of finding the optimal solution with three different target functions, so as to improve the accuracy of error checking. Besides, in order to increase the throughput of decoding, we use a parallel method based on the decoding tree to calculate probability messages of all the nodes in the decoder. Numerical results show that the proposed decoding algorithm achieves better performance than that of some existing decoding algorithms with the same code length. PMID:25540813

Testing of Error-Correcting Sparse Permutation Channel Codes

NASA Technical Reports Server (NTRS)

Shcheglov, Kirill, V.; Orlov, Sergei S.

2008-01-01

A computer program performs Monte Carlo direct numerical simulations for testing sparse permutation channel codes, which offer strong error-correction capabilities at high code rates and are considered especially suitable for storage of digital data in holographic and volume memories. A word in a code of this type is characterized by, among other things, a sparseness parameter (M) and a fixed number (K) of 1 or "on" bits in a channel block length of N.

Neural network decoder for quantum error correcting codes

NASA Astrophysics Data System (ADS)

Krastanov, Stefan; Jiang, Liang

Artificial neural networks form a family of extremely powerful - albeit still poorly understood - tools used in anything from image and sound recognition through text generation to, in our case, decoding. We present a straightforward Recurrent Neural Network architecture capable of deducing the correcting procedure for a quantum error-correcting code from a set of repeated stabilizer measurements. We discuss the fault-tolerance of our scheme and the cost of training the neural network for a system of a realistic size. Such decoders are especially interesting when applied to codes, like the quantum LDPC codes, that lack known efficient decoding schemes.

Introduction to Forward-Error-Correcting Coding

NASA Technical Reports Server (NTRS)

Freeman, Jon C.

1996-01-01

This reference publication introduces forward error correcting (FEC) and stresses definitions and basic calculations for use by engineers. The seven chapters include 41 example problems, worked in detail to illustrate points. A glossary of terms is included, as well as an appendix on the Q function. Block and convolutional codes are covered.

Multichannel error correction code decoder

NASA Technical Reports Server (NTRS)

Wagner, Paul K.; Ivancic, William D.

1993-01-01

A brief overview of a processing satellite for a mesh very-small-aperture (VSAT) communications network is provided. The multichannel error correction code (ECC) decoder system, the uplink signal generation and link simulation equipment, and the time-shared decoder are described. The testing is discussed. Applications of the time-shared decoder are recommended.

Simulation of rare events in quantum error correction

NASA Astrophysics Data System (ADS)

Bravyi, Sergey; Vargo, Alexander

2013-12-01

We consider the problem of calculating the logical error probability for a stabilizer quantum code subject to random Pauli errors. To access the regime of large code distances where logical errors are extremely unlikely we adopt the splitting method widely used in Monte Carlo simulations of rare events and Bennett's acceptance ratio method for estimating the free energy difference between two canonical ensembles. To illustrate the power of these methods in the context of error correction, we calculate the logical error probability PL for the two-dimensional surface code on a square lattice with a pair of holes for all code distances d≤20 and all error rates p below the fault-tolerance threshold. Our numerical results confirm the expected exponential decay PL˜exp[-α(p)d] and provide a simple fitting formula for the decay rate α(p). Both noiseless and noisy syndrome readout circuits are considered.

Reliable Channel-Adapted Error Correction: Bacon-Shor Code Recovery from Amplitude Damping

NASA Astrophysics Data System (ADS)

Piedrafita, Álvaro; Renes, Joseph M.

2017-12-01

We construct two simple error correction schemes adapted to amplitude damping noise for Bacon-Shor codes and investigate their prospects for fault-tolerant implementation. Both consist solely of Clifford gates and require far fewer qubits, relative to the standard method, to achieve exact correction to a desired order in the damping rate. The first, employing one-bit teleportation and single-qubit measurements, needs only one-fourth as many physical qubits, while the second, using just stabilizer measurements and Pauli corrections, needs only half. The improvements stem from the fact that damping events need only be detected, not corrected, and that effective phase errors arising due to undamped qubits occur at a lower rate than damping errors. For error correction that is itself subject to damping noise, we show that existing fault-tolerance methods can be employed for the latter scheme, while the former can be made to avoid potential catastrophic errors and can easily cope with damping faults in ancilla qubits.

Tutorial on Reed-Solomon error correction coding

NASA Technical Reports Server (NTRS)

Geisel, William A.

1990-01-01

This tutorial attempts to provide a frank, step-by-step approach to Reed-Solomon (RS) error correction coding. RS encoding and RS decoding both with and without erasing code symbols are emphasized. There is no need to present rigorous proofs and extreme mathematical detail. Rather, the simple concepts of groups and fields, specifically Galois fields, are presented with a minimum of complexity. Before RS codes are presented, other block codes are presented as a technical introduction into coding. A primitive (15, 9) RS coding example is then completely developed from start to finish, demonstrating the encoding and decoding calculations and a derivation of the famous error-locator polynomial. The objective is to present practical information about Reed-Solomon coding in a manner such that it can be easily understood.

Signal Detection and Frame Synchronization of Multiple Wireless Networking Waveforms

DTIC Science & Technology

2007-09-01

punctured to obtain coding rates of 2 3 and 3 4 . Convolutional forward error correction coding is used to detect and correct bit...likely to be isolated and be correctable by the convolutional decoder. 44 Data rate (Mbps) Modulation Coding Rate Coded bits per subcarrier...binary convolutional code . A shortened Reed-Solomon technique is employed first. The code is shortened depending upon the data

A decoding procedure for the Reed-Solomon codes

NASA Technical Reports Server (NTRS)

Lim, R. S.

1978-01-01

A decoding procedure is described for the (n,k) t-error-correcting Reed-Solomon (RS) code, and an implementation of the (31,15) RS code for the I4-TENEX central system. This code can be used for error correction in large archival memory systems. The principal features of the decoder are a Galois field arithmetic unit implemented by microprogramming a microprocessor, and syndrome calculation by using the g(x) encoding shift register. Complete decoding of the (31,15) code is expected to take less than 500 microsecs. The syndrome calculation is performed by hardware using the encoding shift register and a modified Chien search. The error location polynomial is computed by using Lin's table, which is an interpretation of Berlekamp's iterative algorithm. The error location numbers are calculated by using the Chien search. Finally, the error values are computed by using Forney's method.

Transversal Clifford gates on folded surface codes

DOE PAGES

Moussa, Jonathan E.

2016-10-12

Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surfacemore » codes. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construction is presented generally for qudits of any dimension. Lastly, the specific application of these codes to universal quantum computation based on qubit fusion is also discussed.« less

An extended Reed Solomon decoder design

NASA Technical Reports Server (NTRS)

Chen, J.; Owsley, P.; Purviance, J.

1991-01-01

It has previously been shown that the Reed-Solomon (RS) codes can correct errors beyond the Singleton and Rieger Bounds with an arbitrarily small probability of a miscorrect. That is, an (n,k) RS code can correct more than (n-k)/2 errors. An implementation of such an RS decoder is presented in this paper. An existing RS decoder, the AHA4010, is utilized in this work. This decoder is especially useful for errors which are patterned with a long burst plus some random errors.

Processor register error correction management

DOEpatents

Bose, Pradip; Cher, Chen-Yong; Gupta, Meeta S.

2016-12-27

Processor register protection management is disclosed. In embodiments, a method of processor register protection management can include determining a sensitive logical register for executable code generated by a compiler, generating an error-correction table identifying the sensitive logical register, and storing the error-correction table in a memory accessible by a processor. The processor can be configured to generate a duplicate register of the sensitive logical register identified by the error-correction table.

Fast and Flexible Successive-Cancellation List Decoders for Polar Codes

NASA Astrophysics Data System (ADS)

Hashemi, Seyyed Ali; Condo, Carlo; Gross, Warren J.

2017-11-01

Polar codes have gained significant amount of attention during the past few years and have been selected as a coding scheme for the next generation of mobile broadband standard. Among decoding schemes, successive-cancellation list (SCL) decoding provides a reasonable trade-off between the error-correction performance and hardware implementation complexity when used to decode polar codes, at the cost of limited throughput. The simplified SCL (SSCL) and its extension SSCL-SPC increase the speed of decoding by removing redundant calculations when encountering particular information and frozen bit patterns (rate one and single parity check codes), while keeping the error-correction performance unaltered. In this paper, we improve SSCL and SSCL-SPC by proving that the list size imposes a specific number of bit estimations required to decode rate one and single parity check codes. Thus, the number of estimations can be limited while guaranteeing exactly the same error-correction performance as if all bits of the code were estimated. We call the new decoding algorithms Fast-SSCL and Fast-SSCL-SPC. Moreover, we show that the number of bit estimations in a practical application can be tuned to achieve desirable speed, while keeping the error-correction performance almost unchanged. Hardware architectures implementing both algorithms are then described and implemented: it is shown that our design can achieve 1.86 Gb/s throughput, higher than the best state-of-the-art decoders.

A concatenated coding scheme for error control

NASA Technical Reports Server (NTRS)

Kasami, T.; Fujiwara, T.; Lin, S.

1986-01-01

In this paper, a concatenated coding scheme for error control in data communications is presented and analyzed. In this scheme, the inner code is used for both error correction and detection; however, the outer code is used only for error detection. A retransmission is requested if either the inner code decoder fails to make a successful decoding or the outer code decoder detects the presence of errors after the inner code decoding. Probability of undetected error (or decoding error) of the proposed scheme is derived. An efficient method for computing this probability is presented. Throughput efficiency of the proposed error control scheme incorporated with a selective-repeat ARQ retransmission strategy is also analyzed. Three specific examples are presented. One of the examples is proposed for error control in the NASA Telecommand System.

An analysis of four error detection and correction schemes for the proposed Federal standard 1024 (land mobile radio)

NASA Astrophysics Data System (ADS)

Lohrmann, Carol A.

1990-03-01

Interoperability of commercial Land Mobile Radios (LMR) and the military's tactical LMR is highly desirable if the U.S. government is to respond effectively in a national emergency or in a joint military operation. This ability to talk securely and immediately across agency and military service boundaries is often overlooked. One way to ensure interoperability is to develop and promote Federal communication standards (FS). This thesis surveys one area of the proposed FS 1024 for LMRs; namely, the error detection and correction (EDAC) of the message indicator (MI) bits used for cryptographic synchronization. Several EDAC codes are examined (Hamming, Quadratic Residue, hard decision Golay and soft decision Golay), tested on three FORTRAN programmed channel simulations (INMARSAT, Gaussian and constant burst width), compared and analyzed (based on bit error rates and percent of error-free super-frame runs) so that a best code can be recommended. Out of the four codes under study, the soft decision Golay code (24,12) is evaluated to be the best. This finding is based on the code's ability to detect and correct errors as well as the relative ease of implementation of the algorithm.

A cascaded coding scheme for error control and its performance analysis

NASA Technical Reports Server (NTRS)

Lin, Shu; Kasami, Tadao; Fujiwara, Tohru; Takata, Toyoo

1986-01-01

A coding scheme is investigated for error control in data communication systems. The scheme is obtained by cascading two error correcting codes, called the inner and outer codes. The error performance of the scheme is analyzed for a binary symmetric channel with bit error rate epsilon <1/2. It is shown that if the inner and outer codes are chosen properly, extremely high reliability can be attained even for a high channel bit error rate. Various specific example schemes with inner codes ranging form high rates to very low rates and Reed-Solomon codes as inner codes are considered, and their error probabilities are evaluated. They all provide extremely high reliability even for very high bit error rates. Several example schemes are being considered by NASA for satellite and spacecraft down link error control.

Using concatenated quantum codes for universal fault-tolerant quantum gates.

PubMed

Jochym-O'Connor, Tomas; Laflamme, Raymond

2014-01-10

We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. The concatenation scheme exploits the transversal properties of two different codes, combining them to provide a means to protect against low-weight arbitrary errors. We give the required properties of the error correcting codes to ensure universal fault tolerance and discuss a particular example using the 7-qubit Steane and 15-qubit Reed-Muller codes. Namely, other than computational basis state preparation as required by the DiVincenzo criteria, our scheme requires no special ancillary state preparation to achieve universality, as opposed to schemes such as magic state distillation. We believe that optimizing the codes used in such a scheme could provide a useful alternative to state distillation schemes that exhibit high overhead costs.

Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice

NASA Astrophysics Data System (ADS)

Kim, Isaac H.

2011-05-01

We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.

Topological quantum error correction in the Kitaev honeycomb model

NASA Astrophysics Data System (ADS)

Lee, Yi-Chan; Brell, Courtney G.; Flammia, Steven T.

2017-08-01

The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of topological quantum codes that are typically studied, but its exact solubility makes it more amenable to analysis of effects arising in this noncommutative setting than a generic topologically ordered Hamiltonian. Here we study quantum error correction in the honeycomb model using both analytic and numerical techniques. We first prove explicit exponential bounds on the approximate degeneracy, local indistinguishability, and correctability of the code space. These bounds are tighter than can be achieved using known general properties of topological phases. Our proofs are specialized to the honeycomb model, but some of the methods may nonetheless be of broader interest. Following this, we numerically study noise caused by thermalization processes in the perturbative regime close to the toric code renormalization group fixed point. The appearance of non-topological excitations in this setting has no significant effect on the error correction properties of the honeycomb model in the regimes we study. Although the behavior of this model is found to be qualitatively similar to that of the standard toric code in most regimes, we find numerical evidence of an interesting effect in the low-temperature, finite-size regime where a preferred lattice direction emerges and anyon diffusion is geometrically constrained. We expect this effect to yield an improvement in the scaling of the lifetime with system size as compared to the standard toric code.

RD Optimized, Adaptive, Error-Resilient Transmission of MJPEG2000-Coded Video over Multiple Time-Varying Channels

NASA Astrophysics Data System (ADS)

Bezan, Scott; Shirani, Shahram

2006-12-01

To reliably transmit video over error-prone channels, the data should be both source and channel coded. When multiple channels are available for transmission, the problem extends to that of partitioning the data across these channels. The condition of transmission channels, however, varies with time. Therefore, the error protection added to the data at one instant of time may not be optimal at the next. In this paper, we propose a method for adaptively adding error correction code in a rate-distortion (RD) optimized manner using rate-compatible punctured convolutional codes to an MJPEG2000 constant rate-coded frame of video. We perform an analysis on the rate-distortion tradeoff of each of the coding units (tiles and packets) in each frame and adapt the error correction code assigned to the unit taking into account the bandwidth and error characteristics of the channels. This method is applied to both single and multiple time-varying channel environments. We compare our method with a basic protection method in which data is either not transmitted, transmitted with no protection, or transmitted with a fixed amount of protection. Simulation results show promising performance for our proposed method.

Quantum error correction assisted by two-way noisy communication

PubMed Central

Wang, Zhuo; Yu, Sixia; Fan, Heng; Oh, C. H.

2014-01-01

Pre-shared non-local entanglement dramatically simplifies and improves the performance of quantum error correction via entanglement-assisted quantum error-correcting codes (EAQECCs). However, even considering the noise in quantum communication only, the non-local sharing of a perfectly entangled pair is technically impossible unless additional resources are consumed, such as entanglement distillation, which actually compromises the efficiency of the codes. Here we propose an error-correcting protocol assisted by two-way noisy communication that is more easily realisable: all quantum communication is subjected to general noise and all entanglement is created locally without additional resources consumed. In our protocol the pre-shared noisy entangled pairs are purified simultaneously by the decoding process. For demonstration, we first present an easier implementation of the well-known EAQECC [[4, 1, 3; 1

Quantum error correction assisted by two-way noisy communication.

PubMed

Wang, Zhuo; Yu, Sixia; Fan, Heng; Oh, C H

2014-11-26

Pre-shared non-local entanglement dramatically simplifies and improves the performance of quantum error correction via entanglement-assisted quantum error-correcting codes (EAQECCs). However, even considering the noise in quantum communication only, the non-local sharing of a perfectly entangled pair is technically impossible unless additional resources are consumed, such as entanglement distillation, which actually compromises the efficiency of the codes. Here we propose an error-correcting protocol assisted by two-way noisy communication that is more easily realisable: all quantum communication is subjected to general noise and all entanglement is created locally without additional resources consumed. In our protocol the pre-shared noisy entangled pairs are purified simultaneously by the decoding process. For demonstration, we first present an easier implementation of the well-known EAQECC [[4, 1, 3; 1

The application of LDPC code in MIMO-OFDM system

NASA Astrophysics Data System (ADS)

Liu, Ruian; Zeng, Beibei; Chen, Tingting; Liu, Nan; Yin, Ninghao

2018-03-01

The combination of MIMO and OFDM technology has become one of the key technologies of the fourth generation mobile communication., which can overcome the frequency selective fading of wireless channel, increase the system capacity and improve the frequency utilization. Error correcting coding introduced into the system can further improve its performance. LDPC (low density parity check) code is a kind of error correcting code which can improve system reliability and anti-interference ability, and the decoding is simple and easy to operate. This paper mainly discusses the application of LDPC code in MIMO-OFDM system.

Lithographically encoded polymer microtaggant using high-capacity and error-correctable QR code for anti-counterfeiting of drugs.

PubMed

Han, Sangkwon; Bae, Hyung Jong; Kim, Junhoi; Shin, Sunghwan; Choi, Sung-Eun; Lee, Sung Hoon; Kwon, Sunghoon; Park, Wook

2012-11-20

A QR-coded microtaggant for the anti-counterfeiting of drugs is proposed that can provide high capacity and error-correction capability. It is fabricated lithographically in a microfluidic channel with special consideration of the island patterns in the QR Code. The microtaggant is incorporated in the drug capsule ("on-dose authentication") and can be read by a simple smartphone QR Code reader application when removed from the capsule and washed free of drug. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

3D measurement using combined Gray code and dual-frequency phase-shifting approach

NASA Astrophysics Data System (ADS)

Yu, Shuang; Zhang, Jing; Yu, Xiaoyang; Sun, Xiaoming; Wu, Haibin; Liu, Xin

2018-04-01

The combined Gray code and phase-shifting approach is a commonly used 3D measurement technique. In this technique, an error that equals integer multiples of the phase-shifted fringe period, i.e. period jump error, often exists in the absolute analog code, which can lead to gross measurement errors. To overcome this problem, the present paper proposes 3D measurement using a combined Gray code and dual-frequency phase-shifting approach. Based on 3D measurement using the combined Gray code and phase-shifting approach, one set of low-frequency phase-shifted fringe patterns with an odd-numbered multiple of the original phase-shifted fringe period is added. Thus, the absolute analog code measured value can be obtained by the combined Gray code and phase-shifting approach, and the low-frequency absolute analog code measured value can also be obtained by adding low-frequency phase-shifted fringe patterns. Then, the corrected absolute analog code measured value can be obtained by correcting the former by the latter, and the period jump errors can be eliminated, resulting in reliable analog code unwrapping. For the proposed approach, we established its measurement model, analyzed its measurement principle, expounded the mechanism of eliminating period jump errors by error analysis, and determined its applicable conditions. Theoretical analysis and experimental results show that the proposed approach can effectively eliminate period jump errors, reliably perform analog code unwrapping, and improve the measurement accuracy.

Construction of type-II QC-LDPC codes with fast encoding based on perfect cyclic difference sets

NASA Astrophysics Data System (ADS)

Li, Ling-xiang; Li, Hai-bing; Li, Ji-bi; Jiang, Hua

2017-09-01

In view of the problems that the encoding complexity of quasi-cyclic low-density parity-check (QC-LDPC) codes is high and the minimum distance is not large enough which leads to the degradation of the error-correction performance, the new irregular type-II QC-LDPC codes based on perfect cyclic difference sets (CDSs) are constructed. The parity check matrices of these type-II QC-LDPC codes consist of the zero matrices with weight of 0, the circulant permutation matrices (CPMs) with weight of 1 and the circulant matrices with weight of 2 (W2CMs). The introduction of W2CMs in parity check matrices makes it possible to achieve the larger minimum distance which can improve the error- correction performance of the codes. The Tanner graphs of these codes have no girth-4, thus they have the excellent decoding convergence characteristics. In addition, because the parity check matrices have the quasi-dual diagonal structure, the fast encoding algorithm can reduce the encoding complexity effectively. Simulation results show that the new type-II QC-LDPC codes can achieve a more excellent error-correction performance and have no error floor phenomenon over the additive white Gaussian noise (AWGN) channel with sum-product algorithm (SPA) iterative decoding.

Adaptive decoding of convolutional codes

NASA Astrophysics Data System (ADS)

Hueske, K.; Geldmacher, J.; Götze, J.

2007-06-01

Convolutional codes, which are frequently used as error correction codes in digital transmission systems, are generally decoded using the Viterbi Decoder. On the one hand the Viterbi Decoder is an optimum maximum likelihood decoder, i.e. the most probable transmitted code sequence is obtained. On the other hand the mathematical complexity of the algorithm only depends on the used code, not on the number of transmission errors. To reduce the complexity of the decoding process for good transmission conditions, an alternative syndrome based decoder is presented. The reduction of complexity is realized by two different approaches, the syndrome zero sequence deactivation and the path metric equalization. The two approaches enable an easy adaptation of the decoding complexity for different transmission conditions, which results in a trade-off between decoding complexity and error correction performance.

An investigation of error characteristics and coding performance

NASA Technical Reports Server (NTRS)

Ebel, William J.; Ingels, Frank M.

1993-01-01

The first year's effort on NASA Grant NAG5-2006 was an investigation to characterize typical errors resulting from the EOS dorn link. The analysis methods developed for this effort were used on test data from a March 1992 White Sands Terminal Test. The effectiveness of a concatenated coding scheme of a Reed Solomon outer code and a convolutional inner code versus a Reed Solomon only code scheme has been investigated as well as the effectiveness of a Periodic Convolutional Interleaver in dispersing errors of certain types. The work effort consisted of development of software that allows simulation studies with the appropriate coding schemes plus either simulated data with errors or actual data with errors. The software program is entitled Communication Link Error Analysis (CLEAN) and models downlink errors, forward error correcting schemes, and interleavers.

A cascaded coding scheme for error control and its performance analysis

NASA Technical Reports Server (NTRS)

Lin, S.

1986-01-01

A coding scheme for error control in data communication systems is investigated. The scheme is obtained by cascading two error correcting codes, called the inner and the outer codes. The error performance of the scheme is analyzed for a binary symmetric channel with bit error rate epsilon < 1/2. It is shown that, if the inner and outer codes are chosen properly, extremely high reliability can be attained even for a high channel bit error rate. Various specific example schemes with inner codes ranging from high rates to very low rates and Reed-Solomon codes are considered, and their probabilities are evaluated. They all provide extremely high reliability even for very high bit error rates, say 0.1 to 0.01. Several example schemes are being considered by NASA for satellite and spacecraft down link error control.

Statistical inference of static analysis rules

NASA Technical Reports Server (NTRS)

Engler, Dawson Richards (Inventor)

2009-01-01

Various apparatus and methods are disclosed for identifying errors in program code. Respective numbers of observances of at least one correctness rule by different code instances that relate to the at least one correctness rule are counted in the program code. Each code instance has an associated counted number of observances of the correctness rule by the code instance. Also counted are respective numbers of violations of the correctness rule by different code instances that relate to the correctness rule. Each code instance has an associated counted number of violations of the correctness rule by the code instance. A respective likelihood of the validity is determined for each code instance as a function of the counted number of observances and counted number of violations. The likelihood of validity indicates a relative likelihood that a related code instance is required to observe the correctness rule. The violations may be output in order of the likelihood of validity of a violated correctness rule.

Applications and error correction for adiabatic quantum optimization

NASA Astrophysics Data System (ADS)

Pudenz, Kristen

Adiabatic quantum optimization (AQO) is a fast-developing subfield of quantum information processing which holds great promise in the relatively near future. Here we develop an application, quantum anomaly detection, and an error correction code, Quantum Annealing Correction (QAC), for use with AQO. The motivation for the anomaly detection algorithm is the problematic nature of classical software verification and validation (V&V). The number of lines of code written for safety-critical applications such as cars and aircraft increases each year, and with it the cost of finding errors grows exponentially (the cost of overlooking errors, which can be measured in human safety, is arguably even higher). We approach the V&V problem by using a quantum machine learning algorithm to identify charateristics of software operations that are implemented outside of specifications, then define an AQO to return these anomalous operations as its result. Our error correction work is the first large-scale experimental demonstration of quantum error correcting codes. We develop QAC and apply it to USC's equipment, the first and second generation of commercially available D-Wave AQO processors. We first show comprehensive experimental results for the code's performance on antiferromagnetic chains, scaling the problem size up to 86 logical qubits (344 physical qubits) and recovering significant encoded success rates even when the unencoded success rates drop to almost nothing. A broader set of randomized benchmarking problems is then introduced, for which we observe similar behavior to the antiferromagnetic chain, specifically that the use of QAC is almost always advantageous for problems of sufficient size and difficulty. Along the way, we develop problem-specific optimizations for the code and gain insight into the various on-chip error mechanisms (most prominently thermal noise, since the hardware operates at finite temperature) and the ways QAC counteracts them. We finish by showing that the scheme is robust to qubit loss on-chip, a significant benefit when considering an implemented system.

Multiple description distributed image coding with side information for mobile wireless transmission

NASA Astrophysics Data System (ADS)

Wu, Min; Song, Daewon; Chen, Chang Wen

2005-03-01

Multiple description coding (MDC) is a source coding technique that involves coding the source information into multiple descriptions, and then transmitting them over different channels in packet network or error-prone wireless environment to achieve graceful degradation if parts of descriptions are lost at the receiver. In this paper, we proposed a multiple description distributed wavelet zero tree image coding system for mobile wireless transmission. We provide two innovations to achieve an excellent error resilient capability. First, when MDC is applied to wavelet subband based image coding, it is possible to introduce correlation between the descriptions in each subband. We consider using such a correlation as well as potentially error corrupted description as side information in the decoding to formulate the MDC decoding as a Wyner Ziv decoding problem. If only part of descriptions is lost, however, their correlation information is still available, the proposed Wyner Ziv decoder can recover the description by using the correlation information and the error corrupted description as side information. Secondly, in each description, single bitstream wavelet zero tree coding is very vulnerable to the channel errors. The first bit error may cause the decoder to discard all subsequent bits whether or not the subsequent bits are correctly received. Therefore, we integrate the multiple description scalar quantization (MDSQ) with the multiple wavelet tree image coding method to reduce error propagation. We first group wavelet coefficients into multiple trees according to parent-child relationship and then code them separately by SPIHT algorithm to form multiple bitstreams. Such decomposition is able to reduce error propagation and therefore improve the error correcting capability of Wyner Ziv decoder. Experimental results show that the proposed scheme not only exhibits an excellent error resilient performance but also demonstrates graceful degradation over the packet loss rate.

An investigation of error characteristics and coding performance

NASA Technical Reports Server (NTRS)

Ebel, William J.; Ingels, Frank M.

1992-01-01

The performance of forward error correcting coding schemes on errors anticipated for the Earth Observation System (EOS) Ku-band downlink are studied. The EOS transmits picture frame data to the ground via the Telemetry Data Relay Satellite System (TDRSS) to a ground-based receiver at White Sands. Due to unintentional RF interference from other systems operating in the Ku band, the noise at the receiver is non-Gaussian which may result in non-random errors output by the demodulator. That is, the downlink channel cannot be modeled by a simple memoryless Gaussian-noise channel. From previous experience, it is believed that those errors are bursty. The research proceeded by developing a computer based simulation, called Communication Link Error ANalysis (CLEAN), to model the downlink errors, forward error correcting schemes, and interleavers used with TDRSS. To date, the bulk of CLEAN was written, documented, debugged, and verified. The procedures for utilizing CLEAN to investigate code performance were established and are discussed.

Error-correction coding for digital communications

NASA Astrophysics Data System (ADS)

Clark, G. C., Jr.; Cain, J. B.

This book is written for the design engineer who must build the coding and decoding equipment and for the communication system engineer who must incorporate this equipment into a system. It is also suitable as a senior-level or first-year graduate text for an introductory one-semester course in coding theory. Fundamental concepts of coding are discussed along with group codes, taking into account basic principles, practical constraints, performance computations, coding bounds, generalized parity check codes, polynomial codes, and important classes of group codes. Other topics explored are related to simple nonalgebraic decoding techniques for group codes, soft decision decoding of block codes, algebraic techniques for multiple error correction, the convolutional code structure and Viterbi decoding, syndrome decoding techniques, and sequential decoding techniques. System applications are also considered, giving attention to concatenated codes, coding for the white Gaussian noise channel, interleaver structures for coded systems, and coding for burst noise channels.

Performance Bounds on Two Concatenated, Interleaved Codes

NASA Technical Reports Server (NTRS)

Moision, Bruce; Dolinar, Samuel

2010-01-01

A method has been developed of computing bounds on the performance of a code comprised of two linear binary codes generated by two encoders serially concatenated through an interleaver. Originally intended for use in evaluating the performances of some codes proposed for deep-space communication links, the method can also be used in evaluating the performances of short-block-length codes in other applications. The method applies, more specifically, to a communication system in which following processes take place: At the transmitter, the original binary information that one seeks to transmit is first processed by an encoder into an outer code (Co) characterized by, among other things, a pair of numbers (n,k), where n (n > k)is the total number of code bits associated with k information bits and n k bits are used for correcting or at least detecting errors. Next, the outer code is processed through either a block or a convolutional interleaver. In the block interleaver, the words of the outer code are processed in blocks of I words. In the convolutional interleaver, the interleaving operation is performed bit-wise in N rows with delays that are multiples of B bits. The output of the interleaver is processed through a second encoder to obtain an inner code (Ci) characterized by (ni,ki). The output of the inner code is transmitted over an additive-white-Gaussian- noise channel characterized by a symbol signal-to-noise ratio (SNR) Es/No and a bit SNR Eb/No. At the receiver, an inner decoder generates estimates of bits. Depending on whether a block or a convolutional interleaver is used at the transmitter, the sequence of estimated bits is processed through a block or a convolutional de-interleaver, respectively, to obtain estimates of code words. Then the estimates of the code words are processed through an outer decoder, which generates estimates of the original information along with flags indicating which estimates are presumed to be correct and which are found to be erroneous. From the perspective of the present method, the topic of major interest is the performance of the communication system as quantified in the word-error rate and the undetected-error rate as functions of the SNRs and the total latency of the interleaver and inner code. The method is embodied in equations that describe bounds on these functions. Throughout the derivation of the equations that embody the method, it is assumed that the decoder for the outer code corrects any error pattern of t or fewer errors, detects any error pattern of s or fewer errors, may detect some error patterns of more than s errors, and does not correct any patterns of more than t errors. Because a mathematically complete description of the equations that embody the method and of the derivation of the equations would greatly exceed the space available for this article, it must suffice to summarize by reporting that the derivation includes consideration of several complex issues, including relationships between latency and memory requirements for block and convolutional codes, burst error statistics, enumeration of error-event intersections, and effects of different interleaving depths. In a demonstration, the method was used to calculate bounds on the performances of several communication systems, each based on serial concatenation of a (63,56) expurgated Hamming code with a convolutional inner code through a convolutional interleaver. The bounds calculated by use of the method were compared with results of numerical simulations of performances of the systems to show the regions where the bounds are tight (see figure).

Is QR code an optimal data container in optical encryption systems from an error-correction coding perspective?

PubMed

Jiao, Shuming; Jin, Zhi; Zhou, Changyuan; Zou, Wenbin; Li, Xia

2018-01-01

Quick response (QR) code has been employed as a data carrier for optical cryptosystems in many recent research works, and the error-correction coding mechanism allows the decrypted result to be noise free. However, in this paper, we point out for the first time that the Reed-Solomon coding algorithm in QR code is not a very suitable option for the nonlocally distributed speckle noise in optical cryptosystems from an information coding perspective. The average channel capacity is proposed to measure the data storage capacity and noise-resistant capability of different encoding schemes. We design an alternative 2D barcode scheme based on Bose-Chaudhuri-Hocquenghem (BCH) coding, which demonstrates substantially better average channel capacity than QR code in numerical simulated optical cryptosystems.

Bandwidth efficient CCSDS coding standard proposals

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.; Perez, Lance C.; Wang, Fu-Quan

1992-01-01

The basic concatenated coding system for the space telemetry channel consists of a Reed-Solomon (RS) outer code, a symbol interleaver/deinterleaver, and a bandwidth efficient trellis inner code. A block diagram of this configuration is shown. The system may operate with or without the outer code and interleaver. In this recommendation, the outer code remains the (255,223) RS code over GF(2 exp 8) with an error correcting capability of t = 16 eight bit symbols. This code's excellent performance and the existence of fast, cost effective, decoders justify its continued use. The purpose of the interleaver/deinterleaver is to distribute burst errors out of the inner decoder over multiple codewords of the outer code. This utilizes the error correcting capability of the outer code more efficiently and reduces the probability of an RS decoder failure. Since the space telemetry channel is not considered bursty, the required interleaving depth is primarily a function of the inner decoding method. A diagram of an interleaver with depth 4 that is compatible with the (255,223) RS code is shown. Specific interleaver requirements are discussed after the inner code recommendations.

Error threshold for color codes and random three-body Ising models.

PubMed

Katzgraber, Helmut G; Bombin, H; Martin-Delgado, M A

2009-08-28

We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation, and fault-tolerant quantum computation. We map the error-correction process onto a statistical mechanical random three-body Ising model and study its phase diagram via Monte Carlo simulations. The obtained error threshold of p(c) = 0.109(2) is very close to that of Kitaev's toric code, showing that enhanced computational capabilities do not necessarily imply lower resistance to noise.

Towards self-correcting quantum memories

NASA Astrophysics Data System (ADS)

Michnicki, Kamil

This thesis presents a model of self-correcting quantum memories where quantum states are encoded using topological stabilizer codes and error correction is done using local measurements and local dynamics. Quantum noise poses a practical barrier to developing quantum memories. This thesis explores two types of models for suppressing noise. One model suppresses thermalizing noise energetically by engineering a Hamiltonian with a high energy barrier between code states. Thermalizing dynamics are modeled phenomenologically as a Markovian quantum master equation with only local generators. The second model suppresses stochastic noise with a cellular automaton that performs error correction using syndrome measurements and a local update rule. Several ways of visualizing and thinking about stabilizer codes are presented in order to design ones that have a high energy barrier: the non-local Ising model, the quasi-particle graph and the theory of welded stabilizer codes. I develop the theory of welded stabilizer codes and use it to construct a code with the highest known energy barrier in 3-d for spin Hamiltonians: the welded solid code. Although the welded solid code is not fully self correcting, it has some self correcting properties. It has an increased memory lifetime for an increased system size up to a temperature dependent maximum. One strategy for increasing the energy barrier is by mediating an interaction with an external system. I prove a no-go theorem for a class of Hamiltonians where the interaction terms are local, of bounded strength and commute with the stabilizer group. Under these conditions the energy barrier can only be increased by a multiplicative constant. I develop cellular automaton to do error correction on a state encoded using the toric code. The numerical evidence indicates that while there is no threshold, the model can extend the memory lifetime significantly. While of less theoretical importance, this could be practical for real implementations of quantum memories. Numerical evidence also suggests that the cellular automaton could function as a decoder with a soft threshold.

Author Correction: Single-nucleus analysis of accessible chromatin in developing mouse forebrain reveals cell-type-specific transcriptional regulation.

PubMed

Preissl, Sebastian; Fang, Rongxin; Huang, Hui; Zhao, Yuan; Raviram, Ramya; Gorkin, David U; Zhang, Yanxiao; Sos, Brandon C; Afzal, Veena; Dickel, Diane E; Kuan, Samantha; Visel, Axel; Pennacchio, Len A; Zhang, Kun; Ren, Bing

2018-03-01

In the version of this article initially published online, the accession code was given as GSE1000333. The correct code is GSE100033. The error has been corrected in the print, HTML and PDF versions of the article.

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems.

PubMed

Li, Ying

2016-09-16

Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g., superconducting circuits or quantum dots, is studied in this Letter. Errors caused by topologically unprotected quantum systems need to be corrected with error-correction schemes, for instance, the surface code. We find that the error-correction performance of such a hybrid topological quantum computer is not superior to a normal quantum computer unless the topological charge of Majorana fermions is insusceptible to noise. If errors changing the topological charge are rare, the fault-tolerance threshold is much higher than the threshold of a normal quantum computer and a surface-code logical qubit could be encoded in only tens of topological qubits instead of about 1,000 normal qubits.

Towards Holography via Quantum Source-Channel Codes.

PubMed

Pastawski, Fernando; Eisert, Jens; Wilming, Henrik

2017-07-14

While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics, such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT) indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit nontrivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.

Towards Holography via Quantum Source-Channel Codes

NASA Astrophysics Data System (ADS)

Pastawski, Fernando; Eisert, Jens; Wilming, Henrik

2017-07-01

While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics, such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT) indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit nontrivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.

An engineer's view on genetic information and biological evolution.

PubMed

Battail, Gérard

2004-01-01

We develop ideas on genome replication introduced in Battail [Europhys. Lett. 40 (1997) 343]. Starting with the hypothesis that the genome replication process uses error-correcting means, and the auxiliary one that nested codes are used to this end, we first review the concepts of redundancy and error-correcting codes. Then we show that these hypotheses imply that: distinct species exist with a hierarchical taxonomy, there is a trend of evolution towards complexity, and evolution proceeds by discrete jumps. At least the first two features above may be considered as biological facts so, in the absence of direct evidence, they provide an indirect proof in favour of the hypothesized error-correction system. The very high redundancy of genomes makes it possible. In order to explain how it is implemented, we suggest that soft codes and replication decoding, to be briefly described, are plausible candidates. Experimentally proven properties of long-range correlation of the DNA message substantiate this claim.

Error detection and correction unit with built-in self-test capability for spacecraft applications

NASA Technical Reports Server (NTRS)

Timoc, Constantin

1990-01-01

The objective of this project was to research and develop a 32-bit single chip Error Detection and Correction unit capable of correcting all single bit errors and detecting all double bit errors in the memory systems of a spacecraft. We designed the 32-bit EDAC (Error Detection and Correction unit) based on a modified Hamming code and according to the design specifications and performance requirements. We constructed a laboratory prototype (breadboard) which was converted into a fault simulator. The correctness of the design was verified on the breadboard using an exhaustive set of test cases. A logic diagram of the EDAC was delivered to JPL Section 514 on 4 Oct. 1988.

Virtex-5QV Self Scrubber

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wojahn, Christopher K.

2015-10-20

This HDL code (hereafter referred to as "software") implements circuitry in Xilinx Virtex-5QV Field Programmable Gate Array (FPGA) hardware. This software allows the device to self-check the consistency of its own configuration memory for radiation-induced errors. The software then provides the capability to correct any single-bit errors detected in the memory using the device's inherent circuitry, or reload corrupted memory frames when larger errors occur that cannot be corrected with the device's built-in error correction and detection scheme.

Error-trellis Syndrome Decoding Techniques for Convolutional Codes

NASA Technical Reports Server (NTRS)

Reed, I. S.; Truong, T. K.

1984-01-01

An error-trellis syndrome decoding technique for convolutional codes is developed. This algorithm is then applied to the entire class of systematic convolutional codes and to the high-rate, Wyner-Ash convolutional codes. A special example of the one-error-correcting Wyner-Ash code, a rate 3/4 code, is treated. The error-trellis syndrome decoding method applied to this example shows in detail how much more efficient syndrome decoding is than Viterbi decoding if applied to the same problem. For standard Viterbi decoding, 64 states are required, whereas in the example only 7 states are needed. Also, within the 7 states required for decoding, many fewer transitions are needed between the states.

Error-trellis syndrome decoding techniques for convolutional codes

NASA Technical Reports Server (NTRS)

Reed, I. S.; Truong, T. K.

1985-01-01

An error-trellis syndrome decoding technique for convolutional codes is developed. This algorithm is then applied to the entire class of systematic convolutional codes and to the high-rate, Wyner-Ash convolutional codes. A special example of the one-error-correcting Wyner-Ash code, a rate 3/4 code, is treated. The error-trellis syndrome decoding method applied to this example shows in detail how much more efficient syndrome decordig is than Viterbi decoding if applied to the same problem. For standard Viterbi decoding, 64 states are required, whereas in the example only 7 states are needed. Also, within the 7 states required for decoding, many fewer transitions are needed between the states.

Quantum Error Correction Protects Quantum Search Algorithms Against Decoherence

PubMed Central

Botsinis, Panagiotis; Babar, Zunaira; Alanis, Dimitrios; Chandra, Daryus; Nguyen, Hung; Ng, Soon Xin; Hanzo, Lajos

2016-01-01

When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels’ deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover’s QSA at an aggressive depolarizing probability of 10−3, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane’s quantum error correction code is employed. Finally, apart from Steane’s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered. PMID:27924865

Reed Solomon codes for error control in byte organized computer memory systems

NASA Technical Reports Server (NTRS)

Lin, S.; Costello, D. J., Jr.

1984-01-01

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256K-bit DRAM's are organized in 32Kx8 bit-bytes. Byte oriented codes such as Reed Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special decoding techniques for extended single-and-double-error-correcting RS codes which are capable of high speed operation are presented. These techniques are designed to find the error locations and the error values directly from the syndrome without having to use the iterative algorithm to find the error locator polynomial.

Trace-shortened Reed-Solomon codes

NASA Technical Reports Server (NTRS)

Mceliece, R. J.; Solomon, G.

1994-01-01

Reed-Solomon (RS) codes have been part of standard NASA telecommunications systems for many years. RS codes are character-oriented error-correcting codes, and their principal use in space applications has been as outer codes in concatenated coding systems. However, for a given character size, say m bits, RS codes are limited to a length of, at most, 2(exp m). It is known in theory that longer character-oriented codes would be superior to RS codes in concatenation applications, but until recently no practical class of 'long' character-oriented codes had been discovered. In 1992, however, Solomon discovered an extensive class of such codes, which are now called trace-shortened Reed-Solomon (TSRS) codes. In this article, we will continue the study of TSRS codes. Our main result is a formula for the dimension of any TSRS code, as a function of its error-correcting power. Using this formula, we will give several examples of TSRS codes, some of which look very promising as candidate outer codes in high-performance coded telecommunications systems.

Quantum error-correcting code for ternary logic

NASA Astrophysics Data System (ADS)

Majumdar, Ritajit; Basu, Saikat; Ghosh, Shibashis; Sur-Kolay, Susmita

2018-05-01

Ternary quantum systems are being studied because they provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the coefficient of one of the basis states is zero. Hence both (2 ×2 ) -dimensional and (3 ×3 ) -dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible (2 ×2 ) -dimensional as well as (3 ×3 ) -dimensional Pauli errors in qutrits and show that any pairwise bit swap error can be expressed as a linear combination of shift errors and phase errors, (ii) propose a special type of error called a quantum superposition error and show its equivalence to arbitrary rotation, (iii) formulate a nine-qutrit code which can correct a single error in a qutrit, and (iv) provide its stabilizer and circuit realization.

Final Report: Correctness Tools for Petascale Computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mellor-Crummey, John

2014-10-27

In the course of developing parallel programs for leadership computing systems, subtle programming errors often arise that are extremely difficult to diagnose without tools. To meet this challenge, University of Maryland, the University of Wisconsin—Madison, and Rice University worked to develop lightweight tools to help code developers pinpoint a variety of program correctness errors that plague parallel scientific codes. The aim of this project was to develop software tools that help diagnose program errors including memory leaks, memory access errors, round-off errors, and data races. Research at Rice University focused on developing algorithms and data structures to support efficient monitoringmore » of multithreaded programs for memory access errors and data races. This is a final report about research and development work at Rice University as part of this project.« less

Joint Source-Channel Coding by Means of an Oversampled Filter Bank Code

NASA Astrophysics Data System (ADS)

Marinkovic, Slavica; Guillemot, Christine

2006-12-01

Quantized frame expansions based on block transforms and oversampled filter banks (OFBs) have been considered recently as joint source-channel codes (JSCCs) for erasure and error-resilient signal transmission over noisy channels. In this paper, we consider a coding chain involving an OFB-based signal decomposition followed by scalar quantization and a variable-length code (VLC) or a fixed-length code (FLC). This paper first examines the problem of channel error localization and correction in quantized OFB signal expansions. The error localization problem is treated as an[InlineEquation not available: see fulltext.]-ary hypothesis testing problem. The likelihood values are derived from the joint pdf of the syndrome vectors under various hypotheses of impulse noise positions, and in a number of consecutive windows of the received samples. The error amplitudes are then estimated by solving the syndrome equations in the least-square sense. The message signal is reconstructed from the corrected received signal by a pseudoinverse receiver. We then improve the error localization procedure by introducing a per-symbol reliability information in the hypothesis testing procedure of the OFB syndrome decoder. The per-symbol reliability information is produced by the soft-input soft-output (SISO) VLC/FLC decoders. This leads to the design of an iterative algorithm for joint decoding of an FLC and an OFB code. The performance of the algorithms developed is evaluated in a wavelet-based image coding system.

Error correcting circuit design with carbon nanotube field effect transistors

NASA Astrophysics Data System (ADS)

Liu, Xiaoqiang; Cai, Li; Yang, Xiaokuo; Liu, Baojun; Liu, Zhongyong

2018-03-01

In this work, a parallel error correcting circuit based on (7, 4) Hamming code is designed and implemented with carbon nanotube field effect transistors, and its function is validated by simulation in HSpice with the Stanford model. A grouping method which is able to correct multiple bit errors in 16-bit and 32-bit application is proposed, and its error correction capability is analyzed. Performance of circuits implemented with CNTFETs and traditional MOSFETs respectively is also compared, and the former shows a 34.4% decrement of layout area and a 56.9% decrement of power consumption.

Author Correction: Emission budgets and pathways consistent with limiting warming to 1.5 °C

NASA Astrophysics Data System (ADS)

Millar, Richard J.; Fuglestvedt, Jan S.; Friedlingstein, Pierre; Rogelj, Joeri; Grubb, Michael J.; Matthews, H. Damon; Skeie, Ragnhild B.; Forster, Piers M.; Frame, David J.; Allen, Myles R.

2018-06-01

In the version of this Article originally published, a coding error resulted in the erroneous inclusion of a subset of RCP4.5 and RCP8.5 simulations in the sets used for RCP2.6 and RCP6, respectively, leading to an incorrect depiction of the data of the latter two sets in Fig. 1b and RCP2.6 in Table 2. This coding error has now been corrected. The graphic and quantitative changes in the corrected Fig. 1b and Table 2 are contrasted with the originally published display items below. The core conclusions of the paper are not affected, but some numerical values and statements have also been updated as a result; these are listed below. All these errors have now been corrected in the online versions of this Article.

Smart photodetector arrays for error control in page-oriented optical memory

NASA Astrophysics Data System (ADS)

Schaffer, Maureen Elizabeth

1998-12-01

Page-oriented optical memories (POMs) have been proposed to meet high speed, high capacity storage requirements for input/output intensive computer applications. This technology offers the capability for storage and retrieval of optical data in two-dimensional pages resulting in high throughput data rates. Since currently measured raw bit error rates for these systems fall several orders of magnitude short of industry requirements for binary data storage, powerful error control codes must be adopted. These codes must be designed to take advantage of the two-dimensional memory output. In addition, POMs require an optoelectronic interface to transfer the optical data pages to one or more electronic host systems. Conventional charge coupled device (CCD) arrays can receive optical data in parallel, but the relatively slow serial electronic output of these devices creates a system bottleneck thereby eliminating the POM advantage of high transfer rates. Also, CCD arrays are "unintelligent" interfaces in that they offer little data processing capabilities. The optical data page can be received by two-dimensional arrays of "smart" photo-detector elements that replace conventional CCD arrays. These smart photodetector arrays (SPAs) can perform fast parallel data decoding and error control, thereby providing an efficient optoelectronic interface between the memory and the electronic computer. This approach optimizes the computer memory system by combining the massive parallelism and high speed of optics with the diverse functionality, low cost, and local interconnection efficiency of electronics. In this dissertation we examine the design of smart photodetector arrays for use as the optoelectronic interface for page-oriented optical memory. We review options and technologies for SPA fabrication, develop SPA requirements, and determine SPA scalability constraints with respect to pixel complexity, electrical power dissipation, and optical power limits. Next, we examine data modulation and error correction coding for the purpose of error control in the POM system. These techniques are adapted, where possible, for 2D data and evaluated as to their suitability for a SPA implementation in terms of BER, code rate, decoder time and pixel complexity. Our analysis shows that differential data modulation combined with relatively simple block codes known as array codes provide a powerful means to achieve the desired data transfer rates while reducing error rates to industry requirements. Finally, we demonstrate the first smart photodetector array designed to perform parallel error correction on an entire page of data and satisfy the sustained data rates of page-oriented optical memories. Our implementation integrates a monolithic PN photodiode array and differential input receiver for optoelectronic signal conversion with a cluster error correction code using 0.35-mum CMOS. This approach provides high sensitivity, low electrical power dissipation, and fast parallel correction of 2 x 2-bit cluster errors in an 8 x 8 bit code block to achieve corrected output data rates scalable to 102 Gbps in the current technology increasing to 1.88 Tbps in 0.1-mum CMOS.

Fault-tolerant measurement-based quantum computing with continuous-variable cluster states.

PubMed

Menicucci, Nicolas C

2014-03-28

A long-standing open question about Gaussian continuous-variable cluster states is whether they enable fault-tolerant measurement-based quantum computation. The answer is yes. Initial squeezing in the cluster above a threshold value of 20.5 dB ensures that errors from finite squeezing acting on encoded qubits are below the fault-tolerance threshold of known qubit-based error-correcting codes. By concatenating with one of these codes and using ancilla-based error correction, fault-tolerant measurement-based quantum computation of theoretically indefinite length is possible with finitely squeezed cluster states.

QR Code Mania!

ERIC Educational Resources Information Center

Shumack, Kellie A.; Reilly, Erin; Chamberlain, Nik

2013-01-01

space, has error-correction capacity, and can be read from any direction. These codes are used in manufacturing, shipping, and marketing, as well as in education. QR codes can be created to produce…

FORTRAN Automated Code Evaluation System (faces) system documentation, version 2, mod 0. [error detection codes/user manuals (computer programs)

NASA Technical Reports Server (NTRS)

1975-01-01

A system is presented which processes FORTRAN based software systems to surface potential problems before they become execution malfunctions. The system complements the diagnostic capabilities of compilers, loaders, and execution monitors rather than duplicating these functions. Also, it emphasizes frequent sources of FORTRAN problems which require inordinate manual effort to identify. The principle value of the system is extracting small sections of unusual code from the bulk of normal sequences. Code structures likely to cause immediate or future problems are brought to the user's attention. These messages stimulate timely corrective action of solid errors and promote identification of 'tricky' code. Corrective action may require recoding or simply extending software documentation to explain the unusual technique.

