Optimized iterative decoding method for TPC coded CPM

NASA Astrophysics Data System (ADS)

Ma, Yanmin; Lai, Penghui; Wang, Shilian; Xie, Shunqin; Zhang, Wei

2018-05-01

Turbo Product Code (TPC) coded Continuous Phase Modulation (CPM) system (TPC-CPM) has been widely used in aeronautical telemetry and satellite communication. This paper mainly investigates the improvement and optimization on the TPC-CPM system. We first add the interleaver and deinterleaver to the TPC-CPM system, and then establish an iterative system to iteratively decode. However, the improved system has a poor convergence ability. To overcome this issue, we use the Extrinsic Information Transfer (EXIT) analysis to find the optimal factors for the system. The experiments show our method is efficient to improve the convergence performance.

Hybrid concatenated codes and iterative decoding

NASA Technical Reports Server (NTRS)

Divsalar, Dariush (Inventor); Pollara, Fabrizio (Inventor)

2000-01-01

Several improved turbo code apparatuses and methods. The invention encompasses several classes: (1) A data source is applied to two or more encoders with an interleaver between the source and each of the second and subsequent encoders. Each encoder outputs a code element which may be transmitted or stored. A parallel decoder provides the ability to decode the code elements to derive the original source information d without use of a received data signal corresponding to d. The output may be coupled to a multilevel trellis-coded modulator (TCM). (2) A data source d is applied to two or more encoders with an interleaver between the source and each of the second and subsequent encoders. Each of the encoders outputs a code element. In addition, the original data source d is output from the encoder. All of the output elements are coupled to a TCM. (3) At least two data sources are applied to two or more encoders with an interleaver between each source and each of the second and subsequent encoders. The output may be coupled to a TCM. (4) At least two data sources are applied to two or more encoders with at least two interleavers between each source and each of the second and subsequent encoders. (5) At least one data source is applied to one or more serially linked encoders through at least one interleaver. The output may be coupled to a TCM. The invention includes a novel way of terminating a turbo coder.

Efficient Signal, Code, and Receiver Designs for MIMO Communication Systems

DTIC Science & Technology

2003-06-01

167 5-31 Concatenation of a tilted-QAM inner code with an LDPC outer code with a two component iterative soft-decision decoder. . . . . . . . . 168 5...for AWGN channels has long been studied. There are well-known soft-decision codes like the turbo codes and LDPC codes that can approach capacity to...bits) low density parity check ( LDPC ) code 1. 2. The coded bits are randomly interleaved so that bits nearby go through different sub-channels, and are

Dynamic configuration management of a multi-standard and multi-mode reconfigurable multi-ASIP architecture for turbo decoding

NASA Astrophysics Data System (ADS)

Lapotre, Vianney; Gogniat, Guy; Baghdadi, Amer; Diguet, Jean-Philippe

2017-12-01

The multiplication of connected devices goes along with a large variety of applications and traffic types needing diverse requirements. Accompanying this connectivity evolution, the last years have seen considerable evolutions of wireless communication standards in the domain of mobile telephone networks, local/wide wireless area networks, and Digital Video Broadcasting (DVB). In this context, intensive research has been conducted to provide flexible turbo decoder targeting high throughput, multi-mode, multi-standard, and power consumption efficiency. However, flexible turbo decoder implementations have not often considered dynamic reconfiguration issues in this context that requires high speed configuration switching. Starting from this assessment, this paper proposes the first solution that allows frame-by-frame run-time configuration management of a multi-processor turbo decoder without compromising the decoding performances.