Coded Modulation in C and MATLAB

NASA Technical Reports Server (NTRS)

Hamkins, Jon; Andrews, Kenneth S.

2011-01-01

This software, written separately in C and MATLAB as stand-alone packages with equivalent functionality, implements encoders and decoders for a set of nine error-correcting codes and modulators and demodulators for five modulation types. The software can be used as a single program to simulate the performance of such coded modulation. The error-correcting codes implemented are the nine accumulate repeat-4 jagged accumulate (AR4JA) low-density parity-check (LDPC) codes, which have been approved for international standardization by the Consultative Committee for Space Data Systems, and which are scheduled to fly on a series of NASA missions in the Constellation Program. The software implements the encoder and decoder functions, and contains compressed versions of generator and parity-check matrices used in these operations.

Using Correction Codes to Enhance Understanding of 4-Parts Harmony

ERIC Educational Resources Information Center

Engür, Doruk

2018-01-01

The effective ways of error correction in teaching musical harmony have been neglected. Making students realize their mistakes and have them think over them are assumed to be helpful in harmony teaching. In this sense, correction code technique is thought to be beneficial for students to realize their mistakes and solve them on their own. Forty…

Analysis on applicable error-correcting code strength of storage class memory and NAND flash in hybrid storage

NASA Astrophysics Data System (ADS)

Matsui, Chihiro; Kinoshita, Reika; Takeuchi, Ken

2018-04-01

A hybrid of storage class memory (SCM) and NAND flash is a promising technology for high performance storage. Error correction is inevitable on SCM and NAND flash because their bit error rate (BER) increases with write/erase (W/E) cycles, data retention, and program/read disturb. In addition, scaling and multi-level cell technologies increase BER. However, error-correcting code (ECC) degrades storage performance because of extra memory reading and encoding/decoding time. Therefore, applicable ECC strength of SCM and NAND flash is evaluated independently by fixing ECC strength of one memory in the hybrid storage. As a result, weak BCH ECC with small correctable bit is recommended for the hybrid storage with large SCM capacity because SCM is accessed frequently. In contrast, strong and long-latency LDPC ECC can be applied to NAND flash in the hybrid storage with large SCM capacity because large-capacity SCM improves the storage performance.

Quantum subsystems: Exploring the complementarity of quantum privacy and error correction

NASA Astrophysics Data System (ADS)

Jochym-O'Connor, Tomas; Kribs, David W.; Laflamme, Raymond; Plosker, Sarah

2014-09-01

This paper addresses and expands on the contents of the recent Letter [Phys. Rev. Lett. 111, 030502 (2013), 10.1103/PhysRevLett.111.030502] discussing private quantum subsystems. Here we prove several previously presented results, including a condition for a given random unitary channel to not have a private subspace (although this does not mean that private communication cannot occur, as was previously demonstrated via private subsystems) and algebraic conditions that characterize when a general quantum subsystem or subspace code is private for a quantum channel. These conditions can be regarded as the private analog of the Knill-Laflamme conditions for quantum error correction, and we explore how the conditions simplify in some special cases. The bridge between quantum cryptography and quantum error correction provided by complementary quantum channels motivates the study of a new, more general definition of quantum error-correcting code, and we initiate this study here. We also consider the concept of complementarity for the general notion of a private quantum subsystem.

Syndrome source coding and its universal generalization

NASA Technical Reports Server (NTRS)

Ancheta, T. C., Jr.

1975-01-01

A method of using error-correcting codes to obtain data compression, called syndrome-source-coding, is described in which the source sequence is treated as an error pattern whose syndrome forms the compressed data. It is shown that syndrome-source-coding can achieve arbitrarily small distortion with the number of compressed digits per source digit arbitrarily close to the entropy of a binary memoryless source. A universal generalization of syndrome-source-coding is formulated which provides robustly-effective, distortionless, coding of source ensembles.

Error suppression and correction for quantum annealing

NASA Astrophysics Data System (ADS)

Lidar, Daniel

While adiabatic quantum computing and quantum annealing enjoy a certain degree of inherent robustness against excitations and control errors, there is no escaping the need for error correction or suppression. In this talk I will give an overview of our work on the development of such error correction and suppression methods. We have experimentally tested one such method combining encoding, energy penalties and decoding, on a D-Wave Two processor, with encouraging results. Mean field theory shows that this can be explained in terms of a softening of the closing of the gap due to the energy penalty, resulting in protection against excitations that occur near the quantum critical point. Decoding recovers population from excited states and enhances the success probability of quantum annealing. Moreover, we have demonstrated that using repetition codes with increasing code distance can lower the effective temperature of the annealer. References: K.L. Pudenz, T. Albash, D.A. Lidar, ``Error corrected quantum annealing with hundreds of qubits'', Nature Commun. 5, 3243 (2014). K.L. Pudenz, T. Albash, D.A. Lidar, ``Quantum annealing correction for random Ising problems'', Phys. Rev. A. 91, 042302 (2015). S. Matsuura, H. Nishimori, T. Albash, D.A. Lidar, ``Mean Field Analysis of Quantum Annealing Correction''. arXiv:1510.07709. W. Vinci et al., in preparation.

Both channel coding and wavefront correction on the turbulence mitigation of optical communications using orbital angular momentum multiplexing

NASA Astrophysics Data System (ADS)

Zhao, Shengmei; Wang, Le; Zou, Li; Gong, Longyan; Cheng, Weiwen; Zheng, Baoyu; Chen, Hanwu

2016-10-01

A free-space optical (FSO) communication link with multiplexed orbital angular momentum (OAM) modes has been demonstrated to largely enhance the system capacity without a corresponding increase in spectral bandwidth, but the performance of the link is unavoidably degraded by atmospheric turbulence (AT). In this paper, we propose a turbulence mitigation scheme to improve AT tolerance of the OAM-multiplexed FSO communication link using both channel coding and wavefront correction. In the scheme, we utilize a wavefront correction method to mitigate the phase distortion first, and then we use a channel code to further correct the errors in each OAM mode. The improvement of AT tolerance is discussed over the performance of the link with or without channel coding/wavefront correction. The results show that the bit error rate performance has been improved greatly. The detrimental effect of AT on the OAM-multiplexed FSO communication link could be removed by the proposed scheme even in the relatively strong turbulence regime, such as Cn2 = 3.6 ×10-14m - 2 / 3.

Improved HDRG decoders for qudit and non-Abelian quantum error correction

NASA Astrophysics Data System (ADS)

Hutter, Adrian; Loss, Daniel; Wootton, James R.

2015-03-01

Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction. Due to their versatility, they have been used to decode systems with fractal logical operators, color codes, qudit topological codes, and non-Abelian systems. In this work, we develop a method of performing HDRG decoding which combines strengths of existing decoders and further improves upon them. In particular, we increase the minimal number of errors necessary for a logical error in a system of linear size L from \\Theta ({{L}2/3}) to Ω ({{L}1-ε }) for any ε \\gt 0. We apply our algorithm to decoding D({{{Z}}d}) quantum double models and a non-Abelian anyon model with Fibonacci-like fusion rules, and show that it indeed significantly outperforms previous HDRG decoders. Furthermore, we provide the first study of continuous error correction with imperfect syndrome measurements for the D({{{Z}}d}) quantum double models. The parallelized runtime of our algorithm is poly(log L) for the perfect measurement case. In the continuous case with imperfect syndrome measurements, the averaged runtime is O(1) for Abelian systems, while continuous error correction for non-Abelian anyons stays an open problem.

A concatenated coding scheme for error control

NASA Technical Reports Server (NTRS)

Lin, S.

1985-01-01

A concatenated coding scheme for error control in data communications is analyzed. The inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. The probability of undetected error of the above error control scheme is derived and upper bounded. Two specific exmaples are analyzed. In the first example, the inner code is a distance-4 shortened Hamming code with generator polynomial (X+1)(X(6)+X+1) = X(7)+X(6)+X(2)+1 and the outer code is a distance-4 shortened Hamming code with generator polynomial (X+1)X(15+X(14)+X(13)+X(12)+X(4)+X(3)+X(2)+X+1) = X(16)+X(12)+X(5)+1 which is the X.25 standard for packet-switched data network. This example is proposed for error control on NASA telecommand links. In the second example, the inner code is the same as that in the first example but the outer code is a shortened Reed-Solomon code with symbols from GF(2(8)) and generator polynomial (X+1)(X+alpha) where alpha is a primitive element in GF(z(8)).

The statistical significance of error probability as determined from decoding simulations for long codes

NASA Technical Reports Server (NTRS)

Massey, J. L.

1976-01-01

The very low error probability obtained with long error-correcting codes results in a very small number of observed errors in simulation studies of practical size and renders the usual confidence interval techniques inapplicable to the observed error probability. A natural extension of the notion of a 'confidence interval' is made and applied to such determinations of error probability by simulation. An example is included to show the surprisingly great significance of as few as two decoding errors in a very large number of decoding trials.

Error suppression via complementary gauge choices in Reed-Muller codes

NASA Astrophysics Data System (ADS)

Chamberland, Christopher; Jochym-O'Connor, Tomas

2017-09-01

Concatenation of two quantum error-correcting codes with complementary sets of transversal gates can provide a means toward universal fault-tolerant quantum computation. We first show that it is generally preferable to choose the inner code with the higher pseudo-threshold to achieve lower logical failure rates. We then explore the threshold properties of a wide range of concatenation schemes. Notably, we demonstrate that the concatenation of complementary sets of Reed-Muller codes can increase the code capacity threshold under depolarizing noise when compared to extensions of previously proposed concatenation models. We also analyze the properties of logical errors under circuit-level noise, showing that smaller codes perform better for all sampled physical error rates. Our work provides new insights into the performance of universal concatenated quantum codes for both code capacity and circuit-level noise.

Iterative channel decoding of FEC-based multiple-description codes.

PubMed

Chang, Seok-Ho; Cosman, Pamela C; Milstein, Laurence B

2012-03-01

Multiple description coding has been receiving attention as a robust transmission framework for multimedia services. This paper studies the iterative decoding of FEC-based multiple description codes. The proposed decoding algorithms take advantage of the error detection capability of Reed-Solomon (RS) erasure codes. The information of correctly decoded RS codewords is exploited to enhance the error correction capability of the Viterbi algorithm at the next iteration of decoding. In the proposed algorithm, an intradescription interleaver is synergistically combined with the iterative decoder. The interleaver does not affect the performance of noniterative decoding but greatly enhances the performance when the system is iteratively decoded. We also address the optimal allocation of RS parity symbols for unequal error protection. For the optimal allocation in iterative decoding, we derive mathematical equations from which the probability distributions of description erasures can be generated in a simple way. The performance of the algorithm is evaluated over an orthogonal frequency-division multiplexing system. The results show that the performance of the multiple description codes is significantly enhanced.

Performance and structure of single-mode bosonic codes

NASA Astrophysics Data System (ADS)

Albert, Victor V.; Noh, Kyungjoo; Duivenvoorden, Kasper; Young, Dylan J.; Brierley, R. T.; Reinhold, Philip; Vuillot, Christophe; Li, Linshu; Shen, Chao; Girvin, S. M.; Terhal, Barbara M.; Jiang, Liang

2018-03-01

The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat-binomial-GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multiqubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a multiqudit code.

The random coding bound is tight for the average code.

NASA Technical Reports Server (NTRS)

Gallager, R. G.

1973-01-01

The random coding bound of information theory provides a well-known upper bound to the probability of decoding error for the best code of a given rate and block length. The bound is constructed by upperbounding the average error probability over an ensemble of codes. The bound is known to give the correct exponential dependence of error probability on block length for transmission rates above the critical rate, but it gives an incorrect exponential dependence at rates below a second lower critical rate. Here we derive an asymptotic expression for the average error probability over the ensemble of codes used in the random coding bound. The result shows that the weakness of the random coding bound at rates below the second critical rate is due not to upperbounding the ensemble average, but rather to the fact that the best codes are much better than the average at low rates.

Coordinated design of coding and modulation systems

NASA Technical Reports Server (NTRS)

Massey, J. L.

1976-01-01

Work on partial unit memory codes continued; it was shown that for a given virtual state complexity, the maximum free distance over the class of all convolutional codes is achieved within the class of unit memory codes. The effect of phase-lock loop (PLL) tracking error on coding system performance was studied by using the channel cut-off rate as the measure of quality of a modulation system. Optimum modulation signal sets for a non-white Gaussian channel considered an heuristic selection rule based on a water-filling argument. The use of error correcting codes to perform data compression by the technique of syndrome source coding was researched and a weight-and-error-locations scheme was developed that is closely related to LDSC coding.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Omkar, S.; Srikanth, R., E-mail: srik@poornaprajna.org; Banerjee, Subhashish

A protocol based on quantum error correction based characterization of quantum dynamics (QECCD) is developed for quantum process tomography on a two-qubit system interacting dissipatively with a vacuum bath. The method uses a 5-qubit quantum error correcting code that corrects arbitrary errors on the first two qubits, and also saturates the quantum Hamming bound. The dissipative interaction with a vacuum bath allows for both correlated and independent noise on the two-qubit system. We study the dependence of the degree of the correlation of the noise on evolution time and inter-qubit separation.

Minimizing human error in radiopharmaceutical preparation and administration via a bar code-enhanced nuclear pharmacy management system.

PubMed

Hakala, John L; Hung, Joseph C; Mosman, Elton A

2012-09-01

The objective of this project was to ensure correct radiopharmaceutical administration through the use of a bar code system that links patient and drug profiles with on-site information management systems. This new combined system would minimize the amount of manual human manipulation, which has proven to be a primary source of error. The most common reason for dosing errors is improper patient identification when a dose is obtained from the nuclear pharmacy or when a dose is administered. A standardized electronic transfer of information from radiopharmaceutical preparation to injection will further reduce the risk of misadministration. Value stream maps showing the flow of the patient dose information, as well as potential points of human error, were developed. Next, a future-state map was created that included proposed corrections for the most common critical sites of error. Transitioning the current process to the future state will require solutions that address these sites. To optimize the future-state process, a bar code system that links the on-site radiology management system with the nuclear pharmacy management system was proposed. A bar-coded wristband connects the patient directly to the electronic information systems. The bar code-enhanced process linking the patient dose with the electronic information reduces the number of crucial points for human error and provides a framework to ensure that the prepared dose reaches the correct patient. Although the proposed flowchart is designed for a site with an in-house central nuclear pharmacy, much of the framework could be applied by nuclear medicine facilities using unit doses. An electronic connection between information management systems to allow the tracking of a radiopharmaceutical from preparation to administration can be a useful tool in preventing the mistakes that are an unfortunate reality for any facility.

Ancient DNA sequence revealed by error-correcting codes.

PubMed

Brandão, Marcelo M; Spoladore, Larissa; Faria, Luzinete C B; Rocha, Andréa S L; Silva-Filho, Marcio C; Palazzo, Reginaldo

2015-07-10

A previously described DNA sequence generator algorithm (DNA-SGA) using error-correcting codes has been employed as a computational tool to address the evolutionary pathway of the genetic code. The code-generated sequence alignment demonstrated that a residue mutation revealed by the code can be found in the same position in sequences of distantly related taxa. Furthermore, the code-generated sequences do not promote amino acid changes in the deviant genomes through codon reassignment. A Bayesian evolutionary analysis of both code-generated and homologous sequences of the Arabidopsis thaliana malate dehydrogenase gene indicates an approximately 1 MYA divergence time from the MDH code-generated sequence node to its paralogous sequences. The DNA-SGA helps to determine the plesiomorphic state of DNA sequences because a single nucleotide alteration often occurs in distantly related taxa and can be found in the alternative codon patterns of noncanonical genetic codes. As a consequence, the algorithm may reveal an earlier stage of the evolution of the standard code.

Ancient DNA sequence revealed by error-correcting codes

PubMed Central

Brandão, Marcelo M.; Spoladore, Larissa; Faria, Luzinete C. B.; Rocha, Andréa S. L.; Silva-Filho, Marcio C.; Palazzo, Reginaldo

2015-01-01

A previously described DNA sequence generator algorithm (DNA-SGA) using error-correcting codes has been employed as a computational tool to address the evolutionary pathway of the genetic code. The code-generated sequence alignment demonstrated that a residue mutation revealed by the code can be found in the same position in sequences of distantly related taxa. Furthermore, the code-generated sequences do not promote amino acid changes in the deviant genomes through codon reassignment. A Bayesian evolutionary analysis of both code-generated and homologous sequences of the Arabidopsis thaliana malate dehydrogenase gene indicates an approximately 1 MYA divergence time from the MDH code-generated sequence node to its paralogous sequences. The DNA-SGA helps to determine the plesiomorphic state of DNA sequences because a single nucleotide alteration often occurs in distantly related taxa and can be found in the alternative codon patterns of noncanonical genetic codes. As a consequence, the algorithm may reveal an earlier stage of the evolution of the standard code. PMID:26159228

Crosstalk eliminating and low-density parity-check codes for photochromic dual-wavelength storage

NASA Astrophysics Data System (ADS)

Wang, Meicong; Xiong, Jianping; Jian, Jiqi; Jia, Huibo

2005-01-01

Multi-wavelength storage is an approach to increase the memory density with the problem of crosstalk to be deal with. We apply Low Density Parity Check (LDPC) codes as error-correcting codes in photochromic dual-wavelength optical storage based on the investigation of LDPC codes in optical data storage. A proper method is applied to reduce the crosstalk and simulation results show that this operation is useful to improve Bit Error Rate (BER) performance. At the same time we can conclude that LDPC codes outperform RS codes in crosstalk channel.

A study of high density bit transition requirements versus the effects on BCH error correcting coding

NASA Technical Reports Server (NTRS)

Ingels, F.; Schoggen, W. O.

1981-01-01

The various methods of high bit transition density encoding are presented, their relative performance is compared in so far as error propagation characteristics, transition properties and system constraints are concerned. A computer simulation of the system using the specific PN code recommended, is included.

Dissipative quantum error correction and application to quantum sensing with trapped ions.

PubMed

Reiter, F; Sørensen, A S; Zoller, P; Muschik, C A

2017-11-28

Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error-correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an engineered environment protect the qubit against spin-flips or phase-flips. Our dissipative error correction scheme operates in a continuous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.

Predicted blood glucose from insulin administration based on values from miscoded glucose meters.

PubMed

Raine, Charles H; Pardo, Scott; Parkes, Joan Lee

2008-07-01

The proper use of many types of self-monitored blood glucose (SMBG) meters requires calibration to match strip code. Studies have demonstrated the occurrence and impact on insulin dose of coding errors with SMBG meters. This paper reflects additional analyses performed with data from Raine et al. (JDST, 2:205-210, 2007). It attempts to relate potential insulin dose errors to possible adverse blood glucose outcomes when glucose meters are miscoded. Five sets of glucose meters were used. Two sets of meters were autocoded and therefore could not be miscoded, and three sets required manual coding. Two of each set of manually coded meters were deliberately miscoded, and one from each set was properly coded. Subjects (n = 116) had finger stick blood glucose obtained at fasting, as well as at 1 and 2 hours after a fixed meal (Boost((R)); Novartis Medical Nutrition U.S., Basel, Switzerland). Deviations of meter blood glucose results from the reference method (YSI) were used to predict insulin dose errors and resultant blood glucose outcomes based on these deviations. Using insulin sensitivity data, it was determined that, given an actual blood glucose of 150-400 mg/dl, an error greater than +40 mg/dl would be required to calculate an insulin dose sufficient to produce a blood glucose of less than 70 mg/dl. Conversely, an error less than or equal to -70 mg/dl would be required to derive an insulin dose insufficient to correct an elevated blood glucose to less than 180 mg/dl. For miscoded meters, the estimated probability to produce a blood glucose reduction to less than or equal to 70 mg/dl was 10.40%. The corresponding probabilities for autocoded and correctly coded manual meters were 2.52% (p < 0.0001) and 1.46% (p < 0.0001), respectively. Furthermore, the errors from miscoded meters were large enough to produce a calculated blood glucose outcome less than or equal to 50 mg/dl in 42 of 833 instances. Autocoded meters produced zero (0) outcomes less than or equal to 50 mg/dl out of 279 instances, and correctly coded manual meters produced 1 of 416. Improperly coded blood glucose meters present the potential for insulin dose errors and resultant clinically significant hypoglycemia or hyperglycemia. Patients should be instructed and periodically reinstructed in the proper use of blood glucose meters, particularly for meters that require coding.

Quantum Steganography and Quantum Error-Correction

ERIC Educational Resources Information Center

Shaw, Bilal A.

2010-01-01

Quantum error-correcting codes have been the cornerstone of research in quantum information science (QIS) for more than a decade. Without their conception, quantum computers would be a footnote in the history of science. When researchers embraced the idea that we live in a world where the effects of a noisy environment cannot completely be…

Open quantum systems and error correction

NASA Astrophysics Data System (ADS)

Shabani Barzegar, Alireza

Quantum effects can be harnessed to manipulate information in a desired way. Quantum systems which are designed for this purpose are suffering from harming interaction with their surrounding environment or inaccuracy in control forces. Engineering different methods to combat errors in quantum devices are highly demanding. In this thesis, I focus on realistic formulations of quantum error correction methods. A realistic formulation is the one that incorporates experimental challenges. This thesis is presented in two sections of open quantum system and quantum error correction. Chapters 2 and 3 cover the material on open quantum system theory. It is essential to first study a noise process then to contemplate methods to cancel its effect. In the second chapter, I present the non-completely positive formulation of quantum maps. Most of these results are published in [Shabani and Lidar, 2009b,a], except a subsection on geometric characterization of positivity domain of a quantum map. The real-time formulation of the dynamics is the topic of the third chapter. After introducing the concept of Markovian regime, A new post-Markovian quantum master equation is derived, published in [Shabani and Lidar, 2005a]. The section of quantum error correction is presented in three chapters of 4, 5, 6 and 7. In chapter 4, we introduce a generalized theory of decoherence-free subspaces and subsystems (DFSs), which do not require accurate initialization (published in [Shabani and Lidar, 2005b]). In Chapter 5, we present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the encoding, recovery, or both, and is amenable to approximations that significantly improve computational cost while retaining fidelity (see [Kosut et al., 2008] for a published version). Chapter 6 is devoted to a theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This is a complementary to the second chapter which is published in [Shabani and Lidar, 2007]. In the last chapter 7 before the conclusion, a formulation for evaluating the performance of quantum error correcting codes for a general error model is presented, also published in [Shabani, 2005]. In this formulation, the correlation between errors is quantified by a Hamiltonian description of the noise process. In particular, we consider Calderbank-Shor-Steane codes and observe a better performance in the presence of correlated errors depending on the timing of the error recovery.

Phenotypic Graphs and Evolution Unfold the Standard Genetic Code as the Optimal

NASA Astrophysics Data System (ADS)

Zamudio, Gabriel S.; José, Marco V.

2018-03-01

In this work, we explicitly consider the evolution of the Standard Genetic Code (SGC) by assuming two evolutionary stages, to wit, the primeval RNY code and two intermediate codes in between. We used network theory and graph theory to measure the connectivity of each phenotypic graph. The connectivity values are compared to the values of the codes under different randomization scenarios. An error-correcting optimal code is one in which the algebraic connectivity is minimized. We show that the SGC is optimal in regard to its robustness and error-tolerance when compared to all random codes under different assumptions.

New coding advances for deep space communications

NASA Technical Reports Server (NTRS)

Yuen, Joseph H.

1987-01-01

Advances made in error-correction coding for deep space communications are described. The code believed to be the best is a (15, 1/6) convolutional code, with maximum likelihood decoding; when it is concatenated with a 10-bit Reed-Solomon code, it achieves a bit error rate of 10 to the -6th, at a bit SNR of 0.42 dB. This code outperforms the Voyager code by 2.11 dB. The use of source statics in decoding convolutionally encoded Voyager images from the Uranus encounter is investigated, and it is found that a 2 dB decoding gain can be achieved.

Tailored Codes for Small Quantum Memories

NASA Astrophysics Data System (ADS)

Robertson, Alan; Granade, Christopher; Bartlett, Stephen D.; Flammia, Steven T.

2017-12-01

We demonstrate that small quantum memories, realized via quantum error correction in multiqubit devices, can benefit substantially by choosing a quantum code that is tailored to the relevant error model of the system. For a biased noise model, with independent bit and phase flips occurring at different rates, we show that a single code greatly outperforms the well-studied Steane code across the full range of parameters of the noise model, including for unbiased noise. In fact, this tailored code performs almost optimally when compared with 10 000 randomly selected stabilizer codes of comparable experimental complexity. Tailored codes can even outperform the Steane code with realistic experimental noise, and without any increase in the experimental complexity, as we demonstrate by comparison in the observed error model in a recent seven-qubit trapped ion experiment.

Performance of MIMO-OFDM using convolution codes with QAM modulation

NASA Astrophysics Data System (ADS)

Astawa, I. Gede Puja; Moegiharto, Yoedy; Zainudin, Ahmad; Salim, Imam Dui Agus; Anggraeni, Nur Annisa

2014-04-01

Performance of Orthogonal Frequency Division Multiplexing (OFDM) system can be improved by adding channel coding (error correction code) to detect and correct errors that occur during data transmission. One can use the convolution code. This paper present performance of OFDM using Space Time Block Codes (STBC) diversity technique use QAM modulation with code rate ½. The evaluation is done by analyzing the value of Bit Error Rate (BER) vs Energy per Bit to Noise Power Spectral Density Ratio (Eb/No). This scheme is conducted 256 subcarrier which transmits Rayleigh multipath fading channel in OFDM system. To achieve a BER of 10-3 is required 10dB SNR in SISO-OFDM scheme. For 2×2 MIMO-OFDM scheme requires 10 dB to achieve a BER of 10-3. For 4×4 MIMO-OFDM scheme requires 5 dB while adding convolution in a 4x4 MIMO-OFDM can improve performance up to 0 dB to achieve the same BER. This proves the existence of saving power by 3 dB of 4×4 MIMO-OFDM system without coding, power saving 7 dB of 2×2 MIMO-OFDM and significant power savings from SISO-OFDM system.

Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part II. Homogeneous Lambertian and anisotropic surfaces.

PubMed

Kotchenova, Svetlana Y; Vermote, Eric F

2007-07-10

This is the second part of the validation effort of the recently developed vector version of the 6S (Second Simulation of a Satellite Signal in the Solar Spectrum) radiative transfer code (6SV1), primarily used for the calculation of look-up tables in the Moderate Resolution Imaging Spectroradiometer (MODIS) atmospheric correction algorithm. The 6SV1 code was tested against a Monte Carlo code and Coulson's tabulated values for molecular and aerosol atmospheres bounded by different Lambertian and anisotropic surfaces. The code was also tested in scalar mode against the scalar code SHARM to resolve the previous 6S accuracy issues in the case of an anisotropic surface. All test cases were characterized by good agreement between the 6SV1 and the other codes: The overall relative error did not exceed 0.8%. The study also showed that ignoring the effects of radiation polarization in the atmosphere led to large errors in the simulated top-of-atmosphere reflectances: The maximum observed error was approximately 7.2% for both Lambertian and anisotropic surfaces.

Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part II. Homogeneous Lambertian and anisotropic surfaces

NASA Astrophysics Data System (ADS)

Kotchenova, Svetlana Y.; Vermote, Eric F.

2007-07-01

This is the second part of the validation effort of the recently developed vector version of the 6S (Second Simulation of a Satellite Signal in the Solar Spectrum) radiative transfer code (6SV1), primarily used for the calculation of look-up tables in the Moderate Resolution Imaging Spectroradiometer (MODIS) atmospheric correction algorithm. The 6SV1 code was tested against a Monte Carlo code and Coulson's tabulated values for molecular and aerosol atmospheres bounded by different Lambertian and anisotropic surfaces. The code was also tested in scalar mode against the scalar code SHARM to resolve the previous 6S accuracy issues in the case of an anisotropic surface. All test cases were characterized by good agreement between the 6SV1 and the other codes: The overall relative error did not exceed 0.8%. The study also showed that ignoring the effects of radiation polarization in the atmosphere led to large errors in the simulated top-of-atmosphere reflectances: The maximum observed error was approximately 7.2% for both Lambertian and anisotropic surfaces.

EAC: A program for the error analysis of STAGS results for plates

NASA Technical Reports Server (NTRS)

Sistla, Rajaram; Thurston, Gaylen A.; Bains, Nancy Jane C.

1989-01-01

A computer code is now available for estimating the error in results from the STAGS finite element code for a shell unit consisting of a rectangular orthotropic plate. This memorandum contains basic information about the computer code EAC (Error Analysis and Correction) and describes the connection between the input data for the STAGS shell units and the input data necessary to run the error analysis code. The STAGS code returns a set of nodal displacements and a discrete set of stress resultants; the EAC code returns a continuous solution for displacements and stress resultants. The continuous solution is defined by a set of generalized coordinates computed in EAC. The theory and the assumptions that determine the continuous solution are also outlined in this memorandum. An example of application of the code is presented and instructions on its usage on the Cyber and the VAX machines have been provided.

Neural Decoder for Topological Codes

NASA Astrophysics Data System (ADS)

Torlai, Giacomo; Melko, Roger G.

2017-07-01

We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep learning. We provide a general prescription for the training of the network and a decoding strategy that is applicable to a wide variety of stabilizer codes with very little specialization. We demonstrate the neural decoder numerically on the well-known two-dimensional toric code with phase-flip errors.

Testing and Performance Analysis of the Multichannel Error Correction Code Decoder

NASA Technical Reports Server (NTRS)

Soni, Nitin J.

1996-01-01

This report provides the test results and performance analysis of the multichannel error correction code decoder (MED) system for a regenerative satellite with asynchronous, frequency-division multiple access (FDMA) uplink channels. It discusses the system performance relative to various critical parameters: the coding length, data pattern, unique word value, unique word threshold, and adjacent-channel interference. Testing was performed under laboratory conditions and used a computer control interface with specifically developed control software to vary these parameters. Needed technologies - the high-speed Bose Chaudhuri-Hocquenghem (BCH) codec from Harris Corporation and the TRW multichannel demultiplexer/demodulator (MCDD) - were fully integrated into the mesh very small aperture terminal (VSAT) onboard processing architecture and were demonstrated.

Compression of digital images over local area networks. Appendix 1: Item 3. M.S. Thesis

NASA Technical Reports Server (NTRS)

Gorjala, Bhargavi

1991-01-01

Differential Pulse Code Modulation (DPCM) has been used with speech for many years. It has not been as successful for images because of poor edge performance. The only corruption in DPC is quantizer error but this corruption becomes quite large in the region of an edge because of the abrupt changes in the statistics of the signal. We introduce two improved DPCM schemes; Edge correcting DPCM and Edge Preservation Differential Coding. These two coding schemes will detect the edges and take action to correct them. In an Edge Correcting scheme, the quantizer error for an edge is encoded using a recursive quantizer with entropy coding and sent to the receiver as side information. In an Edge Preserving scheme, when the quantizer input falls in the overload region, the quantizer error is encoded and sent to the receiver repeatedly until the quantizer input falls in the inner levels. Therefore these coding schemes increase the bit rate in the region of an edge and require variable rate channels. We implement these two variable rate coding schemes on a token wing network. Timed token protocol supports two classes of messages; asynchronous and synchronous. The synchronous class provides a pre-allocated bandwidth and guaranteed response time. The remaining bandwidth is dynamically allocated to the asynchronous class. The Edge Correcting DPCM is simulated by considering the edge information under the asynchronous class. For the simulation of the Edge Preserving scheme, the amount of information sent each time is fixed, but the length of the packet or the bit rate for that packet is chosen depending on the availability capacity. The performance of the network, and the performance of the image coding algorithms, is studied.

Bulk locality and quantum error correction in AdS/CFT

NASA Astrophysics Data System (ADS)

Almheiri, Ahmed; Dong, Xi; Harlow, Daniel

2015-04-01

We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard "operator algebra quantum error correction" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.

Performance analysis of the word synchronization properties of the outer code in a TDRSS decoder

NASA Technical Reports Server (NTRS)

Costello, D. J., Jr.; Lin, S.

1984-01-01

A self-synchronizing coding scheme for NASA's TDRSS satellite system is a concatenation of a (2,1,7) inner convolutional code with a (255,223) Reed-Solomon outer code. Both symbol and word synchronization are achieved without requiring that any additional symbols be transmitted. An important parameter which determines the performance of the word sync procedure is the ratio of the decoding failure probability to the undetected error probability. Ideally, the former should be as small as possible compared to the latter when the error correcting capability of the code is exceeded. A computer simulation of a (255,223) Reed-Solomon code as carried out. Results for decoding failure probability and for undetected error probability are tabulated and compared.

MacWilliams Identity for M-Spotty Weight Enumerator

NASA Astrophysics Data System (ADS)

Suzuki, Kazuyoshi; Fujiwara, Eiji

M-spotty byte error control codes are very effective for correcting/detecting errors in semiconductor memory systems that employ recent high-density RAM chips with wide I/O data (e.g., 8, 16, or 32bits). In this case, the width of the I/O data is one byte. A spotty byte error is defined as random t-bit errors within a byte of length b bits, where 1 le t ≤ b. Then, an error is called an m-spotty byte error if at least one spotty byte error is present in a byte. M-spotty byte error control codes are characterized by the m-spotty distance, which includes the Hamming distance as a special case for t =1 or t = b. The MacWilliams identity provides the relationship between the weight distribution of a code and that of its dual code. The present paper presents the MacWilliams identity for the m-spotty weight enumerator of m-spotty byte error control codes. In addition, the present paper clarifies that the indicated identity includes the MacWilliams identity for the Hamming weight enumerator as a special case.

Accumulate-Repeat-Accumulate-Accumulate Codes

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Dolinar, Samuel; Thorpe, Jeremy

2007-01-01

Accumulate-repeat-accumulate-accumulate (ARAA) codes have been proposed, inspired by the recently proposed accumulate-repeat-accumulate (ARA) codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. ARAA codes can be regarded as serial turbolike codes or as a subclass of low-density parity-check (LDPC) codes, and, like ARA codes they have projected graph or protograph representations; these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The objective in proposing ARAA codes as a subclass of ARA codes was to enhance the error-floor performance of ARA codes while maintaining simple encoding structures and low maximum variable node degree.

A forward error correction technique using a high-speed, high-rate single chip codec

NASA Astrophysics Data System (ADS)

Boyd, R. W.; Hartman, W. F.; Jones, Robert E.

The authors describe an error-correction coding approach that allows operation in either burst or continuous modes at data rates of multiple hundreds of megabits per second. Bandspreading is low since the code rate is 7/8 or greater, which is consistent with high-rate link operation. The encoder, along with a hard-decision decoder, fits on a single application-specific integrated circuit (ASIC) chip. Soft-decision decoding is possible utilizing applique hardware in conjunction with the hard-decision decoder. Expected coding gain is a function of the application and is approximately 2.5 dB for hard-decision decoding at 10-5 bit-error rate with phase-shift-keying modulation and additive Gaussian white noise interference. The principal use envisioned for this technique is to achieve a modest amount of coding gain on high-data-rate, bandwidth-constrained channels. Data rates of up to 300 Mb/s can be accommodated by the codec chip. The major objective is burst-mode communications, where code words are composed of 32 n data bits followed by 32 overhead bits.

Adaptive error correction codes for face identification

NASA Astrophysics Data System (ADS)

Hussein, Wafaa R.; Sellahewa, Harin; Jassim, Sabah A.

2012-06-01

Face recognition in uncontrolled environments is greatly affected by fuzziness of face feature vectors as a result of extreme variation in recording conditions (e.g. illumination, poses or expressions) in different sessions. Many techniques have been developed to deal with these variations, resulting in improved performances. This paper aims to model template fuzziness as errors and investigate the use of error detection/correction techniques for face recognition in uncontrolled environments. Error correction codes (ECC) have recently been used for biometric key generation but not on biometric templates. We have investigated error patterns in binary face feature vectors extracted from different image windows of differing sizes and for different recording conditions. By estimating statistical parameters for the intra-class and inter-class distributions of Hamming distances in each window, we encode with appropriate ECC's. The proposed approached is tested for binarised wavelet templates using two face databases: Extended Yale-B and Yale. We shall demonstrate that using different combinations of BCH-based ECC's for different blocks and different recording conditions leads to in different accuracy rates, and that using ECC's results in significantly improved recognition results.

NASTRAN maintenance and enhancement experiences

NASA Technical Reports Server (NTRS)

Schmitz, R. P.

1975-01-01

The current capability is described which includes isoparametric elements, optimization of grid point sequencing, and eigenvalue routine. Overlay and coding errors were corrected for cyclic symmetry, transient response, and differential stiffness rigid formats. Error corrections and program enhancements are discussed along with developments scheduled for the current year and a brief description of analyses being performed using the program.

Five-way smoking status classification using text hot-spot identification and error-correcting output codes.

PubMed

Cohen, Aaron M

2008-01-01

We participated in the i2b2 smoking status classification challenge task. The purpose of this task was to evaluate the ability of systems to automatically identify patient smoking status from discharge summaries. Our submission included several techniques that we compared and studied, including hot-spot identification, zero-vector filtering, inverse class frequency weighting, error-correcting output codes, and post-processing rules. We evaluated our approaches using the same methods as the i2b2 task organizers, using micro- and macro-averaged F1 as the primary performance metric. Our best performing system achieved a micro-F1 of 0.9000 on the test collection, equivalent to the best performing system submitted to the i2b2 challenge. Hot-spot identification, zero-vector filtering, classifier weighting, and error correcting output coding contributed additively to increased performance, with hot-spot identification having by far the largest positive effect. High performance on automatic identification of patient smoking status from discharge summaries is achievable with the efficient and straightforward machine learning techniques studied here.

77 FR 72913 - Defining Larger Participants of the Consumer Debt Collection Market; Correction

Federal Register 2010, 2011, 2012, 2013, 2014

2012-12-07

...;to and codified in the Code of Federal Regulations, which is published #0;under 50 titles pursuant to 44 U.S.C. 1510. #0; #0;The Code of Federal Regulations is sold by the Superintendent of Documents. #0... collection. The final rule contained four typographical errors, which this document corrects. Three of these...

Achieving the Heisenberg limit in quantum metrology using quantum error correction.

PubMed

Zhou, Sisi; Zhang, Mengzhen; Preskill, John; Jiang, Liang

2018-01-08

Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.

Error analysis and correction of discrete solutions from finite element codes

NASA Technical Reports Server (NTRS)

Thurston, G. A.; Stein, P. A.; Knight, N. F., Jr.; Reissner, J. E.

1984-01-01

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Short-Block Protograph-Based LDPC Codes

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Dolinar, Samuel; Jones, Christopher

2010-01-01

Short-block low-density parity-check (LDPC) codes of a special type are intended to be especially well suited for potential applications that include transmission of command and control data, cellular telephony, data communications in wireless local area networks, and satellite data communications. [In general, LDPC codes belong to a class of error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels.] The codes of the present special type exhibit low error floors, low bit and frame error rates, and low latency (in comparison with related prior codes). These codes also achieve low maximum rate of undetected errors over all signal-to-noise ratios, without requiring the use of cyclic redundancy checks, which would significantly increase the overhead for short blocks. These codes have protograph representations; this is advantageous in that, for reasons that exceed the scope of this article, the applicability of protograph representations makes it possible to design highspeed iterative decoders that utilize belief- propagation algorithms.

Topological Qubits from Valence Bond Solids

NASA Astrophysics Data System (ADS)

Wang, Dong-Sheng; Affleck, Ian; Raussendorf, Robert

2018-05-01

Topological qubits based on S U (N )-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with twofold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A logical Z rotation by an angle 2 π /N , for any integer N >2 , is provided by a global twist operation, which is of a topological nature and protected by the energy gap. A general concatenation scheme with standard quantum error-correction codes is also proposed, which can lead to better codes. Generic error-correction properties of symmetry-protected topological order are also demonstrated.

Modulation/demodulation techniques for satellite communications. Part 1: Background

NASA Technical Reports Server (NTRS)

Omura, J. K.; Simon, M. K.

1981-01-01

Basic characteristics of digital data transmission systems described include the physical communication links, the notion of bandwidth, FCC regulations, and performance measurements such as bit rates, bit error probabilities, throughputs, and delays. The error probability performance and spectral characteristics of various modulation/demodulation techniques commonly used or proposed for use in radio and satellite communication links are summarized. Forward error correction with block or convolutional codes is also discussed along with the important coding parameter, channel cutoff rate.

Combining Topological Hardware and Topological Software: Color-Code Quantum Computing with Topological Superconductor Networks

NASA Astrophysics Data System (ADS)

Litinski, Daniel; Kesselring, Markus S.; Eisert, Jens; von Oppen, Felix

2017-07-01

We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely, the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture, including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and we present protocols for realizing topologically protected Clifford gates. These hexagonal-cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome read-out and logical T gates via magic-state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and we give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but it could also be realized in alternative settings such as quantum-Hall-superconductor hybrids.

Topics in quantum cryptography, quantum error correction, and channel simulation

NASA Astrophysics Data System (ADS)

Luo, Zhicheng

In this thesis, we mainly investigate four different topics: efficiently implementable codes for quantum key expansion [51], quantum error-correcting codes based on privacy amplification [48], private classical capacity of quantum channels [44], and classical channel simulation with quantum side information [49, 50]. For the first topic, we propose an efficiently implementable quantum key expansion protocol, capable of increasing the size of a pre-shared secret key by a constant factor. Previously, the Shor-Preskill proof [64] of the security of the Bennett-Brassard 1984 (BB84) [6] quantum key distribution protocol relied on the theoretical existence of good classical error-correcting codes with the "dual-containing" property. But the explicit and efficiently decodable construction of such codes is unknown. We show that we can lift the dual-containing constraint by employing the non-dual-containing codes with excellent performance and efficient decoding algorithms. For the second topic, we propose a construction of Calderbank-Shor-Steane (CSS) [19, 68] quantum error-correcting codes, which are originally based on pairs of mutually dual-containing classical codes, by combining a classical code with a two-universal hash function. We show, using the results of Renner and Koenig [57], that the communication rates of such codes approach the hashing bound on tensor powers of Pauli channels in the limit of large block-length. For the third topic, we prove a regularized formula for the secret key assisted capacity region of a quantum channel for transmitting private classical information. This result parallels the work of Devetak on entanglement assisted quantum communication capacity. This formula provides a new family protocol, the private father protocol, under the resource inequality framework that includes the private classical communication without the assisted secret keys as a child protocol. For the fourth topic, we study and solve the problem of classical channel simulation with quantum side information at the receiver. Our main theorem has two important corollaries: rate-distortion theory with quantum side information and common randomness distillation. Simple proofs of achievability of classical multi-terminal source coding problems can be made via a unified approach using the channel simulation theorem as building blocks. The fully quantum generalization of the problem is also conjectured with outer and inner bounds on the achievable rate pairs.

A /31,15/ Reed-Solomon Code for large memory systems

NASA Technical Reports Server (NTRS)

Lim, R. S.

1979-01-01

This paper describes the encoding and the decoding of a (31,15) Reed-Solomon Code for multiple-burst error correction for large memory systems. The decoding procedure consists of four steps: (1) syndrome calculation, (2) error-location polynomial calculation, (3) error-location numbers calculation, and (4) error values calculation. The principal features of the design are the use of a hardware shift register for both high-speed encoding and syndrome calculation, and the use of a commercially available (31,15) decoder for decoding Steps 2, 3 and 4.

Topological color codes on Union Jack lattices: a stable implementation of the whole Clifford group

DOE Office of Scientific and Technical Information (OSTI.GOV)

Katzgraber, Helmut G.; Theoretische Physik, ETH Zurich, CH-8093 Zurich; Bombin, H.

We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random three-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have a similar error stability to color codes on triangular lattices, as well as to the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respectmore » to triangular lattices and the toric code combined with the inherent robustness of this implementation show good prospects for future stable quantum computer implementations.« less

Enhanced fault-tolerant quantum computing in d-level systems.

PubMed

Campbell, Earl T

2014-12-05

Error-correcting codes protect quantum information and form the basis of fault-tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transversal non-Clifford gate. Codes with the desired property are presented for d-level qudit systems with prime d. The codes use n=d-1 qudits and can detect up to ∼d/3 errors. We quantify the performance of these codes for one approach to quantum computation known as magic-state distillation. Unlike prior work, we find performance is always enhanced by increasing d.

An FPGA design of generalized low-density parity-check codes for rate-adaptive optical transport networks

NASA Astrophysics Data System (ADS)

Zou, Ding; Djordjevic, Ivan B.

2016-02-01

Forward error correction (FEC) is as one of the key technologies enabling the next-generation high-speed fiber optical communications. In this paper, we propose a rate-adaptive scheme using a class of generalized low-density parity-check (GLDPC) codes with a Hamming code as local code. We show that with the proposed unified GLDPC decoder architecture, a variable net coding gains (NCGs) can be achieved with no error floor at BER down to 10-15, making it a viable solution in the next-generation high-speed fiber optical communications.

Fault-tolerant, high-level quantum circuits: form, compilation and description

NASA Astrophysics Data System (ADS)

Paler, Alexandru; Polian, Ilia; Nemoto, Kae; Devitt, Simon J.

2017-06-01

Fault-tolerant quantum error correction is a necessity for any quantum architecture destined to tackle interesting, large-scale problems. Its theoretical formalism has been well founded for nearly two decades. However, we still do not have an appropriate compiler to produce a fault-tolerant, error-corrected description from a higher-level quantum circuit for state-of the-art hardware models. There are many technical hurdles, including dynamic circuit constructions that occur when constructing fault-tolerant circuits with commonly used error correcting codes. We introduce a package that converts high-level quantum circuits consisting of commonly used gates into a form employing all decompositions and ancillary protocols needed for fault-tolerant error correction. We call this form the (I)initialisation, (C)NOT, (M)measurement form (ICM) and consists of an initialisation layer of qubits into one of four distinct states, a massive, deterministic array of CNOT operations and a series of time-ordered X- or Z-basis measurements. The form allows a more flexible approach towards circuit optimisation. At the same time, the package outputs a standard circuit or a canonical geometric description which is a necessity for operating current state-of-the-art hardware architectures using topological quantum codes.

Predicted Blood Glucose from Insulin Administration Based on Values from Miscoded Glucose Meters

PubMed Central

Raine, Charles H.; Pardo, Scott; Parkes, Joan Lee

2008-01-01

Objectives The proper use of many types of self-monitored blood glucose (SMBG) meters requires calibration to match strip code. Studies have demonstrated the occurrence and impact on insulin dose of coding errors with SMBG meters. This paper reflects additional analyses performed with data from Raine et al. (JDST, 2:205–210, 2007). It attempts to relate potential insulin dose errors to possible adverse blood glucose outcomes when glucose meters are miscoded. Methods Five sets of glucose meters were used. Two sets of meters were autocoded and therefore could not be miscoded, and three sets required manual coding. Two of each set of manually coded meters were deliberately miscoded, and one from each set was properly coded. Subjects (n = 116) had finger stick blood glucose obtained at fasting, as well as at 1 and 2 hours after a fixed meal (Boost®; Novartis Medical Nutrition U.S., Basel, Switzerland). Deviations of meter blood glucose results from the reference method (YSI) were used to predict insulin dose errors and resultant blood glucose outcomes based on these deviations. Results Using insulin sensitivity data, it was determined that, given an actual blood glucose of 150–400 mg/dl, an error greater than +40 mg/dl would be required to calculate an insulin dose sufficient to produce a blood glucose of less than 70 mg/dl. Conversely, an error less than or equal to -70 mg/dl would be required to derive an insulin dose insufficient to correct an elevated blood glucose to less than 180 mg/dl. For miscoded meters, the estimated probability to produce a blood glucose reduction to less than or equal to 70 mg/dl was 10.40%. The corresponding probabilities for autocoded and correctly coded manual meters were 2.52% (p < 0.0001) and 1.46% (p < 0.0001), respectively. Furthermore, the errors from miscoded meters were large enough to produce a calculated blood glucose outcome less than or equal to 50 mg/dl in 42 of 833 instances. Autocoded meters produced zero (0) outcomes less than or equal to 50 mg/dl out of 279 instances, and correctly coded manual meters produced 1 of 416. Conclusions Improperly coded blood glucose meters present the potential for insulin dose errors and resultant clinically significant hypoglycemia or hyperglycemia. Patients should be instructed and periodically reinstructed in the proper use of blood glucose meters, particularly for meters that require coding. PMID:19885229

Two high-density recording methods with run-length limited turbo code for holographic data storage system

NASA Astrophysics Data System (ADS)

Nakamura, Yusuke; Hoshizawa, Taku

2016-09-01

Two methods for increasing the data capacity of a holographic data storage system (HDSS) were developed. The first method is called “run-length-limited (RLL) high-density recording”. An RLL modulation has the same effect as enlarging the pixel pitch; namely, it optically reduces the hologram size. Accordingly, the method doubles the raw-data recording density. The second method is called “RLL turbo signal processing”. The RLL turbo code consists of \\text{RLL}(1,∞ ) trellis modulation and an optimized convolutional code. The remarkable point of the developed turbo code is that it employs the RLL modulator and demodulator as parts of the error-correction process. The turbo code improves the capability of error correction more than a conventional LDPC code, even though interpixel interference is generated. These two methods will increase the data density 1.78-fold. Moreover, by simulation and experiment, a data density of 2.4 Tbit/in.2 is confirmed.

Superconducting quantum circuits at the surface code threshold for fault tolerance.

PubMed

Barends, R; Kelly, J; Megrant, A; Veitia, A; Sank, D; Jeffrey, E; White, T C; Mutus, J; Fowler, A G; Campbell, B; Chen, Y; Chen, Z; Chiaro, B; Dunsworth, A; Neill, C; O'Malley, P; Roushan, P; Vainsencher, A; Wenner, J; Korotkov, A N; Cleland, A N; Martinis, John M

2014-04-24

A quantum computer can solve hard problems, such as prime factoring, database searching and quantum simulation, at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection by distributing a logical state among many physical quantum bits (qubits) by means of quantum entanglement. Superconductivity is a useful phenomenon in this regard, because it allows the construction of large quantum circuits and is compatible with microfabrication. For superconducting qubits, the surface code approach to quantum computing is a natural choice for error correction, because it uses only nearest-neighbour coupling and rapidly cycled entangling gates. The gate fidelity requirements are modest: the per-step fidelity threshold is only about 99 per cent. Here we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92 per cent and a two-qubit gate fidelity of up to 99.4 per cent. This places Josephson quantum computing at the fault-tolerance threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger-Horne-Zeilinger state using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

A Survey of Progress in Coding Theory in the Soviet Union. Final Report.