Transmission over UWB channels with OFDM system using LDPC coding

NASA Astrophysics Data System (ADS)

Dziwoki, Grzegorz; Kucharczyk, Marcin; Sulek, Wojciech

2009-06-01

Hostile wireless environment requires use of sophisticated signal processing methods. The paper concerns on Ultra Wideband (UWB) transmission over Personal Area Networks (PAN) including MB-OFDM specification of physical layer. In presented work the transmission system with OFDM modulation was connected with LDPC encoder/decoder. Additionally the frame and bit error rate (FER and BER) of the system was decreased using results from the LDPC decoder in a kind of turbo equalization algorithm for better channel estimation. Computational block using evolutionary strategy, from genetic algorithms family, was also used in presented system. It was placed after SPA (Sum-Product Algorithm) decoder and is conditionally turned on in the decoding process. The result is increased effectiveness of the whole system, especially lower FER. The system was tested with two types of LDPC codes, depending on type of parity check matrices: randomly generated and constructed deterministically, optimized for practical decoder architecture implemented in the FPGA device.

A power-efficient communication system between brain-implantable devices and external computers.

PubMed

Yao, Ning; Lee, Heung-No; Chang, Cheng-Chun; Sclabassi, Robert J; Sun, Mingui

2007-01-01

In this paper, we propose a power efficient communication system for linking a brain-implantable device to an external system. For battery powered implantable devices, the processor and the transmitter power should be reduced in order to both conserve battery power and reduce the health risks associated with transmission. To accomplish this, a joint source-channel coding/decoding system is devised. Low-density generator matrix (LDGM) codes are used in our system due to their low encoding complexity. The power cost for signal processing within the implantable device is greatly reduced by avoiding explicit source encoding. Raw data which is highly correlated is transmitted. At the receiver, a Markov chain source correlation model is utilized to approximate and capture the correlation of raw data. A turbo iterative receiver algorithm is designed which connects the Markov chain source model to the LDGM decoder in a turbo-iterative way. Simulation results show that the proposed system can save up to 1 to 2.5 dB on transmission power.

Error-Rate Bounds for Coded PPM on a Poisson Channel

NASA Technical Reports Server (NTRS)

Moision, Bruce; Hamkins, Jon

2009-01-01

Equations for computing tight bounds on error rates for coded pulse-position modulation (PPM) on a Poisson channel at high signal-to-noise ratio have been derived. These equations and elements of the underlying theory are expected to be especially useful in designing codes for PPM optical communication systems. The equations and the underlying theory apply, more specifically, to a case in which a) At the transmitter, a linear outer code is concatenated with an inner code that includes an accumulator and a bit-to-PPM-symbol mapping (see figure) [this concatenation is known in the art as "accumulate-PPM" (abbreviated "APPM")]; b) The transmitted signal propagates on a memoryless binary-input Poisson channel; and c) At the receiver, near-maximum-likelihood (ML) decoding is effected through an iterative process. Such a coding/modulation/decoding scheme is a variation on the concept of turbo codes, which have complex structures, such that an exact analytical expression for the performance of a particular code is intractable. However, techniques for accurately estimating the performances of turbo codes have been developed. The performance of a typical turbo code includes (1) a "waterfall" region consisting of a steep decrease of error rate with increasing signal-to-noise ratio (SNR) at low to moderate SNR, and (2) an "error floor" region with a less steep decrease of error rate with increasing SNR at moderate to high SNR. The techniques used heretofore for estimating performance in the waterfall region have differed from those used for estimating performance in the error-floor region. For coded PPM, prior to the present derivations, equations for accurate prediction of the performance of coded PPM at high SNR did not exist, so that it was necessary to resort to time-consuming simulations in order to make such predictions. The present derivation makes it unnecessary to perform such time-consuming simulations.

Joint Source-Channel Decoding of Variable-Length Codes with Soft Information: A Survey

NASA Astrophysics Data System (ADS)