ERIC Educational Resources Information Center

Kautz, William H.; Levitt, Karl N.

The results of a comprehensive technical survey of all published Soviet literature in coding theory and its applications--over 400 papers and books appearing before March 1967--are described in this report. Noteworthy Soviet contributions are discussed, including codes for the noiseless channel, codes that correct asymetric errors, decoding for…

Implementation of an experimental fault-tolerant memory system

NASA Technical Reports Server (NTRS)

Carter, W. C.; Mccarthy, C. E.

1976-01-01

The experimental fault-tolerant memory system described in this paper has been designed to enable the modular addition of spares, to validate the theoretical fault-secure and self-testing properties of the translator/corrector, to provide a basis for experiments using the new testing and correction processes for recovery, and to determine the practicality of such systems. The hardware design and implementation are described, together with methods of fault insertion. The hardware/software interface, including a restricted single error correction/double error detection (SEC/DED) code, is specified. Procedures are carefully described which, (1) test for specified physical faults, (2) ensure that single error corrections are not miscorrections due to triple faults, and (3) enable recovery from double errors.

Interactive Video Coding and Transmission over Heterogeneous Wired-to-Wireless IP Networks Using an Edge Proxy

NASA Astrophysics Data System (ADS)

Pei, Yong; Modestino, James W.

2004-12-01

Digital video delivered over wired-to-wireless networks is expected to suffer quality degradation from both packet loss and bit errors in the payload. In this paper, the quality degradation due to packet loss and bit errors in the payload are quantitatively evaluated and their effects are assessed. We propose the use of a concatenated forward error correction (FEC) coding scheme employing Reed-Solomon (RS) codes and rate-compatible punctured convolutional (RCPC) codes to protect the video data from packet loss and bit errors, respectively. Furthermore, the performance of a joint source-channel coding (JSCC) approach employing this concatenated FEC coding scheme for video transmission is studied. Finally, we describe an improved end-to-end architecture using an edge proxy in a mobile support station to implement differential error protection for the corresponding channel impairments expected on the two networks. Results indicate that with an appropriate JSCC approach and the use of an edge proxy, FEC-based error-control techniques together with passive error-recovery techniques can significantly improve the effective video throughput and lead to acceptable video delivery quality over time-varying heterogeneous wired-to-wireless IP networks.

Quantum Error Correction with Biased Noise

NASA Astrophysics Data System (ADS)

Brooks, Peter

Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security. At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level. In this thesis, we look at how additional information about the structure of noise, or "noise bias," can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations. In Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction. In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

What Information is Stored in DNA: Does it Contain Digital Error Correcting Codes?

NASA Astrophysics Data System (ADS)

Liebovitch, Larry

1998-03-01

The longest term correlations in living systems are the information stored in DNA which reflects the evolutionary history of an organism. The 4 bases (A,T,G,C) encode sequences of amino acids as well as locations of binding sites for proteins that regulate DNA. The fidelity of this important information is maintained by ANALOG error check mechanisms. When a single strand of DNA is replicated the complementary base is inserted in the new strand. Sometimes the wrong base is inserted that sticks out disrupting the phosphate backbone. The new base is not yet methylated, so repair enzymes, that slide along the DNA, can tear out the wrong base and replace it with the right one. The bases in DNA form a sequence of 4 different symbols and so the information is encoded in a DIGITAL form. All the digital codes in our society (ISBN book numbers, UPC product codes, bank account numbers, airline ticket numbers) use error checking code, where some digits are functions of other digits to maintain the fidelity of transmitted informaiton. Does DNA also utitlize a DIGITAL error chekcing code to maintain the fidelity of its information and increase the accuracy of replication? That is, are some bases in DNA functions of other bases upstream or downstream? This raises the interesting mathematical problem: How does one determine whether some symbols in a sequence of symbols are a function of other symbols. It also bears on the issue of determining algorithmic complexity: What is the function that generates the shortest algorithm for reproducing the symbol sequence. The error checking codes most used in our technology are linear block codes. We developed an efficient method to test for the presence of such codes in DNA. We coded the 4 bases as (0,1,2,3) and used Gaussian elimination, modified for modulus 4, to test if some bases are linear combinations of other bases. We used this method to analyze the base sequence in the genes from the lac operon and cytochrome C. We did not find evidence for such error correcting codes in these genes. However, we analyzed only a small amount of DNA and if digitial error correcting schemes are present in DNA, they may be more subtle than such simple linear block codes. The basic issue we raise here, is how information is stored in DNA and an appreciation that digital symbol sequences, such as DNA, admit of interesting schemes to store and protect the fidelity of their information content. Liebovitch, Tao, Todorov, Levine. 1996. Biophys. J. 71:1539-1544. Supported by NIH grant EY6234.

Scalable video transmission over Rayleigh fading channels using LDPC codes

NASA Astrophysics Data System (ADS)

Bansal, Manu; Kondi, Lisimachos P.

2005-03-01

In this paper, we investigate an important problem of efficiently utilizing the available resources for video transmission over wireless channels while maintaining a good decoded video quality and resilience to channel impairments. Our system consists of the video codec based on 3-D set partitioning in hierarchical trees (3-D SPIHT) algorithm and employs two different schemes using low-density parity check (LDPC) codes for channel error protection. The first method uses the serial concatenation of the constant-rate LDPC code and rate-compatible punctured convolutional (RCPC) codes. Cyclic redundancy check (CRC) is used to detect transmission errors. In the other scheme, we use the product code structure consisting of a constant rate LDPC/CRC code across the rows of the `blocks' of source data and an erasure-correction systematic Reed-Solomon (RS) code as the column code. In both the schemes introduced here, we use fixed-length source packets protected with unequal forward error correction coding ensuring a strictly decreasing protection across the bitstream. A Rayleigh flat-fading channel with additive white Gaussian noise (AWGN) is modeled for the transmission. The rate-distortion optimization algorithm is developed and carried out for the selection of source coding and channel coding rates using Lagrangian optimization. The experimental results demonstrate the effectiveness of this system under different wireless channel conditions and both the proposed methods (LDPC+RCPC/CRC and RS+LDPC/CRC) outperform the more conventional schemes such as those employing RCPC/CRC.

RETRACTED — PMD mitigation through interleaving LDPC codes with polarization scramblers

NASA Astrophysics Data System (ADS)

Han, Dahai; Chen, Haoran; Xi, Lixia

2012-11-01

The combination of forward error correction (FEC) and distributed fast polarization scramblers (D-FPSs) is approved as an effective method to mitigate polarization mode dispersion (PMD) in high-speed optical fiber communication system. The low-density parity-check (LDPC) codes are newly introduced into the PMD mitigation scheme with D-FPSs in this paper as one of the promising FEC codes to achieve better performance. The scrambling speed of FPS for LDPC (2040, 1903) codes system is discussed, and the reasonable speed 10 MHz is obtained from the simulation results. For easy application in practical large scale integrated (LSI) circuit, the number of iterations in decoding LDPC codes is also investigated. The PMD tolerance and cut-off optical signal-to-noise ratio (OSNR) of LDPC codes are compared with Reed-Solomon (RS) codes in different conditions. In the simulation, the interleaving LDPC codes brings incremental performance of error correction, and the PMD tolerance is 10 ps at OSNR=11.4 dB. The results show that the meaning of the work is that LDPC codes are a substitute for traditional RS codes with D-FPSs and all of the executable code files are open for researchers who have practical LSI platform for PMD mitigation.

PMD mitigation through interleaving LDPC codes with polarization scramblers

NASA Astrophysics Data System (ADS)

Han, Dahai; Chen, Haoran; Xi, Lixia

2013-09-01

The combination of forward error correction (FEC) and distributed fast polarization scramblers (D-FPSs) is approved an effective method to mitigate polarization mode dispersion (PMD) in high-speed optical fiber communication system. The low-density parity-check (LDPC) codes are newly introduced into the PMD mitigation scheme with D-FPSs in this article as one of the promising FEC codes to achieve better performance. The scrambling speed of FPS for LDPC (2040, 1903) codes system is discussed, and the reasonable speed 10MHz is obtained from the simulation results. For easy application in practical large scale integrated (LSI) circuit, the number of iterations in decoding LDPC codes is also investigated. The PMD tolerance and cut-off optical signal-to-noise ratio (OSNR) of LDPC codes are compared with Reed-Solomon (RS) codes in different conditions. In the simulation, the interleaving LDPC codes bring incremental performance of error correction, and the PMD tolerance is 10ps at OSNR=11.4dB. The results show the meaning of the work is that LDPC codes are a substitute for traditional RS codes with D-FPSs and all of the executable code files are open for researchers who have practical LSI platform for PMD mitigation.

Five-wave-packet quantum error correction based on continuous-variable cluster entanglement

PubMed Central

Hao, Shuhong; Su, Xiaolong; Tian, Caixing; Xie, Changde; Peng, Kunchi

2015-01-01

Quantum error correction protects the quantum state against noise and decoherence in quantum communication and quantum computation, which enables one to perform fault-torrent quantum information processing. We experimentally demonstrate a quantum error correction scheme with a five-wave-packet code against a single stochastic error, the original theoretical model of which was firstly proposed by S. L. Braunstein and T. A. Walker. Five submodes of a continuous variable cluster entangled state of light are used for five encoding channels. Especially, in our encoding scheme the information of the input state is only distributed on three of the five channels and thus any error appearing in the remained two channels never affects the output state, i.e. the output quantum state is immune from the error in the two channels. The stochastic error on a single channel is corrected for both vacuum and squeezed input states and the achieved fidelities of the output states are beyond the corresponding classical limit. PMID:26498395

Performance analysis of optical wireless communication system based on two-fold turbo code

NASA Astrophysics Data System (ADS)

Chen, Jun; Huang, Dexiu; Yuan, Xiuhua

2005-11-01

Optical wireless communication (OWC) is beginning to emerge in the telecommunications market as a strategy to meet last-mile demand owing to its unique combination of features. Turbo codes have an impressive near Shannon-limit error correcting performance. Twofold turbo codes have been recently introduced as the least complex member of the multifold turbo code family. In this paper, at first, we present the mathematical model of signal and optical wireless channel with fading and bit error rate model with scintillation, then we provide a new turbo code method to use in OWC system, we can obtain a better BER curse of OWC system with twofold turbo code than with common turbo code.

17 CFR 16.06 - Errors or omissions.

Code of Federal Regulations, 2010 CFR

2010-04-01

..., reporting markets shall file corrections to errors or omissions in data previously filed with the Commission pursuant to §§ 16.00 and 16.01 in the format and using the coding structure and electronic data submission...

Low Density Parity Check Codes: Bandwidth Efficient Channel Coding

NASA Technical Reports Server (NTRS)

Fong, Wai; Lin, Shu; Maki, Gary; Yeh, Pen-Shu

2003-01-01

Low Density Parity Check (LDPC) Codes provide near-Shannon Capacity performance for NASA Missions. These codes have high coding rates R=0.82 and 0.875 with moderate code lengths, n=4096 and 8176. Their decoders have inherently parallel structures which allows for high-speed implementation. Two codes based on Euclidean Geometry (EG) were selected for flight ASIC implementation. These codes are cyclic and quasi-cyclic in nature and therefore have a simple encoder structure. This results in power and size benefits. These codes also have a large minimum distance as much as d,,, = 65 giving them powerful error correcting capabilities and error floors less than lo- BER. This paper will present development of the LDPC flight encoder and decoder, its applications and status.

Experimental implementation of the Bacon-Shor code with 10 entangled photons

NASA Astrophysics Data System (ADS)

Gimeno-Segovia, Mercedes; Sanders, Barry C.

The number of qubits that can be effectively controlled in quantum experiments is growing, reaching a regime where small quantum error-correcting codes can be tested. The Bacon-Shor code is a simple quantum code that protects against the effect of an arbitrary single-qubit error. In this work, we propose an experimental implementation of said code in a post-selected linear optical setup, similar to the recently reported 10-photon GHZ generation experiment. In the procedure we propose, an arbitrary state is encoded into the protected Shor code subspace, and after undergoing a controlled single-qubit error, is successfully decoded. BCS appreciates financial support from Alberta Innovates, NSERC, China's 1000 Talent Plan and the Institute for Quantum Information and Matter, which is an NSF Physics Frontiers Center(NSF Grant PHY-1125565) with support of the Moore Foundation(GBMF-2644).

The proposed coding standard at GSFC

NASA Technical Reports Server (NTRS)

Morakis, J. C.; Helgert, H. J.

1977-01-01

As part of the continuing effort to introduce standardization of spacecraft and ground equipment in satellite systems, NASA's Goddard Space Flight Center and other NASA facilities have supported the development of a set of standards for the use of error control coding in telemetry subsystems. These standards are intended to ensure compatibility between spacecraft and ground encoding equipment, while allowing sufficient flexibility to meet all anticipated mission requirements. The standards which have been developed to date cover the application of block codes in error detection and error correction modes, as well as short and long constraint length convolutional codes decoded via the Viterbi and sequential decoding algorithms, respectively. Included are detailed specifications of the codes, and their implementation. Current effort is directed toward the development of standards covering channels with burst noise characteristics, channels with feedback, and code concatenation.

Classical simulation of quantum error correction in a Fibonacci anyon code

NASA Astrophysics Data System (ADS)

Burton, Simon; Brell, Courtney G.; Flammia, Steven T.

2017-02-01

Classically simulating the dynamics of anyonic excitations in two-dimensional quantum systems is likely intractable in general because such dynamics are sufficient to implement universal quantum computation. However, processes of interest for the study of quantum error correction in anyon systems are typically drawn from a restricted class that displays significant structure over a wide range of system parameters. We exploit this structure to classically simulate, and thereby demonstrate the success of, an error-correction protocol for a quantum memory based on the universal Fibonacci anyon model. We numerically simulate a phenomenological model of the system and noise processes on lattice sizes of up to 128 ×128 sites, and find a lower bound on the error-correction threshold of approximately 0.125 errors per edge, which is comparable to those previously known for Abelian and (nonuniversal) non-Abelian anyon models.

A comparison of VLSI architectures for time and transform domain decoding of Reed-Solomon codes

NASA Technical Reports Server (NTRS)

Hsu, I. S.; Truong, T. K.; Deutsch, L. J.; Satorius, E. H.; Reed, I. S.

1988-01-01

It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial needed to decode a Reed-Solomon (RS) code. It is shown that this algorithm can be used for both time and transform domain decoding by replacing its initial conditions with the Forney syndromes and the erasure locator polynomial. By this means both the errata locator polynomial and the errate evaluator polynomial can be obtained with the Euclidean algorithm. With these ideas, both time and transform domain Reed-Solomon decoders for correcting errors and erasures are simplified and compared. As a consequence, the architectures of Reed-Solomon decoders for correcting both errors and erasures can be made more modular, regular, simple, and naturally suitable for VLSI implementation.

Potts glass reflection of the decoding threshold for qudit quantum error correcting codes

NASA Astrophysics Data System (ADS)

Jiang, Yi; Kovalev, Alexey A.; Pryadko, Leonid P.

We map the maximum likelihood decoding threshold for qudit quantum error correcting codes to the multicritical point in generalized Potts gauge glass models, extending the map constructed previously for qubit codes. An n-qudit quantum LDPC code, where a qudit can be involved in up to m stabilizer generators, corresponds to a ℤd Potts model with n interaction terms which can couple up to m spins each. We analyze general properties of the phase diagram of the constructed model, give several bounds on the location of the transitions, bounds on the energy density of extended defects (non-local analogs of domain walls), and discuss the correlation functions which can be used to distinguish different phases in the original and the dual models. This research was supported in part by the Grants: NSF PHY-1415600 (AAK), NSF PHY-1416578 (LPP), and ARO W911NF-14-1-0272 (LPP).

Golay sequences coded coherent optical OFDM for long-haul transmission

NASA Astrophysics Data System (ADS)

Qin, Cui; Ma, Xiangrong; Hua, Tao; Zhao, Jing; Yu, Huilong; Zhang, Jian

2017-09-01

We propose to use binary Golay sequences in coherent optical orthogonal frequency division multiplexing (CO-OFDM) to improve the long-haul transmission performance. The Golay sequences are generated by binary Reed-Muller codes, which have low peak-to-average power ratio and certain error correction capability. A low-complexity decoding algorithm for the Golay sequences is then proposed to recover the signal. Under same spectral efficiency, the QPSK modulated OFDM with binary Golay sequences coding with and without discrete Fourier transform (DFT) spreading (DFTS-QPSK-GOFDM and QPSK-GOFDM) are compared with the normal BPSK modulated OFDM with and without DFT spreading (DFTS-BPSK-OFDM and BPSK-OFDM) after long-haul transmission. At a 7% forward error correction code threshold (Q2 factor of 8.5 dB), it is shown that DFTS-QPSK-GOFDM outperforms DFTS-BPSK-OFDM by extending the transmission distance by 29% and 18%, in non-dispersion managed and dispersion managed links, respectively.

A family of chaotic pure analog coding schemes based on baker's map function

NASA Astrophysics Data System (ADS)

Liu, Yang; Li, Jing; Lu, Xuanxuan; Yuen, Chau; Wu, Jun

2015-12-01

This paper considers a family of pure analog coding schemes constructed from dynamic systems which are governed by chaotic functions—baker's map function and its variants. Various decoding methods, including maximum likelihood (ML), minimum mean square error (MMSE), and mixed ML-MMSE decoding algorithms, have been developed for these novel encoding schemes. The proposed mirrored baker's and single-input baker's analog codes perform a balanced protection against the fold error (large distortion) and weak distortion and outperform the classical chaotic analog coding and analog joint source-channel coding schemes in literature. Compared to the conventional digital communication system, where quantization and digital error correction codes are used, the proposed analog coding system has graceful performance evolution, low decoding latency, and no quantization noise. Numerical results show that under the same bandwidth expansion, the proposed analog system outperforms the digital ones over a wide signal-to-noise (SNR) range.

Efficient preparation of large-block-code ancilla states for fault-tolerant quantum computation

NASA Astrophysics Data System (ADS)

Zheng, Yi-Cong; Lai, Ching-Yi; Brun, Todd A.

2018-03-01

Fault-tolerant quantum computation (FTQC) schemes that use multiqubit large block codes can potentially reduce the resource overhead to a great extent. A major obstacle is the requirement for a large number of clean ancilla states of different types without correlated errors inside each block. These ancilla states are usually logical stabilizer states of the data-code blocks, which are generally difficult to prepare if the code size is large. Previously, we have proposed an ancilla distillation protocol for Calderbank-Shor-Steane (CSS) codes by classical error-correcting codes. It was assumed that the quantum gates in the distillation circuit were perfect; however, in reality, noisy quantum gates may introduce correlated errors that are not treatable by the protocol. In this paper, we show that additional postselection by another classical error-detecting code can be applied to remove almost all correlated errors. Consequently, the revised protocol is fully fault tolerant and capable of preparing a large set of stabilizer states sufficient for FTQC using large block codes. At the same time, the yield rate can be boosted from O (t-2) to O (1 ) in practice for an [[n ,k ,d =2 t +1

Spirality: A Noval Way to Measure Spiral Arm Pitch Angle

NASA Astrophysics Data System (ADS)

Shields, Douglas W.; Boe, Benjamin; Henderson, Casey L.; Hartley, Matthew; Davis, Benjamin L.; Pour Imani, Hamed; Kennefick, Daniel; Kennefick, Julia D.

2015-01-01

We present the MATLAB code Spirality, a novel method for measuring spiral arm pitch angles by fitting galaxy images to spiral templates of known pitch. For a given pitch angle template, the mean pixel value is found along each of typically 1000 spiral axes. The fitting function, which shows a local maximum at the best-fit pitch angle, is the variance of these means. Error bars are found by varying the inner radius of the measurement annulus and finding the standard deviation of the best-fit pitches. Computation time is typically on the order of 2 minutes per galaxy, assuming at least 8 GB of working memory. We tested the code using 128 synthetic spiral images of known pitch. These spirals varied in the number of spiral arms, pitch angle, degree of logarithmicity, radius, SNR, inclination angle, bar length, and bulge radius. A correct result is defined as a result that matches the true pitch within the error bars, with error bars no greater than ±7°. For the non-logarithmic spiral sample, the correct answer is similarly defined, with the mean pitch as function of radius in place of the true pitch. For all synthetic spirals, correct results were obtained so long as SNR > 0.25, the bar length was no more than 60% of the spiral's diameter (when the bar was included in the measurement), the input center of the spiral was no more than 6% of the spiral radius away from the true center, and the inclination angle was no more than 30°. The synthetic spirals were not deprojected prior to measurement. The code produced the correct result for all barred spirals when the measurement annulus was placed outside the bar. Additionally, we compared the code's results against 2DFFT results for 203 visually selected spiral galaxies in GOODS North and South. Among the entire sample, Spirality's error bars overlapped 2DFFT's error bars 64% of the time. For those galaxies in which Source code is available by email request from the primary author.

Optimal quantum error correcting codes from absolutely maximally entangled states

NASA Astrophysics Data System (ADS)

Raissi, Zahra; Gogolin, Christian; Riera, Arnau; Acín, Antonio

2018-02-01

Absolutely maximally entangled (AME) states are pure multi-partite generalizations of the bipartite maximally entangled states with the property that all reduced states of at most half the system size are in the maximally mixed state. AME states are of interest for multipartite teleportation and quantum secret sharing and have recently found new applications in the context of high-energy physics in toy models realizing the AdS/CFT-correspondence. We work out in detail the connection between AME states of minimal support and classical maximum distance separable (MDS) error correcting codes and, in particular, provide explicit closed form expressions for AME states of n parties with local dimension \

Synthesis of Arbitrary Quantum Circuits to Topological Assembly: Systematic, Online and Compact.

PubMed

Paler, Alexandru; Fowler, Austin G; Wille, Robert

2017-09-05

It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the issues is the efficient placement of magic state distillation sub circuits, so-called distillation boxes, in the space-time volume that abstracts the computation's required resources. This work presents a general, systematic, online method for the synthesis of such circuits. Distillation box placement is controlled by so-called schedulers. The work introduces a greedy scheduler generating compact box placements. The implemented software, whose source code is available at www.github.com/alexandrupaler/tqec, is used to illustrate and discuss synthesis examples. Synthesis and optimisation improvements are proposed.

Applying Jlint to Space Exploration Software

NASA Technical Reports Server (NTRS)

Artho, Cyrille; Havelund, Klaus

2004-01-01

Java is a very successful programming language which is also becoming widespread in embedded systems, where software correctness is critical. Jlint is a simple but highly efficient static analyzer that checks a Java program for several common errors, such as null pointer exceptions, and overflow errors. It also includes checks for multi-threading problems, such as deadlocks and data races. The case study described here shows the effectiveness of Jlint in find-false positives in the multi-threading warnings gives an insight into design patterns commonly used in multi-threaded code. The results show that a few analysis techniques are sufficient to avoid almost all false positives. These techniques include investigating all possible callers and a few code idioms. Verifying the correct application of these patterns is still crucial, because their correct usage is not trivial.

Error-Transparent Quantum Gates for Small Logical Qubit Architectures

NASA Astrophysics Data System (ADS)

Kapit, Eliot

2018-02-01

One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems from a combination of control errors and random single qubit errors from interaction with the environment. While great strides have been made in mitigating control errors, intrinsic qubit error remains a serious problem that limits gate fidelity in modern qubit architectures. Simultaneously, recent developments of small error-corrected logical qubit devices promise significant increases in logical state lifetime, but translating those improvements into increases in gate fidelity is a complex challenge. In this Letter, we construct protocols for gates on and between small logical qubit devices which inherit the parent device's tolerance to single qubit errors which occur at any time before or during the gate. We consider two such devices, a passive implementation of the three-qubit bit flip code, and the author's own [E. Kapit, Phys. Rev. Lett. 116, 150501 (2016), 10.1103/PhysRevLett.116.150501] very small logical qubit (VSLQ) design, and propose error-tolerant gate sets for both. The effective logical gate error rate in these models displays superlinear error reduction with linear increases in single qubit lifetime, proving that passive error correction is capable of increasing gate fidelity. Using a standard phenomenological noise model for superconducting qubits, we demonstrate a realistic, universal one- and two-qubit gate set for the VSLQ, with error rates an order of magnitude lower than those for same-duration operations on single qubits or pairs of qubits. These developments further suggest that incorporating small logical qubits into a measurement based code could substantially improve code performance.

Disjointness of Stabilizer Codes and Limitations on Fault-Tolerant Logical Gates

NASA Astrophysics Data System (ADS)

Jochym-O'Connor, Tomas; Kubica, Aleksander; Yoder, Theodore J.

2018-04-01

Stabilizer codes are among the most successful quantum error-correcting codes, yet they have important limitations on their ability to fault tolerantly compute. Here, we introduce a new quantity, the disjointness of the stabilizer code, which, roughly speaking, is the number of mostly nonoverlapping representations of any given nontrivial logical Pauli operator. The notion of disjointness proves useful in limiting transversal gates on any error-detecting stabilizer code to a finite level of the Clifford hierarchy. For code families, we can similarly restrict logical operators implemented by constant-depth circuits. For instance, we show that it is impossible, with a constant-depth but possibly geometrically nonlocal circuit, to implement a logical non-Clifford gate on the standard two-dimensional surface code.

Unitary reconstruction of secret for stabilizer-based quantum secret sharing

NASA Astrophysics Data System (ADS)

Matsumoto, Ryutaroh

2017-08-01

We propose a unitary procedure to reconstruct quantum secret for a quantum secret sharing scheme constructed from stabilizer quantum error-correcting codes. Erasure correcting procedures for stabilizer codes need to add missing shares for reconstruction of quantum secret, while unitary reconstruction procedures for certain class of quantum secret sharing are known to work without adding missing shares. The proposed procedure also works without adding missing shares.

An investigation of error correcting techniques for OMV and AXAF

NASA Technical Reports Server (NTRS)

Ingels, Frank; Fryer, John

1991-01-01

The original objectives of this project were to build a test system for the NASA 255/223 Reed/Solomon encoding/decoding chip set and circuit board. This test system was then to be interfaced with a convolutional system at MSFC to examine the performance of the concantinated codes. After considerable work, it was discovered that the convolutional system could not function as needed. This report documents the design, construction, and testing of the test apparatus for the R/S chip set. The approach taken was to verify the error correcting behavior of the chip set by injecting known error patterns onto data and observing the results. Error sequences were generated using pseudo-random number generator programs, with Poisson time distribution between errors and Gaussian burst lengths. Sample means, variances, and number of un-correctable errors were calculated for each data set before testing.

Fast transform decoding of nonsystematic Reed-Solomon codes

NASA Technical Reports Server (NTRS)

Truong, T. K.; Cheung, K.-M.; Reed, I. S.; Shiozaki, A.

1989-01-01

A Reed-Solomon (RS) code is considered to be a special case of a redundant residue polynomial (RRP) code, and a fast transform decoding algorithm to correct both errors and erasures is presented. This decoding scheme is an improvement of the decoding algorithm for the RRP code suggested by Shiozaki and Nishida, and can be realized readily on very large scale integration chips.

Analysis on the optical aberration effect on spectral resolution of coded aperture spectroscopy

NASA Astrophysics Data System (ADS)

Hao, Peng; Chi, Mingbo; Wu, Yihui

2017-10-01

The coded aperture spectrometer can achieve high throughput and high spectral resolution by replacing the traditional single slit with two-dimensional array slits manufactured by MEMS technology. However, the sampling accuracy of coding spectrum image will be distorted due to the existence of system aberrations, machining error, fixing errors and so on, resulting in the declined spectral resolution. The influence factor of the spectral resolution come from the decode error, the spectral resolution of each column, and the column spectrum offset correction. For the Czerny-Turner spectrometer, the spectral resolution of each column most depend on the astigmatism, in this coded aperture spectroscopy, the uncorrected astigmatism does result in degraded performance. Some methods must be used to reduce or remove the limiting astigmatism. The curvature of field and the spectral curvature can be result in the spectrum revision errors.

Evaluating software development by analysis of changes: The data from the software engineering laboratory

NASA Technical Reports Server (NTRS)

1982-01-01

An effective data collection methodology for evaluating software development methodologies was applied to four different software development projects. Goals of the data collection included characterizing changes and errors, characterizing projects and programmers, identifying effective error detection and correction techniques, and investigating ripple effects. The data collected consisted of changes (including error corrections) made to the software after code was written and baselined, but before testing began. Data collection and validation were concurrent with software development. Changes reported were verified by interviews with programmers.

Use of CCSDS and OSI Protocols on the Advanced Communications Technology Satellite

NASA Technical Reports Server (NTRS)

Chirieleison, Don

1996-01-01

Although ACTS (Advanced Communications Technology Satellite) provides an almost error-free channel during much of the day and under most conditions, there are times when it is not suitable for reliably error-free data communications when operating in the uncoded mode. Because coded operation is not always available to every earth station, measures must be taken in the end system to maintain adequate throughput when transferring data under adverse conditions. The most effective approach that we tested to improve performance was the addition of an 'outer' Reed-Solomon code through use of CCSDS (Consultative Committee for Space Data Systems) GOS 2 (a forward error correcting code). This addition can benefit all users of an ACTS channel including those applications that do not require totally reliable transport, but it is somewhat expensive because additional hardware is needed. Although we could not characterize the link noise statistically (it appeared to resemble uncorrelated white noise, the type that block codes are least effective in correcting), we did find that CCSDS GOS 2 gave an essentially error-free link at BER's (bit error rate) as high as 6x10(exp -4). For users that demand reliable transport, an ARQ (Automatic Repeat Queuing) protocol such as TCP (Transmission Control Protocol) or TP4 (Transport Protocol, Class 4) will probably be used. In this category, it comes as no surprise that the best choice of the protocol suites tested over ACTS was TP4 using CCSDS GOS 2. TP4 behaves very well over an error-free link which GOS 2 provides up to a point. Without forward error correction, however, TP4 service begins to degrade in the 10(exp -7)-10(exp -6) range and by 4x10(exp -6), it barely gives any throughput at all. If Congestion Avoidance is used in TP4, the degradation is even more pronounced. Fortunately, as demonstrated here, this effect can be more than compensated for by choosing the Selective Acknowledgment option. In fact, this option can enable TP4 to deliver some throughput at error rates as high as 10(exp -5).

Discussion on LDPC Codes and Uplink Coding

NASA Technical Reports Server (NTRS)

Andrews, Ken; Divsalar, Dariush; Dolinar, Sam; Moision, Bruce; Hamkins, Jon; Pollara, Fabrizio

2007-01-01

This slide presentation reviews the progress that the workgroup on Low-Density Parity-Check (LDPC) for space link coding. The workgroup is tasked with developing and recommending new error correcting codes for near-Earth, Lunar, and deep space applications. Included in the presentation is a summary of the technical progress of the workgroup. Charts that show the LDPC decoder sensitivity to symbol scaling errors are reviewed, as well as a chart showing the performance of several frame synchronizer algorithms compared to that of some good codes and LDPC decoder tests at ESTL. Also reviewed is a study on Coding, Modulation, and Link Protocol (CMLP), and the recommended codes. A design for the Pseudo-Randomizer with LDPC Decoder and CRC is also reviewed. A chart that summarizes the three proposed coding systems is also presented.

Error rates and resource overheads of encoded three-qubit gates

NASA Astrophysics Data System (ADS)

Takagi, Ryuji; Yoder, Theodore J.; Chuang, Isaac L.

2017-10-01

A non-Clifford gate is required for universal quantum computation, and, typically, this is the most error-prone and resource-intensive logical operation on an error-correcting code. Small, single-qubit rotations are popular choices for this non-Clifford gate, but certain three-qubit gates, such as Toffoli or controlled-controlled-Z (ccz), are equivalent options that are also more suited for implementing some quantum algorithms, for instance, those with coherent classical subroutines. Here, we calculate error rates and resource overheads for implementing logical ccz with pieceable fault tolerance, a nontransversal method for implementing logical gates. We provide a comparison with a nonlocal magic-state scheme on a concatenated code and a local magic-state scheme on the surface code. We find the pieceable fault-tolerance scheme particularly advantaged over magic states on concatenated codes and in certain regimes over magic states on the surface code. Our results suggest that pieceable fault tolerance is a promising candidate for fault tolerance in a near-future quantum computer.

Ultrahigh Error Threshold for Surface Codes with Biased Noise

NASA Astrophysics Data System (ADS)

Tuckett, David K.; Bartlett, Stephen D.; Flammia, Steven T.

2018-02-01

We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing dominates, is ubiquitous in many quantum architectures. In the limit of pure dephasing noise we find a threshold of 43.7(1)% using a tensor network decoder proposed by Bravyi, Suchara, and Vargo. The threshold remains surprisingly large in the regime of realistic noise bias ratios, for example 28.2(2)% at a bias of 10. The performance is, in fact, at or near the hashing bound for all values of the bias. The modified surface code still uses only weight-4 stabilizers on a square lattice, but merely requires measuring products of Y instead of Z around the faces, as this doubles the number of useful syndrome bits associated with the dominant Z errors. Our results demonstrate that large efficiency gains can be found by appropriately tailoring codes and decoders to realistic noise models, even under the locality constraints of topological codes.

Quantum error correction in crossbar architectures

NASA Astrophysics Data System (ADS)

Helsen, Jonas; Steudtner, Mark; Veldhorst, Menno; Wehner, Stephanie

2018-07-01

A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so-called crossbar architectures. Recently we made a proposal for a large-scale quantum processor (Li et al arXiv:1711.03807 (2017)) to be implemented in silicon quantum dots. This system features a crossbar control architecture which limits parallel single-qubit control, but allows the scheme to overcome control scaling issues that form a major hurdle to large-scale quantum computing systems. In this work, we develop a language that makes it possible to easily map quantum circuits to crossbar systems, taking into account their architecture and control limitations. Using this language we show how to map well known quantum error correction codes such as the planar surface and color codes in this limited control setting with only a small overhead in time. We analyze the logical error behavior of this surface code mapping for estimated experimental parameters of the crossbar system and conclude that logical error suppression to a level useful for real quantum computation is feasible.

5 CFR 890.103 - Correction of errors.

Code of Federal Regulations, 2010 CFR

2010-01-01

... (CONTINUED) FEDERAL EMPLOYEES HEALTH BENEFITS PROGRAM Administration and General Provisions § 890.103... States Code, and permit the individual to enroll in another health benefits plan for purposes of this... health care providers. (e) Retroactive corrections are subject to withholdings and contributions under...

Editing of EIA coded, numerically controlled, machine tool tapes

NASA Technical Reports Server (NTRS)

Weiner, J. M.

1975-01-01

Editing of numerically controlled (N/C) machine tool tapes (8-level paper tape) using an interactive graphic display processor is described. A rapid technique required for correcting production errors in N/C tapes was developed using the interactive text editor on the IMLAC PDS-ID graphic display system and two special programs resident on disk. The correction technique and special programs for processing N/C tapes coded to EIA specifications are discussed.

VLSI single-chip (255,223) Reed-Solomon encoder with interleaver

NASA Technical Reports Server (NTRS)

Hsu, In-Shek (Inventor); Deutsch, Leslie J. (Inventor); Truong, Trieu-Kie (Inventor); Reed, Irving S. (Inventor)

1990-01-01

The invention relates to a concatenated Reed-Solomon/convolutional encoding system consisting of a Reed-Solomon outer code and a convolutional inner code for downlink telemetry in space missions, and more particularly to a Reed-Solomon encoder with programmable interleaving of the information symbols and code correction symbols to combat error bursts in the Viterbi decoder.

Telemetry advances in data compression and channel coding

NASA Technical Reports Server (NTRS)

Miller, Warner H.; Morakis, James C.; Yeh, Pen-Shu

1990-01-01

Addressed in this paper is the dependence of telecommunication channel, forward error correcting coding and source data compression coding on integrated circuit technology. Emphasis is placed on real time high speed Reed Solomon (RS) decoding using full custom VLSI technology. Performance curves of NASA's standard channel coder and a proposed standard lossless data compression coder are presented.

Measurement-based quantum communication with resource states generated by entanglement purification

NASA Astrophysics Data System (ADS)

Wallnöfer, J.; Dür, W.

2017-01-01

We investigate measurement-based quantum communication with noisy resource states that are generated by entanglement purification. We consider the transmission of encoded information via noisy quantum channels using a measurement-based implementation of encoding, error correction, and decoding. We show that such an approach offers advantages over direct transmission, gate-based error correction, and measurement-based schemes with direct generation of resource states. We analyze the noise structure of resource states generated by entanglement purification and show that a local error model, i.e., noise acting independently on all qubits of the resource state, is a good approximation in general, and provides an exact description for Greenberger-Horne-Zeilinger states. The latter are resources for a measurement-based implementation of error-correction codes for bit-flip or phase-flip errors. This provides an approach to link the recently found very high thresholds for fault-tolerant measurement-based quantum information processing based on local error models for resource states with error thresholds for gate-based computational models.

Greater physician involvement improves coding outcomes in endobronchial ultrasound-guided transbronchial needle aspiration procedures.

PubMed

Pillai, Anilkumar; Medford, Andrew R L

2013-01-01

Correct coding is essential for accurate reimbursement for clinical activity. Published data confirm that significant aberrations in coding occur, leading to considerable financial inaccuracies especially in interventional procedures such as endobronchial ultrasound-guided transbronchial needle aspiration (EBUS-TBNA). Previous data reported a 15% coding error for EBUS-TBNA in a U.K. service. We hypothesised that greater physician involvement with coders would reduce EBUS-TBNA coding errors and financial disparity. The study was done as a prospective cohort study in the tertiary EBUS-TBNA service in Bristol. 165 consecutive patients between October 2009 and March 2012 underwent EBUS-TBNA for evaluation of unexplained mediastinal adenopathy on computed tomography. The chief coder was prospectively electronically informed of all procedures and cross-checked on a prospective database and by Trust Informatics. Cost and coding analysis was performed using the 2010-2011 tariffs. All 165 procedures (100%) were coded correctly as verified by Trust Informatics. This compares favourably with the 14.4% coding inaccuracy rate for EBUS-TBNA in a previous U.K. prospective cohort study [odds ratio 201.1 (1.1-357.5), p = 0.006]. Projected income loss was GBP 40,000 per year in the previous study, compared to a GBP 492,195 income here with no coding-attributable loss in revenue. Greater physician engagement with coders prevents coding errors and financial losses which can be significant especially in interventional specialties. The intervention can be as cheap, quick and simple as a prospective email to the coding team with cross-checks by Trust Informatics and against a procedural database. We suggest that all specialties should engage more with their coders using such a simple intervention to prevent revenue losses. Copyright © 2013 S. Karger AG, Basel.

Defense Logistics Agency Disposition Services Afghanistan Disposal Process Needed Improvement

DTIC Science & Technology

2013-11-08

audit, and management was proactive in correcting the deficiencies we identified. DLA DS eliminated backlogs, identified and corrected system ...problems, provided additional system training, corrected coding errors, added personnel to key positions, addressed scale issues, submitted debit...Service Automated Information System to the Reutilization Business Integration2 (RBI) solution. The implementation of RBI in Afghanistan occurred in

78 FR 59313 - Requirement of a Section 4959 Excise Tax Return and Time for Filing the Return; Correction

Federal Register 2010, 2011, 2012, 2013, 2014

2013-09-26

... liable for the excise tax for failure to meet the community health needs assessment requirements for any... Revenue Code. Need for Correction As published, the notice of proposed rulemaking (REG-115300-13) contains errors that are misleading and are in need of clarification. Correction to Publication Accordingly...

Controlling qubit drift by recycling error correction syndromes

NASA Astrophysics Data System (ADS)

Blume-Kohout, Robin

2015-03-01

Physical qubits are susceptible to systematic drift, above and beyond the stochastic Markovian noise that motivates quantum error correction. This parameter drift must be compensated - if it is ignored, error rates will rise to intolerable levels - but compensation requires knowing the parameters' current value, which appears to require halting experimental work to recalibrate (e.g. via quantum tomography). Fortunately, this is untrue. I show how to perform on-the-fly recalibration on the physical qubits in an error correcting code, using only information from the error correction syndromes. The algorithm for detecting and compensating drift is very simple - yet, remarkably, when used to compensate Brownian drift in the qubit Hamiltonian, it achieves a stabilized error rate very close to the theoretical lower bound. Against 1/f noise, it is less effective only because 1/f noise is (like white noise) dominated by high-frequency fluctuations that are uncompensatable. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE

Protecting quantum memories using coherent parity check codes

NASA Astrophysics Data System (ADS)

Roffe, Joschka; Headley, David; Chancellor, Nicholas; Horsman, Dominic; Kendon, Viv

2018-07-01

Coherent parity check (CPC) codes are a new framework for the construction of quantum error correction codes that encode multiple qubits per logical block. CPC codes have a canonical structure involving successive rounds of bit and phase parity checks, supplemented by cross-checks to fix the code distance. In this paper, we provide a detailed introduction to CPC codes using conventional quantum circuit notation. We demonstrate the implementation of a CPC code on real hardware, by designing a [[4, 2, 2

A modified non-binary LDPC scheme based on watermark symbols in high speed optical transmission systems

NASA Astrophysics Data System (ADS)

Wang, Liming; Qiao, Yaojun; Yu, Qian; Zhang, Wenbo

2016-04-01

We introduce a watermark non-binary low-density parity check code (NB-LDPC) scheme, which can estimate the time-varying noise variance by using prior information of watermark symbols, to improve the performance of NB-LDPC codes. And compared with the prior-art counterpart, the watermark scheme can bring about 0.25 dB improvement in net coding gain (NCG) at bit error rate (BER) of 1e-6 and 36.8-81% reduction of the iteration numbers. Obviously, the proposed scheme shows great potential in terms of error correction performance and decoding efficiency.

Halftoning Algorithms and Systems.

DTIC Science & Technology

1996-08-01

TERMS 15. NUMBER IF PAGESi. Halftoning algorithms; error diffusions ; color printing; topographic maps 16. PRICE CODE 17. SECURITY CLASSIFICATION 18...graylevels for each screen level. In the case of error diffusion algorithms, the calibration procedure using the new centering concept manifests itself as a...Novel Centering Concept for Overlapping Correction Paper / Transparency (Patent Applied 5/94)I * Applications To Error Diffusion * To Dithering (IS&T

A secure RFID authentication protocol adopting error correction code.

PubMed

Chen, Chien-Ming; Chen, Shuai-Min; Zheng, Xinying; Chen, Pei-Yu; Sun, Hung-Min

2014-01-01

RFID technology has become popular in many applications; however, most of the RFID products lack security related functionality due to the hardware limitation of the low-cost RFID tags. In this paper, we propose a lightweight mutual authentication protocol adopting error correction code for RFID. Besides, we also propose an advanced version of our protocol to provide key updating. Based on the secrecy of shared keys, the reader and the tag can establish a mutual authenticity relationship. Further analysis of the protocol showed that it also satisfies integrity, forward secrecy, anonymity, and untraceability. Compared with other lightweight protocols, the proposed protocol provides stronger resistance to tracing attacks, compromising attacks and replay attacks. We also compare our protocol with previous works in terms of performance.

A Secure RFID Authentication Protocol Adopting Error Correction Code

PubMed Central

Zheng, Xinying; Chen, Pei-Yu

2014-01-01

RFID technology has become popular in many applications; however, most of the RFID products lack security related functionality due to the hardware limitation of the low-cost RFID tags. In this paper, we propose a lightweight mutual authentication protocol adopting error correction code for RFID. Besides, we also propose an advanced version of our protocol to provide key updating. Based on the secrecy of shared keys, the reader and the tag can establish a mutual authenticity relationship. Further analysis of the protocol showed that it also satisfies integrity, forward secrecy, anonymity, and untraceability. Compared with other lightweight protocols, the proposed protocol provides stronger resistance to tracing attacks, compromising attacks and replay attacks. We also compare our protocol with previous works in terms of performance. PMID:24959619

LDPC-PPM Coding Scheme for Optical Communication

NASA Technical Reports Server (NTRS)

Barsoum, Maged; Moision, Bruce; Divsalar, Dariush; Fitz, Michael

2009-01-01

In a proposed coding-and-modulation/demodulation-and-decoding scheme for a free-space optical communication system, an error-correcting code of the low-density parity-check (LDPC) type would be concatenated with a modulation code that consists of a mapping of bits to pulse-position-modulation (PPM) symbols. Hence, the scheme is denoted LDPC-PPM. This scheme could be considered a competitor of a related prior scheme in which an outer convolutional error-correcting code is concatenated with an interleaving operation, a bit-accumulation operation, and a PPM inner code. Both the prior and present schemes can be characterized as serially concatenated pulse-position modulation (SCPPM) coding schemes. Figure 1 represents a free-space optical communication system based on either the present LDPC-PPM scheme or the prior SCPPM scheme. At the transmitting terminal, the original data (u) are processed by an encoder into blocks of bits (a), and the encoded data are mapped to PPM of an optical signal (c). For the purpose of design and analysis, the optical channel in which the PPM signal propagates is modeled as a Poisson point process. At the receiving terminal, the arriving optical signal (y) is demodulated to obtain an estimate (a^) of the coded data, which is then processed by a decoder to obtain an estimate (u^) of the original data.

FPGA implementation of high-performance QC-LDPC decoder for optical communications

NASA Astrophysics Data System (ADS)

Zou, Ding; Djordjevic, Ivan B.

2015-01-01

Forward error correction is as one of the key technologies enabling the next-generation high-speed fiber optical communications. Quasi-cyclic (QC) low-density parity-check (LDPC) codes have been considered as one of the promising candidates due to their large coding gain performance and low implementation complexity. In this paper, we present our designed QC-LDPC code with girth 10 and 25% overhead based on pairwise balanced design. By FPGAbased emulation, we demonstrate that the 5-bit soft-decision LDPC decoder can achieve 11.8dB net coding gain with no error floor at BER of 10-15 avoiding using any outer code or post-processing method. We believe that the proposed single QC-LDPC code is a promising solution for 400Gb/s optical communication systems and beyond.

Repetition code of 15 qubits

NASA Astrophysics Data System (ADS)

Wootton, James R.; Loss, Daniel

2018-05-01

The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most 15 qubits on the 16 qubit ibmqx3 device. Each experiment is run for a single round of syndrome measurements, achieved using the standard quantum technique of using ancilla qubits and controlled operations. The size of the final syndrome is small enough to allow for lookup table decoding using experimentally obtained data. The results show strong evidence that the logical error rate decays exponentially with code distance, as is expected and required for the development of fault-tolerant quantum computers. The results also give insight into the nature of noise in the device.

Error Correcting Codes and Related Designs

DTIC Science & Technology

1990-09-30

Theory, IT-37 (1991), 1222-1224. 6. Codes and designs, existence and uniqueness, Discrete Math ., to appear. 7. (with R. Brualdi and N. Cai), Orphan...structure of the first order Reed-Muller codes, Discrete Math ., to appear. 8. (with J. H. Conway and N.J.A. Sloane), The binary self-dual codes of length up...18, 1988. 4. "Codes and Designs," Mathematics Colloquium, Technion, Haifa, Israel, March 6, 1989. 5. "On the Covering Radius of Codes," Discrete Math . Group

Enhancing Undergraduate Mathematics Curriculum via Coding Theory and Cryptography

ERIC Educational Resources Information Center

Aydin, Nuh

2009-01-01

The theory of error-correcting codes and cryptography are two relatively recent applications of mathematics to information and communication systems. The mathematical tools used in these fields generally come from algebra, elementary number theory, and combinatorics, including concepts from computational complexity. It is possible to introduce the…

Atmospheric Correction of Satellite Imagery Using Modtran 3.5 Code

NASA Technical Reports Server (NTRS)

Gonzales, Fabian O.; Velez-Reyes, Miguel

1997-01-01

When performing satellite remote sensing of the earth in the solar spectrum, atmospheric scattering and absorption effects provide the sensors corrupted information about the target's radiance characteristics. We are faced with the problem of reconstructing the signal that was reflected from the target, from the data sensed by the remote sensing instrument. This article presents a method for simulating radiance characteristic curves of satellite images using a MODTRAN 3.5 band model (BM) code to solve the radiative transfer equation (RTE), and proposes a method for the implementation of an adaptive system for automated atmospheric corrections. The simulation procedure is carried out as follows: (1) for each satellite digital image a radiance characteristic curve is obtained by performing a digital number (DN) to radiance conversion, (2) using MODTRAN 3.5 a simulation of the images characteristic curves is generated, (3) the output of the code is processed to generate radiance characteristic curves for the simulated cases. The simulation algorithm was used to simulate Landsat Thematic Mapper (TM) images for two types of locations: the ocean surface, and a forest surface. The simulation procedure was validated by computing the error between the empirical and simulated radiance curves. While results in the visible region of the spectrum where not very accurate, those for the infrared region of the spectrum were encouraging. This information can be used for correction of the atmospheric effects. For the simulation over ocean, the lowest error produced in this region was of the order of 105 and up to 14 times smaller than errors in the visible region. For the same spectral region on the forest case, the lowest error produced was of the order of 10-4, and up to 41 times smaller than errors in the visible region,

75 FR 39632 - Regulated Navigation Area; Gulf Intracoastal Waterway, Inner Harbor Navigation Canal, Harvey...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-07-12

..., Algiers Canal, New Orleans, LA; Correction ACTION: Interim rule; Correction. SUMMARY: In the Federal... Area; Gulf Intracoastal Waterway, Inner Harbor Navigation Canal, Harvey Canal, Algiers Canal, New Orleans, LA into the Code of Federal Regulations. That publication contained an error in the DATES section...

Simulations of linear and Hamming codes using SageMath

NASA Astrophysics Data System (ADS)

Timur, Tahta D.; Adzkiya, Dieky; Soleha

2018-03-01

Digital data transmission over a noisy channel could distort the message being transmitted. The goal of coding theory is to ensure data integrity, that is, to find out if and where this noise has distorted the message and what the original message was. Data transmission consists of three stages: encoding, transmission, and decoding. Linear and Hamming codes are codes that we discussed in this work, where encoding algorithms are parity check and generator matrix, and decoding algorithms are nearest neighbor and syndrome. We aim to show that we can simulate these processes using SageMath software, which has built-in class of coding theory in general and linear codes in particular. First we consider the message as a binary vector of size k. This message then will be encoded to a vector with size n using given algorithms. And then a noisy channel with particular value of error probability will be created where the transmission will took place. The last task would be decoding, which will correct and revert the received message back to the original message whenever possible, that is, if the number of error occurred is smaller or equal to the correcting radius of the code. In this paper we will use two types of data for simulations, namely vector and text data.