Guillemot, Christine; Siohan, Pierre

2005-12-01

Multimedia transmission over time-varying wireless channels presents a number of challenges beyond existing capabilities conceived so far for third-generation networks. Efficient quality-of-service (QoS) provisioning for multimedia on these channels may in particular require a loosening and a rethinking of the layer separation principle. In that context, joint source-channel decoding (JSCD) strategies have gained attention as viable alternatives to separate decoding of source and channel codes. A statistical framework based on hidden Markov models (HMM) capturing dependencies between the source and channel coding components sets the foundation for optimal design of techniques of joint decoding of source and channel codes. The problem has been largely addressed in the research community, by considering both fixed-length codes (FLC) and variable-length source codes (VLC) widely used in compression standards. Joint source-channel decoding of VLC raises specific difficulties due to the fact that the segmentation of the received bitstream into source symbols is random. This paper makes a survey of recent theoretical and practical advances in the area of JSCD with soft information of VLC-encoded sources. It first describes the main paths followed for designing efficient estimators for VLC-encoded sources, the key component of the JSCD iterative structure. It then presents the main issues involved in the application of the turbo principle to JSCD of VLC-encoded sources as well as the main approaches to source-controlled channel decoding. This survey terminates by performance illustrations with real image and video decoding systems.

Optical LDPC decoders for beyond 100 Gbits/s optical transmission.

PubMed

Djordjevic, Ivan B; Xu, Lei; Wang, Ting

2009-05-01

We present an optical low-density parity-check (LDPC) decoder suitable for implementation above 100 Gbits/s, which provides large coding gains when based on large-girth LDPC codes. We show that a basic building block, the probabilities multiplier circuit, can be implemented using a Mach-Zehnder interferometer, and we propose corresponding probabilistic-domain sum-product algorithm (SPA). We perform simulations of a fully parallel implementation employing girth-10 LDPC codes and proposed SPA. The girth-10 LDPC(24015,19212) code of the rate of 0.8 outperforms the BCH(128,113)xBCH(256,239) turbo-product code of the rate of 0.82 by 0.91 dB (for binary phase-shift keying at 100 Gbits/s and a bit error rate of 10(-9)), and provides a net effective coding gain of 10.09 dB.

Accumulate repeat accumulate codes

NASA Technical Reports Server (NTRS)

Abbasfar, Aliazam; Divsalar, Dariush; Yao, Kung

2004-01-01

In this paper we propose an innovative channel coding scheme called 'Accumulate Repeat Accumulate codes' (ARA). This class of codes can be viewed as serial turbo-like codes, or as a subclass of Low Density Parity Check (LDPC) codes, thus belief propagation can be used for iterative decoding of ARA codes on a graph. The structure of encoder for this class can be viewed as precoded Repeat Accumulate (RA) code or as precoded Irregular Repeat Accumulate (IRA) code, where simply an accumulator is chosen as a precoder. Thus ARA codes have simple, and very fast encoder structure when they representing LDPC codes. Based on density evolution for LDPC codes through some examples for ARA codes, we show that for maximum variable node degree 5 a minimum bit SNR as low as 0.08 dB from channel capacity for rate 1/2 can be achieved as the block size goes to infinity. Thus based on fixed low maximum variable node degree, its threshold outperforms not only the RA and IRA codes but also the best known LDPC codes with the dame maximum node degree. Furthermore by puncturing the accumulators any desired high rate codes close to code rate 1 can be obtained with thresholds that stay close to the channel capacity thresholds uniformly. Iterative decoding simulation results are provided. The ARA codes also have projected graph or protograph representation that allows for high speed decoder implementation.

Performance Enhancement of MC-CDMA System through Novel Sensitive Bit Algorithm Aided Turbo Multi User Detection

PubMed Central

Kumaravel, Rasadurai; Narayanaswamy, Kumaratharan

2015-01-01

Multi carrier code division multiple access (MC-CDMA) system is a promising multi carrier modulation (MCM) technique for high data rate wireless communication over frequency selective fading channels. MC-CDMA system is a combination of code division multiple access (CDMA) and orthogonal frequency division multiplexing (OFDM). The OFDM parts reduce multipath fading and inter symbol interference (ISI) and the CDMA part increases spectrum utilization. Advantages of this technique are its robustness in case of multipath propagation and improve security with the minimize ISI. Nevertheless, due to the loss of orthogonality at the receiver in a mobile environment, the multiple access interference (MAI) appears. The MAI is one of the factors that degrade the bit error rate (BER) performance of MC-CDMA system. The multiuser detection (MUD) and turbo coding are the two dominant techniques for enhancing the performance of the MC-CDMA systems in terms of BER as a solution of overcome to MAI effects. In this paper a low complexity iterative soft sensitive bits algorithm (SBA) aided logarithmic-Maximum a-Posteriori algorithm (Log MAP) based turbo MUD is proposed. Simulation results show that the proposed method provides better BER performance with low complexity decoding, by mitigating the detrimental effects of MAI. PMID:25714917