BeiDou Geostationary Satellite Code Bias Modeling Using Fengyun-3C Onboard Measurements.

PubMed

Jiang, Kecai; Li, Min; Zhao, Qile; Li, Wenwen; Guo, Xiang

2017-10-27

This study validated and investigated elevation- and frequency-dependent systematic biases observed in ground-based code measurements of the Chinese BeiDou navigation satellite system, using the onboard BeiDou code measurement data from the Chinese meteorological satellite Fengyun-3C. Particularly for geostationary earth orbit satellites, sky-view coverage can be achieved over the entire elevation and azimuth angle ranges with the available onboard tracking data, which is more favorable to modeling code biases. Apart from the BeiDou-satellite-induced biases, the onboard BeiDou code multipath effects also indicate pronounced near-field systematic biases that depend only on signal frequency and the line-of-sight directions. To correct these biases, we developed a proposed code correction model by estimating the BeiDou-satellite-induced biases as linear piece-wise functions in different satellite groups and the near-field systematic biases in a grid approach. To validate the code bias model, we carried out orbit determination using single-frequency BeiDou data with and without code bias corrections applied. Orbit precision statistics indicate that those code biases can seriously degrade single-frequency orbit determination. After the correction model was applied, the orbit position errors, 3D root mean square, were reduced from 150.6 to 56.3 cm.

BeiDou Geostationary Satellite Code Bias Modeling Using Fengyun-3C Onboard Measurements

PubMed Central

Jiang, Kecai; Li, Min; Zhao, Qile; Li, Wenwen; Guo, Xiang

2017-01-01

This study validated and investigated elevation- and frequency-dependent systematic biases observed in ground-based code measurements of the Chinese BeiDou navigation satellite system, using the onboard BeiDou code measurement data from the Chinese meteorological satellite Fengyun-3C. Particularly for geostationary earth orbit satellites, sky-view coverage can be achieved over the entire elevation and azimuth angle ranges with the available onboard tracking data, which is more favorable to modeling code biases. Apart from the BeiDou-satellite-induced biases, the onboard BeiDou code multipath effects also indicate pronounced near-field systematic biases that depend only on signal frequency and the line-of-sight directions. To correct these biases, we developed a proposed code correction model by estimating the BeiDou-satellite-induced biases as linear piece-wise functions in different satellite groups and the near-field systematic biases in a grid approach. To validate the code bias model, we carried out orbit determination using single-frequency BeiDou data with and without code bias corrections applied. Orbit precision statistics indicate that those code biases can seriously degrade single-frequency orbit determination. After the correction model was applied, the orbit position errors, 3D root mean square, were reduced from 150.6 to 56.3 cm. PMID:29076998

Extremal Optimization for estimation of the error threshold in topological subsystem codes at T = 0

NASA Astrophysics Data System (ADS)

Millán-Otoya, Jorge E.; Boettcher, Stefan

2014-03-01

Quantum decoherence is a problem that arises in implementations of quantum computing proposals. Topological subsystem codes (TSC) have been suggested as a way to overcome decoherence. These offer a higher optimal error tolerance when compared to typical error-correcting algorithms. A TSC has been translated into a planar Ising spin-glass with constrained bimodal three-spin couplings. This spin-glass has been considered at finite temperature to determine the phase boundary between the unstable phase and the stable phase, where error recovery is possible.[1] We approach the study of the error threshold problem by exploring ground states of this spin-glass with the Extremal Optimization algorithm (EO).[2] EO has proven to be a effective heuristic to explore ground state configurations of glassy spin-systems.[3

Decoding small surface codes with feedforward neural networks

NASA Astrophysics Data System (ADS)

Varsamopoulos, Savvas; Criger, Ben; Bertels, Koen

2018-01-01

Surface codes reach high error thresholds when decoded with known algorithms, but the decoding time will likely exceed the available time budget, especially for near-term implementations. To decrease the decoding time, we reduce the decoding problem to a classification problem that a feedforward neural network can solve. We investigate quantum error correction and fault tolerance at small code distances using neural network-based decoders, demonstrating that the neural network can generalize to inputs that were not provided during training and that they can reach similar or better decoding performance compared to previous algorithms. We conclude by discussing the time required by a feedforward neural network decoder in hardware.

Validation of prostate-specific antigen laboratory values recorded in Surveillance, Epidemiology, and End Results registries.

PubMed

Adamo, Margaret Peggy; Boten, Jessica A; Coyle, Linda M; Cronin, Kathleen A; Lam, Clara J K; Negoita, Serban; Penberthy, Lynne; Stevens, Jennifer L; Ward, Kevin C

2017-02-15

Researchers have used prostate-specific antigen (PSA) values collected by central cancer registries to evaluate tumors for potential aggressive clinical disease. An independent study collecting PSA values suggested a high error rate (18%) related to implied decimal points. To evaluate the error rate in the Surveillance, Epidemiology, and End Results (SEER) program, a comprehensive review of PSA values recorded across all SEER registries was performed. Consolidated PSA values for eligible prostate cancer cases in SEER registries were reviewed and compared with text documentation from abstracted records. Four types of classification errors were identified: implied decimal point errors, abstraction or coding implementation errors, nonsignificant errors, and changes related to "unknown" values. A total of 50,277 prostate cancer cases diagnosed in 2012 were reviewed. Approximately 94.15% of cases did not have meaningful changes (85.85% correct, 5.58% with a nonsignificant change of <1 ng/mL, and 2.80% with no clinical change). Approximately 5.70% of cases had meaningful changes (1.93% due to implied decimal point errors, 1.54% due to abstract or coding errors, and 2.23% due to errors related to unknown categories). Only 419 of the original 50,277 cases (0.83%) resulted in a change in disease stage due to a corrected PSA value. The implied decimal error rate was only 1.93% of all cases in the current validation study, with a meaningful error rate of 5.81%. The reasons for the lower error rate in SEER are likely due to ongoing and rigorous quality control and visual editing processes by the central registries. The SEER program currently is reviewing and correcting PSA values back to 2004 and will re-release these data in the public use research file. Cancer 2017;123:697-703. © 2016 American Cancer Society. © 2016 The Authors. Cancer published by Wiley Periodicals, Inc. on behalf of American Cancer Society.

Improving the quality of self-monitoring blood glucose measurement: a study in reducing calibration errors.

PubMed

Baum, John M; Monhaut, Nanette M; Parker, Donald R; Price, Christopher P

2006-06-01

Two independent studies reported that 16% of people who self-monitor blood glucose used incorrectly coded meters. The degree of analytical error, however, was not characterized. Our study objectives were to demonstrate that miscoding can cause analytical errors and to characterize the potential amount of bias that can occur. The impact of calibration error with three selfblood glucose monitoring systems (BGMSs), one of which has an autocoding feature, is reported. Fresh capillary fingerstick blood from 50 subjects, 18 men and 32 women ranging in age from 23 to 82 years, was used to measure glucose with three BGMSs. Two BGMSs required manual coding and were purposely miscoded using numbers different from the one recommended for the reagent lot used. Two properly coded meters of each BGMS were included to assess within-system variability. Different reagent lots were used to challenge a third system that had autocoding capability and could not be miscoded. Some within-system comparisons showed deviations of greater than +/-30% when results obtained with miscoded meters were compared with data obtained with ones programmed using the correct code number. Similar erroneous results were found when the miscoded meter results were compared with those obtained with a glucose analyzer. For some miscoded meter and test strip combinations, error grid analysis showed that 90% of results fell into zones indicating altered clinical action. Such inaccuracies were not found with the BGMS having the autocoding feature. When certain meter code number settings of two BGMSs were used in conjunction with test strips having code numbers that did not match, statistically and clinically inaccurate results were obtained. Coding errors resulted in analytical errors of greater than +/-30% (-31.6 to +60.9%). These results confirm the value of a BGMS with an automatic coding feature.

Self-Powered Forward Error-Correcting Biosensor Based on Integration of Paper-Based Microfluidics and Self-Assembled Quick Response Codes.

PubMed

Yuan, Mingquan; Liu, Keng-Ku; Singamaneni, Srikanth; Chakrabartty, Shantanu

2016-10-01

This paper extends our previous work on silver-enhancement based self-assembling structures for designing reliable, self-powered biosensors with forward error correcting (FEC) capability. At the core of the proposed approach is the integration of paper-based microfluidics with quick response (QR) codes that can be optically scanned using a smart-phone. The scanned information is first decoded to obtain the location of a web-server which further processes the self-assembled QR image to determine the concentration of target analytes. The integration substrate for the proposed FEC biosensor is polyethylene and the patterning of the QR code on the substrate has been achieved using a combination of low-cost ink-jet printing and a regular ballpoint dispensing pen. A paper-based microfluidics channel has been integrated underneath the substrate for acquiring, mixing and flowing the sample to areas on the substrate where different parts of the code can self-assemble in presence of immobilized gold nanorods. In this paper we demonstrate the proof-of-concept detection using prototypes of QR encoded FEC biosensors.

Comparison of memory thresholds for planar qudit geometries

NASA Astrophysics Data System (ADS)

Marks, Jacob; Jochym-O'Connor, Tomas; Gheorghiu, Vlad

2017-11-01

We introduce and analyze a new type of decoding algorithm called general color clustering, based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under a generalized bit-flip error model, and is used to obtain the first memory threshold estimates for qudit 6-6-6 color codes. The proposed decoder is compared with similar decoding schemes for qudit surface codes as well as the current leading qubit decoders for both sets of codes. We find that, as with surface codes, clustering performs sub-optimally for qubit color codes, giving a threshold of 5.6 % compared to the 8.0 % obtained through surface projection decoding methods. However, the threshold rate increases by up to 112% for large qudit dimensions, plateauing around 11.9 % . All the analysis is performed using QTop, a new open-source software for simulating and visualizing topological quantum error correcting codes.

Implementing a strand of a scalable fault-tolerant quantum computing fabric.

PubMed

Chow, Jerry M; Gambetta, Jay M; Magesan, Easwar; Abraham, David W; Cross, Andrew W; Johnson, B R; Masluk, Nicholas A; Ryan, Colm A; Smolin, John A; Srinivasan, Srikanth J; Steffen, M

2014-06-24

With favourable error thresholds and requiring only nearest-neighbour interactions on a lattice, the surface code is an error-correcting code that has garnered considerable attention. At the heart of this code is the ability to perform a low-weight parity measurement of local code qubits. Here we demonstrate high-fidelity parity detection of two code qubits via measurement of a third syndrome qubit. With high-fidelity gates, we generate entanglement distributed across three superconducting qubits in a lattice where each code qubit is coupled to two bus resonators. Via high-fidelity measurement of the syndrome qubit, we deterministically entangle the code qubits in either an even or odd parity Bell state, conditioned on the syndrome qubit state. Finally, to fully characterize this parity readout, we develop a measurement tomography protocol. The lattice presented naturally extends to larger networks of qubits, outlining a path towards fault-tolerant quantum computing.

Code Optimization Techniques

DOE Office of Scientific and Technical Information (OSTI.GOV)

MAGEE,GLEN I.

Computers transfer data in a number of different ways. Whether through a serial port, a parallel port, over a modem, over an ethernet cable, or internally from a hard disk to memory, some data will be lost. To compensate for that loss, numerous error detection and correction algorithms have been developed. One of the most common error correction codes is the Reed-Solomon code, which is a special subset of BCH (Bose-Chaudhuri-Hocquenghem) linear cyclic block codes. In the AURA project, an unmanned aircraft sends the data it collects back to earth so it can be analyzed during flight and possible flightmore » modifications made. To counter possible data corruption during transmission, the data is encoded using a multi-block Reed-Solomon implementation with a possibly shortened final block. In order to maximize the amount of data transmitted, it was necessary to reduce the computation time of a Reed-Solomon encoding to three percent of the processor's time. To achieve such a reduction, many code optimization techniques were employed. This paper outlines the steps taken to reduce the processing time of a Reed-Solomon encoding and the insight into modern optimization techniques gained from the experience.« less

Correlated Errors in the Surface Code

NASA Astrophysics Data System (ADS)

Lopez, Daniel; Mucciolo, E. R.; Novais, E.

2012-02-01

A milestone step into the development of quantum information technology would be the ability to design and operate a reliable quantum memory. The greatest obstacle to create such a device has been decoherence due to the unavoidable interaction between the quantum system and its environment. Quantum Error Correction is therefore an essential ingredient to any quantum computing information device. A great deal of attention has been given to surface codes, since it has very good scaling properties. In this seminar, we discuss the time evolution of a qubit encoded in the logical basis of a surface code. The system is interacting with a bosonic environment at zero temperature. Our results show how much spatial and time correlations can be detrimental to the efficiency of the code.

Error control techniques for satellite and space communications

NASA Technical Reports Server (NTRS)

Costello, D. J., Jr.

1986-01-01

High rate concatenated coding systems with trellis inner codes and Reed-Solomon (RS) outer codes for application in satellite communication systems are considered. Two types of inner codes are studied: high rate punctured binary convolutional codes which result in overall effective information rates between 1/2 and 1 bit per channel use; and bandwidth efficient signal space trellis codes which can achieve overall effective information rates greater than 1 bit per channel use. Channel capacity calculations with and without side information performed for the concatenated coding system. Concatenated coding schemes are investigated. In Scheme 1, the inner code is decoded with the Viterbi algorithm and the outer RS code performs error-correction only (decoding without side information). In scheme 2, the inner code is decoded with a modified Viterbi algorithm which produces reliability information along with the decoded output. In this algorithm, path metrics are used to estimate the entire information sequence, while branch metrics are used to provide the reliability information on the decoded sequence. This information is used to erase unreliable bits in the decoded output. An errors-and-erasures RS decoder is then used for the outer code. These two schemes are proposed for use on NASA satellite channels. Results indicate that high system reliability can be achieved with little or no bandwidth expansion.

The Quantum Socket: Wiring for Superconducting Qubits - Part 3

NASA Astrophysics Data System (ADS)

Mariantoni, M.; Bejianin, J. H.; McConkey, T. G.; Rinehart, J. R.; Bateman, J. D.; Earnest, C. T.; McRae, C. H.; Rohanizadegan, Y.; Shiri, D.; Penava, B.; Breul, P.; Royak, S.; Zapatka, M.; Fowler, A. G.

The implementation of a quantum computer requires quantum error correction codes, which allow to correct errors occurring on physical quantum bits (qubits). Ensemble of physical qubits will be grouped to form a logical qubit with a lower error rate. Reaching low error rates will necessitate a large number of physical qubits. Thus, a scalable qubit architecture must be developed. Superconducting qubits have been used to realize error correction. However, a truly scalable qubit architecture has yet to be demonstrated. A critical step towards scalability is the realization of a wiring method that allows to address qubits densely and accurately. A quantum socket that serves this purpose has been designed and tested at microwave frequencies. In this talk, we show results where the socket is used at millikelvin temperatures to measure an on-chip superconducting resonator. The control electronics is another fundamental element for scalability. We will present a proposal based on the quantum socket to interconnect a classical control hardware to a superconducting qubit hardware, where both are operated at millikelvin temperatures.

[MODIS Investigation

NASA Technical Reports Server (NTRS)

Abbott, Mark R.

1996-01-01

Our first activity is based on delivery of code to Bob Evans (University of Miami) for integration and eventual delivery to the MODIS Science Data Support Team. As we noted in our previous semi-annual report, coding required the development and analysis of an end-to-end model of fluorescence line height (FLH) errors and sensitivity. This model is described in a paper in press in Remote Sensing of the Environment. Once the code was delivered to Miami, we continue to use this error analysis to evaluate proposed changes in MODIS sensor specifications and performance. Simply evaluating such changes on a band by band basis may obscure the true impacts of changes in sensor performance that are manifested in the complete algorithm. This is especially true with FLH that is sensitive to band placement and width. The error model will be used by Howard Gordon (Miami) to evaluate the effects of absorbing aerosols on the FLH algorithm performance. Presently, FLH relies only on simple corrections for atmospheric effects (viewing geometry, Rayleigh scattering) without correcting for aerosols. Our analysis suggests that aerosols should have a small impact relative to changes in the quantum yield of fluorescence in phytoplankton. However, the effect of absorbing aerosol is a new process and will be evaluated by Gordon.

High rate concatenated coding systems using bandwidth efficient trellis inner codes

NASA Technical Reports Server (NTRS)

Deng, Robert H.; Costello, Daniel J., Jr.

1989-01-01

High-rate concatenated coding systems with bandwidth-efficient trellis inner codes and Reed-Solomon (RS) outer codes are investigated for application in high-speed satellite communication systems. Two concatenated coding schemes are proposed. In one the inner code is decoded with soft-decision Viterbi decoding, and the outer RS code performs error-correction-only decoding (decoding without side information). In the other, the inner code is decoded with a modified Viterbi algorithm, which produces reliability information along with the decoded output. In this algorithm, path metrics are used to estimate the entire information sequence, whereas branch metrics are used to provide reliability information on the decoded sequence. This information is used to erase unreliable bits in the decoded output. An errors-and-erasures RS decoder is then used for the outer code. The two schemes have been proposed for high-speed data communication on NASA satellite channels. The rates considered are at least double those used in current NASA systems, and the results indicate that high system reliability can still be achieved.

Information Theory, Inference and Learning Algorithms

NASA Astrophysics Data System (ADS)

Mackay, David J. C.

2003-10-01

Information theory and inference, often taught separately, are here united in one entertaining textbook. These topics lie at the heart of many exciting areas of contemporary science and engineering - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics, and cryptography. This textbook introduces theory in tandem with applications. Information theory is taught alongside practical communication systems, such as arithmetic coding for data compression and sparse-graph codes for error-correction. A toolbox of inference techniques, including message-passing algorithms, Monte Carlo methods, and variational approximations, are developed alongside applications of these tools to clustering, convolutional codes, independent component analysis, and neural networks. The final part of the book describes the state of the art in error-correcting codes, including low-density parity-check codes, turbo codes, and digital fountain codes -- the twenty-first century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, David MacKay's groundbreaking book is ideal for self-learning and for undergraduate or graduate courses. Interludes on crosswords, evolution, and sex provide entertainment along the way. In sum, this is a textbook on information, communication, and coding for a new generation of students, and an unparalleled entry point into these subjects for professionals in areas as diverse as computational biology, financial engineering, and machine learning.

Decodoku: Quantum error rorrection as a simple puzzle game

NASA Astrophysics Data System (ADS)

Wootton, James

To build quantum computers, we need to detect and manage any noise that occurs. This will be done using quantum error correction. At the hardware level, QEC is a multipartite system that stores information non-locally. Certain measurements are made which do not disturb the stored information, but which do allow signatures of errors to be detected. Then there is a software problem. How to take these measurement outcomes and determine: a) The errors that caused them, and (b) how to remove their effects. For qubit error correction, the algorithms required to do this are well known. For qudits, however, current methods are far from optimal. We consider the error correction problem of qubit surface codes. At the most basic level, this is a problem that can be expressed in terms of a grid of numbers. Using this fact, we take the inherent problem at the heart of quantum error correction, remove it from its quantum context, and presented in terms of simple grid based puzzle games. We have developed three versions of these puzzle games, focussing on different aspects of the required algorithms. These have been presented and iOS and Android apps, allowing the public to try their hand at developing good algorithms to solve the puzzles. For more information, see www.decodoku.com. Funding from the NCCR QSIT.

Apply network coding for H.264/SVC multicasting

NASA Astrophysics Data System (ADS)

Wang, Hui; Kuo, C.-C. Jay

2008-08-01

In a packet erasure network environment, video streaming benefits from error control in two ways to achieve graceful degradation. The first approach is application-level (or the link-level) forward error-correction (FEC) to provide erasure protection. The second error control approach is error concealment at the decoder end to compensate lost packets. A large amount of research work has been done in the above two areas. More recently, network coding (NC) techniques have been proposed for efficient data multicast over networks. It was shown in our previous work that multicast video streaming benefits from NC for its throughput improvement. An algebraic model is given to analyze the performance in this work. By exploiting the linear combination of video packets along nodes in a network and the SVC video format, the system achieves path diversity automatically and enables efficient video delivery to heterogeneous receivers in packet erasure channels. The application of network coding can protect video packets against the erasure network environment. However, the rank defficiency problem of random linear network coding makes the error concealment inefficiently. It is shown by computer simulation that the proposed NC video multicast scheme enables heterogenous receiving according to their capacity constraints. But it needs special designing to improve the video transmission performance when applying network coding.

An investigation of error correcting techniques for OMV data

NASA Technical Reports Server (NTRS)

Ingels, Frank; Fryer, John

1992-01-01

Papers on the following topics are presented: considerations of testing the Orbital Maneuvering Vehicle (OMV) system with CLASS; OMV CLASS test results (first go around); equivalent system gain available from R-S encoding versus a desire to lower the power amplifier from 25 watts to 20 watts for OMV; command word acceptance/rejection rates for OMV; a memo concerning energy-to-noise ratio for the Viterbi-BSC Channel and the impact of Manchester coding loss; and an investigation of error correcting techniques for OMV and Advanced X-ray Astrophysics Facility (AXAF).

Free Space Laser Communication Experiments from Earth to the Lunar Reconnaissance Orbiter in Lunar Orbit

NASA Technical Reports Server (NTRS)

Sun, Xiaoli; Skillman, David R.; Hoffman, Evan D.; Mao, Dandan; McGarry, Jan F.; Zellar, Ronald S.; Fong, Wai H; Krainak, Michael A.; Neumann, Gregory A.; Smith, David E.

2013-01-01

Laser communication and ranging experiments were successfully conducted from the satellite laser ranging (SLR) station at NASA Goddard Space Flight Center (GSFC) to the Lunar Reconnaissance Orbiter (LRO) in lunar orbit. The experiments used 4096-ary pulse position modulation (PPM) for the laser pulses during one-way LRO Laser Ranging (LR) operations. Reed-Solomon forward error correction codes were used to correct the PPM symbol errors due to atmosphere turbulence and pointing jitter. The signal fading was measured and the results were compared to the model.

A study of redundancy management strategy for tetrad strap-down inertial systems. [error detection codes

NASA Technical Reports Server (NTRS)

Hruby, R. J.; Bjorkman, W. S.; Schmidt, S. F.; Carestia, R. A.

1979-01-01

Algorithms were developed that attempt to identify which sensor in a tetrad configuration has experienced a step failure. An algorithm is also described that provides a measure of the confidence with which the correct identification was made. Experimental results are presented from real-time tests conducted on a three-axis motion facility utilizing an ortho-skew tetrad strapdown inertial sensor package. The effects of prediction errors and of quantization on correct failure identification are discussed as well as an algorithm for detecting second failures through prediction.

Design the RS(255,239) encoder and interleaving in the space laser communication system

NASA Astrophysics Data System (ADS)

Lang, Yue; Tong, Shou-feng

2013-08-01

Space laser communication is researched by more and more countries. Space laser communication deserves to be researched. We can acquire higher transmission speed and better transmission quality between satellite and satellite, satellite and earth by setting up laser link. But in the space laser communication system，the reliability is under influences of many factors of atmosphere，detector noise, optical platform jitter and other factors. The intensity of the signal which is attenuated because of the long transmission distance is demanded to have higher intensity to acquire low BER. The channel code technology can enhance the anti-interference ability of the system. The theory of channel coding technology is that some redundancies is added to information codes. So it can make use of the checkout polynomial to correct errors at the sink port. It help the system to get low BER rate and coding gain. Reed-Solomon (RS) code is one of the channel code, and it is one kind of multi-ary BCH code, and it can correct both burst errors and random errors, and it is widely used in the error-control schemes. The new method of the RS encoder and interleaving based on the FPGA is proposed, aiming at satisfying the needs of the widely-used error control technology in the space laser communication field. An improved method for Finite Galois Field multiplier of encoding is proposed, and it is suitable for FPGA implementation. Comparison of the XOR gates cost between the optimization and original, the number of XOR gates is lessen more than 40% .Then give a new structure of interleaving by using the FPGA. By controlling the in-data stream and out-data stream of encoder, the asynchronous process of the whole frame is accomplished, while by using multi-level pipeline, the real-time transfer of the data is achieved. By controlling the read-address and write-address of the block RAM, the interleaving operation of the arbitrary depth is synchronously implemented. Compared with the normal method, it could reduce the complexity of the channel encoder and the hardware requirement effectively.

Quantization of high dimensional Gaussian vector using permutation modulation with application to information reconciliation in continuous variable QKD

NASA Astrophysics Data System (ADS)

Daneshgaran, Fred; Mondin, Marina; Olia, Khashayar

This paper is focused on the problem of Information Reconciliation (IR) for continuous variable Quantum Key Distribution (QKD). The main problem is quantization and assignment of labels to the samples of the Gaussian variables observed at Alice and Bob. Trouble is that most of the samples, assuming that the Gaussian variable is zero mean which is de-facto the case, tend to have small magnitudes and are easily disturbed by noise. Transmission over longer and longer distances increases the losses corresponding to a lower effective Signal-to-Noise Ratio (SNR) exasperating the problem. Quantization over higher dimensions is advantageous since it allows for fractional bit per sample accuracy which may be needed at very low SNR conditions whereby the achievable secret key rate is significantly less than one bit per sample. In this paper, we propose to use Permutation Modulation (PM) for quantization of Gaussian vectors potentially containing thousands of samples. PM is applied to the magnitudes of the Gaussian samples and we explore the dependence of the sign error probability on the magnitude of the samples. At very low SNR, we may transmit the entire label of the PM code from Bob to Alice in Reverse Reconciliation (RR) over public channel. The side information extracted from this label can then be used by Alice to characterize the sign error probability of her individual samples. Forward Error Correction (FEC) coding can be used by Bob on each subset of samples with similar sign error probability to aid Alice in error correction. This can be done for different subsets of samples with similar sign error probabilities leading to an Unequal Error Protection (UEP) coding paradigm.

Lexical architecture based on a hierarchy of codes for high-speed string correction

NASA Astrophysics Data System (ADS)

de Bertrand de Beuvron, Francois; Trigano, Philippe

1992-03-01

AI systems for the general public have to be really tolerant to errors. These errors could be of several kinds: typographic, phonetic, grammatical, or semantic. A special lexical dictionary architecture has been designed to deal with the first two. It extends the hierarchical file method of E. Tanaka and Y. Kojima.

Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping

NASA Astrophysics Data System (ADS)

Kubica, Aleksander; Beverland, Michael E.; Brandão, Fernando; Preskill, John; Svore, Krysta M.

2018-05-01

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p3DCC (1 )≃1.9 % and p3DCC (2 )≃27.6 % . We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

Fault-tolerance thresholds for the surface code with fabrication errors

NASA Astrophysics Data System (ADS)

Auger, James M.; Anwar, Hussain; Gimeno-Segovia, Mercedes; Stace, Thomas M.; Browne, Dan E.

2017-10-01

The construction of topological error correction codes requires the ability to fabricate a lattice of physical qubits embedded on a manifold with a nontrivial topology such that the quantum information is encoded in the global degrees of freedom (i.e., the topology) of the manifold. However, the manufacturing of large-scale topological devices will undoubtedly suffer from fabrication errors—permanent faulty components such as missing physical qubits or failed entangling gates—introducing permanent defects into the topology of the lattice and hence significantly reducing the distance of the code and the quality of the encoded logical qubits. In this work we investigate how fabrication errors affect the performance of topological codes, using the surface code as the test bed. A known approach to mitigate defective lattices involves the use of primitive swap gates in a long sequence of syndrome extraction circuits. Instead, we show that in the presence of fabrication errors the syndrome can be determined using the supercheck operator approach and the outcome of the defective gauge stabilizer generators without any additional computational overhead or use of swap gates. We report numerical fault-tolerance thresholds in the presence of both qubit fabrication and gate fabrication errors using a circuit-based noise model and the minimum-weight perfect-matching decoder. Our numerical analysis is most applicable to two-dimensional chip-based technologies, but the techniques presented here can be readily extended to other topological architectures. We find that in the presence of 8 % qubit fabrication errors, the surface code can still tolerate a computational error rate of up to 0.1 % .

Improve homology search sensitivity of PacBio data by correcting frameshifts.

PubMed

Du, Nan; Sun, Yanni

2016-09-01

Single-molecule, real-time sequencing (SMRT) developed by Pacific BioSciences produces longer reads than secondary generation sequencing technologies such as Illumina. The long read length enables PacBio sequencing to close gaps in genome assembly, reveal structural variations, and identify gene isoforms with higher accuracy in transcriptomic sequencing. However, PacBio data has high sequencing error rate and most of the errors are insertion or deletion errors. During alignment-based homology search, insertion or deletion errors in genes will cause frameshifts and may only lead to marginal alignment scores and short alignments. As a result, it is hard to distinguish true alignments from random alignments and the ambiguity will incur errors in structural and functional annotation. Existing frameshift correction tools are designed for data with much lower error rate and are not optimized for PacBio data. As an increasing number of groups are using SMRT, there is an urgent need for dedicated homology search tools for PacBio data. In this work, we introduce Frame-Pro, a profile homology search tool for PacBio reads. Our tool corrects sequencing errors and also outputs the profile alignments of the corrected sequences against characterized protein families. We applied our tool to both simulated and real PacBio data. The results showed that our method enables more sensitive homology search, especially for PacBio data sets of low sequencing coverage. In addition, we can correct more errors when comparing with a popular error correction tool that does not rely on hybrid sequencing. The source code is freely available at https://sourceforge.net/projects/frame-pro/ yannisun@msu.edu. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Multiplier Architecture for Coding Circuits

NASA Technical Reports Server (NTRS)

Wang, C. C.; Truong, T. K.; Shao, H. M.; Deutsch, L. J.

1986-01-01

Multipliers based on new algorithm for Galois-field (GF) arithmetic regular and expandable. Pipeline structures used for computing both multiplications and inverses. Designs suitable for implementation in very-large-scale integrated (VLSI) circuits. This general type of inverter and multiplier architecture especially useful in performing finite-field arithmetic of Reed-Solomon error-correcting codes and of some cryptographic algorithms.

Coding for Efficient Image Transmission

NASA Technical Reports Server (NTRS)

Rice, R. F.; Lee, J. J.

1986-01-01

NASA publication second in series on data-coding techniques for noiseless channels. Techniques used even in noisy channels, provided data further processed with Reed-Solomon or other error-correcting code. Techniques discussed in context of transmission of monochrome imagery from Voyager II spacecraft but applicable to other streams of data. Objective of this type coding to "compress" data; that is, to transmit using as few bits as possible by omitting as much as possible of portion of information repeated in subsequent samples (or picture elements).

Simultaneous Laser Ranging and Communication from an Earth-Based Satellite Laser Ranging Station to the Lunar Reconnaissance Orbiter in Lunar Orbit

NASA Technical Reports Server (NTRS)

Sun, Xiaoli; Skillman, David R.; Hoffman, Evan D.; Mao, Dandan; McGarry, Jan F.; Neumann, Gregory A.; McIntire, Leva; Zellar, Ronald S.; Davidson, Frederic M.; Fong, Wai H.;

The Space Telescope SI C&DH system. [Scientific Instrument Control and Data Handling Subsystem

NASA Technical Reports Server (NTRS)

Gadwal, Govind R.; Barasch, Ronald S.

1990-01-01

The Hubble Space Telescope Scientific Instrument Control and Data Handling Subsystem (SI C&DH) is designed to interface with five scientific instruments of the Space Telescope to provide ground and autonomous control and collect health and status information using the Standard Telemetry and Command Components (STACC) multiplex data bus. It also formats high throughput science data into packets. The packetized data is interleaved and Reed-Solomon encoded for error correction and Pseudo Random encoded. An inner convolutional coding with the outer Reed-Solomon coding provides excellent error correction capability. The subsystem is designed with the capacity for orbital replacement in order to meet a mission life of fifteen years. The spacecraft computer and the SI C&DH computer coordinate the activities of the spacecraft and the scientific instruments to achieve the mission objectives.

Self-dual random-plaquette gauge model and the quantum toric code

NASA Astrophysics Data System (ADS)

Takeda, Koujin; Nishimori, Hidetoshi

2004-05-01

We study the four-dimensional Z2 random-plaquette lattice gauge theory as a model of topological quantum memory, the toric code in particular. In this model, the procedure of quantum error correction works properly in the ordered (Higgs) phase, and phase boundary between the ordered (Higgs) and disordered (confinement) phases gives the accuracy threshold of error correction. Using self-duality of the model in conjunction with the replica method, we show that this model has exactly the same mathematical structure as that of the two-dimensional random-bond Ising model, which has been studied very extensively. This observation enables us to derive a conjecture on the exact location of the multicritical point (accuracy threshold) of the model, pc=0.889972…, and leads to several nontrivial results including bounds on the accuracy threshold in three dimensions.

A method to compute SEU fault probabilities in memory arrays with error correction

NASA Technical Reports Server (NTRS)

Gercek, Gokhan

1994-01-01

With the increasing packing densities in VLSI technology, Single Event Upsets (SEU) due to cosmic radiations are becoming more of a critical issue in the design of space avionics systems. In this paper, a method is introduced to compute the fault (mishap) probability for a computer memory of size M words. It is assumed that a Hamming code is used for each word to provide single error correction. It is also assumed that every time a memory location is read, single errors are corrected. Memory is read randomly whose distribution is assumed to be known. In such a scenario, a mishap is defined as two SEU's corrupting the same memory location prior to a read. The paper introduces a method to compute the overall mishap probability for the entire memory for a mission duration of T hours.

Extending Moore's Law via Computationally Error Tolerant Computing.

DOE PAGES

Deng, Bobin; Srikanth, Sriseshan; Hein, Eric R.; ...

2018-03-01

Dennard scaling has ended. Lowering the voltage supply (V dd) to sub-volt levels causes intermittent losses in signal integrity, rendering further scaling (down) no longer acceptable as a means to lower the power required by a processor core. However, it is possible to correct the occasional errors caused due to lower V dd in an efficient manner and effectively lower power. By deploying the right amount and kind of redundancy, we can strike a balance between overhead incurred in achieving reliability and energy savings realized by permitting lower V dd. One promising approach is the Redundant Residue Number System (RRNS)more » representation. Unlike other error correcting codes, RRNS has the important property of being closed under addition, subtraction and multiplication, thus enabling computational error correction at a fraction of an overhead compared to conventional approaches. We use the RRNS scheme to design a Computationally-Redundant, Energy-Efficient core, including the microarchitecture, Instruction Set Architecture (ISA) and RRNS centered algorithms. Finally, from the simulation results, this RRNS system can reduce the energy-delay-product by about 3× for multiplication intensive workloads and by about 2× in general, when compared to a non-error-correcting binary core.« less

Extending Moore's Law via Computationally Error Tolerant Computing.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng, Bobin; Srikanth, Sriseshan; Hein, Eric R.

Dennard scaling has ended. Lowering the voltage supply (V dd) to sub-volt levels causes intermittent losses in signal integrity, rendering further scaling (down) no longer acceptable as a means to lower the power required by a processor core. However, it is possible to correct the occasional errors caused due to lower V dd in an efficient manner and effectively lower power. By deploying the right amount and kind of redundancy, we can strike a balance between overhead incurred in achieving reliability and energy savings realized by permitting lower V dd. One promising approach is the Redundant Residue Number System (RRNS)more » representation. Unlike other error correcting codes, RRNS has the important property of being closed under addition, subtraction and multiplication, thus enabling computational error correction at a fraction of an overhead compared to conventional approaches. We use the RRNS scheme to design a Computationally-Redundant, Energy-Efficient core, including the microarchitecture, Instruction Set Architecture (ISA) and RRNS centered algorithms. Finally, from the simulation results, this RRNS system can reduce the energy-delay-product by about 3× for multiplication intensive workloads and by about 2× in general, when compared to a non-error-correcting binary core.« less

FPGA implementation of advanced FEC schemes for intelligent aggregation networks

NASA Astrophysics Data System (ADS)

Zou, Ding; Djordjevic, Ivan B.

2016-02-01

In state-of-the-art fiber-optics communication systems the fixed forward error correction (FEC) and constellation size are employed. While it is important to closely approach the Shannon limit by using turbo product codes (TPC) and low-density parity-check (LDPC) codes with soft-decision decoding (SDD) algorithm; rate-adaptive techniques, which enable increased information rates over short links and reliable transmission over long links, are likely to become more important with ever-increasing network traffic demands. In this invited paper, we describe a rate adaptive non-binary LDPC coding technique, and demonstrate its flexibility and good performance exhibiting no error floor at BER down to 10-15 in entire code rate range, by FPGA-based emulation, making it a viable solution in the next-generation high-speed intelligent aggregation networks.

Convolutional coding at 50 Mbps for the Shuttle Ku-band return link

NASA Technical Reports Server (NTRS)

Batson, B. H.; Huth, G. K.

1976-01-01

Error correcting coding is required for 50 Mbps data link from the Shuttle Orbiter through the Tracking and Data Relay Satellite System (TDRSS) to the ground because of severe power limitations. Convolutional coding has been chosen because the decoding algorithms (sequential and Viterbi) provide significant coding gains at the required bit error probability of one in 10 to the sixth power and can be implemented at 50 Mbps with moderate hardware. While a 50 Mbps sequential decoder has been built, the highest data rate achieved for a Viterbi decoder is 10 Mbps. Thus, five multiplexed 10 Mbps Viterbi decoders must be used to provide a 50 Mbps data rate. This paper discusses the tradeoffs which were considered when selecting the multiplexed Viterbi decoder approach for this application.

Fade-resistant forward error correction method for free-space optical communications systems

DOEpatents

Johnson, Gary W.; Dowla, Farid U.; Ruggiero, Anthony J.

2007-10-02

Free-space optical (FSO) laser communication systems offer exceptionally wide-bandwidth, secure connections between platforms that cannot other wise be connected via physical means such as optical fiber or cable. However, FSO links are subject to strong channel fading due to atmospheric turbulence and beam pointing errors, limiting practical performance and reliability. We have developed a fade-tolerant architecture based on forward error correcting codes (FECs) combined with delayed, redundant, sub-channels. This redundancy is made feasible though dense wavelength division multiplexing (WDM) and/or high-order M-ary modulation. Experiments and simulations show that error-free communications is feasible even when faced with fades that are tens of milliseconds long. We describe plans for practical implementation of a complete system operating at 2.5 Gbps.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olama, Mohammed M; Matalgah, Mustafa M; Bobrek, Miljko

Traditional encryption techniques require packet overhead, produce processing time delay, and suffer from severe quality of service deterioration due to fades and interference in wireless channels. These issues reduce the effective transmission data rate (throughput) considerably in wireless communications, where data rate with limited bandwidth is the main constraint. In this paper, performance evaluation analyses are conducted for an integrated signaling-encryption mechanism that is secure and enables improved throughput and probability of bit-error in wireless channels. This mechanism eliminates the drawbacks stated herein by encrypting only a small portion of an entire transmitted frame, while the rest is not subjectmore » to traditional encryption but goes through a signaling process (designed transformation) with the plaintext of the portion selected for encryption. We also propose to incorporate error correction coding solely on the small encrypted portion of the data to drastically improve the overall bit-error rate performance while not noticeably increasing the required bit-rate. We focus on validating the signaling-encryption mechanism utilizing Hamming and convolutional error correction coding by conducting an end-to-end system-level simulation-based study. The average probability of bit-error and throughput of the encryption mechanism are evaluated over standard Gaussian and Rayleigh fading-type channels and compared to the ones of the conventional advanced encryption standard (AES).« less

A novel QC-LDPC code based on the finite field multiplicative group for optical communications

NASA Astrophysics Data System (ADS)

Yuan, Jian-guo; Xu, Liang; Tong, Qing-zhen

2013-09-01

A novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) code is proposed based on the finite field multiplicative group, which has easier construction, more flexible code-length code-rate adjustment and lower encoding/decoding complexity. Moreover, a regular QC-LDPC(5334,4962) code is constructed. The simulation results show that the constructed QC-LDPC(5334,4962) code can gain better error correction performance under the condition of the additive white Gaussian noise (AWGN) channel with iterative decoding sum-product algorithm (SPA). At the bit error rate (BER) of 10-6, the net coding gain (NCG) of the constructed QC-LDPC(5334,4962) code is 1.8 dB, 0.9 dB and 0.2 dB more than that of the classic RS(255,239) code in ITU-T G.975, the LDPC(32640,30592) code in ITU-T G.975.1 and the SCG-LDPC(3969,3720) code constructed by the random method, respectively. So it is more suitable for optical communication systems.

Entanglement-assisted quantum convolutional coding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wilde, Mark M.; Brun, Todd A.

2010-04-15

We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted quantum convolutional coding. Our construction produces a Calderbank-Shor-Steane (CSS) entanglement-assisted quantum convolutional code from two arbitrary classical binary convolutional codes. The rate and error-correcting properties of the classical convolutional codes directly determine the corresponding properties of the resulting entanglement-assisted quantum convolutional code. We explain how to encode our CSS entanglement-assisted quantum convolutional codes starting from a stream of information qubits, ancilla qubits, and shared entangled bits.

Simulating a transmon implementation of the surface code, Part II

NASA Astrophysics Data System (ADS)

O'Brien, Thomas; Tarasinski, Brian; Rol, Adriaan; Bultink, Niels; Fu, Xiang; Criger, Ben; Dicarlo, Leonardo

The majority of quantum error correcting circuit simulations use Pauli error channels, as they can be efficiently calculated. This raises two questions: what is the effect of more complicated physical errors on the logical qubit error rate, and how much more efficient can decoders become when accounting for realistic noise? To answer these questions, we design a minimal weight perfect matching decoder parametrized by a physically motivated noise model and test it on the full density matrix simulation of Surface-17, a distance-3 surface code. We compare performance against other decoders, for a range of physical parameters. Particular attention is paid to realistic sources of error for transmon qubits in a circuit QED architecture, and the requirements for real-time decoding via an FPGA Research funded by the Foundation for Fundamental Research on Matter (FOM), the Netherlands Organization for Scientific Research (NWO/OCW), IARPA, an ERC Synergy Grant, the China Scholarship Council, and Intel Corporation.

Using Analysis Increments (AI) to Estimate and Correct Systematic Errors in the Global Forecast System (GFS) Online

NASA Astrophysics Data System (ADS)

Bhargava, K.; Kalnay, E.; Carton, J.; Yang, F.

2017-12-01

Systematic forecast errors, arising from model deficiencies, form a significant portion of the total forecast error in weather prediction models like the Global Forecast System (GFS). While much effort has been expended to improve models, substantial model error remains. The aim here is to (i) estimate the model deficiencies in the GFS that lead to systematic forecast errors, (ii) implement an online correction (i.e., within the model) scheme to correct GFS following the methodology of Danforth et al. [2007] and Danforth and Kalnay [2008, GRL]. Analysis Increments represent the corrections that new observations make on, in this case, the 6-hr forecast in the analysis cycle. Model bias corrections are estimated from the time average of the analysis increments divided by 6-hr, assuming that initial model errors grow linearly and first ignoring the impact of observation bias. During 2012-2016, seasonal means of the 6-hr model bias are generally robust despite changes in model resolution and data assimilation systems, and their broad continental scales explain their insensitivity to model resolution. The daily bias dominates the sub-monthly analysis increments and consists primarily of diurnal and semidiurnal components, also requiring a low dimensional correction. Analysis increments in 2015 and 2016 are reduced over oceans, which is attributed to improvements in the specification of the SSTs. These results encourage application of online correction, as suggested by Danforth and Kalnay, for mean, seasonal and diurnal and semidiurnal model biases in GFS to reduce both systematic and random errors. As the error growth in the short-term is still linear, estimated model bias corrections can be added as a forcing term in the model tendency equation to correct online. Preliminary experiments with GFS, correcting temperature and specific humidity online show reduction in model bias in 6-hr forecast. This approach can then be used to guide and optimize the design of sub-grid scale physical parameterizations, more accurate discretization of the model dynamics, boundary conditions, radiative transfer codes, and other potential model improvements which can then replace the empirical correction scheme. The analysis increments also provide guidance in testing new physical parameterizations.

An approach enabling adaptive FEC for OFDM in fiber-VLLC system

NASA Astrophysics Data System (ADS)

Wei, Yiran; He, Jing; Deng, Rui; Shi, Jin; Chen, Shenghai; Chen, Lin

2017-12-01

In this paper, we propose an orthogonal circulant matrix transform (OCT)-based adaptive frame-level-forward error correction (FEC) scheme for fiber-visible laser light communication (VLLC) system and experimentally demonstrate by Reed-Solomon (RS) Code. In this method, no extra bits are spent for adaptive message, except training sequence (TS), which is simultaneously used for synchronization and channel estimation. Therefore, RS-coding can be adaptively performed frames by frames via the last received codeword-error-rate (CER) feedback estimated by the TSs of the previous few OFDM frames. In addition, the experimental results exhibit that over 20 km standard single-mode fiber (SSMF) and 8 m visible light transmission, the costs of RS codewords are at most 14.12% lower than those of conventional adaptive subcarrier-RS-code based 16-QAM OFDM at bit error rate (BER) of 10-5.

Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping.

PubMed

Kubica, Aleksander; Beverland, Michael E; Brandão, Fernando; Preskill, John; Svore, Krysta M

2018-05-04

Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p_{3DCC}^{(1)}≃1.9% and p_{3DCC}^{(2)}≃27.6%. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

Comparing Zeeman qubits to hyperfine qubits in the context of the surface code: +174Yb and +171Yb

NASA Astrophysics Data System (ADS)

Brown, Natalie C.; Brown, Kenneth R.

2018-05-01

Many systems used for quantum computing possess additional states beyond those defining the qubit. Leakage out of the qubit subspace must be considered when designing quantum error correction codes. Here we consider trapped ion qubits manipulated by Raman transitions. Zeeman qubits do not suffer from leakage errors but are sensitive to magnetic fields to first order. Hyperfine qubits can be encoded in clock states that are insensitive to magnetic fields to first order, but spontaneous scattering during the Raman transition can lead to leakage. Here we compare a Zeeman qubit (+174Yb) to a hyperfine qubit (+171Yb) in the context of the surface code. We find that the number of physical qubits required to reach a specific logical qubit error can be reduced by using +174Yb if the magnetic field can be stabilized with fluctuations smaller than 10 μ G .

Measuring Data Quality Through a Source Data Verification Audit in a Clinical Research Setting.

PubMed

Houston, Lauren; Probst, Yasmine; Humphries, Allison

2015-01-01

Health data has long been scrutinised in relation to data quality and integrity problems. Currently, no internationally accepted or "gold standard" method exists measuring data quality and error rates within datasets. We conducted a source data verification (SDV) audit on a prospective clinical trial dataset. An audit plan was applied to conduct 100% manual verification checks on a 10% random sample of participant files. A quality assurance rule was developed, whereby if >5% of data variables were incorrect a second 10% random sample would be extracted from the trial data set. Error was coded: correct, incorrect (valid or invalid), not recorded or not entered. Audit-1 had a total error of 33% and audit-2 36%. The physiological section was the only audit section to have <5% error. Data not recorded to case report forms had the greatest impact on error calculations. A significant association (p=0.00) was found between audit-1 and audit-2 and whether or not data was deemed correct or incorrect. Our study developed a straightforward method to perform a SDV audit. An audit rule was identified and error coding was implemented. Findings demonstrate that monitoring data quality by a SDV audit can identify data quality and integrity issues within clinical research settings allowing quality improvement to be made. The authors suggest this approach be implemented for future research.

Percolation bounds for decoding thresholds with correlated erasures in quantum LDPC codes

NASA Astrophysics Data System (ADS)

Hamilton, Kathleen; Pryadko, Leonid

Correlations between errors can dramatically affect decoding thresholds, in some cases eliminating the threshold altogether. We analyze the existence of a threshold for quantum low-density parity-check (LDPC) codes in the case of correlated erasures. When erasures are positively correlated, the corresponding multi-variate Bernoulli distribution can be modeled in terms of cluster errors, where qubits in clusters of various size can be marked all at once. In a code family with distance scaling as a power law of the code length, erasures can be always corrected below percolation on a qubit adjacency graph associated with the code. We bound this correlated percolation transition by weighted (uncorrelated) percolation on a specially constructed cluster connectivity graph, and apply our recent results to construct several bounds for the latter. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-14-1-0272.

Use the Bar Code System to Improve Accuracy of the Patient and Sample Identification.

PubMed

Chuang, Shu-Hsia; Yeh, Huy-Pzu; Chi, Kun-Hung; Ku, Hsueh-Chen

2018-01-01

In time and correct sample collection were highly related to patient's safety. The sample error rate was 11.1%, because misbranded patient information and wrong sample containers during January to April, 2016. We developed a barcode system of "Specimens Identify System" through process of reengineering of TRM, used bar code scanners, add sample container instructions, and mobile APP. Conclusion, the bar code systems improved the patient safety and created green environment.

High data rate Reed-Solomon encoding and decoding using VLSI technology

NASA Technical Reports Server (NTRS)

Miller, Warner; Morakis, James

1987-01-01

Presented as an implementation of a Reed-Solomon encode and decoder, which is 16-symbol error correcting, each symbol is 8 bits. This Reed-Solomon (RS) code is an efficient error correcting code that the National Aeronautics and Space Administration (NASA) will use in future space communications missions. A Very Large Scale Integration (VLSI) implementation of the encoder and decoder accepts data rates up 80 Mbps. A total of seven chips are needed for the decoder (four of the seven decoding chips are customized using 3-micron Complementary Metal Oxide Semiconduction (CMOS) technology) and one chip is required for the encoder. The decoder operates with the symbol clock being the system clock for the chip set. Approximately 1.65 billion Galois Field (GF) operations per second are achieved with the decoder chip set and 640 MOPS are achieved with the encoder chip.

Logical qubit fusion

NASA Astrophysics Data System (ADS)

Moussa, Jonathan; Ryan-Anderson, Ciaran

The canonical modern plan for universal quantum computation is a Clifford+T gate set implemented in a topological error-correcting code. This plan has the basic disparity that logical Clifford gates are natural for codes in two spatial dimensions while logical T gates are natural in three. Recent progress has reduced this disparity by proposing logical T gates in two dimensions with doubled, stacked, or gauge color codes, but these proposals lack an error threshold. An alternative universal gate set is Clifford+F, where a fusion (F) gate converts two logical qubits into a logical qudit. We show that logical F gates can be constructed by identifying compatible pairs of qubit and qudit codes that stabilize the same logical subspace, much like the original Bravyi-Kitaev construction of magic state distillation. The simplest example of high-distance compatible codes results in a proposal that is very similar to the stacked color code with the key improvement of retaining an error threshold. Sandia National Labs is a multi-program laboratory managed and operated by Sandia Corp, a wholly owned subsidiary of Lockheed Martin Corp, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Adiabatic topological quantum computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cesare, Chris; Landahl, Andrew J.; Bacon, Dave

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev’s surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computationmore » size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.« less

Adiabatic topological quantum computing

DOE PAGES

Cesare, Chris; Landahl, Andrew J.; Bacon, Dave; ...