Capacity Maximizing Constellations

NASA Technical Reports Server (NTRS)

Barsoum, Maged; Jones, Christopher

2010-01-01

Some non-traditional signal constellations have been proposed for transmission of data over the Additive White Gaussian Noise (AWGN) channel using such channel-capacity-approaching codes as low-density parity-check (LDPC) or turbo codes. Computational simulations have shown performance gains of more than 1 dB over traditional constellations. These gains could be translated to bandwidth- efficient communications, variously, over longer distances, using less power, or using smaller antennas. The proposed constellations have been used in a bit-interleaved coded modulation system employing state-ofthe-art LDPC codes. In computational simulations, these constellations were shown to afford performance gains over traditional constellations as predicted by the gap between the parallel decoding capacity of the constellations and the Gaussian capacity

Toward enhancing the distributed video coder under a multiview video codec framework

NASA Astrophysics Data System (ADS)

Lee, Shih-Chieh; Chen, Jiann-Jone; Tsai, Yao-Hong; Chen, Chin-Hua

2016-11-01

The advance of video coding technology enables multiview video (MVV) or three-dimensional television (3-D TV) display for users with or without glasses. For mobile devices or wireless applications, a distributed video coder (DVC) can be utilized to shift the encoder complexity to decoder under the MVV coding framework, denoted as multiview distributed video coding (MDVC). We proposed to exploit both inter- and intraview video correlations to enhance side information (SI) and improve the MDVC performance: (1) based on the multiview motion estimation (MVME) framework, a categorized block matching prediction with fidelity weights (COMPETE) was proposed to yield a high quality SI frame for better DVC reconstructed images. (2) The block transform coefficient properties, i.e., DCs and ACs, were exploited to design the priority rate control for the turbo code, such that the DVC decoding can be carried out with fewest parity bits. In comparison, the proposed COMPETE method demonstrated lower time complexity, while presenting better reconstructed video quality. Simulations show that the proposed COMPETE can reduce the time complexity of MVME to 1.29 to 2.56 times smaller, as compared to previous hybrid MVME methods, while the image peak signal to noise ratios (PSNRs) of a decoded video can be improved 0.2 to 3.5 dB, as compared to H.264/AVC intracoding.

Accumulate-Repeat-Accumulate-Accumulate-Codes

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Dolinar, Sam; Thorpe, Jeremy

2004-01-01

Inspired by recently proposed Accumulate-Repeat-Accumulate (ARA) codes [15], in this paper we propose a channel coding scheme called Accumulate-Repeat-Accumulate-Accumulate (ARAA) codes. These codes can be seen as serial turbo-like codes or as a subclass of Low Density Parity Check (LDPC) codes, and they have a projected graph or protograph representation; this allows for a high-speed iterative decoder implementation using belief propagation. An ARAA code can be viewed as a precoded Repeat-and-Accumulate (RA) code with puncturing in concatenation with another accumulator, where simply an accumulator is chosen as the precoder; thus ARAA codes have a very fast encoder structure. Using density evolution on their associated protographs, we find examples of rate-lJ2 ARAA codes with maximum variable node degree 4 for which a minimum bit-SNR as low as 0.21 dB from the channel capacity limit can be achieved as the block size goes to infinity. Such a low threshold cannot be achieved by RA or Irregular RA (IRA) or unstructured irregular LDPC codes with the same constraint on the maximum variable node degree. Furthermore by puncturing the accumulators we can construct families of higher rate ARAA codes with thresholds that stay close to their respective channel capacity thresholds uniformly. Iterative decoding simulation results show comparable performance with the best-known LDPC codes but with very low error floor even at moderate block sizes.

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.

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.

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.