2015-07-31

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev’s surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computationmore » size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.« less

Effect of ancilla's structure on quantum error correction using the seven-qubit Calderbank-Shor-Steane code

NASA Astrophysics Data System (ADS)

Salas, P. J.; Sanz, A. L.

2004-05-01

In this work we discuss the ability of different types of ancillas to control the decoherence of a qubit interacting with an environment. The error is introduced into the numerical simulation via a depolarizing isotropic channel. The ranges of values considered are 10-4 ⩽ɛ⩽ 10-2 for memory errors and 3× 10-5 ⩽γ/7⩽ 10-2 for gate errors. After the correction we calculate the fidelity as a quality criterion for the qubit recovered. We observe that a recovery method with a three-qubit ancilla provides reasonably good results bearing in mind its economy. If we want to go further, we have to use fault tolerant ancillas with a high degree of parallelism, even if this condition implies introducing additional ancilla verification qubits.

An evaluation of the effect of JPEG, JPEG2000, and H.264/AVC on CQR codes decoding process

NASA Astrophysics Data System (ADS)

Vizcarra Melgar, Max E.; Farias, Mylène C. Q.; Zaghetto, Alexandre

2015-02-01

This paper presents a binarymatrix code based on QR Code (Quick Response Code), denoted as CQR Code (Colored Quick Response Code), and evaluates the effect of JPEG, JPEG2000 and H.264/AVC compression on the decoding process. The proposed CQR Code has three additional colors (red, green and blue), what enables twice as much storage capacity when compared to the traditional black and white QR Code. Using the Reed-Solomon error-correcting code, the CQR Code model has a theoretical correction capability of 38.41%. The goal of this paper is to evaluate the effect that degradations inserted by common image compression algorithms have on the decoding process. Results show that a successful decoding process can be achieved for compression rates up to 0.3877 bits/pixel, 0.1093 bits/pixel and 0.3808 bits/pixel for JPEG, JPEG2000 and H.264/AVC formats, respectively. The algorithm that presents the best performance is the H.264/AVC, followed by the JPEG2000, and JPEG.

Digital to synchro converter

NASA Technical Reports Server (NTRS)

Predina, Joseph P. (Inventor)

1989-01-01

A digital-to-synchro converter is provided where a binary input code specifies a desired shaft angle and where an resolver type position transducer is employed with additional circuitry to generate a shaft position error signal indicative of the angular difference between the desired shaft angle and the actual shaft angle. The additional circuitry corrects for known and calculated errors in the shaft position detection process and equipment.

Uncertainty Analysis Principles and Methods

DTIC Science & Technology

2007-09-01

error source . The Data Processor converts binary coded numbers to values, performs D/A curve fitting and applies any correction factors that may be...describes the stages or modules involved in the measurement process. We now need to identify all relevant error sources and develop the mathematical... sources , gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden

Some partial-unit-memory convolutional codes

NASA Technical Reports Server (NTRS)

Abdel-Ghaffar, K.; Mceliece, R. J.; Solomon, G.

1991-01-01

The results of a study on a class of error correcting codes called partial unit memory (PUM) codes are presented. This class of codes, though not entirely new, has until now remained relatively unexplored. The possibility of using the well developed theory of block codes to construct a large family of promising PUM codes is shown. The performance of several specific PUM codes are compared with that of the Voyager standard (2, 1, 6) convolutional code. It was found that these codes can outperform the Voyager code with little or no increase in decoder complexity. This suggests that there may very well be PUM codes that can be used for deep space telemetry that offer both increased performance and decreased implementational complexity over current coding systems.

Rate-compatible punctured convolutional codes (RCPC codes) and their applications

NASA Astrophysics Data System (ADS)

Hagenauer, Joachim

1988-04-01

The concept of punctured convolutional codes is extended by punctuating a low-rate 1/N code periodically with period P to obtain a family of codes with rate P/(P + l), where l can be varied between 1 and (N - 1)P. A rate-compatibility restriction on the puncturing tables ensures that all code bits of high rate codes are used by the lower-rate codes. This allows transmission of incremental redundancy in ARQ/FEC (automatic repeat request/forward error correction) schemes and continuous rate variation to change from low to high error protection within a data frame. Families of RCPC codes with rates between 8/9 and 1/4 are given for memories M from 3 to 6 (8 to 64 trellis states) together with the relevant distance spectra. These codes are almost as good as the best known general convolutional codes of the respective rates. It is shown that the same Viterbi decoder can be used for all RCPC codes of the same M. The application of RCPC codes to hybrid ARQ/FEC schemes is discussed for Gaussian and Rayleigh fading channels using channel-state information to optimize throughput.

Ensemble codes involving hippocampal neurons are at risk during delayed performance tests.

PubMed

Hampson, R E; Deadwyler, S A

1996-11-26

Multielectrode recording techniques were used to record ensemble activity from 10 to 16 simultaneously active CA1 and CA3 neurons in the rat hippocampus during performance of a spatial delayed-nonmatch-to-sample task. Extracted sources of variance were used to assess the nature of two different types of errors that accounted for 30% of total trials. The two types of errors included ensemble "miscodes" of sample phase information and errors associated with delay-dependent corruption or disappearance of sample information at the time of the nonmatch response. Statistical assessment of trial sequences and associated "strength" of hippocampal ensemble codes revealed that miscoded error trials always followed delay-dependent error trials in which encoding was "weak," indicating that the two types of errors were "linked." It was determined that the occurrence of weakly encoded, delay-dependent error trials initiated an ensemble encoding "strategy" that increased the chances of being correct on the next trial and avoided the occurrence of further delay-dependent errors. Unexpectedly, the strategy involved "strongly" encoding response position information from the prior (delay-dependent) error trial and carrying it forward to the sample phase of the next trial. This produced a miscode type error on trials in which the "carried over" information obliterated encoding of the sample phase response on the next trial. Application of this strategy, irrespective of outcome, was sufficient to reorient the animal to the proper between trial sequence of response contingencies (nonmatch-to-sample) and boost performance to 73% correct on subsequent trials. The capacity for ensemble analyses of strength of information encoding combined with statistical assessment of trial sequences therefore provided unique insight into the "dynamic" nature of the role hippocampus plays in delay type memory tasks.

Least Reliable Bits Coding (LRBC) for high data rate satellite communications

NASA Technical Reports Server (NTRS)

Vanderaar, Mark; Wagner, Paul; Budinger, James

1992-01-01

An analysis and discussion of a bandwidth efficient multi-level/multi-stage block coded modulation technique called Least Reliable Bits Coding (LRBC) is presented. LRBC uses simple multi-level component codes that provide increased error protection on increasingly unreliable modulated bits in order to maintain an overall high code rate that increases spectral efficiency. Further, soft-decision multi-stage decoding is used to make decisions on unprotected bits through corrections made on more protected bits. Using analytical expressions and tight performance bounds it is shown that LRBC can achieve increased spectral efficiency and maintain equivalent or better power efficiency compared to that of Binary Phase Shift Keying (BPSK). Bit error rates (BER) vs. channel bit energy with Additive White Gaussian Noise (AWGN) are given for a set of LRB Reed-Solomon (RS) encoded 8PSK modulation formats with an ensemble rate of 8/9. All formats exhibit a spectral efficiency of 2.67 = (log2(8))(8/9) information bps/Hz. Bit by bit coded and uncoded error probabilities with soft-decision information are determined. These are traded with with code rate to determine parameters that achieve good performance. The relative simplicity of Galois field algebra vs. the Viterbi algorithm and the availability of high speed commercial Very Large Scale Integration (VLSI) for block codes indicates that LRBC using block codes is a desirable method for high data rate implementations.

Analysis and correction of linear optics errors, and operational improvements in the Indus-2 storage ring

NASA Astrophysics Data System (ADS)

Husain, Riyasat; Ghodke, A. D.

2017-08-01

Estimation and correction of the optics errors in an operational storage ring is always vital to achieve the design performance. To achieve this task, the most suitable and widely used technique, called linear optics from closed orbit (LOCO) is used in almost all storage ring based synchrotron radiation sources. In this technique, based on the response matrix fit, errors in the quadrupole strengths, beam position monitor (BPM) gains, orbit corrector calibration factors etc. can be obtained. For correction of the optics, suitable changes in the quadrupole strengths can be applied through the driving currents of the quadrupole power supplies to achieve the desired optics. The LOCO code has been used at the Indus-2 storage ring for the first time. The estimation of linear beam optics errors and their correction to minimize the distortion of linear beam dynamical parameters by using the installed number of quadrupole power supplies is discussed. After the optics correction, the performance of the storage ring is improved in terms of better beam injection/accumulation, reduced beam loss during energy ramping, and improvement in beam lifetime. It is also useful in controlling the leakage in the orbit bump required for machine studies or for commissioning of new beamlines.

Scalable effective-temperature reduction for quantum annealers via nested quantum annealing correction

NASA Astrophysics Data System (ADS)

Vinci, Walter; Lidar, Daniel A.

2018-02-01

Nested quantum annealing correction (NQAC) is an error-correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. The encoding replaces each logical qubit by a complete graph of degree C . The nesting level C represents the distance of the error-correcting code and controls the amount of protection against thermal and control errors. Theoretical mean-field analyses and empirical data obtained with a D-Wave Two quantum annealer (supporting up to 512 qubits) showed that NQAC has the potential to achieve a scalable effective-temperature reduction, Teff˜C-η , with 0 <η ≤2 . We confirm that this scaling is preserved when NQAC is tested on a D-Wave 2000Q device (supporting up to 2048 qubits). In addition, we show that NQAC can also be used in sampling problems to lower the effective-temperature of a quantum annealer. Such effective-temperature reduction is relevant for machine-learning applications. Since we demonstrate that NQAC achieves error correction via a reduction of the effective-temperature of the quantum annealing device, our results address the problem of the "temperature scaling law for quantum annealers," which requires the temperature of quantum annealers to be reduced as problems of larger sizes are attempted to be solved.

Subspace Arrangement Codes and Cryptosystems

DTIC Science & Technology

2011-05-09

any other prov1sion of law, no person shall be subject to any penalty for failing to comply w1th a collection of information if it does not display a...NUMBER OF PAGES 49 19a. NAME OF RESPONSIBLE PERSON 19b. TELEPHONE NUMBER (Include area code) Standard Form 298 (Rev. 8/98) Prescribed by ANSI Std...theory is finding codes that have a small number of digits (length) with a high number codewords (dimension), as well as good error-correction properties

A TDM link with channel coding and digital voice.

NASA Technical Reports Server (NTRS)

Jones, M. W.; Tu, K.; Harton, P. L.

1972-01-01

The features of a TDM (time-division multiplexed) link model are described. A PCM telemetry sequence was coded for error correction and multiplexed with a digitized voice channel. An all-digital implementation of a variable-slope delta modulation algorithm was used to digitize the voice channel. The results of extensive testing are reported. The measured coding gain and the system performance over a Gaussian channel are compared with theoretical predictions and computer simulations. Word intelligibility scores are reported as a measure of voice channel performance.

Recognition of medical errors’ reporting system dimensions in educational hospitals

PubMed Central

Yarmohammadian, Mohammad H.; Mohammadinia, Leila; Tavakoli, Nahid; Ghalriz, Parvin; Haghshenas, Abbas

2014-01-01

Introduction and Objective: Nowadays medical errors are one of the serious issues in the health-care system and carry to account of the patient's safety threat. The most important step for achieving safety promotion is identifying errors and their causes in order to recognize, correct and omit them. Concerning about repeating medical errors and harms, which were received via theses errors concluded to designing and establishing medical error reporting systems for hospitals and centers that are presenting therapeutic services. The aim of this study is the recognition of medical errors’ reporting system dimensions in educational hospitals. Materials and Methods: This research is a descriptive-analytical and qualities’ study, which has been carried out in Shahid Beheshti educational therapeutic center in Isfahan during 2012. In this study, relevant information was collected through 15 face to face interviews. That each of interviews take place in about 1hr and creation of five focused discussion groups through 45 min for each section, they were composed of Metron, educational supervisor, health officer, health education, and all of the head nurses. Concluded data interviews and discussion sessions were coded, then achieved results were extracted in the presence of clear-sighted persons and after their feedback perception, they were categorized. In order to make sure of information correctness, tables were presented to the research's interviewers and final the corrections were confirmed based on their view. Finding: The extracted information from interviews and discussion groups have been divided into nine main categories after content analyzing and subject coding and their subsets have been completely expressed. Achieved dimensions are composed of nine domains of medical error concept, error cases according to nurses’ prospection, medical error reporting barriers, employees’ motivational factors for error reporting, purposes of medical error reporting system, error reporting's challenges and opportunities, a desired system characteristics, and the quality of error experiences’ transmission in the health-care system. Conclusion: Although, appropriate achievements have been assured in Shahid Beheshti Hospital, but it seems necessary that in order to immune promotion not only in this hospital, but in the other organizations, necessary infrastructures have been provided for an error reporting system performance. An appropriate medical error reporting system could be educated and prevent the occurrence of repeated errors. PMID:25250342

Demonstration of Weight-Four Parity Measurements in the Surface Code Architecture.

PubMed

Takita, Maika; Córcoles, A D; Magesan, Easwar; Abdo, Baleegh; Brink, Markus; Cross, Andrew; Chow, Jerry M; Gambetta, Jay M

2016-11-18

We present parity measurements on a five-qubit lattice with connectivity amenable to the surface code quantum error correction architecture. Using all-microwave controls of superconducting qubits coupled via resonators, we encode the parities of four data qubit states in either the X or the Z basis. Given the connectivity of the lattice, we perform a full characterization of the static Z interactions within the set of five qubits, as well as dynamical Z interactions brought along by single- and two-qubit microwave drives. The parity measurements are significantly improved by modifying the microwave two-qubit gates to dynamically remove nonideal Z errors.

A study of high density bit transition requirements versus the effects on BCH error correcting coding

NASA Technical Reports Server (NTRS)

Ingels, F.; Schoggen, W. O.

1981-01-01

Several methods for increasing bit transition densities in a data stream are summarized, discussed in detail, and compared against constraints imposed by the 2 MHz data link of the space shuttle high rate multiplexer unit. These methods include use of alternate pulse code modulation waveforms, data stream modification by insertion, alternate bit inversion, differential encoding, error encoding, and use of bit scramblers. The psuedo-random cover sequence generator was chosen for application to the 2 MHz data link of the space shuttle high rate multiplexer unit. This method is fully analyzed and a design implementation proposed.

Fault tolerance with noisy and slow measurements and preparation.

PubMed

Paz-Silva, Gerardo A; Brennen, Gavin K; Twamley, Jason

2010-09-03

It is not so well known that measurement-free quantum error correction protocols can be designed to achieve fault-tolerant quantum computing. Despite their potential advantages in terms of the relaxation of accuracy, speed, and addressing requirements, they have usually been overlooked since they are expected to yield a very bad threshold. We show that this is not the case. We design fault-tolerant circuits for the 9-qubit Bacon-Shor code and find an error threshold for unitary gates and preparation of p((p,g)thresh)=3.76×10(-5) (30% of the best known result for the same code using measurement) while admitting up to 1/3 error rates for measurements and allocating no constraints on measurement speed. We further show that demanding gate error rates sufficiently below the threshold pushes the preparation threshold up to p((p)thresh)=1/3.

Combined group ECC protection and subgroup parity protection

DOEpatents

Gara, Alan G.; Chen, Dong; Heidelberger, Philip; Ohmacht, Martin

2013-06-18

A method and system are disclosed for providing combined error code protection and subgroup parity protection for a given group of n bits. The method comprises the steps of identifying a number, m, of redundant bits for said error protection; and constructing a matrix P, wherein multiplying said given group of n bits with P produces m redundant error correction code (ECC) protection bits, and two columns of P provide parity protection for subgroups of said given group of n bits. In the preferred embodiment of the invention, the matrix P is constructed by generating permutations of m bit wide vectors with three or more, but an odd number of, elements with value one and the other elements with value zero; and assigning said vectors to rows of the matrix P.

Stem revenue losses with effective CDM management.

PubMed

Alwell, Michael

2003-09-01

Effective CDM management not only minimizes revenue losses due to denied claims, but also helps eliminate administrative costs associated with correcting coding errors. Accountability for CDM management should be assigned to a single individual, who ideally reports to the CFO or high-level finance director. If your organization is prone to making billing errors due to CDM deficiencies, you should consider purchasing CDM software to help you manage your CDM.

Multipath noise reduction spread spectrum signals

NASA Technical Reports Server (NTRS)

Meehan, Thomas K. (Inventor)

1994-01-01

The concepts of early-prompt delay tracking, multipath correction of early-prompt delay tracking from correlation shape, and carrier phase multipath correction are addressed. In early-prompt delay tracking, since multipath is always delayed with respect to the direct signals, the system derives phase and pseudorange observables from earlier correlation lags. In multipath correction of early-prompt delay tracking from correlation shape, the system looks for relative variations of amplitude across the code correlation function that do not match the predicted multipath-free code cross-correlation shape. The system then uses deviations from the multipath-free shape to infer the magnitude of multipath, and to generate corrections pseudorange observables. In carrier phase multipath correction, the system looks for variations of phase among plural early and prompt lags. The system uses the measured phase variations, along with the general principle that the multipath errors are larger for later lags, to infer the presence of multipath, and to generate corrections for carrier-phase observables.

Error correcting code with chip kill capability and power saving enhancement

DOEpatents

Gara, Alan G [Mount Kisco, NY; Chen, Dong [Croton On Husdon, NY; Coteus, Paul W [Yorktown Heights, NY; Flynn, William T [Rochester, MN; Marcella, James A [Rochester, MN; Takken, Todd [Brewster, NY; Trager, Barry M [Yorktown Heights, NY; Winograd, Shmuel [Scarsdale, NY

2011-08-30

A method and system are disclosed for detecting memory chip failure in a computer memory system. The method comprises the steps of accessing user data from a set of user data chips, and testing the user data for errors using data from a set of system data chips. This testing is done by generating a sequence of check symbols from the user data, grouping the user data into a sequence of data symbols, and computing a specified sequence of syndromes. If all the syndromes are zero, the user data has no errors. If one of the syndromes is non-zero, then a set of discriminator expressions are computed, and used to determine whether a single or double symbol error has occurred. In the preferred embodiment, less than two full system data chips are used for testing and correcting the user data.

Locality-preserving logical operators in topological stabilizer codes

NASA Astrophysics Data System (ADS)

Webster, Paul; Bartlett, Stephen D.

2018-01-01

Locality-preserving logical operators in topological codes are naturally fault tolerant, since they preserve the correctability of local errors. Using a correspondence between such operators and gapped domain walls, we describe a procedure for finding all locality-preserving logical operators admitted by a large and important class of topological stabilizer codes. In particular, we focus on those equivalent to a stack of a finite number of surface codes of any spatial dimension, where our procedure fully specifies the group of locality-preserving logical operators. We also present examples of how our procedure applies to codes with different boundary conditions, including color codes and toric codes, as well as more general codes such as Abelian quantum double models and codes with fermionic excitations in more than two dimensions.

A surface code quantum computer in silicon

PubMed Central

Hill, Charles D.; Peretz, Eldad; Hile, Samuel J.; House, Matthew G.; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y.; Hollenberg, Lloyd C. L.

2015-01-01

The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel—posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited. PMID:26601310

A surface code quantum computer in silicon.

PubMed

Hill, Charles D; Peretz, Eldad; Hile, Samuel J; House, Matthew G; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y; Hollenberg, Lloyd C L

2015-10-01

The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.

Simulating the performance of a distance-3 surface code in a linear ion trap

NASA Astrophysics Data System (ADS)

Trout, Colin J.; Li, Muyuan; Gutiérrez, Mauricio; Wu, Yukai; Wang, Sheng-Tao; Duan, Luming; Brown, Kenneth R.

2018-04-01

We explore the feasibility of implementing a small surface code with 9 data qubits and 8 ancilla qubits, commonly referred to as surface-17, using a linear chain of 171Yb+ ions. Two-qubit gates can be performed between any two ions in the chain with gate time increasing linearly with ion distance. Measurement of the ion state by fluorescence requires that the ancilla qubits be physically separated from the data qubits to avoid errors on the data due to scattered photons. We minimize the time required to measure one round of stabilizers by optimizing the mapping of the two-dimensional surface code to the linear chain of ions. We develop a physically motivated Pauli error model that allows for fast simulation and captures the key sources of noise in an ion trap quantum computer including gate imperfections and ion heating. Our simulations showed a consistent requirement of a two-qubit gate fidelity of ≥99.9% for the logical memory to have a better fidelity than physical two-qubit operations. Finally, we perform an analysis of the error subsets from the importance sampling method used to bound the logical error rates to gain insight into which error sources are particularly detrimental to error correction.

LDPC Codes with Minimum Distance Proportional to Block Size

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Jones, Christopher; Dolinar, Samuel; Thorpe, Jeremy

2009-01-01

Low-density parity-check (LDPC) codes characterized by minimum Hamming distances proportional to block sizes have been demonstrated. Like the codes mentioned in the immediately preceding article, the present codes are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. The previously mentioned codes have low decoding thresholds and reasonably low error floors. However, the minimum Hamming distances of those codes do not grow linearly with code-block sizes. Codes that have this minimum-distance property exhibit very low error floors. Examples of such codes include regular LDPC codes with variable degrees of at least 3. Unfortunately, the decoding thresholds of regular LDPC codes are high. Hence, there is a need for LDPC codes characterized by both low decoding thresholds and, in order to obtain acceptably low error floors, minimum Hamming distances that are proportional to code-block sizes. The present codes were developed to satisfy this need. The minimum Hamming distances of the present codes have been shown, through consideration of ensemble-average weight enumerators, to be proportional to code block sizes. As in the cases of irregular ensembles, the properties of these codes are sensitive to the proportion of degree-2 variable nodes. A code having too few such nodes tends to have an iterative decoding threshold that is far from the capacity threshold. A code having too many such nodes tends not to exhibit a minimum distance that is proportional to block size. Results of computational simulations have shown that the decoding thresholds of codes of the present type are lower than those of regular LDPC codes. Included in the simulations were a few examples from a family of codes characterized by rates ranging from low to high and by thresholds that adhere closely to their respective channel capacity thresholds; the simulation results from these examples showed that the codes in question have low error floors as well as low decoding thresholds. As an example, the illustration shows the protograph (which represents the blueprint for overall construction) of one proposed code family for code rates greater than or equal to 1.2. Any size LDPC code can be obtained by copying the protograph structure N times, then permuting the edges. The illustration also provides Field Programmable Gate Array (FPGA) hardware performance simulations for this code family. In addition, the illustration provides minimum signal-to-noise ratios (Eb/No) in decibels (decoding thresholds) to achieve zero error rates as the code block size goes to infinity for various code rates. In comparison with the codes mentioned in the preceding article, these codes have slightly higher decoding thresholds.

A novel construction method of QC-LDPC codes based on CRT for optical communications

NASA Astrophysics Data System (ADS)

Yuan, Jian-guo; Liang, Meng-qi; Wang, Yong; Lin, Jin-zhao; Pang, Yu

2016-05-01

A novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes is proposed based on Chinese remainder theory (CRT). The method can not only increase the code length without reducing the girth, but also greatly enhance the code rate, so it is easy to construct a high-rate code. The simulation results show that at the bit error rate ( BER) of 10-7, the net coding gain ( NCG) of the regular QC-LDPC(4 851, 4 546) code is respectively 2.06 dB, 1.36 dB, 0.53 dB and 0.31 dB more than those of the classic RS(255, 239) code in ITU-T G.975, the LDPC(32 640, 30 592) code in ITU-T G.975.1, the QC-LDPC(3 664, 3 436) code constructed by the improved combining construction method based on CRT and the irregular QC-LDPC(3 843, 3 603) code constructed by the construction method based on the Galois field ( GF( q)) multiplicative group. Furthermore, all these five codes have the same code rate of 0.937. Therefore, the regular QC-LDPC(4 851, 4 546) code constructed by the proposed construction method has excellent error-correction performance, and can be more suitable for optical transmission systems.

Unitals and ovals of symmetric block designs in LDPC and space-time coding

NASA Astrophysics Data System (ADS)

Andriamanalimanana, Bruno R.

2004-08-01

An approach to the design of LDPC (low density parity check) error-correction and space-time modulation codes involves starting with known mathematical and combinatorial structures, and deriving code properties from structure properties. This paper reports on an investigation of unital and oval configurations within generic symmetric combinatorial designs, not just classical projective planes, as the underlying structure for classes of space-time LDPC outer codes. Of particular interest are the encoding and iterative (sum-product) decoding gains that these codes may provide. Various small-length cases have been numerically implemented in Java and Matlab for a number of channel models.

High-efficiency Gaussian key reconciliation in continuous variable quantum key distribution

NASA Astrophysics Data System (ADS)

Bai, ZengLiang; Wang, XuYang; Yang, ShenShen; Li, YongMin

2016-01-01

Efficient reconciliation is a crucial step in continuous variable quantum key distribution. The progressive-edge-growth (PEG) algorithm is an efficient method to construct relatively short block length low-density parity-check (LDPC) codes. The qua-sicyclic construction method can extend short block length codes and further eliminate the shortest cycle. In this paper, by combining the PEG algorithm and qua-si-cyclic construction method, we design long block length irregular LDPC codes with high error-correcting capacity. Based on these LDPC codes, we achieve high-efficiency Gaussian key reconciliation with slice recon-ciliation based on multilevel coding/multistage decoding with an efficiency of 93.7%.

Integrating automated structured analysis and design with Ada programming support environments

NASA Technical Reports Server (NTRS)

Hecht, Alan; Simmons, Andy

1986-01-01

Ada Programming Support Environments (APSE) include many powerful tools that address the implementation of Ada code. These tools do not address the entire software development process. Structured analysis is a methodology that addresses the creation of complete and accurate system specifications. Structured design takes a specification and derives a plan to decompose the system subcomponents, and provides heuristics to optimize the software design to minimize errors and maintenance. It can also produce the creation of useable modules. Studies have shown that most software errors result from poor system specifications, and that these errors also become more expensive to fix as the development process continues. Structured analysis and design help to uncover error in the early stages of development. The APSE tools help to insure that the code produced is correct, and aid in finding obscure coding errors. However, they do not have the capability to detect errors in specifications or to detect poor designs. An automated system for structured analysis and design TEAMWORK, which can be integrated with an APSE to support software systems development from specification through implementation is described. These tools completement each other to help developers improve quality and productivity, as well as to reduce development and maintenance costs. Complete system documentation and reusable code also resultss from the use of these tools. Integrating an APSE with automated tools for structured analysis and design provide capabilities and advantages beyond those realized with any of these systems used by themselves.

Study of a co-designed decision feedback equalizer, deinterleaver, and decoder

NASA Technical Reports Server (NTRS)

Peile, Robert E.; Welch, Loyd

1990-01-01

A technique that promises better quality data from band limited channels at lower received power in digital transmission systems is presented. Data transmission, in such systems often suffers from intersymbol interference (ISI) and noise. Two separate techniques, channel coding and equalization, have caused considerable advances in the state of communication systems and both concern themselves with removing the undesired effects of a communication channel. Equalizers mitigate the ISI whereas coding schemes are used to incorporate error-correction. In the past, most of the research in these two areas has been carried out separately. However, the individual techniques have strengths and weaknesses that are complementary in many applications: an integrated approach realizes gains in excess to that of a simple juxtaposition. Coding schemes have been successfully used in cascade with linear equalizers which in the absence of ISI provide excellent performance. However, when both ISI and the noise level are relatively high, nonlinear receivers like the decision feedback equalizer (DFE) perform better. The DFE has its drawbacks: it suffers from error propagation. The technique presented here takes advantage of interleaving to integrate the two approaches so that the error propagation in DFE can be reduced with the help of error correction provided by the decoder. The results of simulations carried out for both, binary, and non-binary, channels confirm that significant gain can be obtained by codesigning equalizer and decoder. Although, systems with time-invariant channels and simple DFE having linear filters were looked into, the technique is fairly general and can easily be modified for more sophisticated equalizers to obtain even larger gains.

From Verified Models to Verifiable Code

NASA Technical Reports Server (NTRS)

Lensink, Leonard; Munoz, Cesar A.; Goodloe, Alwyn E.

2009-01-01

Declarative specifications of digital systems often contain parts that can be automatically translated into executable code. Automated code generation may reduce or eliminate the kinds of errors typically introduced through manual code writing. For this approach to be effective, the generated code should be reasonably efficient and, more importantly, verifiable. This paper presents a prototype code generator for the Prototype Verification System (PVS) that translates a subset of PVS functional specifications into an intermediate language and subsequently to multiple target programming languages. Several case studies are presented to illustrate the tool's functionality. The generated code can be analyzed by software verification tools such as verification condition generators, static analyzers, and software model-checkers to increase the confidence that the generated code is correct.

A fault-tolerant information processing concept for space vehicles.

NASA Technical Reports Server (NTRS)

Hopkins, A. L., Jr.

1971-01-01

A distributed fault-tolerant information processing system is proposed, comprising a central multiprocessor, dedicated local processors, and multiplexed input-output buses connecting them together. The processors in the multiprocessor are duplicated for error detection, which is felt to be less expensive than using coded redundancy of comparable effectiveness. Error recovery is made possible by a triplicated scratchpad memory in each processor. The main multiprocessor memory uses replicated memory for error detection and correction. Local processors use any of three conventional redundancy techniques: voting, duplex pairs with backup, and duplex pairs in independent subsystems.

Assessing the utility of the Oxford Nanopore MinION for snake venom gland cDNA sequencing.

PubMed

Hargreaves, Adam D; Mulley, John F

2015-01-01

Portable DNA sequencers such as the Oxford Nanopore MinION device have the potential to be truly disruptive technologies, facilitating new approaches and analyses and, in some cases, taking sequencing out of the lab and into the field. However, the capabilities of these technologies are still being revealed. Here we show that single-molecule cDNA sequencing using the MinION accurately characterises venom toxin-encoding genes in the painted saw-scaled viper, Echis coloratus. We find the raw sequencing error rate to be around 12%, improved to 0-2% with hybrid error correction and 3% with de novo error correction. Our corrected data provides full coding sequences and 5' and 3' UTRs for 29 of 33 candidate venom toxins detected, far superior to Illumina data (13/40 complete) and Sanger-based ESTs (15/29). We suggest that, should the current pace of improvement continue, the MinION will become the default approach for cDNA sequencing in a variety of species.

Assessing the utility of the Oxford Nanopore MinION for snake venom gland cDNA sequencing

PubMed Central

Hargreaves, Adam D.

2015-01-01

Portable DNA sequencers such as the Oxford Nanopore MinION device have the potential to be truly disruptive technologies, facilitating new approaches and analyses and, in some cases, taking sequencing out of the lab and into the field. However, the capabilities of these technologies are still being revealed. Here we show that single-molecule cDNA sequencing using the MinION accurately characterises venom toxin-encoding genes in the painted saw-scaled viper, Echis coloratus. We find the raw sequencing error rate to be around 12%, improved to 0–2% with hybrid error correction and 3% with de novo error correction. Our corrected data provides full coding sequences and 5′ and 3′ UTRs for 29 of 33 candidate venom toxins detected, far superior to Illumina data (13/40 complete) and Sanger-based ESTs (15/29). We suggest that, should the current pace of improvement continue, the MinION will become the default approach for cDNA sequencing in a variety of species. PMID:26623194

428-Gb/s single-channel coherent optical OFDM transmission over 960-km SSMF with constellation expansion and LDPC coding.

PubMed

Yang, Qi; Al Amin, Abdullah; Chen, Xi; Ma, Yiran; Chen, Simin; Shieh, William

2010-08-02

High-order modulation formats and advanced error correcting codes (ECC) are two promising techniques for improving the performance of ultrahigh-speed optical transport networks. In this paper, we present record receiver sensitivity for 107 Gb/s CO-OFDM transmission via constellation expansion to 16-QAM and rate-1/2 LDPC coding. We also show the single-channel transmission of a 428-Gb/s CO-OFDM signal over 960-km standard-single-mode-fiber (SSMF) without Raman amplification.

Combined group ECC protection and subgroup parity protection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gara, Alan; Cheng, Dong; Heidelberger, Philip

A method and system are disclosed for providing combined error code protection and subgroup parity protection for a given group of n bits. The method comprises the steps of identifying a number, m, of redundant bits for said error protection; and constructing a matrix P, wherein multiplying said given group of n bits with P produces m redundant error correction code (ECC) protection bits, and two columns of P provide parity protection for subgroups of said given group of n bits. In the preferred embodiment of the invention, the matrix P is constructed by generating permutations of m bit widemore » vectors with three or more, but an odd number of, elements with value one and the other elements with value zero; and assigning said vectors to rows of the matrix P.« less

Nonlinear, nonbinary cyclic group codes

NASA Technical Reports Server (NTRS)

Solomon, G.

1992-01-01

New cyclic group codes of length 2(exp m) - 1 over (m - j)-bit symbols are introduced. These codes can be systematically encoded and decoded algebraically. The code rates are very close to Reed-Solomon (RS) codes and are much better than Bose-Chaudhuri-Hocquenghem (BCH) codes (a former alternative). The binary (m - j)-tuples are identified with a subgroup of the binary m-tuples which represents the field GF(2 exp m). Encoding is systematic and involves a two-stage procedure consisting of the usual linear feedback register (using the division or check polynomial) and a small table lookup. For low rates, a second shift-register encoding operation may be invoked. Decoding uses the RS error-correcting procedures for the m-tuple codes for m = 4, 5, and 6.

Channel coding in the space station data system network

NASA Technical Reports Server (NTRS)

Healy, T.

1982-01-01

A detailed discussion of the use of channel coding for error correction, privacy/secrecy, channel separation, and synchronization is presented. Channel coding, in one form or another, is an established and common element in data systems. No analysis and design of a major new system would fail to consider ways in which channel coding could make the system more effective. The presence of channel coding on TDRS, Shuttle, the Advanced Communication Technology Satellite Program system, the JSC-proposed Space Operations Center, and the proposed 30/20 GHz Satellite Communication System strongly support the requirement for the utilization of coding for the communications channel. The designers of the space station data system have to consider the use of channel coding.

New quantum codes constructed from quaternary BCH codes

NASA Astrophysics Data System (ADS)

Xu, Gen; Li, Ruihu; Guo, Luobin; Ma, Yuena

2016-10-01

In this paper, we firstly study construction of new quantum error-correcting codes (QECCs) from three classes of quaternary imprimitive BCH codes. As a result, the improved maximal designed distance of these narrow-sense imprimitive Hermitian dual-containing quaternary BCH codes are determined to be much larger than the result given according to Aly et al. (IEEE Trans Inf Theory 53:1183-1188, 2007) for each different code length. Thus, families of new QECCs are newly obtained, and the constructed QECCs have larger distance than those in the previous literature. Secondly, we apply a combinatorial construction to the imprimitive BCH codes with their corresponding primitive counterpart and construct many new linear quantum codes with good parameters, some of which have parameters exceeding the finite Gilbert-Varshamov bound for linear quantum codes.

Use of FEC coding to improve statistical multiplexing performance for video transport over ATM networks

NASA Astrophysics Data System (ADS)

Kurceren, Ragip; Modestino, James W.

1998-12-01

The use of forward error-control (FEC) coding, possibly in conjunction with ARQ techniques, has emerged as a promising approach for video transport over ATM networks for cell-loss recovery and/or bit error correction, such as might be required for wireless links. Although FEC provides cell-loss recovery capabilities it also introduces transmission overhead which can possibly cause additional cell losses. A methodology is described to maximize the number of video sources multiplexed at a given quality of service (QoS), measured in terms of decoded cell loss probability, using interlaced FEC codes. The transport channel is modelled as a block interference channel (BIC) and the multiplexer as single server, deterministic service, finite buffer supporting N users. Based upon an information-theoretic characterization of the BIC and large deviation bounds on the buffer overflow probability, the described methodology provides theoretically achievable upper limits on the number of sources multiplexed. Performance of specific coding techniques using interlaced nonbinary Reed-Solomon (RS) codes and binary rate-compatible punctured convolutional (RCPC) codes is illustrated.

Soft-Decision-Data Reshuffle to Mitigate Pulsed Radio Frequency Interference Impact on Low-Density-Parity-Check Code Performance

NASA Technical Reports Server (NTRS)

Ni, Jianjun David

2011-01-01

This presentation briefly discusses a research effort on mitigation techniques of pulsed radio frequency interference (RFI) on a Low-Density-Parity-Check (LDPC) code. This problem is of considerable interest in the context of providing reliable communications to the space vehicle which might suffer severe degradation due to pulsed RFI sources such as large radars. The LDPC code is one of modern forward-error-correction (FEC) codes which have the decoding performance to approach the Shannon Limit. The LDPC code studied here is the AR4JA (2048, 1024) code recommended by the Consultative Committee for Space Data Systems (CCSDS) and it has been chosen for some spacecraft design. Even though this code is designed as a powerful FEC code in the additive white Gaussian noise channel, simulation data and test results show that the performance of this LDPC decoder is severely degraded when exposed to the pulsed RFI specified in the spacecraft s transponder specifications. An analysis work (through modeling and simulation) has been conducted to evaluate the impact of the pulsed RFI and a few implemental techniques have been investigated to mitigate the pulsed RFI impact by reshuffling the soft-decision-data available at the input of the LDPC decoder. The simulation results show that the LDPC decoding performance of codeword error rate (CWER) under pulsed RFI can be improved up to four orders of magnitude through a simple soft-decision-data reshuffle scheme. This study reveals that an error floor of LDPC decoding performance appears around CWER=1E-4 when the proposed technique is applied to mitigate the pulsed RFI impact. The mechanism causing this error floor remains unknown, further investigation is necessary.

Physical implementation of protected qubits

NASA Astrophysics Data System (ADS)

Douçot, B.; Ioffe, L. B.

2012-07-01

We review the general notion of topological protection of quantum states in spin models and its relation with the ideas of quantum error correction. We show that topological protection can be viewed as a Hamiltonian realization of error correction: for a quantum code for which the minimal number of errors that remain undetected is N, the corresponding Hamiltonian model of the effects of the environment noise appears only in the Nth order of the perturbation theory. We discuss the simplest model Hamiltonians that realize topological protection and their implementation in superconducting arrays. We focus on two dual realizations: in one the protected state is stored in the parity of the Cooper pair number, in the other, in the parity of the flux number. In both cases the superconducting arrays allow a number of fault-tolerant operations that should make the universal quantum computation possible.

Universal fault-tolerant quantum computation with only transversal gates and error correction.

PubMed

Paetznick, Adam; Reichardt, Ben W

2013-08-30

Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. Though transversal gates alone cannot be computationally universal, they can be combined with specially distilled resource states in order to achieve universality. We show that "triorthogonal" stabilizer codes, introduced for state distillation by Bravyi and Haah [Phys. Rev. A 86, 052329 (2012)], admit transversal implementation of the controlled-controlled-Z gate. We then construct a universal set of fault-tolerant gates without state distillation by using only transversal controlled-controlled-Z, transversal Hadamard, and fault-tolerant error correction. We also adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes.

Reliability of Memories Protected by Multibit Error Correction Codes Against MBUs

NASA Astrophysics Data System (ADS)

Ming, Zhu; Yi, Xiao Li; Chang, Liu; Wei, Zhang Jian

2011-02-01

As technology scales, more and more memory cells can be placed in a die. Therefore, the probability that a single event induces multiple bit upsets (MBUs) in adjacent memory cells gets greater. Generally, multibit error correction codes (MECCs) are effective approaches to mitigate MBUs in memories. In order to evaluate the robustness of protected memories, reliability models have been widely studied nowadays. Instead of irradiation experiments, the models can be used to quickly evaluate the reliability of memories in the early design. To build an accurate model, some situations should be considered. Firstly, when MBUs are presented in memories, the errors induced by several events may overlap each other, which is more frequent than single event upset (SEU) case. Furthermore, radiation experiments show that the probability of MBUs strongly depends on angles of the radiation event. However, reliability models which consider the overlap of multiple bit errors and angles of radiation event have not been proposed in the present literature. In this paper, a more accurate model of memories with MECCs is presented. Both the overlap of multiple bit errors and angles of event are considered in the model, which produces a more precise analysis in the calculation of mean time to failure (MTTF) for memory systems under MBUs. In addition, memories with scrubbing and nonscrubbing are analyzed in the proposed model. Finally, we evaluate the reliability of memories under MBUs in Matlab. The simulation results verify the validity of the proposed model.

Error Prevention Aid

NASA Technical Reports Server (NTRS)

1987-01-01

In a complex computer environment there is ample opportunity for error, a mistake by a programmer, or a software-induced undesirable side effect. In insurance, errors can cost a company heavily, so protection against inadvertent change is a must for the efficient firm. The data processing center at Transport Life Insurance Company has taken a step to guard against accidental changes by adopting a software package called EQNINT (Equations Interpreter Program). EQNINT cross checks the basic formulas in a program against the formulas that make up the major production system. EQNINT assures that formulas are coded correctly and helps catch errors before they affect the customer service or its profitability.

47 CFR 101.521 - Spectrum utilization.

Code of Federal Regulations, 2010 CFR

2010-10-01

... applicants for DEMS frequencies in the 10.6 GHz band must submit as part of the original application a... contain detailed descriptions of the modulation method, the channel time sharing method, any error detecting and/or correcting codes, any spatial frequency reuse system and the total data throughput capacity...

[Critical analysis of French DRG based information system (PMSI) databases for the epidemiology of cancer: a longitudinal approach becomes possible].

PubMed

Olive, F; Gomez, F; Schott, A-M; Remontet, L; Bossard, N; Mitton, N; Polazzi, S; Colonna, M; Trombert-Paviot, B

2011-02-01

Use of French Diagnosis Related Groups (DRGs) program databases, apart from financial purposes, has recently been improved since a unique anonymous patient identification number has been created for each inpatient in administrative case mix database. Based on the work of the group for cancer epidemiological observation in the Rhône-Alpes area, (ONC-EPI group), we review the remaining difficulties in the use of DRG data for epidemiological purposes and we consider a longitudinal approach based on analysis of database over several years. We also discuss limitations of this approach. The main problems are related to a lack of quality of administrative data, especially coding of diagnoses. These errors come from missing or inappropriate codes, or not being in accordance with prioritization rules (causing an over- or under-reporting or inconsistencies in coding over time). One difficulty, partly due to the hierarchy of coding and the type of cancer, is the choice of an extraction algorithm. In two studies designed to estimate the incidence of cancer cared in hospitals (breast, colon-rectum, kidney, ovaries), a first algorithm, including a code of cancer as principal diagnosis with a selection of surgical procedures less performed than the second one including a code of cancer as principal diagnosis only, for which the number of hospitalizations per patient ratio was stable across time and space. The chaining over several years allows, by tracing the trajectory of the patient, to detect and correct inaccuracies, errors and missing values, and for incidence studies, to correct incident cases by removing prevalent cases. However, linkage, complete only since 2007, does not correct data in all cases. Ways of future improvement certainly pass through improved algorithms for case identification and especially by linking DRG data with other databases. Copyright © 2010 Elsevier Masson SAS. All rights reserved.

Code for the calculation of the instrumental profile: preliminary results. (Spanish Title: Código para el cálculo del perfil instrumental: resultados preliminares)

NASA Astrophysics Data System (ADS)

Pintado, O. I.; Santillán, L.; Marquetti, M. E.

All images obtained with a telescope are distorted by the instrument. This distorsion is known as instrumental profile or instrumental broadening. The deformations in the spectra could introduce large errors in the determination of different parameters, especially in those dependent on the spectral lines shapes, such as chemical abundances, winds, microturbulence, etc. To correct this distortion, in some cases, the spectral lines are convolved with a Gaussian function and in others the lines are widened with a fixed value. Some codes used to calculate synthetic spectra, as SYNTHE, include this corrections. We present results obtained for the spectrograph REOSC and EBASIM of CASLEO.

Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part I: Path radiance

NASA Astrophysics Data System (ADS)

Kotchenova, Svetlana Y.; Vermote, Eric F.; Matarrese, Raffaella; Klemm, Frank J., Jr.

2006-09-01

A vector version of the 6S (Second Simulation of a Satellite Signal in the Solar Spectrum) radiative transfer code (6SV1), which enables accounting for radiation polarization, has been developed and validated against a Monte Carlo code, Coulson's tabulated values, and MOBY (Marine Optical Buoy System) water-leaving reflectance measurements. The developed code was also tested against the scalar codes SHARM, DISORT, and MODTRAN to evaluate its performance in scalar mode and the influence of polarization. The obtained results have shown a good agreement of 0.7% in comparison with the Monte Carlo code, 0.2% for Coulson's tabulated values, and 0.001-0.002 for the 400-550 nm region for the MOBY reflectances. Ignoring the effects of polarization led to large errors in calculated top-of-atmosphere reflectances: more than 10% for a molecular atmosphere and up to 5% for an aerosol atmosphere. This new version of 6S is intended to replace the previous scalar version used for calculation of lookup tables in the MODIS (Moderate Resolution Imaging Spectroradiometer) atmospheric correction algorithm.

Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part I: path radiance.

PubMed

Kotchenova, Svetlana Y; Vermote, Eric F; Matarrese, Raffaella; Klemm, Frank J

2006-09-10

A vector version of the 6S (Second Simulation of a Satellite Signal in the Solar Spectrum) radiative transfer code (6SV1), which enables accounting for radiation polarization, has been developed and validated against a Monte Carlo code, Coulson's tabulated values, and MOBY (Marine Optical Buoy System) water-leaving reflectance measurements. The developed code was also tested against the scalar codes SHARM, DISORT, and MODTRAN to evaluate its performance in scalar mode and the influence of polarization. The obtained results have shown a good agreement of 0.7% in comparison with the Monte Carlo code, 0.2% for Coulson's tabulated values, and 0.001-0.002 for the 400-550 nm region for the MOBY reflectances. Ignoring the effects of polarization led to large errors in calculated top-of-atmosphere reflectances: more than 10% for a molecular atmosphere and up to 5% for an aerosol atmosphere. This new version of 6S is intended to replace the previous scalar version used for calculation of lookup tables in the MODIS (Moderate Resolution Imaging Spectroradiometer) atmospheric correction algorithm.

The solar vector error within the SNPP Common GEO code, the correction, and the effects on the VIIRS SDR RSB calibration

NASA Astrophysics Data System (ADS)

Fulbright, Jon; Anderson, Samuel; Lei, Ning; Efremova, Boryana; Wang, Zhipeng; McIntire, Jeffrey; Chiang, Kwofu; Xiong, Xiaoxiong

2014-11-01

Due to a software error, the solar and lunar vectors reported in the on-board calibrator intermediate product (OBC-IP) files for SNPP VIIRS are incorrect. The magnitude of the error is about 0.2 degree, and the magnitude is increasing by about 0.01 degree per year. This error, although small, has an effect on the radiometric calibration of the reflective solar bands (RSB) because accurate solar angles are required for calculating the screen transmission functions and for calculating the illumination of the Solar Diffuser panel. In this paper, we describe the error in the Common GEO code, and how it may be fixed. We present evidence for the error from within the OBC-IP data. We also describe the effects of the solar vector error on the RSB calibration and the Sensor Data Record (SDR). In order to perform this evaluation, we have reanalyzed the yaw-maneuver data to compute the vignetting functions required for the on-orbit SD RSB radiometric calibration. After the reanalysis, we find effect of up to 0.5% on the shortwave infrared (SWIR) RSB calibration.

Coding for Communication Channels with Dead-Time Constraints

NASA Technical Reports Server (NTRS)

Moision, Bruce; Hamkins, Jon

2004-01-01

Coding schemes have been designed and investigated specifically for optical and electronic data-communication channels in which information is conveyed via pulse-position modulation (PPM) subject to dead-time constraints. These schemes involve the use of error-correcting codes concatenated with codes denoted constrained codes. These codes are decoded using an interactive method. In pulse-position modulation, time is partitioned into frames of Mslots of equal duration. Each frame contains one pulsed slot (all others are non-pulsed). For a given channel, the dead-time constraints are defined as a maximum and a minimum on the allowable time between pulses. For example, if a Q-switched laser is used to transmit the pulses, then the minimum allowable dead time is the time needed to recharge the laser for the next pulse. In the case of bits recorded on a magnetic medium, the minimum allowable time between pulses depends on the recording/playback speed and the minimum distance between pulses needed to prevent interference between adjacent bits during readout. The maximum allowable dead time for a given channel is the maximum time for which it is possible to satisfy the requirement to synchronize slots. In mathematical shorthand, the dead-time constraints for a given channel are represented by the pair of integers (d,k), where d is the minimum allowable number of zeroes between ones and k is the maximum allowable number of zeroes between ones. A system of the type to which the present schemes apply is represented by a binary- input, real-valued-output channel model illustrated in the figure. At the transmitting end, information bits are first encoded by use of an error-correcting code, then further encoded by use of a constrained code. Several constrained codes for channels subject to constraints of (d,infinity) have been investigated theoretically and computationally. The baseline codes chosen for purposes of comparison were simple PPM codes characterized by M-slot PPM frames separated by d-slot dead times.

Characterizing a four-qubit planar lattice for arbitrary error detection

NASA Astrophysics Data System (ADS)

Chow, Jerry M.; Srinivasan, Srikanth J.; Magesan, Easwar; Córcoles, A. D.; Abraham, David W.; Gambetta, Jay M.; Steffen, Matthias

2015-05-01

Quantum error correction will be a necessary component towards realizing scalable quantum computers with physical qubits. Theoretically, it is possible to perform arbitrarily long computations if the error rate is below a threshold value. The two-dimensional surface code permits relatively high fault-tolerant thresholds at the ~1% level, and only requires a latticed network of qubits with nearest-neighbor interactions. Superconducting qubits have continued to steadily improve in coherence, gate, and readout fidelities, to become a leading candidate for implementation into larger quantum networks. Here we describe characterization experiments and calibration of a system of four superconducting qubits arranged in a planar lattice, amenable to the surface code. Insights into the particular qubit design and comparison between simulated parameters and experimentally determined parameters are given. Single- and two-qubit gate tune-up procedures are described and results for simultaneously benchmarking pairs of two-qubit gates are given. All controls are eventually used for an arbitrary error detection protocol described in separate work [Corcoles et al., Nature Communications, 6, 2015].