Iterative Code-Aided ML Phase Estimation and Phase Ambiguity Resolution

NASA Astrophysics Data System (ADS)

Wymeersch, Henk; Moeneclaey, Marc

2005-12-01

As many coded systems operate at very low signal-to-noise ratios, synchronization becomes a very difficult task. In many cases, conventional algorithms will either require long training sequences or result in large BER degradations. By exploiting code properties, these problems can be avoided. In this contribution, we present several iterative maximum-likelihood (ML) algorithms for joint carrier phase estimation and ambiguity resolution. These algorithms operate on coded signals by accepting soft information from the MAP decoder. Issues of convergence and initialization are addressed in detail. Simulation results are presented for turbo codes, and are compared to performance results of conventional algorithms. Performance comparisons are carried out in terms of BER performance and mean square estimation error (MSEE). We show that the proposed algorithm reduces the MSEE and, more importantly, the BER degradation. Additionally, phase ambiguity resolution can be performed without resorting to a pilot sequence, thus improving the spectral efficiency.

Weight distributions for turbo codes using random and nonrandom permutations

NASA Technical Reports Server (NTRS)

Dolinar, S.; Divsalar, D.

1995-01-01

This article takes a preliminary look at the weight distributions achievable for turbo codes using random, nonrandom, and semirandom permutations. Due to the recursiveness of the encoders, it is important to distinguish between self-terminating and non-self-terminating input sequences. The non-self-terminating sequences have little effect on decoder performance, because they accumulate high encoded weight until they are artificially terminated at the end of the block. From probabilistic arguments based on selecting the permutations randomly, it is concluded that the self-terminating weight-2 data sequences are the most important consideration in the design of constituent codes; higher-weight self-terminating sequences have successively decreasing importance. Also, increasing the number of codes and, correspondingly, the number of permutations makes it more and more likely that the bad input sequences will be broken up by one or more of the permuters. It is possible to design nonrandom permutations that ensure that the minimum distance due to weight-2 input sequences grows roughly as the square root of (2N), where N is the block length. However, these nonrandom permutations amplify the bad effects of higher-weight inputs, and as a result they are inferior in performance to randomly selected permutations. But there are 'semirandom' permutations that perform nearly as well as the designed nonrandom permutations with respect to weight-2 input sequences and are not as susceptible to being foiled by higher-weight inputs.

Error control techniques for satellite and space communications

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.

1995-01-01

This report focuses on the results obtained during the PI's recent sabbatical leave at the Swiss Federal Institute of Technology (ETH) in Zurich, Switzerland, from January 1, 1995 through June 30, 1995. Two projects investigated various properties of TURBO codes, a new form of concatenated coding that achieves near channel capacity performance at moderate bit error rates. The performance of TURBO codes is explained in terms of the code's distance spectrum. These results explain both the near capacity performance of the TURBO codes and the observed 'error floor' for moderate and high signal-to-noise ratios (SNR's). A semester project, entitled 'The Realization of the Turbo-Coding System,' involved a thorough simulation study of the performance of TURBO codes and verified the results claimed by previous authors. A copy of the final report for this project is included as Appendix A. A diploma project, entitled 'On the Free Distance of Turbo Codes and Related Product Codes,' includes an analysis of TURBO codes and an explanation for their remarkable performance. A copy of the final report for this project is included as Appendix B.

A Direct Mapping of Max k-SAT and High Order Parity Checks to a Chimera Graph

PubMed Central

Chancellor, N.; Zohren, S.; Warburton, P. A.; Benjamin, S. C.; Roberts, S.