Impact of Uncertainties and Errors in Converting NWS Radiosonde Hygristor Resistances to Relative Humidity

NASA Technical Reports Server (NTRS)

Westphal, Douglas L.; Russell, Philip (Technical Monitor)

1994-01-01

A set of 2,600 6-second, National Weather Service soundings from NASA's FIRE-II Cirrus field experiment are used to illustrate previously known errors and new potential errors in the VIZ and SDD brand relative humidity (RH) sensors and the MicroART processing software. The entire spectrum of RH is potentially affected by at least one of these errors. (These errors occur before being converted to dew point temperature.) Corrections to the errors are discussed. Examples are given of the effect that these errors and biases may have on numerical weather prediction and radiative transfer. The figure shows the OLR calculated for the corrected and uncorrected soundings using an 18-band radiative transfer code. The OLR differences are sufficiently large to warrant consideration when validating line-by-line radiation calculations that use radiosonde data to specify the atmospheric state, or when validating satellite retrievals. In addition, a comparison of observations of RE during FIRE-II derived from GOES satellite, raman lidar, MAPS analyses, NCAR CLASS sondes, and the NWS sondes reveals disagreement in the RH distribution and underlines our lack of an understanding of the climatology of water vapor.

Impact of Uncertainties and Errors in Converting NWS Radiosonde Hygristor Resistances to Relative Humidity

NASA Technical Reports Server (NTRS)

Westphal, Douglas L.; Russell, Philip B. (Technical Monitor)

1994-01-01

A set of 2,600 6-second, National Weather Service soundings from NASA's FIRE-II Cirrus field experiment are used to illustrate previously known errors and new potential errors in the VIZ and SDD ) brand relative humidity (RH) sensors and the MicroART processing software. The entire spectrum of RH is potentially affected by at least one of these errors. (These errors occur before being converted to dew point temperature.) Corrections to the errors are discussed. Examples are given of the effect that these errors and biases may have on numerical weather prediction and radiative transfer. The figure shows the OLR calculated for the corrected and uncorrected soundings using an 18-band radiative transfer code. The OLR differences are sufficiently large to warrant consideration when validating line-by-line radiation calculations that use radiosonde data to specify the atmospheric state, or when validating satellite retrievals. in addition, a comparison of observations of RH during FIRE-II derived from GOES satellite, raman lidar, MAPS analyses, NCAR CLASS sondes, and the NWS sondes reveals disagreement in the RH distribution and underlines our lack of an understanding of the climatology of water vapor.

Resolving Ethical Disputes Through Arbitration: An Alternative to Code Penalties.

ERIC Educational Resources Information Center

Barwis, Gail Lund

Arbitration cases involving journalism ethics can be grouped into three major categories: outside activities that lead to conflicts of interest, acceptance of gifts that compromise journalistic objectivity, and writing false or misleading information or failing to check facts or correct errors. In most instances, failure to adhere to ethical…

Fix Broken and Redirected Links Using Group Dashboard Link Report

EPA Pesticide Factsheets

Learn how to use the tools provided by Drupal in the Group Dashboard to find and correct links on your site that are broken (404 and 403 error codes), or that redirect (301 and 302), for example to a homepage rather than the originally intended content.

Distillation with Sublogarithmic Overhead.

PubMed

Hastings, Matthew B; Haah, Jeongwan

2018-02-02

It has been conjectured that, for any distillation protocol for magic states for the T gate, the number of noisy input magic states required per output magic state at output error rate ε is Ω[log(1/ε)]. We show that this conjecture is false. We find a family of quantum error correcting codes of parameters ⟦∑[under i=w+1][over m](m/i),∑[under i=0][over w](m/i),∑[under i=w+1][over r+1](r+1/i)⟧ for any integers m>2r, r>w≥0, by puncturing quantum Reed-Muller codes. When m>νr, our code admits a transversal logical gate at the νth level of Clifford hierarchy. In a distillation protocol for magic states at the level ν=3 (T gate), the ratio of input to output magic states is O(log^{γ}(1/ε)), where γ=log(n/k)/log(d)<0.678 for some m, r, w. The smallest code in our family for which γ<1 is on ≈2^{58} qubits.

Highly fault-tolerant parallel computation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spielman, D.A.

We re-introduce the coded model of fault-tolerant computation in which the input and output of a computational device are treated as words in an error-correcting code. A computational device correctly computes a function in the coded model if its input and output, once decoded, are a valid input and output of the function. In the coded model, it is reasonable to hope to simulate all computational devices by devices whose size is greater by a constant factor but which are exponentially reliable even if each of their components can fail with some constant probability. We consider fine-grained parallel computations inmore » which each processor has a constant probability of producing the wrong output at each time step. We show that any parallel computation that runs for time t on w processors can be performed reliably on a faulty machine in the coded model using w log{sup O(l)} w processors and time t log{sup O(l)} w. The failure probability of the computation will be at most t {center_dot} exp(-w{sup 1/4}). The codes used to communicate with our fault-tolerant machines are generalized Reed-Solomon codes and can thus be encoded and decoded in O(n log{sup O(1)} n) sequential time and are independent of the machine they are used to communicate with. We also show how coded computation can be used to self-correct many linear functions in parallel with arbitrarily small overhead.« less

New nonbinary quantum codes with larger distance constructed from BCH codes over 𝔽q2

NASA Astrophysics Data System (ADS)

Xu, Gen; Li, Ruihu; Fu, Qiang; Ma, Yuena; Guo, Luobin

2017-03-01

This paper concentrates on construction of new nonbinary quantum error-correcting codes (QECCs) from three classes of narrow-sense imprimitive BCH codes over finite field 𝔽q2 (q ≥ 3 is an odd prime power). By a careful analysis on properties of cyclotomic cosets in defining set T of these BCH codes, the improved maximal designed distance of these narrow-sense imprimitive Hermitian dual-containing BCH codes is determined to be much larger than the result given according to Aly et al. [S. A. Aly, A. Klappenecker and P. K. Sarvepalli, IEEE Trans. Inf. Theory 53, 1183 (2007)] for each different code length. Thus families of new nonbinary QECCs are constructed, and the newly obtained QECCs have larger distance than those in previous literature.

Validation of a general practice audit and data extraction tool.

PubMed

Peiris, David; Agaliotis, Maria; Patel, Bindu; Patel, Anushka

2013-11-01

We assessed how accurately a common general practitioner (GP) audit tool extracts data from two software systems. First, pathology test codes were audited at 33 practices covering nine companies. Second, a manual audit of chronic disease data from 200 random patient records at two practices was compared with audit tool data. Pathology review: all companies assigned correct codes for cholesterol, creatinine and glycated haemoglobin; four companies assigned incorrect codes for albuminuria tests, precluding accurate detection with the audit tool. Case record review: there was strong agreement between the manual audit and the tool for all variables except chronic kidney disease diagnoses, which was due to a tool-related programming error. The audit tool accurately detected most chronic disease data in two GP record systems. The one exception, however, highlights the importance of surveillance systems to promptly identify errors. This will maximise potential for audit tools to improve healthcare quality.

Performance Analysis of a JTIDS/Link-16-type Waveform Transmitted over Slow, Flat Nakagami Fading Channels in the Presence of Narrowband Interference

DTIC Science & Technology

2008-12-01

The effective two-way tactical data rate is 3,060 bits per second. Note that there is no parity check or forward error correction (FEC) coding used in...of 1800 bits per second. With the use of FEC coding , the channel data rate is 2250 bits per second; however, the information data rate is still the...Link-11. If the parity bits are included, the channel data rate is 28,800 bps. If FEC coding is considered, the channel data rate is 59,520 bps

Development of an LSI maximum-likelihood convolutional decoder for advanced forward error correction capability on the NASA 30/20 GHz program

NASA Technical Reports Server (NTRS)

Clark, R. T.; Mccallister, R. D.

1982-01-01

The particular coding option identified as providing the best level of coding gain performance in an LSI-efficient implementation was the optimal constraint length five, rate one-half convolutional code. To determine the specific set of design parameters which optimally matches this decoder to the LSI constraints, a breadboard MCD (maximum-likelihood convolutional decoder) was fabricated and used to generate detailed performance trade-off data. The extensive performance testing data gathered during this design tradeoff study are summarized, and the functional and physical MCD chip characteristics are presented.

Fault tolerant computing: A preamble for assuring viability of large computer systems

NASA Technical Reports Server (NTRS)

Lim, R. S.

1977-01-01

The need for fault-tolerant computing is addressed from the viewpoints of (1) why it is needed, (2) how to apply it in the current state of technology, and (3) what it means in the context of the Phoenix computer system and other related systems. To this end, the value of concurrent error detection and correction is described. User protection, program retry, and repair are among the factors considered. The technology of algebraic codes to protect memory systems and arithmetic codes to protect memory systems and arithmetic codes to protect arithmetic operations is discussed.

The design plan of a VLSI single chip (255, 223) Reed-Solomon decoder

NASA Technical Reports Server (NTRS)

Hsu, I. S.; Shao, H. M.; Deutsch, L. J.

1987-01-01

The very large-scale integration (VLSI) architecture of a single chip (255, 223) Reed-Solomon decoder for decoding both errors and erasures is described. A decoding failure detection capability is also included in this system so that the decoder will recognize a failure to decode instead of introducing additional errors. This could happen whenever the received word contains too many errors and erasures for the code to correct. The number of transistors needed to implement this decoder is estimated at about 75,000 if the delay for received message is not included. This is in contrast to the older transform decoding algorithm which needs about 100,000 transistors. However, the transform decoder is simpler in architecture than the time decoder. It is therefore possible to implement a single chip (255, 223) Reed-Solomon decoder with today's VLSI technology. An implementation strategy for the decoder system is presented. This represents the first step in a plan to take advantage of advanced coding techniques to realize a 2.0 dB coding gain for future space missions.

Random access to mobile networks with advanced error correction

NASA Technical Reports Server (NTRS)

Dippold, Michael

1990-01-01

A random access scheme for unreliable data channels is investigated in conjunction with an adaptive Hybrid-II Automatic Repeat Request (ARQ) scheme using Rate Compatible Punctured Codes (RCPC) Forward Error Correction (FEC). A simple scheme with fixed frame length and equal slot sizes is chosen and reservation is implicit by the first packet transmitted randomly in a free slot, similar to Reservation Aloha. This allows the further transmission of redundancy if the last decoding attempt failed. Results show that a high channel utilization and superior throughput can be achieved with this scheme that shows a quite low implementation complexity. For the example of an interleaved Rayleigh channel and soft decision utilization and mean delay are calculated. A utilization of 40 percent may be achieved for a frame with the number of slots being equal to half the station number under high traffic load. The effects of feedback channel errors and some countermeasures are discussed.

An extensible circuit QED architecture for quantum computation

NASA Astrophysics Data System (ADS)

Dicarlo, Leo

Realizing a logical qubit robust to single errors in its constituent physical elements is an immediate challenge for quantum information processing platforms. A longer-term challenge will be achieving quantum fault tolerance, i.e., improving logical qubit resilience by increasing redundancy in the underlying quantum error correction code (QEC). In QuTech, we target these challenges in collaboration with industrial and academic partners. I will present the circuit QED quantum hardware, room-temperature control electronics, and software components of the complete architecture. I will show the extensibility of each component to the Surface-17 and -49 circuits needed to reach the objectives with surface-code QEC, and provide an overview of latest developments. Research funded by IARPA and Intel Corporation.

Complete chloroplast genome sequence of MD-2 pineapple and its comparative analysis among nine other plants from the subclass Commelinidae.

PubMed

Redwan, R M; Saidin, A; Kumar, S V

2015-08-12

Pineapple (Ananas comosus var. comosus) is known as the king of fruits for its crown and is the third most important tropical fruit after banana and citrus. The plant, which is indigenous to South America, is the most important species in the Bromeliaceae family and is largely traded for fresh fruit consumption. Here, we report the complete chloroplast sequence of the MD-2 pineapple that was sequenced using the PacBio sequencing technology. In this study, the high error rate of PacBio long sequence reads of A. comosus's total genomic DNA were improved by leveraging on the high accuracy but short Illumina reads for error-correction via the latest error correction module from Novocraft. Error corrected long PacBio reads were assembled by using a single tool to produce a contig representing the pineapple chloroplast genome. The genome of 159,636 bp in length is featured with the conserved quadripartite structure of chloroplast containing a large single copy region (LSC) with a size of 87,482 bp, a small single copy region (SSC) with a size of 18,622 bp and two inverted repeat regions (IRA and IRB) each with the size of 26,766 bp. Overall, the genome contained 117 unique coding regions and 30 were repeated in the IR region with its genes contents, structure and arrangement similar to its sister taxon, Typha latifolia. A total of 35 repeats structure were detected in both the coding and non-coding regions with a majority being tandem repeats. In addition, 205 SSRs were detected in the genome with six protein-coding genes contained more than two SSRs. Comparative chloroplast genomes from the subclass Commelinidae revealed a conservative protein coding gene albeit located in a highly divergence region. Analysis of selection pressure on protein-coding genes using Ka/Ks ratio showed significant positive selection exerted on the rps7 gene of the pineapple chloroplast with P less than 0.05. Phylogenetic analysis confirmed the recent taxonomical relation among the member of commelinids which support the monophyly relationship between Arecales and Dasypogonaceae and between Zingiberales to the Poales, which includes the A. comosus. The complete sequence of the chloroplast of pineapple provides insights to the divergence of genic chloroplast sequences from the members of the subclass Commelinidae. The complete pineapple chloroplast will serve as a reference for in-depth taxonomical studies in the Bromeliaceae family when more species under the family are sequenced in the future. The genetic sequence information will also make feasible other molecular applications of the pineapple chloroplast for plant genetic improvement.

Development and Positioning Accuracy Assessment of Single-Frequency Precise Point Positioning Algorithms by Combining GPS Code-Pseudorange Measurements with Real-Time SSR Corrections

PubMed Central

Kim, Miso; Park, Kwan-Dong

2017-01-01

We have developed a suite of real-time precise point positioning programs to process GPS pseudorange observables, and validated their performance through static and kinematic positioning tests. To correct inaccurate broadcast orbits and clocks, and account for signal delays occurring from the ionosphere and troposphere, we applied State Space Representation (SSR) error corrections provided by the Seoul Broadcasting System (SBS) in South Korea. Site displacements due to solid earth tide loading are also considered for the purpose of improving the positioning accuracy, particularly in the height direction. When the developed algorithm was tested under static positioning, Kalman-filtered solutions produced a root-mean-square error (RMSE) of 0.32 and 0.40 m in the horizontal and vertical directions, respectively. For the moving platform, the RMSE was found to be 0.53 and 0.69 m in the horizontal and vertical directions. PMID:28598403

Orthogonal patterns in binary neural networks

NASA Technical Reports Server (NTRS)

Baram, Yoram

1988-01-01

A binary neural network that stores only mutually orthogonal patterns is shown to converge, when probed by any pattern, to a pattern in the memory space, i.e., the space spanned by the stored patterns. The latter are shown to be the only members of the memory space under a certain coding condition, which allows maximum storage of M=(2N) sup 0.5 patterns, where N is the number of neurons. The stored patterns are shown to have basins of attraction of radius N/(2M), within which errors are corrected with probability 1 in a single update cycle. When the probe falls outside these regions, the error correction capability can still be increased to 1 by repeatedly running the network with the same probe.

JWL equation of state coefficients for high explosives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, E.; Finger, M.; Collins, W.

1973-01-16

The compilation of equetions of state for high explosives now includes some 38 entries. Additions and revisions have recently introduced errors in Previous lists should be discarded. To avoid transcribing errors, we have computerized the list and will issue computer updates periodically. If you are maintaining equation of state files for hydrodynamic codes and would like IBM card records of our lists, we will be happy to send you a copy of our card deck. We have noted those entries where changes or corrections have been made. Of special note for t h i s update are the corrections tmore » o PBX-9404 and IX-04 from the most recent memo, dated August 23, 1972.« less

IEEE International Symposium on Information Theory (ISIT): Abstracts of Papers, Held in Ann Arbor, Michigan on 6-9 October 1986.

DTIC Science & Technology

1986-10-01

BUZO, and FEDERICO KUHLMANN, Universidad Nacional Autdnoma de Mixico, Facultad de Ingenieria , Divisidn Estudios de Posgrado, P.O. Box 70-256, 04510...unsuccess- ful in this area for a long time. It was felt, e.g., in the voiceband modem industry , that the coding gains achievable by error-correction coding...without bandwidth expansion or data rate reduction, when compared to uncoded modulation. The concept was quickly adopted by industry , and is now becoming

High-density digital recording

NASA Technical Reports Server (NTRS)

Kalil, F. (Editor); Buschman, A. (Editor)

1985-01-01

The problems associated with high-density digital recording (HDDR) are discussed. Five independent users of HDDR systems and their problems, solutions, and insights are provided as guidance for other users of HDDR systems. Various pulse code modulation coding techniques are reviewed. An introduction to error detection and correction head optimization theory and perpendicular recording are provided. Competitive tape recorder manufacturers apply all of the above theories and techniques and present their offerings. The methodology used by the HDDR Users Subcommittee of THIC to evaluate parallel HDDR systems is presented.

Photonic entanglement-assisted quantum low-density parity-check encoders and decoders.

PubMed

Djordjevic, Ivan B

2010-05-01

I propose encoder and decoder architectures for entanglement-assisted (EA) quantum low-density parity-check (LDPC) codes suitable for all-optical implementation. I show that two basic gates needed for EA quantum error correction, namely, controlled-NOT (CNOT) and Hadamard gates can be implemented based on Mach-Zehnder interferometer. In addition, I show that EA quantum LDPC codes from balanced incomplete block designs of unitary index require only one entanglement qubit to be shared between source and destination.

Linear-time general decoding algorithm for the surface code

NASA Astrophysics Data System (ADS)

Darmawan, Andrew S.; Poulin, David

2018-05-01

A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including coherences and correlations. We demonstrate that the decoder significantly outperforms the conventional matching algorithm on a variety of noise models, including non-Pauli noise and spatially correlated noise. The algorithm is based on an approximate calculation of the logical channel using a tensor-network description of the noisy state.

Analysis and Compensation for Lateral Chromatic Aberration in a Color Coding Structured Light 3D Measurement System.

PubMed

Huang, Junhui; Xue, Qi; Wang, Zhao; Gao, Jianmin

2016-09-03

While color-coding methods have improved the measuring efficiency of a structured light three-dimensional (3D) measurement system, they decreased the measuring accuracy significantly due to lateral chromatic aberration (LCA). In this study, the LCA in a structured light measurement system is analyzed, and a method is proposed to compensate the error caused by the LCA. Firstly, based on the projective transformation, a 3D error map of LCA is constructed in the projector images by using a flat board and comparing the image coordinates of red, green and blue circles with the coordinates of white circles at preselected sample points within the measurement volume. The 3D map consists of the errors, which are the equivalent errors caused by LCA of the camera and projector. Then in measurements, error values of LCA are calculated and compensated to correct the projector image coordinates through the 3D error map and a tri-linear interpolation method. Eventually, 3D coordinates with higher accuracy are re-calculated according to the compensated image coordinates. The effectiveness of the proposed method is verified in the following experiments.

Analysis and Compensation for Lateral Chromatic Aberration in a Color Coding Structured Light 3D Measurement System

PubMed Central

Huang, Junhui; Xue, Qi; Wang, Zhao; Gao, Jianmin

2016-01-01

While color-coding methods have improved the measuring efficiency of a structured light three-dimensional (3D) measurement system, they decreased the measuring accuracy significantly due to lateral chromatic aberration (LCA). In this study, the LCA in a structured light measurement system is analyzed, and a method is proposed to compensate the error caused by the LCA. Firstly, based on the projective transformation, a 3D error map of LCA is constructed in the projector images by using a flat board and comparing the image coordinates of red, green and blue circles with the coordinates of white circles at preselected sample points within the measurement volume. The 3D map consists of the errors, which are the equivalent errors caused by LCA of the camera and projector. Then in measurements, error values of LCA are calculated and compensated to correct the projector image coordinates through the 3D error map and a tri-linear interpolation method. Eventually, 3D coordinates with higher accuracy are re-calculated according to the compensated image coordinates. The effectiveness of the proposed method is verified in the following experiments. PMID:27598174

Mapping and correction of the CMM workspace error with the use of an electronic gyroscope and neural networks--practical application.

PubMed

Swornowski, Pawel J

2013-01-01

The article presents the application of neural networks in determining and correction of the deformation of a coordinate measuring machine (CMM) workspace. The information about the CMM errors is acquired using an ADXRS401 electronic gyroscope. A test device (PS-20 module) was built and integrated with a commercial measurement system based on the SP25M passive scanning probe and with a PH10M module (Renishaw). The proposed solution was tested on a Kemco 600 CMM and on a DEA Global Clima CMM. In the former case, correction of the CMM errors was performed using the source code of WinIOS software owned by The Institute of Advanced Manufacturing Technology, Cracow, Poland and in the latter on an external PC. Optimum parameters of full and simplified mapping of a given layer of the CMM workspace were determined for practical applications. The proposed method can be employed for the interim check (ISO 10360-2 procedure) or to detect local CMM deformations, occurring when the CMM works at high scanning speeds (>20 mm/s). © Wiley Periodicals, Inc.

On the decoding process in ternary error-correcting output codes.

PubMed

Escalera, Sergio; Pujol, Oriol; Radeva, Petia

2010-01-01

A common way to model multiclass classification problems is to design a set of binary classifiers and to combine them. Error-Correcting Output Codes (ECOC) represent a successful framework to deal with these type of problems. Recent works in the ECOC framework showed significant performance improvements by means of new problem-dependent designs based on the ternary ECOC framework. The ternary framework contains a larger set of binary problems because of the use of a "do not care" symbol that allows us to ignore some classes by a given classifier. However, there are no proper studies that analyze the effect of the new symbol at the decoding step. In this paper, we present a taxonomy that embeds all binary and ternary ECOC decoding strategies into four groups. We show that the zero symbol introduces two kinds of biases that require redefinition of the decoding design. A new type of decoding measure is proposed, and two novel decoding strategies are defined. We evaluate the state-of-the-art coding and decoding strategies over a set of UCI Machine Learning Repository data sets and into a real traffic sign categorization problem. The experimental results show that, following the new decoding strategies, the performance of the ECOC design is significantly improved.

Morse Monte Carlo Radiation Transport Code System

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emmett, M.B.

1975-02-01

The report contains sections containing descriptions of the MORSE and PICTURE codes, input descriptions, sample problems, deviations of the physical equations and explanations of the various error messages. The MORSE code is a multipurpose neutron and gamma-ray transport Monte Carlo code. Time dependence for both shielding and criticality problems is provided. General three-dimensional geometry may be used with an albedo option available at any material surface. The PICTURE code provide aid in preparing correct input data for the combinatorial geometry package CG. It provides a printed view of arbitrary two-dimensional slices through the geometry. By inspecting these pictures one maymore » determine if the geometry specified by the input cards is indeed the desired geometry. 23 refs. (WRF)« less

Embedded feature ranking for ensemble MLP classifiers.

PubMed

Windeatt, Terry; Duangsoithong, Rakkrit; Smith, Raymond

2011-06-01

A feature ranking scheme for multilayer perceptron (MLP) ensembles is proposed, along with a stopping criterion based upon the out-of-bootstrap estimate. To solve multi-class problems feature ranking is combined with modified error-correcting output coding. Experimental results on benchmark data demonstrate the versatility of the MLP base classifier in removing irrelevant features.

Measurement Techniques for Transmit Source Clock Jitter for Weak Serial RF Links

NASA Technical Reports Server (NTRS)

Lansdowne, Chatwin A.; Schlesinger, Adam M.

2010-01-01

Techniques for filtering clock jitter measurements are developed, in the context of controlling data modulation jitter on an RF carrier to accommodate low signal-to-noise ratio thresholds of high-performance error correction codes. Measurement artifacts from sampling are considered, and a tutorial on interpretation of direct readings is included.

Common data buffer

NASA Technical Reports Server (NTRS)

Byrne, F.

1981-01-01

Time-shared interface speeds data processing in distributed computer network. Two-level high-speed scanning approach routes information to buffer, portion of which is reserved for series of "first-in, first-out" memory stacks. Buffer address structure and memory are protected from noise or failed components by error correcting code. System is applicable to any computer or processing language.

Improved Algorithm For Finite-Field Normal-Basis Multipliers

NASA Technical Reports Server (NTRS)

Wang, C. C.

1989-01-01

Improved algorithm reduces complexity of calculations that must precede design of Massey-Omura finite-field normal-basis multipliers, used in error-correcting-code equipment and cryptographic devices. Algorithm represents an extension of development reported in "Algorithm To Design Finite-Field Normal-Basis Multipliers" (NPO-17109), NASA Tech Briefs, Vol. 12, No. 5, page 82.

SSDA code to apply data assimilation in soil water flow modeling: Documentation and user manual

USDA-ARS?s Scientific Manuscript database

Soil water flow models are based on simplified assumptions about the mechanisms, processes, and parameters of water retention and flow. That causes errors in soil water flow model predictions. Data assimilation (DA) with the ensemble Kalman filter (EnKF) corrects modeling results based on measured s...

Efficient Bit-to-Symbol Likelihood Mappings

NASA Technical Reports Server (NTRS)

Moision, Bruce E.; Nakashima, Michael A.

2010-01-01

This innovation is an efficient algorithm designed to perform bit-to-symbol and symbol-to-bit likelihood mappings that represent a significant portion of the complexity of an error-correction code decoder for high-order constellations. Recent implementation of the algorithm in hardware has yielded an 8- percent reduction in overall area relative to the prior design.

Reed-Muller Codes in Error Correction in Wireless Adhoc Networks

DTIC Science & Technology

2004-03-01

resulting spectrum is the spectrum of the windowed signal. Therefore, the window width is an important pa- rameter that affects the BER performanceof ... compare the results, the same random message was used. The seed value in msg.m was changed only for comparing the PAPR values of the system with

75 FR 74607 - Correction of Administrative Errors

Federal Register 2010, 2011, 2012, 2013, 2014

2010-12-01

... established for private-sector employees under section 401(k) of the Internal Revenue Code (26 U.S.C. 401(k... regulation on state, local, and tribal governments and the private sector have been assessed. This regulation... governments, in the aggregate, or by the private sector. Therefore, a statement under section 1532 is not...

Non-binary LDPC-coded modulation for high-speed optical metro networks with backpropagation

NASA Astrophysics Data System (ADS)

Arabaci, Murat; Djordjevic, Ivan B.; Saunders, Ross; Marcoccia, Roberto M.

2010-01-01

To simultaneously mitigate the linear and nonlinear channel impairments in high-speed optical communications, we propose the use of non-binary low-density-parity-check-coded modulation in combination with a coarse backpropagation method. By employing backpropagation, we reduce the memory in the channel and in return obtain significant reductions in the complexity of the channel equalizer which is exponentially proportional to the channel memory. We then compensate for the remaining channel distortions using forward error correction based on non-binary LDPC codes. We propose non-binary-LDPC-coded modulation scheme because, compared to bit-interleaved binary-LDPC-coded modulation scheme employing turbo equalization, the proposed scheme lowers the computational complexity and latency of the overall system while providing impressively larger coding gains.

Least reliable bits coding (LRBC) for high data rate satellite communications

NASA Technical Reports Server (NTRS)

Vanderaar, Mark; Budinger, James; Wagner, Paul

1992-01-01

LRBC, a bandwidth efficient multilevel/multistage block-coded modulation technique, is analyzed. LRBC uses simple multilevel component codes that provide increased error protection on increasingly unreliable modulated bits in order to maintain an overall high code rate that increases spectral efficiency. Soft-decision multistage decoding is used to make decisions on unprotected bits through corrections made on more protected bits. Analytical expressions and tight performance bounds are used to show that LRBC can achieve increased spectral efficiency and maintain equivalent or better power efficiency compared to that of BPSK. The relative simplicity of Galois field algebra vs the Viterbi algorithm and the availability of high-speed commercial VLSI for block codes indicates that LRBC using block codes is a desirable method for high data rate implementations.

High-Threshold Fault-Tolerant Quantum Computation with Analog Quantum Error Correction

NASA Astrophysics Data System (ADS)

Fukui, Kosuke; Tomita, Akihisa; Okamoto, Atsushi; Fujii, Keisuke

2018-04-01

To implement fault-tolerant quantum computation with continuous variables, the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important technological element. However, it is still challenging to experimentally generate the GKP qubit with the required squeezing level, 14.8 dB, of the existing fault-tolerant quantum computation. To reduce this requirement, we propose a high-threshold fault-tolerant quantum computation with GKP qubits using topologically protected measurement-based quantum computation with the surface code. By harnessing analog information contained in the GKP qubits, we apply analog quantum error correction to the surface code. Furthermore, we develop a method to prevent the squeezing level from decreasing during the construction of the large-scale cluster states for the topologically protected, measurement-based, quantum computation. We numerically show that the required squeezing level can be relaxed to less than 10 dB, which is within the reach of the current experimental technology. Hence, this work can considerably alleviate this experimental requirement and take a step closer to the realization of large-scale quantum computation.

The performance of trellis coded multilevel DPSK on a fading mobile satellite channel

NASA Technical Reports Server (NTRS)

Simon, Marvin K.; Divsalar, Dariush

1987-01-01

The performance of trellis coded multilevel differential phase-shift-keying (MDPSK) over Rician and Rayleigh fading channels is discussed. For operation at L-Band, this signalling technique leads to a more robust system than the coherent system with dual pilot tone calibration previously proposed for UHF. The results are obtained using a combination of analysis and simulation. The analysis shows that the design criterion for trellis codes to be operated on fading channels with interleaving/deinterleaving is no longer free Euclidean distance. The correct design criterion for optimizing bit error probability of trellis coded MDPSK over fading channels will be presented along with examples illustrating its application.

a Climatology of Global Precipitation.

NASA Astrophysics Data System (ADS)

Legates, David Russell

A global climatology of mean monthly precipitation has been developed using traditional land-based gage measurements as well as derived oceanic data. These data have been screened for coding errors and redundant entries have been removed. Oceanic precipitation estimates are most often extrapolated from coastal and island observations because few gage estimates of oceanic precipitation exist. One such procedure, developed by Dorman and Bourke and used here, employs a derived relationship between observed rainfall totals and the "current weather" at coastal stations. The combined data base contains 24,635 independent terrestial station records and 2223 oceanic grid-point records. Raingage catches are known to underestimate actual precipitation. Errors in the gage catch result from wind -field deformation, wetting losses, and evaporation from the gage and can amount to nearly 8, 2, and 1 percent of the global catch, respectively. A procedure has been developed to correct many of these errors and has been used to adjust the gage estimates of global precipitation. Space-time variations in gage type, air temperature, wind speed, and natural vegetation were incorporated into the correction procedure. Corrected data were then interpolated to the nodes of a 0.5^circ of latitude by 0.5^circ of longitude lattice using a spherically-based interpolation algorithm. Interpolation errors are largest in areas of low station density, rugged topography, and heavy precipitation. Interpolated estimates also were compared with a digital filtering technique to access the aliasing of high-frequency "noise" into the lower frequency signals. Isohyetal maps displaying the mean annual, seasonal, and monthly precipitation are presented. Gage corrections and the standard error of the corrected estimates also are mapped. Results indicate that mean annual global precipitation is 1123 mm with 1251 mm falling over the oceans and 820 mm over land. Spatial distributions of monthly precipitation generally are consistent with existing precipitation climatologies.

Multiple component codes based generalized LDPC codes for high-speed optical transport.

PubMed

Djordjevic, Ivan B; Wang, Ting

2014-07-14

A class of generalized low-density parity-check (GLDPC) codes suitable for optical communications is proposed, which consists of multiple local codes. It is shown that Hamming, BCH, and Reed-Muller codes can be used as local codes, and that the maximum a posteriori probability (MAP) decoding of these local codes by Ashikhmin-Lytsin algorithm is feasible in terms of complexity and performance. We demonstrate that record coding gains can be obtained from properly designed GLDPC codes, derived from multiple component codes. We then show that several recently proposed classes of LDPC codes such as convolutional and spatially-coupled codes can be described using the concept of GLDPC coding, which indicates that the GLDPC coding can be used as a unified platform for advanced FEC enabling ultra-high speed optical transport. The proposed class of GLDPC codes is also suitable for code-rate adaption, to adjust the error correction strength depending on the optical channel conditions.

Interactive QR code beautification with full background image embedding

NASA Astrophysics Data System (ADS)

Lin, Lijian; Wu, Song; Liu, Sijiang; Jiang, Bo

2017-06-01

QR (Quick Response) code is a kind of two dimensional barcode that was first developed in automotive industry. Nowadays, QR code has been widely used in commercial applications like product promotion, mobile payment, product information management, etc. Traditional QR codes in accordance with the international standard are reliable and fast to decode, but are lack of aesthetic appearance to demonstrate visual information to customers. In this work, we present a novel interactive method to generate aesthetic QR code. By given information to be encoded and an image to be decorated as full QR code background, our method accepts interactive user's strokes as hints to remove undesired parts of QR code modules based on the support of QR code error correction mechanism and background color thresholds. Compared to previous approaches, our method follows the intention of the QR code designer, thus can achieve more user pleasant result, while keeping high machine readability.

Improved Iterative Decoding of Network-Channel Codes for Multiple-Access Relay Channel.

PubMed

Majumder, Saikat; Verma, Shrish

2015-01-01

Cooperative communication using relay nodes is one of the most effective means of exploiting space diversity for low cost nodes in wireless network. In cooperative communication, users, besides communicating their own information, also relay the information of other users. In this paper we investigate a scheme where cooperation is achieved using a common relay node which performs network coding to provide space diversity for two information nodes transmitting to a base station. We propose a scheme which uses Reed-Solomon error correcting code for encoding the information bit at the user nodes and convolutional code as network code, instead of XOR based network coding. Based on this encoder, we propose iterative soft decoding of joint network-channel code by treating it as a concatenated Reed-Solomon convolutional code. Simulation results show significant improvement in performance compared to existing scheme based on compound codes.

Error and Error Mitigation in Low-Coverage Genome Assemblies

PubMed Central

Hubisz, Melissa J.; Lin, Michael F.; Kellis, Manolis; Siepel, Adam

2011-01-01

The recent release of twenty-two new genome sequences has dramatically increased the data available for mammalian comparative genomics, but twenty of these new sequences are currently limited to ∼2× coverage. Here we examine the extent of sequencing error in these 2× assemblies, and its potential impact in downstream analyses. By comparing 2× assemblies with high-quality sequences from the ENCODE regions, we estimate the rate of sequencing error to be 1–4 errors per kilobase. While this error rate is fairly modest, sequencing error can still have surprising effects. For example, an apparent lineage-specific insertion in a coding region is more likely to reflect sequencing error than a true biological event, and the length distribution of coding indels is strongly distorted by error. We find that most errors are contributed by a small fraction of bases with low quality scores, in particular, by the ends of reads in regions of single-read coverage in the assembly. We explore several approaches for automatic sequencing error mitigation (SEM), making use of the localized nature of sequencing error, the fact that it is well predicted by quality scores, and information about errors that comes from comparisons across species. Our automatic methods for error mitigation cannot replace the need for additional sequencing, but they do allow substantial fractions of errors to be masked or eliminated at the cost of modest amounts of over-correction, and they can reduce the impact of error in downstream phylogenomic analyses. Our error-mitigated alignments are available for download. PMID:21340033

Probabilistic Amplitude Shaping With Hard Decision Decoding and Staircase Codes

NASA Astrophysics Data System (ADS)

Sheikh, Alireza; Amat, Alexandre Graell i.; Liva, Gianluigi; Steiner, Fabian

2018-05-01

We consider probabilistic amplitude shaping (PAS) as a means of increasing the spectral efficiency of fiber-optic communication systems. In contrast to previous works in the literature, we consider probabilistic shaping with hard decision decoding (HDD). In particular, we apply the PAS recently introduced by B\\"ocherer \\emph{et al.} to a coded modulation (CM) scheme with bit-wise HDD that uses a staircase code as the forward error correction code. We show that the CM scheme with PAS and staircase codes yields significant gains in spectral efficiency with respect to the baseline scheme using a staircase code and a standard constellation with uniformly distributed signal points. Using a single staircase code, the proposed scheme achieves performance within $0.57$--$1.44$ dB of the corresponding achievable information rate for a wide range of spectral efficiencies.

Checking Questionable Entry of Personally Identifiable Information Encrypted by One-Way Hash Transformation

PubMed Central

Chen, Xianlai; Fann, Yang C; McAuliffe, Matthew; Vismer, David

2017-01-01

Background As one of the several effective solutions for personal privacy protection, a global unique identifier (GUID) is linked with hash codes that are generated from combinations of personally identifiable information (PII) by a one-way hash algorithm. On the GUID server, no PII is permitted to be stored, and only GUID and hash codes are allowed. The quality of PII entry is critical to the GUID system. Objective The goal of our study was to explore a method of checking questionable entry of PII in this context without using or sending any portion of PII while registering a subject. Methods According to the principle of GUID system, all possible combination patterns of PII fields were analyzed and used to generate hash codes, which were stored on the GUID server. Based on the matching rules of the GUID system, an error-checking algorithm was developed using set theory to check PII entry errors. We selected 200,000 simulated individuals with randomly-planted errors to evaluate the proposed algorithm. These errors were placed in the required PII fields or optional PII fields. The performance of the proposed algorithm was also tested in the registering system of study subjects. Results There are 127,700 error-planted subjects, of which 114,464 (89.64%) can still be identified as the previous one and remaining 13,236 (10.36%, 13,236/127,700) are discriminated as new subjects. As expected, 100% of nonidentified subjects had errors within the required PII fields. The possibility that a subject is identified is related to the count and the type of incorrect PII field. For all identified subjects, their errors can be found by the proposed algorithm. The scope of questionable PII fields is also associated with the count and the type of the incorrect PII field. The best situation is to precisely find the exact incorrect PII fields, and the worst situation is to shrink the questionable scope only to a set of 13 PII fields. In the application, the proposed algorithm can give a hint of questionable PII entry and perform as an effective tool. Conclusions The GUID system has high error tolerance and may correctly identify and associate a subject even with few PII field errors. Correct data entry, especially required PII fields, is critical to avoiding false splits. In the context of one-way hash transformation, the questionable input of PII may be identified by applying set theory operators based on the hash codes. The count and the type of incorrect PII fields play an important role in identifying a subject and locating questionable PII fields. PMID:28213343

Checking Questionable Entry of Personally Identifiable Information Encrypted by One-Way Hash Transformation.

PubMed

Chen, Xianlai; Fann, Yang C; McAuliffe, Matthew; Vismer, David; Yang, Rong

2017-02-17

As one of the several effective solutions for personal privacy protection, a global unique identifier (GUID) is linked with hash codes that are generated from combinations of personally identifiable information (PII) by a one-way hash algorithm. On the GUID server, no PII is permitted to be stored, and only GUID and hash codes are allowed. The quality of PII entry is critical to the GUID system. The goal of our study was to explore a method of checking questionable entry of PII in this context without using or sending any portion of PII while registering a subject. According to the principle of GUID system, all possible combination patterns of PII fields were analyzed and used to generate hash codes, which were stored on the GUID server. Based on the matching rules of the GUID system, an error-checking algorithm was developed using set theory to check PII entry errors. We selected 200,000 simulated individuals with randomly-planted errors to evaluate the proposed algorithm. These errors were placed in the required PII fields or optional PII fields. The performance of the proposed algorithm was also tested in the registering system of study subjects. There are 127,700 error-planted subjects, of which 114,464 (89.64%) can still be identified as the previous one and remaining 13,236 (10.36%, 13,236/127,700) are discriminated as new subjects. As expected, 100% of nonidentified subjects had errors within the required PII fields. The possibility that a subject is identified is related to the count and the type of incorrect PII field. For all identified subjects, their errors can be found by the proposed algorithm. The scope of questionable PII fields is also associated with the count and the type of the incorrect PII field. The best situation is to precisely find the exact incorrect PII fields, and the worst situation is to shrink the questionable scope only to a set of 13 PII fields. In the application, the proposed algorithm can give a hint of questionable PII entry and perform as an effective tool. The GUID system has high error tolerance and may correctly identify and associate a subject even with few PII field errors. Correct data entry, especially required PII fields, is critical to avoiding false splits. In the context of one-way hash transformation, the questionable input of PII may be identified by applying set theory operators based on the hash codes. The count and the type of incorrect PII fields play an important role in identifying a subject and locating questionable PII fields. ©Xianlai Chen, Yang C Fann, Matthew McAuliffe, David Vismer, Rong Yang. Originally published in JMIR Medical Informatics (http://medinform.jmir.org), 17.02.2017.

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

DOE PAGES

Grout, Ray; Kolla, Hemanth; Minion, Michael; ...

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering frommore » soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. Here, we demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grout, Ray; Kolla, Hemanth; Minion, Michael

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited tomore » recovering from soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual on the first correction iteration and changes slowly between successive iterations. We demonstrate the effectiveness of this strategy for both canonical test problems and a comprehen- sive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grout, Ray; Kolla, Hemanth; Minion, Michael

2017-05-08

Spectral deferred corrections (SDC) is an iterative approach for constructing higher-order-accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering frommore » soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual of the first correction iteration and changes slowly between successive iterations. We demonstrate the effectiveness of this strategy for both canonical test problems and a comprehensive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.« less

Atmospheric Phase Delay Correction of D-Insar Based on SENTINEL-1A

NASA Astrophysics Data System (ADS)

Li, X.; Huang, G.; Kong, Q.

2018-04-01

In this paper, we used the Generic Atmospheric Correction Online Service for InSAR (GACOS) tropospheric delay maps to correct the atmospheric phase delay of the differential interferometric synthetic aperture radar (D-InSAR) monitoring, and we improved the accuracy of subsidence monitoring using D-InSAR technology. Atmospheric phase delay, as one of the most important errors that limit the monitoring accuracy of InSAR, would lead to the masking of true phase in subsidence monitoring. For the problem, this paper used the Sentinel-1A images and the tropospheric delay maps got from GACOS to monitor the subsidence of the Yellow River Delta in Shandong Province. The conventional D-InSAR processing was performed using the GAMMA software. The MATLAB codes were used to correct the atmospheric delay of the D-InSAR results. The results before and after the atmospheric phase delay correction were verified and analyzed in the main subsidence area. The experimental results show that atmospheric phase influences the deformation results to a certain extent. After the correction, the measurement error of vertical deformation is reduced by about 18 mm, which proves that the removal of atmospheric effects can improve the accuracy of the D-InSAR monitoring.

Communications and information research: Improved space link performance via concatenated forward error correction coding

NASA Technical Reports Server (NTRS)

Rao, T. R. N.; Seetharaman, G.; Feng, G. L.

1996-01-01

With the development of new advanced instruments for remote sensing applications, sensor data will be generated at a rate that not only requires increased onboard processing and storage capability, but imposes demands on the space to ground communication link and ground data management-communication system. Data compression and error control codes provide viable means to alleviate these demands. Two types of data compression have been studied by many researchers in the area of information theory: a lossless technique that guarantees full reconstruction of the data, and a lossy technique which generally gives higher data compaction ratio but incurs some distortion in the reconstructed data. To satisfy the many science disciplines which NASA supports, lossless data compression becomes a primary focus for the technology development. While transmitting the data obtained by any lossless data compression, it is very important to use some error-control code. For a long time, convolutional codes have been widely used in satellite telecommunications. To more efficiently transform the data obtained by the Rice algorithm, it is required to meet the a posteriori probability (APP) for each decoded bit. A relevant algorithm for this purpose has been proposed which minimizes the bit error probability in the decoding linear block and convolutional codes and meets the APP for each decoded bit. However, recent results on iterative decoding of 'Turbo codes', turn conventional wisdom on its head and suggest fundamentally new techniques. During the past several months of this research, the following approaches have been developed: (1) a new lossless data compression algorithm, which is much better than the extended Rice algorithm for various types of sensor data, (2) a new approach to determine the generalized Hamming weights of the algebraic-geometric codes defined by a large class of curves in high-dimensional spaces, (3) some efficient improved geometric Goppa codes for disk memory systems and high-speed mass memory systems, and (4) a tree based approach for data compression using dynamic programming.

Erratum: The Hubble Space Telescope Key Project on the Extragalactic Distance Scale. XXVIII. Combining the Constraints on the Hubble Constant

NASA Astrophysics Data System (ADS)

Mould, Jeremy R.; Huchra, John P.; Freedman, Wendy L.; Kennicutt, Robert C., Jr.; Ferrarese, Laura; Ford, Holland C.; Gibson, Brad K.; Graham, John A.; Hughes, Shaun M. G.; Illingworth, Garth D.; Kelson, Daniel D.; Macri, Lucas M.; Madore, Barry F.; Sakai, Shoko; Sebo, Kim M.; Silbermann, Nancy A.; Stetson, Peter B.

2000-12-01

In the article ``The Hubble Space Telescope Key Project on the Extragalactic Distance Scale. XXVIII. Combining the Constraints on the Hubble Constant'' (ApJ, 529, 786 [2000]), by Jeremy R. Mould, John P. Huchra, Wendy L. Freedman, Robert C. Kennicutt, Jr., Laura Ferrarese, Holland C. Ford, Brad K. Gibson, John A. Graham, Shaun M. G. Hughes, Garth D. Illingworth, Daniel D. Kelson, Lucas M. Macri, Barry F. Madore, Shoko Sakai, Kim M. Sebo, Nancy A. Silbermann, and Peter B. Stetson, some sign errors need to be corrected. 1. In equation (A2) the minus signs should be plus signs. The correct version is Vcosmic=VH+Vc,LG+Vin,Virgo+Vin,GA+Vin,Shap+... 2. In Table A1 the declination of the Great Attractor (GA) is -44°, and that of the Shapley supercluster is -31°, i.e., south declination, not north, as implied in the table. The first error is the authors' and the second occurred in the publication process. In both cases the computer code was correct, and the errors are in the published representation. None of the results presented in the paper are therefore affected in any way. The authors thank Dr. Jim Condon for pointing out the error in equation (A2)

Experimental Demonstration of Fault-Tolerant State Preparation with Superconducting Qubits.

PubMed

Takita, Maika; Cross, Andrew W; Córcoles, A D; Chow, Jerry M; Gambetta, Jay M

2017-11-03

Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting storage errors, but applications require not just storing information; we must accurately compute even with faulty operations. The theory of fault-tolerant quantum computing illuminates a way forward by providing a foundation and collection of techniques for limiting the spread of errors. Here we implement one of the smallest quantum codes in a five-qubit superconducting transmon device and demonstrate fault-tolerant state preparation. We characterize the resulting code words through quantum process tomography and study the free evolution of the logical observables. Our results are consistent with fault-tolerant state preparation in a protected qubit subspace.

SOL - SIZING AND OPTIMIZATION LANGUAGE COMPILER

NASA Technical Reports Server (NTRS)

Scotti, S. J.

1994-01-01

SOL is a computer language which is geared to solving design problems. SOL includes the mathematical modeling and logical capabilities of a computer language like FORTRAN but also includes the additional power of non-linear mathematical programming methods (i.e. numerical optimization) at the language level (as opposed to the subroutine level). The language-level use of optimization has several advantages over the traditional, subroutine-calling method of using an optimizer: first, the optimization problem is described in a concise and clear manner which closely parallels the mathematical description of optimization; second, a seamless interface is automatically established between the optimizer subroutines and the mathematical model of the system being optimized; third, the results of an optimization (objective, design variables, constraints, termination criteria, and some or all of the optimization history) are output in a form directly related to the optimization description; and finally, automatic error checking and recovery from an ill-defined system model or optimization description is facilitated by the language-level specification of the optimization problem. Thus, SOL enables rapid generation of models and solutions for optimum design problems with greater confidence that the problem is posed correctly. The SOL compiler takes SOL-language statements and generates the equivalent FORTRAN code and system calls. Because of this approach, the modeling capabilities of SOL are extended by the ability to incorporate existing FORTRAN code into a SOL program. In addition, SOL has a powerful MACRO capability. The MACRO capability of the SOL compiler effectively gives the user the ability to extend the SOL language and can be used to develop easy-to-use shorthand methods of generating complex models and solution strategies. The SOL compiler provides syntactic and semantic error-checking, error recovery, and detailed reports containing cross-references to show where each variable was used. The listings summarize all optimizations, listing the objective functions, design variables, and constraints. The compiler offers error-checking specific to optimization problems, so that simple mistakes will not cost hours of debugging time. The optimization engine used by and included with the SOL compiler is a version of Vanderplatt's ADS system (Version 1.1) modified specifically to work with the SOL compiler. SOL allows the use of the over 100 ADS optimization choices such as Sequential Quadratic Programming, Modified Feasible Directions, interior and exterior penalty function and variable metric methods. Default choices of the many control parameters of ADS are made for the user, however, the user can override any of the ADS control parameters desired for each individual optimization. The SOL language and compiler were developed with an advanced compiler-generation system to ensure correctness and simplify program maintenance. Thus, SOL's syntax was defined precisely by a LALR(1) grammar and the SOL compiler's parser was generated automatically from the LALR(1) grammar with a parser-generator. Hence unlike ad hoc, manually coded interfaces, the SOL compiler's lexical analysis insures that the SOL compiler recognizes all legal SOL programs, can recover from and correct for many errors and report the location of errors to the user. This version of the SOL compiler has been implemented on VAX/VMS computer systems and requires 204 KB of virtual memory to execute. Since the SOL compiler produces FORTRAN code, it requires the VAX FORTRAN compiler to produce an executable program. The SOL compiler consists of 13,000 lines of Pascal code. It was developed in 1986 and last updated in 1988. The ADS and other utility subroutines amount to 14,000 lines of FORTRAN code and were also updated in 1988.

Construction of self-dual codes in the Rosenbloom-Tsfasman metric

NASA Astrophysics Data System (ADS)

Krisnawati, Vira Hari; Nisa, Anzi Lina Ukhtin

2017-12-01

Linear code is a very basic code and very useful in coding theory. Generally, linear code is a code over finite field in Hamming metric. Among the most interesting families of codes, the family of self-dual code is a very important one, because it is the best known error-correcting code. The concept of Hamming metric is develop into Rosenbloom-Tsfasman metric (RT-metric). The inner product in RT-metric is different from Euclid inner product that is used to define duality in Hamming metric. Most of the codes which are self-dual in Hamming metric are not so in RT-metric. And, generator matrix is very important to construct a code because it contains basis of the code. Therefore in this paper, we give some theorems and methods to construct self-dual codes in RT-metric by considering properties of the inner product and generator matrix. Also, we illustrate some examples for every kind of the construction.

Handling the satellite inter-frequency biases in triple-frequency observations

NASA Astrophysics Data System (ADS)

Zhao, Lewen; Ye, Shirong; Song, Jia

2017-04-01

The new generation of GNSS satellites, including BDS, Galileo, modernized GPS, and GLONASS, transmit navigation sdata at more frequencies. Multi-frequency signals open new prospects for precise positioning, but satellite code and phase inter-frequency biases (IFB) induced by the third frequency need to be handled. Satellite code IFB can be corrected using products estimated by different strategies, the theoretical and numerical compatibility of these methods need to be proved. Furthermore, a new type of phase IFB, which changes with the relative sun-spacecraft-earth geometry, has been observed. It is necessary to investigate the cause and possible impacts of phase Time-variant IFB (TIFB). Therefore, we present systematic analysis to illustrate the relevancy between satellite clocks and phase TIFB, and compare the handling strategies of the code and phase IFB in triple-frequency positioning. First, the un-differenced L1/L2 satellite clock corrections considering the hardware delays are derived. And IFB induced by the dual-frequency satellite clocks to triple-frequency PPP model is detailed. The analysis shows that estimated satellite clocks actually contain the time-variant phase hardware delays, which can be compensated in L1/L2 ionosphere-free combinations. However, the time-variant hardware delays will lead to TIFB if the third frequency is used. Then, the methods used to correct the code and phase IFB are discussed. Standard point positioning (SPP) and precise point positioning (PPP) using BDS observations are carried out to validate the improvement of different IFB correction strategies. Experiments show that code IFB derived from DCB or geometry-free and ionosphere-free combination show an agreement of 0.3 ns for all satellites. Positioning results and error distribution with two different code IFB correcting strategies achieve similar tendency, which shows their substitutability. The original and wavelet filtered phase TIFB long-term series show significant periodical characteristic for most GEO and IGSO satellites, with the magnitude varies between - 5 cm and 5 cm. Finally, BDS L1/L3 kinematic PPP is conducted with code IFB corrected with DCB combinations, and TIFB corrected with filtered series. Results show that the IFB corrected L1/L3 PPP can achieve comparable convergence and positioning accuracy as L1/L2 combinations in static and kinematic mode.

Energy efficient rateless codes for high speed data transfer over free space optical channels

NASA Astrophysics Data System (ADS)

Prakash, Geetha; Kulkarni, Muralidhar; Acharya, U. S.

2015-03-01

Terrestrial Free Space Optical (FSO) links transmit information by using the atmosphere (free space) as a medium. In this paper, we have investigated the use of Luby Transform (LT) codes as a means to mitigate the effects of data corruption induced by imperfect channel which usually takes the form of lost or corrupted packets. LT codes, which are a class of Fountain codes, can be used independent of the channel rate and as many code words as required can be generated to recover all the message bits irrespective of the channel performance. Achieving error free high data rates with limited energy resources is possible with FSO systems if error correction codes with minimal overheads on the power can be used. We also employ a combination of Binary Phase Shift Keying (BPSK) with provision for modification of threshold and optimized LT codes with belief propagation for decoding. These techniques provide additional protection even under strong turbulence regimes. Automatic Repeat Request (ARQ) is another method of improving link reliability. Performance of ARQ is limited by the number of retransmissions and the corresponding time delay. We prove through theoretical computations and simulations that LT codes consume less energy per bit. We validate the feasibility of using energy efficient LT codes over ARQ for FSO links to be used in optical wireless sensor networks within the eye safety limits.

A novel construction method of QC-LDPC codes based on the subgroup of the finite field multiplicative group for optical transmission systems

NASA Astrophysics Data System (ADS)

Yuan, Jian-guo; Zhou, Guang-xiang; Gao, Wen-chun; Wang, Yong; Lin, Jin-zhao; Pang, Yu

2016-01-01

According to the requirements of the increasing development for optical transmission systems, a novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes based on the subgroup of the finite field multiplicative group is proposed. Furthermore, this construction method can effectively avoid the girth-4 phenomena and has the advantages such as simpler construction, easier implementation, lower encoding/decoding complexity, better girth properties and more flexible adjustment for the code length and code rate. The simulation results show that the error correction performance of the QC-LDPC(3 780,3 540) code with the code rate of 93.7% constructed by this proposed method is excellent, its net coding gain is respectively 0.3 dB, 0.55 dB, 1.4 dB and 1.98 dB higher than those of the QC-LDPC(5 334,4 962) code constructed by the method based on the inverse element characteristics in the finite field multiplicative group, the SCG-LDPC(3 969,3 720) code constructed by the systematically constructed Gallager (SCG) random construction method, the LDPC(32 640,30 592) code in ITU-T G.975.1 and the classic RS(255,239) code which is widely used in optical transmission systems in ITU-T G.975 at the bit error rate ( BER) of 10-7. Therefore, the constructed QC-LDPC(3 780,3 540) code is more suitable for optical transmission systems.

Step-by-step magic state encoding for efficient fault-tolerant quantum computation

PubMed Central

Goto, Hayato

2014-01-01

Quantum error correction allows one to make quantum computers fault-tolerant against unavoidable errors due to decoherence and imperfect physical gate operations. However, the fault-tolerant quantum computation requires impractically large computational resources for useful applications. This is a current major obstacle to the realization of a quantum computer. In particular, magic state distillation, which is a standard approach to universality, consumes the most resources in fault-tolerant quantum computation. For the resource problem, here we propose step-by-step magic state encoding for concatenated quantum codes, where magic states are encoded step by step from the physical level to the logical one. To manage errors during the encoding, we carefully use error detection. Since the sizes of intermediate codes are small, it is expected that the resource overheads will become lower than previous approaches based on the distillation at the logical level. Our simulation results suggest that the resource requirements for a logical magic state will become comparable to those for a single logical controlled-NOT gate. Thus, the present method opens a new possibility for efficient fault-tolerant quantum computation. PMID:25511387

Step-by-step magic state encoding for efficient fault-tolerant quantum computation.

PubMed

Goto, Hayato

2014-12-16

Quantum error correction allows one to make quantum computers fault-tolerant against unavoidable errors due to decoherence and imperfect physical gate operations. However, the fault-tolerant quantum computation requires impractically large computational resources for useful applications. This is a current major obstacle to the realization of a quantum computer. In particular, magic state distillation, which is a standard approach to universality, consumes the most resources in fault-tolerant quantum computation. For the resource problem, here we propose step-by-step magic state encoding for concatenated quantum codes, where magic states are encoded step by step from the physical level to the logical one. To manage errors during the encoding, we carefully use error detection. Since the sizes of intermediate codes are small, it is expected that the resource overheads will become lower than previous approaches based on the distillation at the logical level. Our simulation results suggest that the resource requirements for a logical magic state will become comparable to those for a single logical controlled-NOT gate. Thus, the present method opens a new possibility for efficient fault-tolerant quantum computation.

Does Menstruation Explain Gender Gaps in Work Absenteeism?

ERIC Educational Resources Information Center

Herrmann, Mariesa A.; Rockoff, Jonah E.

2012-01-01

Ichino and Moretti (2009) find that menstruation may contribute to gender gaps in absenteeism and earnings, based on evidence that absences of young female Italian bank employees follow a 28-day cycle. We find this evidence is not robust to the correction of coding errors or small changes in specification, and we find no evidence of increased…

Telling Mathematical Stories with Live Editing

ERIC Educational Resources Information Center

Thomson, Ian

2017-01-01

Using "live editing" it is possible to write code that can be run a section at a time. This makes it easier to spot and correct errors. It can also be used to create an interactive mathematical story. This brief article shows how MATLAB software can be used to take the user on a mathematical journey with historical connections.

The Big Picture in Bilingual Education: A Meta-Analysis Corrected for Gersten's Coding Error

ERIC Educational Resources Information Center

Rolstad, Kellie; Mahoney, Kate; Glass, Gene V.

2008-01-01

In light of a recent revelation that Gersten (1985) included erroneous information on one of two programs for English Language Learners (ELLs), the authors re-calculate results of their earlier meta-analysis of program effectiveness studies for ELLs in which Gersten's studies had behaved as outliers (Rolstad, Mahoney & Glass, 2005). The correction…

Additional development of the XTRAN3S computer program

NASA Technical Reports Server (NTRS)

Borland, C. J.

1989-01-01

Additional developments and enhancements to the XTRAN3S computer program, a code for calculation of steady and unsteady aerodynamics, and associated aeroelastic solutions, for 3-D wings in the transonic flow regime are described. Algorithm improvements for the XTRAN3S program were provided including an implicit finite difference scheme to enhance the allowable time step and vectorization for improved computational efficiency. The code was modified to treat configurations with a fuselage, multiple stores/nacelles/pylons, and winglets. Computer program changes (updates) for error corrections and updates for version control are provided.

Pre-engineering Spaceflight Validation of Environmental Models and the 2005 HZETRN Simulation Code

NASA Technical Reports Server (NTRS)

Nealy, John E.; Cucinotta, Francis A.; Wilson, John W.; Badavi, Francis F.; Dachev, Ts. P.; Tomov, B. T.; Walker, Steven A.; DeAngelis, Giovanni; Blattnig, Steve R.; Atwell, William

2006-01-01

The HZETRN code has been identified by NASA for engineering design in the next phase of space exploration highlighting a return to the Moon in preparation for a Mars mission. In response, a new series of algorithms beginning with 2005 HZETRN, will be issued by correcting some prior limitations and improving control of propagated errors along with established code verification processes. Code validation processes will use new/improved low Earth orbit (LEO) environmental models with a recently improved International Space Station (ISS) shield model to validate computational models and procedures using measured data aboard ISS. These validated models will provide a basis for flight-testing the designs of future space vehicles and systems of the Constellation program in the LEO environment.

Detection and avoidance of errors in computer software

NASA Technical Reports Server (NTRS)

Kinsler, Les

1989-01-01

The acceptance test errors of a computer software project to determine if the errors could be detected or avoided in earlier phases of development. GROAGSS (Gamma Ray Observatory Attitude Ground Support System) was selected as the software project to be examined. The development of the software followed the standard Flight Dynamics Software Development methods. GROAGSS was developed between August 1985 and April 1989. The project is approximately 250,000 lines of code of which approximately 43,000 lines are reused from previous projects. GROAGSS had a total of 1715 Change Report Forms (CRFs) submitted during the entire development and testing. These changes contained 936 errors. Of these 936 errors, 374 were found during the acceptance testing. These acceptance test errors were first categorized into methods of avoidance including: more clearly written requirements; detail review; code reading; structural unit testing; and functional system integration testing. The errors were later broken down in terms of effort to detect and correct, class of error, and probability that the prescribed detection method would be successful. These determinations were based on Software Engineering Laboratory (SEL) documents and interviews with the project programmers. A summary of the results of the categorizations is presented. The number of programming errors at the beginning of acceptance testing can be significantly reduced. The results of the existing development methodology are examined for ways of improvements. A basis is provided for the definition is a new development/testing paradigm. Monitoring of the new scheme will objectively determine its effectiveness on avoiding and detecting errors.

Modified linear predictive coding approach for moving target tracking by Doppler radar

NASA Astrophysics Data System (ADS)

Ding, Yipeng; Lin, Xiaoyi; Sun, Ke-Hui; Xu, Xue-Mei; Liu, Xi-Yao

2016-07-01

Doppler radar is a cost-effective tool for moving target tracking, which can support a large range of civilian and military applications. A modified linear predictive coding (LPC) approach is proposed to increase the target localization accuracy of the Doppler radar. Based on the time-frequency analysis of the received echo, the proposed approach first real-time estimates the noise statistical parameters and constructs an adaptive filter to intelligently suppress the noise interference. Then, a linear predictive model is applied to extend the available data, which can help improve the resolution of the target localization result. Compared with the traditional LPC method, which empirically decides the extension data length, the proposed approach develops an error array to evaluate the prediction accuracy and thus, adjust the optimum extension data length intelligently. Finally, the prediction error array is superimposed with the predictor output to correct the prediction error. A series of experiments are conducted to illustrate the validity and performance of the proposed techniques.

Genetic Code Analysis Toolkit: A novel tool to explore the coding properties of the genetic code and DNA sequences

NASA Astrophysics Data System (ADS)

Kraljić, K.; Strüngmann, L.; Fimmel, E.; Gumbel, M.

2018-01-01

The genetic code is degenerated and it is assumed that redundancy provides error detection and correction mechanisms in the translation process. However, the biological meaning of the code's structure is still under current research. This paper presents a Genetic Code Analysis Toolkit (GCAT) which provides workflows and algorithms for the analysis of the structure of nucleotide sequences. In particular, sets or sequences of codons can be transformed and tested for circularity, comma-freeness, dichotomic partitions and others. GCAT comes with a fertile editor custom-built to work with the genetic code and a batch mode for multi-sequence processing. With the ability to read FASTA files or load sequences from GenBank, the tool can be used for the mathematical and statistical analysis of existing sequence data. GCAT is Java-based and provides a plug-in concept for extensibility. Availability: Open source Homepage:http://www.gcat.bio/

The decoding of Reed-Solomon codes

NASA Technical Reports Server (NTRS)

Mceliece, R. J.

1988-01-01

Reed-Solomon (RS) codes form an important part of the high-rate downlink telemetry system for the Magellan mission, and the RS decoding function for this project will be done by DSN. Although the basic idea behind all Reed-Solomon decoding algorithms was developed by Berlekamp in 1968, there are dozens of variants of Berlekamp's algorithm in current use. An attempt to restore order is made by presenting a mathematical theory which explains the working of almost all known RS decoding algorithms. The key innovation that makes this possible is the unified approach to the solution of the key equation, which simultaneously describes the Berlekamp, Berlekamp-Massey, Euclid, and continued fractions approaches. Additionally, a detailed analysis is made of what can happen to a generic RS decoding algorithm when the number of errors and erasures exceeds the code's designed correction capability, and it is shown that while most published algorithms do not detect as many of these error-erasure patterns as possible, by making a small change in the algorithms, this problem can be overcome.

SeqLib: a C ++ API for rapid BAM manipulation, sequence alignment and sequence assembly

PubMed Central

Wala, Jeremiah; Beroukhim, Rameen

2017-01-01

Abstract We present SeqLib, a C ++ API and command line tool that provides a rapid and user-friendly interface to BAM/SAM/CRAM files, global sequence alignment operations and sequence assembly. Four C libraries perform core operations in SeqLib: HTSlib for BAM access, BWA-MEM and BLAT for sequence alignment and Fermi for error correction and sequence assembly. Benchmarking indicates that SeqLib has lower CPU and memory requirements than leading C ++ sequence analysis APIs. We demonstrate an example of how minimal SeqLib code can extract, error-correct and assemble reads from a CRAM file and then align with BWA-MEM. SeqLib also provides additional capabilities, including chromosome-aware interval queries and read plotting. Command line tools are available for performing integrated error correction, micro-assemblies and alignment. Availability and Implementation: SeqLib is available on Linux and OSX for the C ++98 standard and later at github.com/walaj/SeqLib. SeqLib is released under the Apache2 license. Additional capabilities for BLAT alignment are available under the BLAT license. Contact: jwala@broadinstitue.org; rameen@broadinstitute.org PMID:28011768

Two-step single slope/SAR ADC with error correction for CMOS image sensor.

PubMed

Tang, Fang; Bermak, Amine; Amira, Abbes; Amor Benammar, Mohieddine; He, Debiao; Zhao, Xiaojin

2014-01-01

Conventional two-step ADC for CMOS image sensor requires full resolution noise performance in the first stage single slope ADC, leading to high power consumption and large chip area. This paper presents an 11-bit two-step single slope/successive approximation register (SAR) ADC scheme for CMOS image sensor applications. The first stage single slope ADC generates a 3-bit data and 1 redundant bit. The redundant bit is combined with the following 8-bit SAR ADC output code using a proposed error correction algorithm. Instead of requiring full resolution noise performance, the first stage single slope circuit of the proposed ADC can tolerate up to 3.125% quantization noise. With the proposed error correction mechanism, the power consumption and chip area of the single slope ADC are significantly reduced. The prototype ADC is fabricated using 0.18 μ m CMOS technology. The chip area of the proposed ADC is 7 μ m × 500 μ m. The measurement results show that the energy efficiency figure-of-merit (FOM) of the proposed ADC core is only 125 pJ/sample under 1.4 V power supply and the chip area efficiency is 84 k  μ m(2) · cycles/sample.

SeqLib: a C ++ API for rapid BAM manipulation, sequence alignment and sequence assembly.

PubMed

Wala, Jeremiah; Beroukhim, Rameen

2017-03-01

We present SeqLib, a C ++ API and command line tool that provides a rapid and user-friendly interface to BAM/SAM/CRAM files, global sequence alignment operations and sequence assembly. Four C libraries perform core operations in SeqLib: HTSlib for BAM access, BWA-MEM and BLAT for sequence alignment and Fermi for error correction and sequence assembly. Benchmarking indicates that SeqLib has lower CPU and memory requirements than leading C ++ sequence analysis APIs. We demonstrate an example of how minimal SeqLib code can extract, error-correct and assemble reads from a CRAM file and then align with BWA-MEM. SeqLib also provides additional capabilities, including chromosome-aware interval queries and read plotting. Command line tools are available for performing integrated error correction, micro-assemblies and alignment. SeqLib is available on Linux and OSX for the C ++98 standard and later at github.com/walaj/SeqLib. SeqLib is released under the Apache2 license. Additional capabilities for BLAT alignment are available under the BLAT license. jwala@broadinstitue.org ; rameen@broadinstitute.org. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Nonuniform code concatenation for universal fault-tolerant quantum computing

NASA Astrophysics Data System (ADS)

Nikahd, Eesa; Sedighi, Mehdi; Saheb Zamani, Morteza

2017-09-01

Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state distillation, code switching, or code concatenation to achieve universality. In this paper we propose an alternative approach for universal fault-tolerant quantum computing, mainly based on the code concatenation approach proposed in [T. Jochym-O'Connor and R. Laflamme, Phys. Rev. Lett. 112, 010505 (2014), 10.1103/PhysRevLett.112.010505], but in a nonuniform fashion. The proposed approach is described based on nonuniform concatenation of the 7-qubit Steane code with the 15-qubit Reed-Muller code, as well as the 5-qubit code with the 15-qubit Reed-Muller code, which lead to two 49-qubit and 47-qubit codes, respectively. These codes can correct any arbitrary single physical error with the ability to perform a universal set of fault-tolerant gates, without using magic state distillation.

A burst-mode photon counting receiver with automatic channel estimation and bit rate detection

NASA Astrophysics Data System (ADS)

Rao, Hemonth G.; DeVoe, Catherine E.; Fletcher, Andrew S.; Gaschits, Igor D.; Hakimi, Farhad; Hamilton, Scott A.; Hardy, Nicholas D.; Ingwersen, John G.; Kaminsky, Richard D.; Moores, John D.; Scheinbart, Marvin S.; Yarnall, Timothy M.

2016-04-01

We demonstrate a multi-rate burst-mode photon-counting receiver for undersea communication at data rates up to 10.416 Mb/s over a 30-foot water channel. To the best of our knowledge, this is the first demonstration of burst-mode photon-counting communication. With added attenuation, the maximum link loss is 97.1 dB at λ=517 nm. In clear ocean water, this equates to link distances up to 148 meters. For λ=470 nm, the achievable link distance in clear ocean water is 450 meters. The receiver incorporates soft-decision forward error correction (FEC) based on a product code of an inner LDPC code and an outer BCH code. The FEC supports multiple code rates to achieve error-free performance. We have selected a burst-mode receiver architecture to provide robust performance with respect to unpredictable channel obstructions. The receiver is capable of on-the-fly data rate detection and adapts to changing levels of signal and background light. The receiver updates its phase alignment and channel estimates every 1.6 ms, allowing for rapid changes in water quality as well as motion between transmitter and receiver. We demonstrate on-the-fly rate detection, channel BER within 0.2 dB of theory across all data rates, and error-free performance within 1.82 dB of soft-decision capacity across all tested code rates. All signal processing is done in FPGAs and runs continuously in real time.

Effect of initial phase on error in electron energy obtained using paraxial approximation for a focused laser pulse in vacuum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Kunwar Pal, E-mail: k-psingh@yahoo.com; Department of Physics, Shri Venkateshwara University, Gajraula, Amroha, Uttar Pradesh 244236; Arya, Rashmi

2015-09-14

We have investigated the effect of initial phase on error in electron energy obtained using paraxial approximation to study electron acceleration by a focused laser pulse in vacuum using a three dimensional test-particle simulation code. The error is obtained by comparing the energy of the electron for paraxial approximation and seventh-order correction description of the fields of Gaussian laser. The paraxial approximation predicts wrong laser divergence and wrong electron escape time from the pulse which leads to prediction of higher energy. The error shows strong phase dependence for the electrons lying along the axis of the laser for linearly polarizedmore » laser pulse. The relative error may be significant for some specific values of initial phase even at moderate values of laser spot sizes. The error does not show initial phase dependence for a circularly laser pulse.« less

Modeling error distributions of growth curve models through Bayesian methods.

PubMed

Zhang, Zhiyong

2016-06-01

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is proposed to flexibly model normal and non-normal data through the explicit specification of the error distributions. A simulation study shows when the distribution of the error is correctly specified, one can avoid the loss in the efficiency of standard error estimates. A real example on the analysis of mathematical ability growth data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 is used to show the application of the proposed methods. Instructions and code on how to conduct growth curve analysis with both normal and non-normal error distributions using the the MCMC procedure of SAS are provided.

Surface code quantum communication.

PubMed

Fowler, Austin G; Wang, David S; Hill, Charles D; Ladd, Thaddeus D; Van Meter, Rodney; Hollenberg, Lloyd C L

2010-05-07

Quantum communication typically involves a linear chain of repeater stations, each capable of reliable local quantum computation and connected to their nearest neighbors by unreliable communication links. The communication rate of existing protocols is low as two-way classical communication is used. By using a surface code across the repeater chain and generating Bell pairs between neighboring stations with probability of heralded success greater than 0.65 and fidelity greater than 0.96, we show that two-way communication can be avoided and quantum information can be sent over arbitrary distances with arbitrarily low error at a rate limited only by the local gate speed. This is achieved by using the unreliable Bell pairs to measure nonlocal stabilizers and feeding heralded failure information into post-transmission error correction. Our scheme also applies when the probability of heralded success is arbitrarily low.

Flow-Centric, Back-in-Time Debugging

NASA Astrophysics Data System (ADS)

Lienhard, Adrian; Fierz, Julien; Nierstrasz, Oscar

Conventional debugging tools present developers with means to explore the run-time context in which an error has occurred. In many cases this is enough to help the developer discover the faulty source code and correct it. However, rather often errors occur due to code that has executed in the past, leaving certain objects in an inconsistent state. The actual run-time error only occurs when these inconsistent objects are used later in the program. So-called back-in-time debuggers help developers step back through earlier states of the program and explore execution contexts not available to conventional debuggers. Nevertheless, even Back-in-Time Debuggers do not help answer the question, “Where did this object come from?” The Object-Flow Virtual Machine, which we have proposed in previous work, tracks the flow of objects to answer precisely such questions, but this VM does not provide dedicated debugging support to explore faulty programs. In this paper we present a novel debugger, called Compass, to navigate between conventional run-time stack-oriented control flow views and object flows. Compass enables a developer to effectively navigate from an object contributing to an error back-in-time through all the code that has touched the object. We present the design and implementation of Compass, and we demonstrate how flow-centric, back-in-time debugging can be used to effectively locate the source of hard-to-find bugs.

Crack Turning and Arrest Mechanisms for Integral Structure

NASA Technical Reports Server (NTRS)

Pettit, Richard; Ingraffea, Anthony

1999-01-01

In the course of several years of research efforts to predict crack turning and flapping in aircraft fuselage structures and other problems related to crack turning, the 2nd order maximum tangential stress theory has been identified as the theory most capable of predicting the observed test results. This theory requires knowledge of a material specific characteristic length, and also a computation of the stress intensity factors and the T-stress, or second order term in the asymptotic stress field in the vicinity of the crack tip. A characteristic length, r(sub c), is proposed for ductile materials pertaining to the onset of plastic instability, as opposed to the void spacing theories espoused by previous investigators. For the plane stress case, an approximate estimate of r(sub c), is obtained from the asymptotic field for strain hardening materials given by Hutchinson, Rice and Rosengren (HRR). A previous study using of high order finite element methods to calculate T-stresses by contour integrals resulted in extremely high accuracy values obtained for selected test specimen geometries, and a theoretical error estimation parameter was defined. In the present study, it is shown that a large portion of the error in finite element computations of both K and T are systematic, and can be corrected after the initial solution if the finite element implementation utilizes a similar crack tip discretization scheme for all problems. This scheme is applied for two-dimensional problems to a both a p-version finite element code, showing that sufficiently accurate values of both K(sub I) and T can be obtained with fairly low order elements if correction is used. T-stress correction coefficients are also developed for the singular crack tip rosette utilized in the adaptive mesh finite element code FRANC2D, and shown to reduce the error in the computed T-stress significantly. Stress intensity factor correction was not attempted for FRANC2D because it employs a highly accurate quarter-point scheme to obtain stress intensity factors.

Erratum: Binary neutron stars with arbitrary spins in numerical relativity [Phys. Rev. D 92, 124012 (2015)

NASA Astrophysics Data System (ADS)

Tacik, Nick; Foucart, Francois; Pfeiffer, Harald P.; Haas, Roland; Ossokine, Serguei; Kaplan, Jeff; Muhlberger, Curran; Duez, Matt D.; Kidder, Lawrence E.; Scheel, Mark A.; Szilágyi, Béla

2016-08-01

The code used in [Phys. Rev. D 92, 124012 (2015)] erroneously computed the enthalpy at the center of the neutron stars. Upon correcting this error, density oscillations in evolutions of rotating neutron stars are significantly reduced (from ˜20 % to ˜0.5 % ). Furthermore, it is possible to construct neutron stars with faster rotation rates.

ERRATUM: "Search for High-Energy Muon Neutrinos from the "Naked-Eye" GRB 080319B with the Icecube Neutrino Telescope" (2009, ApJ, 701, 1721)

NASA Astrophysics Data System (ADS)

Abbasi, R.; Abdou, Y.; Ackermann, M.; Adams, J.; Ahlers, M.; Andeen, K.; Auffenberg, J.; Bai, X.; Baker, M.; Barwick, S. W.; Bay, R.; Bazo Alba, J. L.; Beattie, K.; Bechet, S.; Becker, J. K.; Becker, K.-H.; Benabderrahmane, M. L.; Berdermann, J.; Berghaus, P.; Berley, D.; Bernardini, E.; Bertrand, D.; Besson, D. Z.; Bissok, M.; Blaufuss, E.; Boersma, D. J.; Bohm, C.; Bolmont, J.; Böser, S.; Botner, O.; Bradley, L.; Braun, J.; Breder, D.; Burgess, T.; Castermans, T.; Chirkin, D.; Christy, B.; Clem, J.; Cohen, S.; Cowen, D. F.; D'Agostino, M. V.; Danninger, M.; Day, C. T.; De Clercq, C.; Demirörs, L.; Depaepe, O.; Descamps, F.; Desiati, P.; de Vries-Uiterweerd, G.; DeYoung, T.; Diaz-Velez, J. C.; Dreyer, J.; Dumm, J. P.; Duvoort, M. R.; Edwards, W. R.; Ehrlich, R.; Eisch, J.; Ellsworth, R. W.; Engdegård, O.; Euler, S.; Evenson, P. A.; Fadiran, O.; Fazely, A. R.; Feusels, T.; Filimonov, K.; Finley, C.; Foerster, M. M.; Fox, B. D.; Franckowiak, A.; Franke, R.; Gaisser, T. K.; Gallagher, J.; Ganugapati, R.; Gerhardt, L.; Gladstone, L.; Goldschmidt, A.; Goodman, J. A.; Gozzini, R.; Grant, D.; Griesel, T.; Groß, A.; Grullon, S.; Gunasingha, R. M.; Gurtner, M.; Ha, C.; Hallgren, A.; Halzen, F.; Han, K.; Hanson, K.; Hasegawa, Y.; Heise, J.; Helbing, K.; Herquet, P.; Hickford, S.; Hill, G. C.; Hoffman, K. D.; Hoshina, K.; Hubert, D.; Huelsnitz, W.; Hülß, J.-P.; Hulth, P. O.; Hultqvist, K.; Hussain, S.; Imlay, R. L.; Inaba, M.; Ishihara, A.; Jacobsen, J.; Japaridze, G. S.; Johansson, H.; Joseph, J. M.; Kampert, K.-H.; Kappes, A.; Karg, T.; Karle, A.; Kelley, J. L.; Kenny, P.; Kiryluk, J.; Kislat, F.; Klein, S. R.; Klepser, S.; Knops, S.; Kohnen, G.; Kolanoski, H.; Köpke, L.; Kowalski, M.; Kowarik, T.; Krasberg, M.; Kuehn, K.; Kuwabara, T.; Labare, M.; Laihem, K.; Landsman, H.; Lauer, R.; Leich, H.; Lennarz, D.; Lucke, A.; Lundberg, J.; Lünemann, J.; Madsen, J.; Majumdar, P.; Maruyama, R.; Mase, K.; Matis, H. S.; McParland, C. P.; Meagher, K.; Merck, M.; Mészáros, P.; Middell, E.; Milke, N.; Miyamoto, H.; Mohr, A.; Montaruli, T.; Morse, R.; Movit, S. M.; Münich, K.; Nahnhauer, R.; Nam, J. W.; Nießen, P.; Nygren, D. R.; Odrowski, S.; Olivas, A.; Olivo, M.; Ono, M.; Panknin, S.; Patton, S.; Pérez de los Heros, C.; Petrovic, J.; Piegsa, A.; Pieloth, D.; Pohl, A. C.; Porrata, R.; Potthoff, N.; Price, P. B.; Prikockis, M.; Przybylski, G. T.; Rawlins, K.; Redl, P.; Resconi, E.; Rhode, W.; Ribordy, M.; Rizzo, A.; Rodrigues, J. P.; Roth, P.; Rothmaier, F.; Rott, C.; Roucelle, C.; Rutledge, D.; Ryckbosch, D.; Sander, H.-G.; Sarkar, S.; Satalecka, K.; Schlenstedt, S.; Schmidt, T.; Schneider, D.; Schukraft, A.; Schulz, O.; Schunck, M.; Seckel, D.; Semburg, B.; Seo, S. H.; Sestayo, Y.; Seunarine, S.; Silvestri, A.; Slipak, A.; Spiczak, G. M.; Spiering, C.; Stamatikos, M.; Stanev, T.; Stephens, G.; Stezelberger, T.; Stokstad, R. G.; Stoufer, M. C.; Stoyanov, S.; Strahler, E. A.; Straszheim, T.; Sulanke, K.-H.; Sullivan, G. W.; Swillens, Q.; Taboada, I.; Tarasova, O.; Tepe, A.; Ter-Antonyan, S.; Terranova, C.; Tilav, S.; Tluczykont, M.; Toale, P. A.; Tosi, D.; Turčan, D.; van Eijndhoven, N.; Vandenbroucke, J.; Van Overloop, A.; Voigt, B.; Walck, C.; Waldenmaier, T.; Walter, M.; Wendt, C.; Westerhoff, S.; Whitehorn, N.; Wiebusch, C. H.; Wiedemann, A.; Wikström, G.; Williams, D. R.; Wischnewski, R.; Wissing, H.; Woschnagg, K.; Xu, X. W.; Yodh, G.; Yoshida, S.; IceCube Collaboration

2010-01-01

We have noticed some mistakes in formulae (A2) and (A5) in the appendix of our paper. The errors are not present in the code used in the analysis and hence none of the plots or results is affected. The correct formulae are

Integrated source and channel encoded digital communication system design study

NASA Technical Reports Server (NTRS)

Huth, G. K.; Trumpis, B. D.; Udalov, S.

1975-01-01

Various aspects of space shuttle communication systems were studied. The following major areas were investigated: burst error correction for shuttle command channels; performance optimization and design considerations for Costas receivers with and without bandpass limiting; experimental techniques for measuring low level spectral components of microwave signals; and potential modulation and coding techniques for the Ku-band return link. Results are presented.

Sequencing artifacts in the type A influenza databases and attempts to correct them.

PubMed

Suarez, David L; Chester, Nikki; Hatfield, Jason

2014-07-01

There are over 276 000 influenza gene sequences in public databases, with the quality of the sequences determined by the contributor. As part of a high school class project, influenza sequences with possible errors were identified in the public databases based on the size of the gene being longer than expected, with the hypothesis that these sequences would have an error. Students contacted sequence submitters alerting them of the possible sequence issue(s) and requested they the suspect sequence(s) be correct as appropriate. Type A influenza viruses were screened, and gene segments longer than the accepted size were identified for further analysis. Attention was placed on sequences with additional nucleotides upstream or downstream of the highly conserved non-coding ends of the viral segments. A total of 1081 sequences were identified that met this criterion. Three types of errors were commonly observed: non-influenza primer sequence wasn't removed from the sequence; PCR product was cloned and plasmid sequence was included in the sequence; and Taq polymerase added an adenine at the end of the PCR product. Internal insertions of nucleotide sequence were also commonly observed, but in many cases it was unclear if the sequence was correct or actually contained an error. A total of 215 sequences, or 22.8% of the suspect sequences, were corrected in the public databases in the first year of the student project. Unfortunately 138 additional sequences with possible errors were added to the databases in the second year. Additional awareness of the need for data integrity of sequences submitted to public databases is needed to fully reap the benefits of these large data sets. © 2014 The Authors. Influenza and Other Respiratory Viruses Published by John Wiley & Sons Ltd.

Reliable Wireless Broadcast with Linear Network Coding for Multipoint-to-Multipoint Real-Time Communications

NASA Astrophysics Data System (ADS)

Kondo, Yoshihisa; Yomo, Hiroyuki; Yamaguchi, Shinji; Davis, Peter; Miura, Ryu; Obana, Sadao; Sampei, Seiichi

This paper proposes multipoint-to-multipoint (MPtoMP) real-time broadcast transmission using network coding for ad-hoc networks like video game networks. We aim to achieve highly reliable MPtoMP broadcasting using IEEE 802.11 media access control (MAC) that does not include a retransmission mechanism. When each node detects packets from the other nodes in a sequence, the correctly detected packets are network-encoded, and the encoded packet is broadcasted in the next sequence as a piggy-back for its native packet. To prevent increase of overhead in each packet due to piggy-back packet transmission, network coding vector for each node is exchanged between all nodes in the negotiation phase. Each user keeps using the same coding vector generated in the negotiation phase, and only coding information that represents which user signal is included in the network coding process is transmitted along with the piggy-back packet. Our simulation results show that the proposed method can provide higher reliability than other schemes using multi point relay (MPR) or redundant transmissions such as forward error correction (FEC). We also implement the proposed method in a wireless testbed, and show that the proposed method achieves high reliability in a real-world environment with a practical degree of complexity when installed on current wireless devices.

Extensions and improvements on XTRAN3S

NASA Technical Reports Server (NTRS)

Borland, C. J.

1989-01-01

Improvements to the XTRAN3S computer program are summarized. Work on this code, for steady and unsteady aerodynamic and aeroelastic analysis in the transonic flow regime has concentrated on the following areas: (1) Maintenance of the XTRAN3S code, including correction of errors, enhancement of operational capability, and installation on the Cray X-MP system; (2) Extension of the vectorization concepts in XTRAN3S to include additional areas of the code for improved execution speed; (3) Modification of the XTRAN3S algorithm for improved numerical stability for swept, tapered wing cases and improved computational efficiency; and (4) Extension of the wing-only version of XTRAN3S to include pylon and nacelle or external store capability.

Machine Learned Replacement of N-Labels for Basecalled Sequences in DNA Barcoding.

PubMed

Ma, Eddie Y T; Ratnasingham, Sujeevan; Kremer, Stefan C

2018-01-01

This study presents a machine learning method that increases the number of identified bases in Sanger Sequencing. The system post-processes a KB basecalled chromatogram. It selects a recoverable subset of N-labels in the KB-called chromatogram to replace with basecalls (A,C,G,T). An N-label correction is defined given an additional read of the same sequence, and a human finished sequence. Corrections are added to the dataset when an alignment determines the additional read and human agree on the identity of the N-label. KB must also rate the replacement with quality value of in the additional read. Corrections are only available during system training. Developing the system, nearly 850,000 N-labels are obtained from Barcode of Life Datasystems, the premier database of genetic markers called DNA Barcodes. Increasing the number of correct bases improves reference sequence reliability, increases sequence identification accuracy, and assures analysis correctness. Keeping with barcoding standards, our system maintains an error rate of percent. Our system only applies corrections when it estimates low rate of error. Tested on this data, our automation selects and recovers: 79 percent of N-labels from COI (animal barcode); 80 percent from matK and rbcL (plant barcodes); and 58 percent from non-protein-coding sequences (across eukaryotes).

Decoder synchronization for deep space missions

NASA Technical Reports Server (NTRS)

Statman, J. I.; Cheung, K.-M.; Chauvin, T. H.; Rabkin, J.; Belongie, M. L.

1994-01-01

The Consultative Committee for Space Data Standards (CCSDS) recommends that space communication links employ a concatenated, error-correcting, channel-coding system in which the inner code is a convolutional (7,1/2) code and the outer code is a (255,223) Reed-Solomon code. The traditional implementation is to perform the node synchronization for the Viterbi decoder and the frame synchronization for the Reed-Solomon decoder as separate, sequential operations. This article discusses a unified synchronization technique that is required for deep space missions that have data rates and signal-to-noise ratios (SNR's) that are extremely low. This technique combines frame synchronization in the bit and symbol domains and traditional accumulated-metric growth techniques to establish a joint frame and node synchronization. A variation on this technique is used for the Galileo spacecraft on its Jupiter-bound mission.

H.264 Layered Coded Video over Wireless Networks: Channel Coding and Modulation Constraints

NASA Astrophysics Data System (ADS)

Ghandi, M. M.; Barmada, B.; Jones, E. V.; Ghanbari, M.

2006-12-01

This paper considers the prioritised transmission of H.264 layered coded video over wireless channels. For appropriate protection of video data, methods such as prioritised forward error correction coding (FEC) or hierarchical quadrature amplitude modulation (HQAM) can be employed, but each imposes system constraints. FEC provides good protection but at the price of a high overhead and complexity. HQAM is less complex and does not introduce any overhead, but permits only fixed data ratios between the priority layers. Such constraints are analysed and practical solutions are proposed for layered transmission of data-partitioned and SNR-scalable coded video where combinations of HQAM and FEC are used to exploit the advantages of both coding methods. Simulation results show that the flexibility of SNR scalability and absence of picture drift imply that SNR scalability as modelled is superior to data partitioning in such applications.

Application of Exactly Linearized Error Transport Equations to AIAA CFD Prediction Workshops

NASA Technical Reports Server (NTRS)

Derlaga, Joseph M.; Park, Michael A.; Rallabhandi, Sriram

2017-01-01

The computational fluid dynamics (CFD) prediction workshops sponsored by the AIAA have created invaluable opportunities in which to discuss the predictive capabilities of CFD in areas in which it has struggled, e.g., cruise drag, high-lift, and sonic boom pre diction. While there are many factors that contribute to disagreement between simulated and experimental results, such as modeling or discretization error, quantifying the errors contained in a simulation is important for those who make decisions based on the computational results. The linearized error transport equations (ETE) combined with a truncation error estimate is a method to quantify one source of errors. The ETE are implemented with a complex-step method to provide an exact linearization with minimal source code modifications to CFD and multidisciplinary analysis methods. The equivalency of adjoint and linearized ETE functional error correction is demonstrated. Uniformly refined grids from a series of AIAA prediction workshops demonstrate the utility of ETE for multidisciplinary analysis with a connection between estimated discretization error and (resolved or under-resolved) flow features.

High speed fault tolerant secure communication for muon chamber using FPGA based GBTx emulator

NASA Astrophysics Data System (ADS)

Sau, Suman; Mandal, Swagata; Saini, Jogender; Chakrabarti, Amlan; Chattopadhyay, Subhasis

2015-12-01

The Compressed Baryonic Matter (CBM) experiment is a part of the Facility for Antiproton and Ion Research (FAIR) in Darmstadt at the GSI. The CBM experiment will investigate the highly compressed nuclear matter using nucleus-nucleus collisions. This experiment will examine lieavy-ion collisions in fixed target geometry and will be able to measure hadrons, electrons and muons. CBM requires precise time synchronization, compact hardware, radiation tolerance, self-triggered front-end electronics, efficient data aggregation schemes and capability to handle high data rate (up to several TB/s). As a part of the implementation of read out chain of Muon Cliamber(MUCH) [1] in India, we have tried to implement FPGA based emulator of GBTx in India. GBTx is a radiation tolerant ASIC that can be used to implement multipurpose high speed bidirectional optical links for high-energy physics (HEP) experiments and is developed by CERN. GBTx will be used in highly irradiated area and more prone to be affected by multi bit error. To mitigate this effect instead of single bit error correcting RS code we have used two bit error correcting (15, 7) BCH code. It will increase the redundancy which in turn increases the reliability of the coded data. So the coded data will be less prone to be affected by noise due to radiation. The data will go from detector to PC through multiple nodes through the communication channel. The computing resources are connected to a network which can be accessed by authorized person to prevent unauthorized data access which might happen by compromising the network security. Thus data encryption is essential. In order to make the data communication secure, advanced encryption standard [2] (AES - a symmetric key cryptography) and RSA [3], [4] (asymmetric key cryptography) are used after the channel coding. We have implemented GBTx emulator on two Xilinx Kintex-7 boards (KC705). One will act as transmitter and other will act as receiver and they are connected through optical fiber through small form-factor pluggable (SFP) port. We have tested the setup in the runtime environment using Xilinx Cliipscope Pro Analyzer. We also measure the resource utilization, throughput., power optimization of implemented design.

Enhanced intercarrier interference mitigation based on encoded bit-sequence distribution inside optical superchannels

NASA Astrophysics Data System (ADS)

Torres, Jhon James Granada; Soto, Ana María Cárdenas; González, Neil Guerrero

2016-10-01

In the context of gridless optical multicarrier systems, we propose a method for intercarrier interference (ICI) mitigation which allows bit error correction in scenarios of nonspectral flatness between the subcarriers composing the multicarrier system and sub-Nyquist carrier spacing. We propose a hybrid ICI mitigation technique which exploits the advantages of signal equalization at both levels: the physical level for any digital and analog pulse shaping, and the bit-data level and its ability to incorporate advanced correcting codes. The concatenation of these two complementary techniques consists of a nondata-aided equalizer applied to each optical subcarrier, and a hard-decision forward error correction applied to the sequence of bits distributed along the optical subcarriers regardless of prior subchannel quality assessment as performed in orthogonal frequency-division multiplexing modulations for the implementation of the bit-loading technique. The impact of the ICI is systematically evaluated in terms of bit-error-rate as a function of the carrier frequency spacing and the roll-off factor of the digital pulse-shaping filter for a simulated 3×32-Gbaud single-polarization quadrature phase shift keying Nyquist-wavelength division multiplexing system. After the ICI mitigation, a back-to-back error-free decoding was obtained for sub-Nyquist carrier spacings of 28.5 and 30 GHz and roll-off values of 0.1 and 0.4, respectively.

Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Armstrong, Derek Elswick

This report discusses the mathematical procedures used to convert raw interferograms from Fourier transform infrared (FTIR) sensors to calibrated spectra. The work discussed in this report was completed as part of the Helios project at Los Alamos National Laboratory. MATLAB code was developed to convert the raw interferograms to calibrated spectra. The report summarizes the developed MATLAB scripts and functions, along with a description of the mathematical methods used by the code. The first step in working with raw interferograms is to convert them to uncalibrated spectra by applying an apodization function to the raw data and then by performingmore » a Fourier transform. The developed MATLAB code also addresses phase error correction by applying the Mertz method. This report provides documentation for the MATLAB scripts.« less

Embodying Others in Immersive Virtual Reality: Electro-Cortical Signatures of Monitoring the Errors in the Actions of an Avatar Seen from a First-Person Perspective.

PubMed

Pavone, Enea Francesco; Tieri, Gaetano; Rizza, Giulia; Tidoni, Emmanuele; Grisoni, Luigi; Aglioti, Salvatore Maria

2016-01-13

Brain monitoring of errors in one's own and other's actions is crucial for a variety of processes, ranging from the fine-tuning of motor skill learning to important social functions, such as reading out and anticipating the intentions of others. Here, we combined immersive virtual reality and EEG recording to explore whether embodying the errors of an avatar by seeing it from a first-person perspective may activate the error monitoring system in the brain of an onlooker. We asked healthy participants to observe, from a first- or third-person perspective, an avatar performing a correct or an incorrect reach-to-grasp movement toward one of two virtual mugs placed on a table. At the end of each trial, participants reported verbally how much they embodied the avatar's arm. Ratings were maximal in first-person perspective, indicating that immersive virtual reality can be a powerful tool to induce embodiment of an artificial agent, even through mere visual perception and in the absence of any cross-modal boosting. Observation of erroneous grasping from a first-person perspective enhanced error-related negativity and medial-frontal theta power in the trials where human onlookers embodied the virtual character, hinting at the tight link between early, automatic coding of error detection and sense of embodiment. Error positivity was similar in 1PP and 3PP, suggesting that conscious coding of errors is similar for self and other. Thus, embodiment plays an important role in activating specific components of the action monitoring system when others' errors are coded as if they are one's own errors. Detecting errors in other's actions is crucial for social functions, such as reading out and anticipating the intentions of others. Using immersive virtual reality and EEG recording, we explored how the brain of an onlooker reacted to the errors of an avatar seen from a first-person perspective. We found that mere observation of erroneous actions enhances electrocortical markers of error detection in the trials where human onlookers embodied the virtual character. Thus, the cerebral system for action monitoring is maximally activated when others' errors are coded as if they are one's own errors. The results have important implications for understanding how the brain can control the external world and thus creating new brain-computer interfaces. Copyright © 2016 the authors 0270-6474/16/360268-12$15.00/0.

Fault-tolerant logical gates in quantum error-correcting codes

NASA Astrophysics Data System (ADS)

Pastawski, Fernando; Yoshida, Beni

2015-01-01

Recently, S. Bravyi and R. König [Phys. Rev. Lett. 110, 170503 (2013), 10.1103/PhysRevLett.110.170503] have shown that there is a trade-off between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a constant-depth geometrically local circuit and are thus fault tolerant by construction. In particular, they show that, for local stabilizer codes in D spatial dimensions, locality-preserving gates are restricted to a set of unitary gates known as the D th level of the Clifford hierarchy. In this paper, we explore this idea further by providing several extensions and applications of their characterization to qubit stabilizer and subsystem codes. First, we present a no-go theorem for self-correcting quantum memory. Namely, we prove that a three-dimensional stabilizer Hamiltonian with a locality-preserving implementation of a non-Clifford gate cannot have a macroscopic energy barrier. This result implies that non-Clifford gates do not admit such implementations in Haah's cubic code and Michnicki's welded code. Second, we prove that the code distance of a D -dimensional local stabilizer code with a nontrivial locality-preserving m th -level Clifford logical gate is upper bounded by O (LD +1 -m) . For codes with non-Clifford gates (m >2 ), this improves the previous best bound by S. Bravyi and B. Terhal [New. J. Phys. 11, 043029 (2009), 10.1088/1367-2630/11/4/043029]. Topological color codes, introduced by H. Bombin and M. A. Martin-Delgado [Phys. Rev. Lett. 97, 180501 (2006), 10.1103/PhysRevLett.97.180501; Phys. Rev. Lett. 98, 160502 (2007), 10.1103/PhysRevLett.98.160502; Phys. Rev. B 75, 075103 (2007), 10.1103/PhysRevB.75.075103], saturate the bound for m =D . Third, we prove that the qubit erasure threshold for codes with a nontrivial transversal m th -level Clifford logical gate is upper bounded by 1 /m . This implies that no family of fault-tolerant codes with transversal gates in increasing level of the Clifford hierarchy may exist. This result applies to arbitrary stabilizer and subsystem codes and is not restricted to geometrically local codes. Fourth, we extend the result of Bravyi and König to subsystem codes. Unlike stabilizer codes, the so-called union lemma does not apply to subsystem codes. This problem is avoided by assuming the presence of an error threshold in a subsystem code, and a conclusion analogous to that of Bravyi and König is recovered.

Selection of neural network structure for system error correction of electro-optical tracker system with horizontal gimbal

NASA Astrophysics Data System (ADS)

Liu, Xing-fa; Cen, Ming

2007-12-01

Neural Network system error correction method is more precise than lest square system error correction method and spheric harmonics function system error correction method. The accuracy of neural network system error correction method is mainly related to the frame of Neural Network. Analysis and simulation prove that both BP neural network system error correction method and RBF neural network system error correction method have high correction accuracy; it is better to use RBF Network system error correction method than BP Network system error correction method for little studying stylebook considering training rate and neural network scale.

A multidisciplinary approach to vascular surgery procedure coding improves coding accuracy, work relative value unit assignment, and reimbursement.