2016-01-01

We demonstrate a direct mapping of max k-SAT problems (and weighted max k-SAT) to a Chimera graph, which is the non-planar hardware graph of the devices built by D-Wave Systems Inc. We further show that this mapping can be used to map a similar class of maximum satisfiability problems where the clauses are replaced by parity checks over potentially large numbers of bits. The latter is of specific interest for applications in decoding for communication. We discuss an example in which the decoding of a turbo code, which has been demonstrated to perform near the Shannon limit, can be mapped to a Chimera graph. The weighted max k-SAT problem is the most general class of satisfiability problems, so our result effectively demonstrates how any satisfiability problem may be directly mapped to a Chimera graph. Our methods faithfully reproduce the low energy spectrum of the target problems, so therefore may also be used for maximum entropy inference. PMID:27857179

Application of Aeroelastic Solvers Based on Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Srivastava, Rakesh

1998-01-01

A pre-release version of the Navier-Stokes solver (TURBO) was obtained from MSU. Along with Dr. Milind Bakhle of the University of Toledo, subroutines for aeroelastic analysis were developed and added to the TURBO code to develop versions 1 and 2 of the TURBO-AE code. For specified mode shape, frequency and inter-blade phase angle the code calculates the work done by the fluid on the rotor for a prescribed sinusoidal motion. Positive work on the rotor indicates instability of the rotor. The version 1 of the code calculates the work for in-phase blade motions only. In version 2 of the code, the capability for analyzing all possible inter-blade phase angles, was added. The version 2 of TURBO-AE code was validated and delivered to NASA and the industry partners of the AST project. The capabilities and the features of the code are summarized in Refs. [1] & [2]. To release the version 2 of TURBO-AE, a workshop was organized at NASA Lewis, by Dr. Srivastava and Dr. M. A. Bakhle, both of the University of Toledo, in October of 1996 for the industry partners of NASA Lewis. The workshop provided the potential users of TURBO-AE, all the relevant information required in preparing the input data, executing the code, interpreting the results and bench marking the code on their computer systems. After the code was delivered to the industry partners, user support was also provided. A new version of the Navier-Stokes solver (TURBO) was later released by MSU. This version had significant changes and upgrades over the previous version. This new version was merged with the TURBO-AE code. Also, new boundary conditions for 3-D unsteady non-reflecting boundaries, were developed by researchers from UTRC, Ref. [3]. Time was spent on understanding, familiarizing, executing and implementing the new boundary conditions into the TURBO-AE code. Work was started on the phase lagged (time-shifted) boundary condition version (version 4) of the code. This will allow the users to calculate non-zero interblade phase angles using, only one blade passage for analysis.

Hardware Implementation of Serially Concatenated PPM Decoder

NASA Technical Reports Server (NTRS)

Moision, Bruce; Hamkins, Jon; Barsoum, Maged; Cheng, Michael; Nakashima, Michael

2009-01-01

A prototype decoder for a serially concatenated pulse position modulation (SCPPM) code has been implemented in a field-programmable gate array (FPGA). At the time of this reporting, this is the first known hardware SCPPM decoder. The SCPPM coding scheme, conceived for free-space optical communications with both deep-space and terrestrial applications in mind, is an improvement of several dB over the conventional Reed-Solomon PPM scheme. The design of the FPGA SCPPM decoder is based on a turbo decoding algorithm that requires relatively low computational complexity while delivering error-rate performance within approximately 1 dB of channel capacity. The SCPPM encoder consists of an outer convolutional encoder, an interleaver, an accumulator, and an inner modulation encoder (more precisely, a mapping of bits to PPM symbols). Each code is describable by a trellis (a finite directed graph). The SCPPM decoder consists of an inner soft-in-soft-out (SISO) module, a de-interleaver, an outer SISO module, and an interleaver connected in a loop (see figure). Each SISO module applies the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm to compute a-posteriori bit log-likelihood ratios (LLRs) from apriori LLRs by traversing the code trellis in forward and backward directions. The SISO modules iteratively refine the LLRs by passing the estimates between one another much like the working of a turbine engine. Extrinsic information (the difference between the a-posteriori and a-priori LLRs) is exchanged rather than the a-posteriori LLRs to minimize undesired feedback. All computations are performed in the logarithmic domain, wherein multiplications are translated into additions, thereby reducing complexity and sensitivity to fixed-point implementation roundoff errors. To lower the required memory for storing channel likelihood data and the amounts of data transfer between the decoder and the receiver, one can discard the majority of channel likelihoods, using only the remainder in operation of the decoder. This is accomplished in the receiver by transmitting only a subset consisting of the likelihoods that correspond to time slots containing the largest numbers of observed photons during each PPM symbol period. The assumed number of observed photons in the remaining time slots is set to the mean of a noise slot. In low background noise, the selection of a small subset in this manner results in only negligible loss. Other features of the decoder design to reduce complexity and increase speed include (1) quantization of metrics in an efficient procedure chosen to incur no more than a small performance loss and (2) the use of the max-star function that allows sum of exponentials to be computed by simple operations that involve only an addition, a subtraction, and a table lookup. Another prominent feature of the design is a provision for access to interleaver and de-interleaver memory in a single clock cycle, eliminating the multiple clock-cycle latency characteristic of prior interleaver and de-interleaver designs.

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.

Identification and Classification of Orthogonal Frequency Division Multiple Access (OFDMA) Signals Used in Next Generation Wireless Systems

DTIC Science & Technology

2012-03-01

advanced antenna systems AMC adaptive modulation and coding AWGN additive white Gaussian noise BPSK binary phase shift keying BS base station BTC ...QAM-16, and QAM-64, and coding types include convolutional coding (CC), convolutional turbo coding (CTC), block turbo coding ( BTC ), zero-terminating

Multi-stage decoding for multi-level block modulation codes

NASA Technical Reports Server (NTRS)

Lin, Shu; Kasami, Tadao

1991-01-01

Various types of multistage decoding for multilevel block modulation codes, in which the decoding of a component code at each stage can be either soft decision or hard decision, maximum likelihood or bounded distance are discussed. Error performance for codes is analyzed for a memoryless additive channel based on various types of multi-stage decoding, and upper bounds on the probability of an incorrect decoding are derived. It was found that, if component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity. It was found that the difference in performance between the suboptimum multi-stage soft decision maximum likelihood decoding of a modulation code and the single stage optimum decoding of the overall code is very small, only a fraction of dB loss in SNR at the probability of an incorrect decoding for a block of 10(exp -6). Multi-stage decoding of multi-level modulation codes really offers a way to achieve the best of three worlds, bandwidth efficiency, coding gain, and decoding complexity.

A high throughput architecture for a low complexity soft-output demapping algorithm

NASA Astrophysics Data System (ADS)

Ali, I.; Wasenmüller, U.; Wehn, N.

2015-11-01

Iterative channel decoders such as Turbo-Code and LDPC decoders show exceptional performance and therefore they are a part of many wireless communication receivers nowadays. These decoders require a soft input, i.e., the logarithmic likelihood ratio (LLR) of the received bits with a typical quantization of 4 to 6 bits. For computing the LLR values from a received complex symbol, a soft demapper is employed in the receiver. The implementation cost of traditional soft-output demapping methods is relatively large in high order modulation systems, and therefore low complexity demapping algorithms are indispensable in low power receivers. In the presence of multiple wireless communication standards where each standard defines multiple modulation schemes, there is a need to have an efficient demapper architecture covering all the flexibility requirements of these standards. Another challenge associated with hardware implementation of the demapper is to achieve a very high throughput in double iterative systems, for instance, MIMO and Code-Aided Synchronization. In this paper, we present a comprehensive communication and hardware performance evaluation of low complexity soft-output demapping algorithms to select the best algorithm for implementation. The main goal of this work is to design a high throughput, flexible, and area efficient architecture. We describe architectures to execute the investigated algorithms. We implement these architectures on a FPGA device to evaluate their hardware performance. The work has resulted in a hardware architecture based on the figured out best low complexity algorithm delivering a high throughput of 166 Msymbols/second for Gray mapped 16-QAM modulation on Virtex-5. This efficient architecture occupies only 127 slice registers, 248 slice LUTs and 2 DSP48Es.