PubMed

Aiello, Francesco A; Judelson, Dejah R; Messina, Louis M; Indes, Jeffrey; FitzGerald, Gordon; Doucet, Danielle R; Simons, Jessica P; Schanzer, Andres

2016-08-01

Vascular surgery procedural reimbursement depends on accurate procedural coding and documentation. Despite the critical importance of correct coding, there has been a paucity of research focused on the effect of direct physician involvement. We hypothesize that direct physician involvement in procedural coding will lead to improved coding accuracy, increased work relative value unit (wRVU) assignment, and increased physician reimbursement. This prospective observational cohort study evaluated procedural coding accuracy of fistulograms at an academic medical institution (January-June 2014). All fistulograms were coded by institutional coders (traditional coding) and by a single vascular surgeon whose codes were verified by two institution coders (multidisciplinary coding). The coding methods were compared, and differences were translated into revenue and wRVUs using the Medicare Physician Fee Schedule. Comparison between traditional and multidisciplinary coding was performed for three discrete study periods: baseline (period 1), after a coding education session for physicians and coders (period 2), and after a coding education session with implementation of an operative dictation template (period 3). The accuracy of surgeon operative dictations during each study period was also assessed. An external validation at a second academic institution was performed during period 1 to assess and compare coding accuracy. During period 1, traditional coding resulted in a 4.4% (P = .004) loss in reimbursement and a 5.4% (P = .01) loss in wRVUs compared with multidisciplinary coding. During period 2, no significant difference was found between traditional and multidisciplinary coding in reimbursement (1.3% loss; P = .24) or wRVUs (1.8% loss; P = .20). During period 3, traditional coding yielded a higher overall reimbursement (1.3% gain; P = .26) than multidisciplinary coding. This increase, however, was due to errors by institution coders, with six inappropriately used codes resulting in a higher overall reimbursement that was subsequently corrected. Assessment of physician documentation showed improvement, with decreased documentation errors at each period (11% vs 3.1% vs 0.6%; P = .02). Overall, between period 1 and period 3, multidisciplinary coding resulted in a significant increase in additional reimbursement ($17.63 per procedure; P = .004) and wRVUs (0.50 per procedure; P = .01). External validation at a second academic institution was performed to assess coding accuracy during period 1. Similar to institution 1, traditional coding revealed an 11% loss in reimbursement ($13,178 vs $14,630; P = .007) and a 12% loss in wRVU (293 vs 329; P = .01) compared with multidisciplinary coding. Physician involvement in the coding of endovascular procedures leads to improved procedural coding accuracy, increased wRVU assignments, and increased physician reimbursement. Copyright © 2016 Society for Vascular Surgery. Published by Elsevier Inc. All rights reserved.

Maximum aposteriori joint source/channel coding

NASA Technical Reports Server (NTRS)

Sayood, Khalid; Gibson, Jerry D.

1991-01-01

A maximum aposteriori probability (MAP) approach to joint source/channel coder design is presented in this paper. This method attempts to explore a technique for designing joint source/channel codes, rather than ways of distributing bits between source coders and channel coders. For a nonideal source coder, MAP arguments are used to design a decoder which takes advantage of redundancy in the source coder output to perform error correction. Once the decoder is obtained, it is analyzed with the purpose of obtaining 'desirable properties' of the channel input sequence for improving overall system performance. Finally, an encoder design which incorporates these properties is proposed.

Pilot self-coding applied in optical OFDM systems

NASA Astrophysics Data System (ADS)

Li, Changping; Yi, Ying; Lee, Kyesan

2015-04-01

This paper studies the frequency offset correction technique which can be applied in optical OFDM systems. Through theoretical analysis and computer simulations, we can observe that our proposed scheme named pilot self-coding (PSC) has a distinct influence for rectifying the frequency offset, which could mitigate the OFDM performance deterioration because of inter-carrier interference and common phase error. The main approach is to assign a pilot subcarrier before data subcarriers and copy this subcarrier sequence to the symmetric side. The simulation results verify that our proposed PSC is indeed effective against the high degree of frequency offset.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strait, R.S.; Pearson, P.K.; Sengupta, S.K.

A password system comprises a set of codewords spaced apart from one another by a Hamming distance (HD) that exceeds twice the variability that can be projected for a series of biometric measurements for a particular individual and that is less than the HD that can be encountered between two individuals. To enroll an individual, a biometric measurement is taken and exclusive-ORed with a random codeword to produce a reference value. To verify the individual later, a biometric measurement is taken and exclusive-ORed with the reference value to reproduce the original random codeword or its approximation. If the reproduced valuemore » is not a codeword, the nearest codeword to it is found, and the bits that were corrected to produce the codeword to it is found, and the bits that were corrected to produce the codeword are also toggled in the biometric measurement taken and the codeword generated during enrollment. The correction scheme can be implemented by any conventional error correction code such as Reed-Muller code R(m,n). In the implementation using a hand geometry device an R(2,5) code has been used in this invention. Such codeword and biometric measurement can then be used to see if the individual is an authorized user. Conventional Diffie-Hellman public key encryption schemes and hashing procedures can then be used to secure the communications lines carrying the biometric information and to secure the database of authorized users.« less

Transfer Error and Correction Approach in Mobile Network

NASA Astrophysics Data System (ADS)

Xiao-kai, Wu; Yong-jin, Shi; Da-jin, Chen; Bing-he, Ma; Qi-li, Zhou

With the development of information technology and social progress, human demand for information has become increasingly diverse, wherever and whenever people want to be able to easily, quickly and flexibly via voice, data, images and video and other means to communicate. Visual information to the people direct and vivid image, image / video transmission also been widespread attention. Although the third generation mobile communication systems and the emergence and rapid development of IP networks, making video communications is becoming the main business of the wireless communications, however, the actual wireless and IP channel will lead to error generation, such as: wireless channel multi- fading channels generated error and blocking IP packet loss and so on. Due to channel bandwidth limitations, the video communication compression coding of data is often beyond the data, and compress data after the error is very sensitive to error conditions caused a serious decline in image quality.

Using LDPC Code Constraints to Aid Recovery of Symbol Timing

NASA Technical Reports Server (NTRS)

Jones, Christopher; Villasnor, John; Lee, Dong-U; Vales, Esteban

2008-01-01

A method of utilizing information available in the constraints imposed by a low-density parity-check (LDPC) code has been proposed as a means of aiding the recovery of symbol timing in the reception of a binary-phase-shift-keying (BPSK) signal representing such a code in the presence of noise, timing error, and/or Doppler shift between the transmitter and the receiver. This method and the receiver architecture in which it would be implemented belong to a class of timing-recovery methods and corresponding receiver architectures characterized as pilotless in that they do not require transmission and reception of pilot signals. Acquisition and tracking of a signal of the type described above have traditionally been performed upstream of, and independently of, decoding and have typically involved utilization of a phase-locked loop (PLL). However, the LDPC decoding process, which is iterative, provides information that can be fed back to the timing-recovery receiver circuits to improve performance significantly over that attainable in the absence of such feedback. Prior methods of coupling LDPC decoding with timing recovery had focused on the use of output code words produced as the iterations progress. In contrast, in the present method, one exploits the information available from the metrics computed for the constraint nodes of an LDPC code during the decoding process. In addition, the method involves the use of a waveform model that captures, better than do the waveform models of the prior methods, distortions introduced by receiver timing errors and transmitter/ receiver motions. An LDPC code is commonly represented by use of a bipartite graph containing two sets of nodes. In the graph corresponding to an (n,k) code, the n variable nodes correspond to the code word symbols and the n-k constraint nodes represent the constraints that the code places on the variable nodes in order for them to form a valid code word. The decoding procedure involves iterative computation of values associated with these nodes. A constraint node represents a parity-check equation using a set of variable nodes as inputs. A valid decoded code word is obtained if all parity-check equations are satisfied. After each iteration, the metrics associated with each constraint node can be evaluated to determine the status of the associated parity check. Heretofore, normally, these metrics would be utilized only within the LDPC decoding process to assess whether or not variable nodes had converged to a codeword. In the present method, it is recognized that these metrics can be used to determine accuracy of the timing estimates used in acquiring the sampled data that constitute the input to the LDPC decoder. In fact, the number of constraints that are satisfied exhibits a peak near the optimal timing estimate. Coarse timing estimation (or first-stage estimation as described below) is found via a parametric search for this peak. The present method calls for a two-stage receiver architecture illustrated in the figure. The first stage would correct large time delays and frequency offsets; the second stage would track random walks and correct residual time and frequency offsets. In the first stage, constraint-node feedback from the LDPC decoder would be employed in a search algorithm in which the searches would be performed in successively narrower windows to find the correct time delay and/or frequency offset. The second stage would include a conventional first-order PLL with a decision-aided timing-error detector that would utilize, as its decision aid, decoded symbols from the LDPC decoder. The method has been tested by means of computational simulations in cases involving various timing and frequency errors. The results of the simulations ined in the ideal case of perfect timing in the receiver.

[INVITED] Luminescent QR codes for smart labelling and sensing

NASA Astrophysics Data System (ADS)

Ramalho, João F. C. B.; António, L. C. F.; Correia, S. F. H.; Fu, L. S.; Pinho, A. S.; Brites, C. D. S.; Carlos, L. D.; André, P. S.; Ferreira, R. A. S.

2018-05-01

QR (Quick Response) codes are two-dimensional barcodes composed of special geometric patterns of black modules in a white square background that can encode different types of information with high density and robustness, correct errors and physical damages, thus keeping the stored information protected. Recently, these codes have gained increased attention as they offer a simple physical tool for quick access to Web sites for advertising and social interaction. Challenges encompass the increase of the storage capacity limit, even though they can store approximately 350 times more information than common barcodes, and encode different types of characters (e.g., numeric, alphanumeric, kanji and kana). In this work, we fabricate luminescent QR codes based on a poly(methyl methacrylate) substrate coated with organic-inorganic hybrid materials doped with trivalent terbium (Tb3+) and europium (Eu3+) ions, demonstrating the increase of storage capacity per unit area by a factor of two by using the colour multiplexing, when compared to conventional QR codes. A novel methodology to decode the multiplexed QR codes is developed based on a colour separation threshold where a decision level is calculated through a maximum-likelihood criteria to minimize the error probability of the demultiplexed modules, maximizing the foreseen total storage capacity. Moreover, the thermal dependence of the emission colour coordinates of the Eu3+/Tb3+-based hybrids enables the simultaneously QR code colour-multiplexing and may be used to sense temperature (reproducibility higher than 93%), opening new fields of applications for QR codes as smart labels for sensing.

Distillation with Sublogarithmic Overhead

NASA Astrophysics Data System (ADS)

Hastings, Matthew B.; Haah, Jeongwan

2018-02-01

It has been conjectured that, for any distillation protocol for magic states for the T gate, the number of noisy input magic states required per output magic state at output error rate ɛ is Ω [log (1 /ɛ )] . We show that this conjecture is false. We find a family of quantum error correcting codes of parameters ⟦ ∑ i =w +1 m (m i ),∑ i =0 w (m i ),∑ i =w +1 r +1 (r +1 i )⟧ for any integers m >2 r , r >w ≥0 , by puncturing quantum Reed-Muller codes. When m >ν r , our code admits a transversal logical gate at the ν th level of Clifford hierarchy. In a distillation protocol for magic states at the level ν =3 (T gate), the ratio of input to output magic states is O (logγ(1 /ɛ )) , where γ =log (n /k )/log (d )<0.678 for some m , r , w . The smallest code in our family for which γ <1 is on ≈258 qubits.

Coded throughput performance simulations for the time-varying satellite channel. M.S. Thesis

NASA Technical Reports Server (NTRS)

Han, LI

1995-01-01

The design of a reliable satellite communication link involving the data transfer from a small, low-orbit satellite to a ground station, but through a geostationary satellite, was examined. In such a scenario, the received signal power to noise density ratio increases as the transmitting low-orbit satellite comes into view, and then decreases as it then departs, resulting in a short-duration, time-varying communication link. The optimal values of the small satellite antenna beamwidth, signaling rate, modulation scheme and the theoretical link throughput (in bits per day) have been determined. The goal of this thesis is to choose a practical coding scheme which maximizes the daily link throughput while satisfying a prescribed probability of error requirement. We examine the throughput of both fixed rate and variable rate concatenated forward error correction (FEC) coding schemes for the additive white Gaussian noise (AWGN) channel, and then examine the effect of radio frequency interference (RFI) on the best coding scheme among them. Interleaving is used to mitigate degradation due to RFI. It was found that the variable rate concatenated coding scheme could achieve 74 percent of the theoretical throughput, equivalent to 1.11 Gbits/day based on the cutoff rate R(sub 0). For comparison, 87 percent is achievable for AWGN-only case.

Study on advanced information processing system

NASA Technical Reports Server (NTRS)

Shin, Kang G.; Liu, Jyh-Charn

1992-01-01

Issues related to the reliability of a redundant system with large main memory are addressed. In particular, the Fault-Tolerant Processor (FTP) for Advanced Launch System (ALS) is used as a basis for our presentation. When the system is free of latent faults, the probability of system crash due to nearly-coincident channel faults is shown to be insignificant even when the outputs of computing channels are infrequently voted on. In particular, using channel error maskers (CEMs) is shown to improve reliability more effectively than increasing the number of channels for applications with long mission times. Even without using a voter, most memory errors can be immediately corrected by CEMs implemented with conventional coding techniques. In addition to their ability to enhance system reliability, CEMs--with a low hardware overhead--can be used to reduce not only the need of memory realignment, but also the time required to realign channel memories in case, albeit rare, such a need arises. Using CEMs, we have developed two schemes, called Scheme 1 and Scheme 2, to solve the memory realignment problem. In both schemes, most errors are corrected by CEMs, and the remaining errors are masked by a voter.

Study on fault-tolerant processors for advanced launch system

NASA Technical Reports Server (NTRS)

Shin, Kang G.; Liu, Jyh-Charn

1990-01-01

Issues related to the reliability of a redundant system with large main memory are addressed. The Fault-Tolerant Processor (FTP) for the Advanced Launch System (ALS) is used as a basis for the presentation. When the system is free of latent faults, the probability of system crash due to multiple channel faults is shown to be insignificant even when voting on the outputs of computing channels is infrequent. Using channel error maskers (CEMs) is shown to improve reliability more effectively than increasing redundancy or the number of channels for applications with long mission times. Even without using a voter, most memory errors can be immediately corrected by those CEMs implemented with conventional coding techniques. In addition to their ability to enhance system reliability, CEMs (with a very low hardware overhead) can be used to dramatically reduce not only the need of memory realignment, but also the time required to realign channel memories in case, albeit rare, such a need arises. Using CEMs, two different schemes were developed to solve the memory realignment problem. In both schemes, most errors are corrected by CEMs, and the remaining errors are masked by a voter.

Seaworthy Quantum Key Distribution Design and Validation (SEAKEY)

DTIC Science & Technology

2014-10-30

to single photon detection, at comparable detection efficiencies. On the other hand, error-correction codes are better developed for small-alphabet...protocol is several orders of magnitude better than the Shapiro protocol, which needs entangled states. The bits/mode performance achieved by our...putting together a software tool implemented in MATLAB , which talks to the MODTRAN database via an intermediate numerical dump of transmission data

Precision and Accuracy of Intercontinental Distance Determinations Using Radio Interferometry.

DTIC Science & Technology

1983-07-01

applicsible) Air Forcc Gc.’!physics Laborator - LWG F19628-82-K- 0002 Sc ADDRESS ICity,. State and ZIP Code) 10. SOURCE OF FUNDING NOS. [lanscon AFB, MA...error in the calibration phase, E. Hence E tan-’[( Acsin, s- Acoso )/A ] (3.2.5)4s obs s obs cal and the corrected calibration phase will be given by cal m

State-of-the-Art Assessment of Testing and Testability of Custom LSI/VLSI Circuits. Volume VI. Redundancy, Testing Circuits, and Codes.

DTIC Science & Technology

1982-10-01

e.g., providing voters in TMR systems and detection-switching requirements in standby-sparing sys- tems. The application of mathematical thoery of...and time redundancy required for error detection and correction, are interrelated. Mathematical modeling, when applied to fault tolerant systems, can...9 1.1 Some Fundamental Principles............................. 11 1.2 Mathematical Theory of

Documentation for the machine-readable version of the general catalogue of 33342 stars for the epoch 1950 (Boss 1937)

NASA Technical Reports Server (NTRS)

Roman, N. G.; Warren, W. H., Jr.

1983-01-01

A revised and corrected version of the machine-readable catalog has been prepared. Cross identifications of the GC stars to the HD and DM catalogs have been replaced by data from the new SAO-HD-GC-DM Cross Index (Roman, Warren and Schofield 1983), including component identifications for multiple SAO entries having identical DM numbers in the SAO Catalog, supplemental Bonner Durchmusterung stars (lower case letter designations) and codes for multiple HD stars. Additional individual corrections have been incorporated based upon errors found during analyses of other catalogs.

Sum of the Magnitude for Hard Decision Decoding Algorithm Based on Loop Update Detection.

PubMed

Meng, Jiahui; Zhao, Danfeng; Tian, Hai; Zhang, Liang

2018-01-15

In order to improve the performance of non-binary low-density parity check codes (LDPC) hard decision decoding algorithm and to reduce the complexity of decoding, a sum of the magnitude for hard decision decoding algorithm based on loop update detection is proposed. This will also ensure the reliability, stability and high transmission rate of 5G mobile communication. The algorithm is based on the hard decision decoding algorithm (HDA) and uses the soft information from the channel to calculate the reliability, while the sum of the variable nodes' (VN) magnitude is excluded for computing the reliability of the parity checks. At the same time, the reliability information of the variable node is considered and the loop update detection algorithm is introduced. The bit corresponding to the error code word is flipped multiple times, before this is searched in the order of most likely error probability to finally find the correct code word. Simulation results show that the performance of one of the improved schemes is better than the weighted symbol flipping (WSF) algorithm under different hexadecimal numbers by about 2.2 dB and 2.35 dB at the bit error rate (BER) of 10 -5 over an additive white Gaussian noise (AWGN) channel, respectively. Furthermore, the average number of decoding iterations is significantly reduced.

Robust video transmission with distributed source coded auxiliary channel.

PubMed

Wang, Jiajun; Majumdar, Abhik; Ramchandran, Kannan

2009-12-01

We propose a novel solution to the problem of robust, low-latency video transmission over lossy channels. Predictive video codecs, such as MPEG and H.26x, are very susceptible to prediction mismatch between encoder and decoder or "drift" when there are packet losses. These mismatches lead to a significant degradation in the decoded quality. To address this problem, we propose an auxiliary codec system that sends additional information alongside an MPEG or H.26x compressed video stream to correct for errors in decoded frames and mitigate drift. The proposed system is based on the principles of distributed source coding and uses the (possibly erroneous) MPEG/H.26x decoder reconstruction as side information at the auxiliary decoder. The distributed source coding framework depends upon knowing the statistical dependency (or correlation) between the source and the side information. We propose a recursive algorithm to analytically track the correlation between the original source frame and the erroneous MPEG/H.26x decoded frame. Finally, we propose a rate-distortion optimization scheme to allocate the rate used by the auxiliary encoder among the encoding blocks within a video frame. We implement the proposed system and present extensive simulation results that demonstrate significant gains in performance both visually and objectively (on the order of 2 dB in PSNR over forward error correction based solutions and 1.5 dB in PSNR over intrarefresh based solutions for typical scenarios) under tight latency constraints.

Recent Updates to the MELCOR 1.8.2 Code for ITER Applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Merrill, Brad J

This report documents recent changes made to the MELCOR 1.8.2 computer code for application to the International Thermonuclear Experimental Reactor (ITER), as required by ITER Task Agreement ITA 81-18. There are four areas of change documented by this report. The first area is the addition to this code of a model for transporting HTO. The second area is the updating of the material oxidation correlations to match those specified in the ITER Safety Analysis Data List (SADL). The third area replaces a modification to an aerosol tranpsort subroutine that specified the nominal aerosol density internally with one that now allowsmore » the user to specify this density through user input. The fourth area corrected an error that existed in an air condensation subroutine of previous versions of this modified MELCOR code. The appendices of this report contain FORTRAN listings of the coding for these modifications.« less

Environmental boundaries as a mechanism for correcting and anchoring spatial maps

PubMed Central

2016-01-01

Abstract Ubiquitous throughout the animal kingdom, path integration‐based navigation allows an animal to take a circuitous route out from a home base and using only self‐motion cues, calculate a direct vector back. Despite variation in an animal's running speed and direction, medial entorhinal grid cells fire in repeating place‐specific locations, pointing to the medial entorhinal circuit as a potential neural substrate for path integration‐based spatial navigation. Supporting this idea, grid cells appear to provide an environment‐independent metric representation of the animal's location in space and preserve their periodic firing structure even in complete darkness. However, a series of recent experiments indicate that spatially responsive medial entorhinal neurons depend on environmental cues in a more complex manner than previously proposed. While multiple types of landmarks may influence entorhinal spatial codes, environmental boundaries have emerged as salient landmarks that both correct error in entorhinal grid cells and bind internal spatial representations to the geometry of the external spatial world. The influence of boundaries on error correction and grid symmetry points to medial entorhinal border cells, which fire at a high rate only near environmental boundaries, as a potential neural substrate for landmark‐driven control of spatial codes. The influence of border cells on other entorhinal cell populations, such as grid cells, could depend on plasticity, raising the possibility that experience plays a critical role in determining how external cues influence internal spatial representations. PMID:26563618

Reduced circuit implementation of encoder and syndrome generator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trager, Barry M; Winograd, Shmuel

An error correction method and system includes an Encoder and Syndrome-generator that operate in parallel to reduce the amount of circuitry used to compute check symbols and syndromes for error correcting codes. The system and method computes the contributions to the syndromes and check symbols 1 bit at a time instead of 1 symbol at a time. As a result, the even syndromes can be computed as powers of the odd syndromes. Further, the system assigns symbol addresses so that there are, for an example GF(2.sup.8) which has 72 symbols, three (3) blocks of addresses which differ by a cubemore » root of unity to allow the data symbols to be combined for reducing size and complexity of odd syndrome circuits. Further, the implementation circuit for generating check symbols is derived from syndrome circuit using the inverse of the part of the syndrome matrix for check locations.« less

Remembering a criminal conversation: beyond eyewitness testimony.

PubMed

Campos, Laura; Alonso-Quecuty, María L

2006-01-01

Unlike the important body of work on eyewitness memory, little research has been done on the accuracy and completeness of "earwitness" memory for conversations. The present research examined the effects of mode of presentation (audiovisual/ auditory-only) on witnesses' free recall for utterances in a criminal conversation at different retention intervals (immediate/delayed) within a single experiment. Different forms of correct recall (verbatim/gist) of the verbal information as well as different types of errors (distortions/fabrications) were also examined. It was predicted that participants in the audiovisual modality would provide more correct information, and fewer errors than participants in the auditory-only modality. Participants' recall was predicted to be impaired over time, dropping to a greater extent after a delay in the auditory-only modality. Results confirmed these hypotheses. Interpretations of the overall findings are offered within the context of dual-coding theory, and within the theoretical frameworks of source monitoring and fuzzy-trace theory.

Bandwidth efficient bidirectional 5 Gb/s overlapped-SCM WDM PON with electronic equalization and forward-error correction.

PubMed

Buset, Jonathan M; El-Sahn, Ziad A; Plant, David V

2012-06-18

We demonstrate an improved overlapped-subcarrier multiplexed (O-SCM) WDM PON architecture transmitting over a single feeder using cost sensitive intensity modulation/direct detection transceivers, data re-modulation and simple electronics. Incorporating electronic equalization and Reed-Solomon forward-error correction codes helps to overcome the bandwidth limitation of a remotely seeded reflective semiconductor optical amplifier (RSOA)-based ONU transmitter. The O-SCM architecture yields greater spectral efficiency and higher bit rates than many other SCM techniques while maintaining resilience to upstream impairments. We demonstrate full-duplex 5 Gb/s transmission over 20 km and analyze BER performance as a function of transmitted and received power. The architecture provides flexibility to network operators by relaxing common design constraints and enabling full-duplex operation at BER ∼ 10(-10) over a wide range of OLT launch powers from 3.5 to 8 dBm.

Qubits in phase space: Wigner-function approach to quantum-error correction and the mean-king problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paz, Juan Pablo; Roncaglia, Augusto Jose; Theoretical Division, LANL, MSB213, Los Alamos, New Mexico 87545

2005-07-15

We analyze and further develop a method to represent the quantum state of a system of n qubits in a phase-space grid of NxN points (where N=2{sup n}). The method, which was recently proposed by Wootters and co-workers (Gibbons et al., Phys. Rev. A 70, 062101 (2004).), is based on the use of the elements of the finite field GF(2{sup n}) to label the phase-space axes. We present a self-contained overview of the method, we give insights into some of its features, and we apply it to investigate problems which are of interest for quantum-information theory: We analyze the phase-spacemore » representation of stabilizer states and quantum error-correction codes and present a phase-space solution to the so-called mean king problem.« less

A methodology for the rigorous verification of plasma simulation codes

NASA Astrophysics Data System (ADS)

Riva, Fabio

2016-10-01

The methodology used to assess the reliability of numerical simulation codes constitutes the Verification and Validation (V&V) procedure. V&V is composed by two separate tasks: the verification, which is a mathematical issue targeted to assess that the physical model is correctly solved, and the validation, which determines the consistency of the code results, and therefore of the physical model, with experimental data. In the present talk we focus our attention on the verification, which in turn is composed by the code verification, targeted to assess that a physical model is correctly implemented in a simulation code, and the solution verification, that quantifies the numerical error affecting a simulation. Bridging the gap between plasma physics and other scientific domains, we introduced for the first time in our domain a rigorous methodology for the code verification, based on the method of manufactured solutions, as well as a solution verification based on the Richardson extrapolation. This methodology was applied to GBS, a three-dimensional fluid code based on a finite difference scheme, used to investigate the plasma turbulence in basic plasma physics experiments and in the tokamak scrape-off layer. Overcoming the difficulty of dealing with a numerical method intrinsically affected by statistical noise, we have now generalized the rigorous verification methodology to simulation codes based on the particle-in-cell algorithm, which are employed to solve Vlasov equation in the investigation of a number of plasma physics phenomena.

Performance enhancement of wireless mobile adhoc networks through improved error correction and ICI cancellation

NASA Astrophysics Data System (ADS)

Sabir, Zeeshan; Babar, M. Inayatullah; Shah, Syed Waqar

2012-12-01

Mobile adhoc network (MANET) refers to an arrangement of wireless mobile nodes that have the tendency of dynamically and freely self-organizing into temporary and arbitrary network topologies. Orthogonal frequency division multiplexing (OFDM) is the foremost choice for MANET system designers at the Physical Layer due to its inherent property of high data rate transmission that corresponds to its lofty spectrum efficiency. The downside of OFDM includes its sensitivity to synchronization errors (frequency offsets and symbol time). Most of the present day techniques employing OFDM for data transmission support mobility as one of the primary features. This mobility causes small frequency offsets due to the production of Doppler frequencies. It results in intercarrier interference (ICI) which degrades the signal quality due to a crosstalk between the subcarriers of OFDM symbol. An efficient frequency-domain block-type pilot-assisted ICI mitigation scheme is proposed in this article which nullifies the effect of channel frequency offsets from the received OFDM symbols. Second problem addressed in this article is the noise effect induced by different sources into the received symbol increasing its bit error rate and making it unsuitable for many applications. Forward-error-correcting turbo codes have been employed into the proposed model which adds redundant bits into the system which are later used for error detection and correction purpose. At the receiver end, maximum a posteriori (MAP) decoding algorithm is implemented using two component MAP decoders. These decoders tend to exchange interleaved extrinsic soft information among each other in the form of log likelihood ratio improving the previous estimate regarding the decoded bit in each iteration.

Hybrid optical CDMA-FSO communications network under spatially correlated gamma-gamma scintillation.

PubMed

Jurado-Navas, Antonio; Raddo, Thiago R; Garrido-Balsells, José María; Borges, Ben-Hur V; Olmos, Juan José Vegas; Monroy, Idelfonso Tafur

2016-07-25

In this paper, we propose a new hybrid network solution based on asynchronous optical code-division multiple-access (OCDMA) and free-space optical (FSO) technologies for last-mile access networks, where fiber deployment is impractical. The architecture of the proposed hybrid OCDMA-FSO network is thoroughly described. The users access the network in a fully asynchronous manner by means of assigned fast frequency hopping (FFH)-based codes. In the FSO receiver, an equal gain-combining technique is employed along with intensity modulation and direct detection. New analytical formalisms for evaluating the average bit error rate (ABER) performance are also proposed. These formalisms, based on the spatially correlated gamma-gamma statistical model, are derived considering three distinct scenarios, namely, uncorrelated, totally correlated, and partially correlated channels. Numerical results show that users can successfully achieve error-free ABER levels for the three scenarios considered as long as forward error correction (FEC) algorithms are employed. Therefore, OCDMA-FSO networks can be a prospective alternative to deliver high-speed communication services to access networks with deficient fiber infrastructure.

Polarization entanglement purification for concatenated Greenberger-Horne-Zeilinger state

NASA Astrophysics Data System (ADS)

Zhou, Lan; Sheng, Yu-Bo

2017-10-01

Entanglement purification plays a fundamental role in long-distance quantum communication. In the paper, we put forward the first polarization entanglement purification protocol (EPP) for one type of nonlocal logic-qubit entanglement, i.e., concatenated Greenberger-Horne-Zeilinger (C-GHZ) state, resorting to the photon-atom interaction in low-quality (Q) cavity. In contrast to existing EPPs, this protocol can purify the bit-flip error and phase-flip error in both physic and logic level. Instead of measuring the photons directly, this protocol only requires to measure the atom states to judge whether the protocol is successful. In this way, the purified logic entangled states can be preserved for further application. Moreover, it makes this EPP repeatable so as to obtain a higher fidelity of logic entangled states. As the logic-qubit entanglement utilizes the quantum error correction (QEC) codes, which has an inherent stability against noise and decoherence, this EPP combined with the QEC codes may provide a double protection for the entanglement from the channel noise and may have potential applications in long-distance quantum communication.

Information-reduced Carrier Synchronization of Iterative Decoded BPSK and QPSK using Soft Decision (Extrinsic) Feedback

NASA Technical Reports Server (NTRS)

Simon, Marvin; Valles, Esteban; Jones, Christopher

2008-01-01

This paper addresses the carrier-phase estimation problem under low SNR conditions as are typical of turbo- and LDPC-coded applications. In previous publications by the first author, closed-loop carrier synchronization schemes for error-correction coded BPSK and QPSK modulation were proposed that were based on feeding back hard data decisions at the input of the loop, the purpose being to remove the modulation prior to attempting to track the carrier phase as opposed to the more conventional decision-feedback schemes that incorporate such feedback inside the loop. In this paper, we consider an alternative approach wherein the extrinsic soft information from the iterative decoder of turbo or LDPC codes is instead used as the feedback.

Video Transmission for Third Generation Wireless Communication Systems

PubMed Central

Gharavi, H.; Alamouti, S. M.

2001-01-01

This paper presents a twin-class unequal protected video transmission system over wireless channels. Video partitioning based on a separation of the Variable Length Coded (VLC) Discrete Cosine Transform (DCT) coefficients within each block is considered for constant bitrate transmission (CBR). In the splitting process the fraction of bits assigned to each of the two partitions is adjusted according to the requirements of the unequal error protection scheme employed. Subsequently, partitioning is applied to the ITU-T H.263 coding standard. As a transport vehicle, we have considered one of the leading third generation cellular radio standards known as WCDMA. A dual-priority transmission system is then invoked on the WCDMA system where the video data, after being broken into two streams, is unequally protected. We use a very simple error correction coding scheme for illustration and then propose more sophisticated forms of unequal protection of the digitized video signals. We show that this strategy results in a significantly higher quality of the reconstructed video data when it is transmitted over time-varying multipath fading channels. PMID:27500033

Embedding intensity image into a binary hologram with strong noise resistant capability

NASA Astrophysics Data System (ADS)

Zhuang, Zhaoyong; Jiao, Shuming; Zou, Wenbin; Li, Xia

2017-11-01

A digital hologram can be employed as a host image for image watermarking applications to protect information security. Past research demonstrates that a gray level intensity image can be embedded into a binary Fresnel hologram by error diffusion method or bit truncation coding method. However, the fidelity of the retrieved watermark image from binary hologram is generally not satisfactory, especially when the binary hologram is contaminated with noise. To address this problem, we propose a JPEG-BCH encoding method in this paper. First, we employ the JPEG standard to compress the intensity image into a binary bit stream. Next, we encode the binary bit stream with BCH code to obtain error correction capability. Finally, the JPEG-BCH code is embedded into the binary hologram. By this way, the intensity image can be retrieved with high fidelity by a BCH-JPEG decoder even if the binary hologram suffers from serious noise contamination. Numerical simulation results show that the image quality of retrieved intensity image with our proposed method is superior to the state-of-the-art work reported.

Emodiversity and the emotional ecosystem.

PubMed

Quoidbach, Jordi; Gruber, June; Mikolajczak, Moïra; Kogan, Alexsandr; Kotsou, Ilios; Norton, Michael I

2014-12-01

[Correction Notice: An Erratum for this article was reported in Vol 143(6) of Journal of Experimental Psychology: General (see record 2014-49316-001). There is a color coding error in Figure 2. The correct color coding is explained in the erratum.] Bridging psychological research exploring emotional complexity and research in the natural sciences on the measurement of biodiversity, we introduce--and demonstrate the benefits of--emodiversity: the variety and relative abundance of the emotions that humans experience. Two cross-sectional studies across more than 37,000 respondents demonstrate that emodiversity is an independent predictor of mental and physical health--such as decreased depression and doctor's visits--over and above mean levels of positive and negative emotion. These results remained robust after controlling for gender, age, and the 5 main dimensions of personality. Emodiversity is a practically important and previously unidentified metric for assessing the health of the human emotional ecosystem. PsycINFO Database Record (c) 2014 APA, all rights reserved.

Mathematical fundamentals for the noise immunity of the genetic code.

PubMed

Fimmel, Elena; Strüngmann, Lutz

2018-02-01

Symmetry is one of the essential and most visible patterns that can be seen in nature. Starting from the left-right symmetry of the human body, all types of symmetry can be found in crystals, plants, animals and nature as a whole. Similarly, principals of symmetry are also some of the fundamental and most useful tools in modern mathematical natural science that play a major role in theory and applications. As a consequence, it is not surprising that the desire to understand the origin of life, based on the genetic code, forces us to involve symmetry as a mathematical concept. The genetic code can be seen as a key to biological self-organisation. All living organisms have the same molecular bases - an alphabet consisting of four letters (nitrogenous bases): adenine, cytosine, guanine, and thymine. Linearly ordered sequences of these bases contain the genetic information for synthesis of proteins in all forms of life. Thus, one of the most fascinating riddles of nature is to explain why the genetic code is as it is. Genetic coding possesses noise immunity which is the fundamental feature that allows to pass on the genetic information from parents to their descendants. Hence, since the time of the discovery of the genetic code, scientists have tried to explain the noise immunity of the genetic information. In this chapter we will discuss recent results in mathematical modelling of the genetic code with respect to noise immunity, in particular error-detection and error-correction. We will focus on two central properties: Degeneracy and frameshift correction. Different amino acids are encoded by different quantities of codons and a connection between this degeneracy and the noise immunity of genetic information is a long standing hypothesis. Biological implications of the degeneracy have been intensively studied and whether the natural code is a frozen accident or a highly optimised product of evolution is still controversially discussed. Symmetries in the structure of degeneracy of the genetic code are essential and give evidence of substantial advantages of the natural code over other possible ones. In the present chapter we will present a recent approach to explain the degeneracy of the genetic code by algorithmic methods from bioinformatics, and discuss its biological consequences. The biologists recognised this problem immediately after the detection of the non-overlapping structure of the genetic code, i.e., coding sequences are to be read in a unique way determined by their reading frame. But how does the reading head of the ribosome recognises an error in the grouping of codons, caused by e.g. insertion or deletion of a base, that can be fatal during the translation process and may result in nonfunctional proteins? In this chapter we will discuss possible solutions to the frameshift problem with a focus on the theory of so-called circular codes that were discovered in large gene populations of prokaryotes and eukaryotes in the early 90s. Circular codes allow to detect a frameshift of one or two positions and recently a beautiful theory of such codes has been developed using statistics, group theory and graph theory. Copyright © 2017 Elsevier B.V. All rights reserved.

Read Code Quality Assurance

PubMed Central

Schulz, Erich; Barrett, James W.; Price, Colin

1998-01-01

As controlled clinical vocabularies assume an increasing role in modern clinical information systems, so the issue of their quality demands greater attention. In order to meet the resulting stringent criteria for completeness and correctness, a quality assurance system comprising a database of more than 500 rules is being developed and applied to the Read Thesaurus. The authors discuss the requirement to apply quality assurance processes to their dynamic editing database in order to ensure the quality of exported products. Sources of errors include human, hardware, and software factors as well as new rules and transactions. The overall quality strategy includes prevention, detection, and correction of errors. The quality assurance process encompasses simple data specification, internal consistency, inspection procedures and, eventually, field testing. The quality assurance system is driven by a small number of tables and UNIX scripts, with “business rules” declared explicitly as Structured Query Language (SQL) statements. Concurrent authorship, client-server technology, and an initial failure to implement robust transaction control have all provided valuable lessons. The feedback loop for error management needs to be short. PMID:9670131

Read Code quality assurance: from simple syntax to semantic stability.

PubMed

Schulz, E B; Barrett, J W; Price, C

1998-01-01

As controlled clinical vocabularies assume an increasing role in modern clinical information systems, so the issue of their quality demands greater attention. In order to meet the resulting stringent criteria for completeness and correctness, a quality assurance system comprising a database of more than 500 rules is being developed and applied to the Read Thesaurus. The authors discuss the requirement to apply quality assurance processes to their dynamic editing database in order to ensure the quality of exported products. Sources of errors include human, hardware, and software factors as well as new rules and transactions. The overall quality strategy includes prevention, detection, and correction of errors. The quality assurance process encompasses simple data specification, internal consistency, inspection procedures and, eventually, field testing. The quality assurance system is driven by a small number of tables and UNIX scripts, with "business rules" declared explicitly as Structured Query Language (SQL) statements. Concurrent authorship, client-server technology, and an initial failure to implement robust transaction control have all provided valuable lessons. The feedback loop for error management needs to be short.

Chroma intra prediction based on inter-channel correlation for HEVC.

PubMed

Zhang, Xingyu; Gisquet, Christophe; François, Edouard; Zou, Feng; Au, Oscar C

2014-01-01

In this paper, we investigate a new inter-channel coding mode called LM mode proposed for the next generation video coding standard called high efficiency video coding. This mode exploits inter-channel correlation using reconstructed luma to predict chroma linearly with parameters derived from neighboring reconstructed luma and chroma pixels at both encoder and decoder to avoid overhead signaling. In this paper, we analyze the LM mode and prove that the LM parameters for predicting original chroma and reconstructed chroma are statistically the same. We also analyze the error sensitivity of the LM parameters. We identify some LM mode problematic situations and propose three novel LM-like modes called LMA, LML, and LMO to address the situations. To limit the increase in complexity due to the LM-like modes, we propose some fast algorithms with the help of some new cost functions. We further identify some potentially-problematic conditions in the parameter estimation (including regression dilution problem) and introduce a novel model correction technique to detect and correct those conditions. Simulation results suggest that considerable BD-rate reduction can be achieved by the proposed LM-like modes and model correction technique. In addition, the performance gain of the two techniques appears to be essentially additive when combined.

TRIGA: Telecommunications Protocol Processing Subsystem Using Reconfigurable Interoperable Gate Arrays

NASA Technical Reports Server (NTRS)

Pang, Jackson; Pingree, Paula J.; Torgerson, J. Leigh

2006-01-01

We present the Telecommunications protocol processing subsystem using Reconfigurable Interoperable Gate Arrays (TRIGA), a novel approach that unifies fault tolerance, error correction coding and interplanetary communication protocol off-loading to implement CCSDS File Delivery Protocol and Datalink layers. The new reconfigurable architecture offers more than one order of magnitude throughput increase while reducing footprint requirements in memory, command and data handling processor utilization, communication system interconnects and power consumption.

Reduction of PAPR in coded OFDM using fast Reed-Solomon codes over prime Galois fields

NASA Astrophysics Data System (ADS)

Motazedi, Mohammad Reza; Dianat, Reza

2017-02-01

In this work, two new techniques using Reed-Solomon (RS) codes over GF(257) and GF(65,537) are proposed for peak-to-average power ratio (PAPR) reduction in coded orthogonal frequency division multiplexing (OFDM) systems. The lengths of these codes are well-matched to the length of OFDM frames. Over these fields, the block lengths of codes are powers of two and we fully exploit the radix-2 fast Fourier transform algorithms. Multiplications and additions are simple modulus operations. These codes provide desirable randomness with a small perturbation in information symbols that is essential for generation of different statistically independent candidates. Our simulations show that the PAPR reduction ability of RS codes is the same as that of conventional selected mapping (SLM), but contrary to SLM, we can get error correction capability. Also for the second proposed technique, the transmission of side information is not needed. To the best of our knowledge, this is the first work using RS codes for PAPR reduction in single-input single-output systems.

Author Correction: Intergenerational equity can help to prevent climate change and extinction.

PubMed

Treves, Adrian; Artelle, Kyle A; Darimont, Chris T; Lynn, William S; Paquet, Paul; Santiago-Ávila, Francisco J; Shaw, Rance; Wood, Mary C

2018-05-01

The original Article mistakenly coded the constitutional rights of Australia as containing a governmental duty to protect the environment (blue in the figures); this has been corrected to containing no explicit mention of environmental protection (orange in the figures). The original Article also neglected to code the constitutional rights of the Cayman Islands (no data; yellow in the figures); this has been corrected to containing a governmental duty to protect the environment (blue in the figures).Although no inferences changed as a result of these errors, many values changed slightly and have been corrected. The proportion of the world's nations having constitutional rights to a healthy environment changed from 75% to 74%. The proportions of nations in different categories given in the Fig. 1 caption all changed except purple countries (3.1%): green countries changed from 47.2% to 46.9%; blue countries changed from 24.4% to 24.2%; and orange countries changed from 25.3% to 25.8%. The proportion of the global atmospheric CO 2 emitted by the 144 nations changed from 72.6% to 74.4%; the proportion of the world's population represented by the 144 nations changed from 84.9% to 85%. The values of annual average CO 2 emissions for blue countries changed from 363,000 Gg to 353,000 Gg and for orange countries from 195,000 Gg to 201,000 Gg. The proportion of threatened mammals endemic to a single country represented by the 144 countries changed from 91% to 84%. Figures 1-3 have been updated to show the correct values and map colours and the Supplementary Information has been updated to give the correct country codes.

Palmprint Based Multidimensional Fuzzy Vault Scheme

PubMed Central

Liu, Hailun; Sun, Dongmei; Xiong, Ke; Qiu, Zhengding

2014-01-01

Fuzzy vault scheme (FVS) is one of the most popular biometric cryptosystems for biometric template protection. However, error correcting code (ECC) proposed in FVS is not appropriate to deal with real-valued biometric intraclass variances. In this paper, we propose a multidimensional fuzzy vault scheme (MDFVS) in which a general subspace error-tolerant mechanism is designed and embedded into FVS to handle intraclass variances. Palmprint is one of the most important biometrics; to protect palmprint templates; a palmprint based MDFVS implementation is also presented. Experimental results show that the proposed scheme not only can deal with intraclass variances effectively but also could maintain the accuracy and meanwhile enhance security. PMID:24892094

High-speed architecture for the decoding of trellis-coded modulation

NASA Technical Reports Server (NTRS)

Osborne, William P.

1992-01-01

Since 1971, when the Viterbi Algorithm was introduced as the optimal method of decoding convolutional codes, improvements in circuit technology, especially VLSI, have steadily increased its speed and practicality. Trellis-Coded Modulation (TCM) combines convolutional coding with higher level modulation (non-binary source alphabet) to provide forward error correction and spectral efficiency. For binary codes, the current stare-of-the-art is a 64-state Viterbi decoder on a single CMOS chip, operating at a data rate of 25 Mbps. Recently, there has been an interest in increasing the speed of the Viterbi Algorithm by improving the decoder architecture, or by reducing the algorithm itself. Designs employing new architectural techniques are now in existence, however these techniques are currently applied to simpler binary codes, not to TCM. The purpose of this report is to discuss TCM architectural considerations in general, and to present the design, at the logic gate level, or a specific TCM decoder which applies these considerations to achieve high-speed decoding.

Improving software quality - The use of formal inspections at the Jet Propulsion Laboratory

NASA Technical Reports Server (NTRS)

Bush, Marilyn

1990-01-01

The introduction of software formal inspections (Fagan Inspections) at JPL for finding and fixing defects early in the software development life cycle are reviewed. It is estimated that, by the year 2000, some software efforts will rise to as much as 80 percent of the total. Software problems are especially important at NASA as critical flight software must be error-free. It is shown that formal inspections are particularly effective at finding and removing defects having to do with clarity, correctness, consistency, and completeness. A very significant discovery was that code audits were not as effective at finding defects as code inspections.

Motion artifact detection and correction in functional near-infrared spectroscopy: a new hybrid method based on spline interpolation method and Savitzky-Golay filtering.

PubMed

Jahani, Sahar; Setarehdan, Seyed K; Boas, David A; Yücel, Meryem A

2018-01-01

Motion artifact contamination in near-infrared spectroscopy (NIRS) data has become an important challenge in realizing the full potential of NIRS for real-life applications. Various motion correction algorithms have been used to alleviate the effect of motion artifacts on the estimation of the hemodynamic response function. While smoothing methods, such as wavelet filtering, are excellent in removing motion-induced sharp spikes, the baseline shifts in the signal remain after this type of filtering. Methods, such as spline interpolation, on the other hand, can properly correct baseline shifts; however, they leave residual high-frequency spikes. We propose a hybrid method that takes advantage of different correction algorithms. This method first identifies the baseline shifts and corrects them using a spline interpolation method or targeted principal component analysis. The remaining spikes, on the other hand, are corrected by smoothing methods: Savitzky-Golay (SG) filtering or robust locally weighted regression and smoothing. We have compared our new approach with the existing correction algorithms in terms of hemodynamic response function estimation using the following metrics: mean-squared error, peak-to-peak error ([Formula: see text]), Pearson's correlation ([Formula: see text]), and the area under the receiver operator characteristic curve. We found that spline-SG hybrid method provides reasonable improvements in all these metrics with a relatively short computational time. The dataset and the code used in this study are made available online for the use of all interested researchers.

Error properties of Argos satellite telemetry locations using least squares and Kalman filtering.

PubMed

Boyd, Janice D; Brightsmith, Donald J

2013-01-01

Study of animal movements is key for understanding their ecology and facilitating their conservation. The Argos satellite system is a valuable tool for tracking species which move long distances, inhabit remote areas, and are otherwise difficult to track with traditional VHF telemetry and are not suitable for GPS systems. Previous research has raised doubts about the magnitude of position errors quoted by the satellite service provider CLS. In addition, no peer-reviewed publications have evaluated the usefulness of the CLS supplied error ellipses nor the accuracy of the new Kalman filtering (KF) processing method. Using transmitters hung from towers and trees in southeastern Peru, we show the Argos error ellipses generally contain <25% of the true locations and therefore do not adequately describe the true location errors. We also find that KF processing does not significantly increase location accuracy. The errors for both LS and KF processing methods were found to be lognormally distributed, which has important repercussions for error calculation, statistical analysis, and data interpretation. In brief, "good" positions (location codes 3, 2, 1, A) are accurate to about 2 km, while 0 and B locations are accurate to about 5-10 km. However, due to the lognormal distribution of the errors, larger outliers are to be expected in all location codes and need to be accounted for in the user's data processing. We evaluate five different empirical error estimates and find that 68% lognormal error ellipses provided the most useful error estimates. Longitude errors are larger than latitude errors by a factor of 2 to 3, supporting the use of elliptical error ellipses. Numerous studies over the past 15 years have also found fault with the CLS-claimed error estimates yet CLS has failed to correct their misleading information. We hope this will be reversed in the near future.

Method and system for normalizing biometric variations to authenticate users from a public database and that ensures individual biometric data privacy

DOEpatents

Strait, Robert S.; Pearson, Peter K.; Sengupta, Sailes K.

2000-01-01

A password system comprises a set of codewords spaced apart from one another by a Hamming distance (HD) that exceeds twice the variability that can be projected for a series of biometric measurements for a particular individual and that is less than the HD that can be encountered between two individuals. To enroll an individual, a biometric measurement is taken and exclusive-ORed with a random codeword to produce a "reference value." To verify the individual later, a biometric measurement is taken and exclusive-ORed with the reference value to reproduce the original random codeword or its approximation. If the reproduced value is not a codeword, the nearest codeword to it is found, and the bits that were corrected to produce the codeword to it is found, and the bits that were corrected to produce the codeword are also toggled in the biometric measurement taken and the codeword generated during enrollment. The correction scheme can be implemented by any conventional error correction code such as Reed-Muller code R(m,n). In the implementation using a hand geometry device an R(2,5) code has been used in this invention. Such codeword and biometric measurement can then be used to see if the individual is an authorized user. Conventional Diffie-Hellman public key encryption schemes and hashing procedures can then be used to secure the communications lines carrying the biometric information and to secure the database of authorized users.

Obtaining correct compile results by absorbing mismatches between data types representations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horie, Michihiro; Horii, Hiroshi H.; Kawachiya, Kiyokuni

Methods and a system are provided. A method includes implementing a function, which a compiler for a first language does not have, using a compiler for a second language. The implementing step includes generating, by the compiler for the first language, a first abstract syntax tree. The implementing step further includes converting, by a converter, the first abstract syntax tree to a second abstract syntax tree of the compiler for the second language using a conversion table from data representation types in the first language to data representation types in the second language. When a compilation error occurs, the implementingmore » step also includes generating a special node for error processing in the second abstract syntax tree and storing an error token in the special node. When unparsing, the implementing step additionally includes outputting the error token, in the form of source code written in the first language.« less

Obtaining correct compile results by absorbing mismatches between data types representations

DOEpatents

Horie, Michihiro; Horii, Hiroshi H.; Kawachiya, Kiyokuni; Takeuchi, Mikio

2017-03-21

Methods and a system are provided. A method includes implementing a function, which a compiler for a first language does not have, using a compiler for a second language. The implementing step includes generating, by the compiler for the first language, a first abstract syntax tree. The implementing step further includes converting, by a converter, the first abstract syntax tree to a second abstract syntax tree of the compiler for the second language using a conversion table from data representation types in the first language to data representation types in the second language. When a compilation error occurs, the implementing step also includes generating a special node for error processing in the second abstract syntax tree and storing an error token in the special node. When unparsing, the implementing step additionally includes outputting the error token, in the form of source code written in the first language.

Obtaining correct compile results by absorbing mismatches between data types representations

DOEpatents

Horie, Michihiro; Horii, Hiroshi H.; Kawachiya, Kiyokuni; Takeuchi, Mikio

2017-11-21

Methods and a system are provided. A method includes implementing a function, which a compiler for a first language does not have, using a compiler for a second language. The implementing step includes generating, by the compiler for the first language, a first abstract syntax tree. The implementing step further includes converting, by a converter, the first abstract syntax tree to a second abstract syntax tree of the compiler for the second language using a conversion table from data representation types in the first language to data representation types in the second language. When a compilation error occurs, the implementing step also includes generating a special node for error processing in the second abstract syntax tree and storing an error token in the special node. When unparsing, the implementing step additionally includes outputting the error token, in the form of source code written in the first language.