Channel coding for underwater acoustic single-carrier CDMA communication system

NASA Astrophysics Data System (ADS)

Liu, Lanjun; Zhang, Yonglei; Zhang, Pengcheng; Zhou, Lin; Niu, Jiong

2017-01-01

CDMA is an effective multiple access protocol for underwater acoustic networks, and channel coding can effectively reduce the bit error rate (BER) of the underwater acoustic communication system. For the requirements of underwater acoustic mobile networks based on CDMA, an underwater acoustic single-carrier CDMA communication system (UWA/SCCDMA) based on the direct-sequence spread spectrum is proposed, and its channel coding scheme is studied based on convolution, RA, Turbo and LDPC coding respectively. The implementation steps of the Viterbi algorithm of convolutional coding, BP and minimum sum algorithms of RA coding, Log-MAP and SOVA algorithms of Turbo coding, and sum-product algorithm of LDPC coding are given. An UWA/SCCDMA simulation system based on Matlab is designed. Simulation results show that the UWA/SCCDMA based on RA, Turbo and LDPC coding have good performance such that the communication BER is all less than 10-6 in the underwater acoustic channel with low signal to noise ratio (SNR) from -12 dB to -10dB, which is about 2 orders of magnitude lower than that of the convolutional coding. The system based on Turbo coding with Log-MAP algorithm has the best performance.

Multi-stage decoding for multi-level block modulation codes

NASA Technical Reports Server (NTRS)

Lin, Shu

1991-01-01

In this paper, we investigate various types of multi-stage decoding for multi-level block modulation codes, in which the decoding of a component code at each stage can be either soft-decision or hard-decision, maximum likelihood or bounded-distance. Error performance of codes is analyzed for a memoryless additive channel based on various types of multi-stage decoding, and upper bounds on the probability of an incorrect decoding are derived. Based on our study and computation results, we find that, if component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity. In particular, we find that the difference in performance between the suboptimum multi-stage soft-decision maximum likelihood decoding of a modulation code and the single-stage optimum decoding of the overall code is very small: only a fraction of dB loss in SNR at the probability of an incorrect decoding for a block of 10(exp -6). Multi-stage decoding of multi-level modulation codes really offers a way to achieve the best of three worlds, bandwidth efficiency, coding gain, and decoding complexity.

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.

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.

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

NASA Technical Reports Server (NTRS)

Lin, Shu

1998-01-01

A code trellis is a graphical representation of a code, block or convolutional, in which every path represents a codeword (or a code sequence for a convolutional code). This representation makes it possible to implement Maximum Likelihood Decoding (MLD) of a code with reduced decoding complexity. The most well known trellis-based MLD algorithm is the Viterbi algorithm. The trellis representation was first introduced and used for convolutional codes [23]. This representation, together with the Viterbi decoding algorithm, has resulted in a wide range of applications of convolutional codes for error control in digital communications over the last two decades. There are two major reasons for this inactive period of research in this area. First, most coding theorists at that time believed that block codes did not have simple trellis structure like convolutional codes and maximum likelihood decoding of linear block codes using the Viterbi algorithm was practically impossible, except for very short block codes. Second, since almost all of the linear block codes are constructed algebraically or based on finite geometries, it was the belief of many coding theorists that algebraic decoding was the only way to decode these codes. These two reasons seriously hindered the development of efficient soft-decision decoding methods for linear block codes and their applications to error control in digital communications. This led to a general belief that block codes are inferior to convolutional codes and hence, that they were not useful. Chapter 2 gives a brief review of linear block codes. The goal is to provide the essential background material for the development of trellis structure and trellis-based decoding algorithms for linear block codes in the later chapters. Chapters 3 through 6 present the fundamental concepts, finite-state machine model, state space formulation, basic structural properties, state labeling, construction procedures, complexity, minimality, and sectionalization of trellises. Chapter 7 discusses trellis decomposition and subtrellises for low-weight codewords. Chapter 8 first presents well known methods for constructing long powerful codes from short component codes or component codes of smaller dimensions, and then provides methods for constructing their trellises which include Shannon and Cartesian product techniques. Chapter 9 deals with convolutional codes, puncturing, zero-tail termination and tail-biting.Chapters 10 through 13 present various trellis-based decoding algorithms, old and new. Chapter 10 first discusses the application of the well known Viterbi decoding algorithm to linear block codes, optimum sectionalization of a code trellis to minimize computation complexity, and design issues for IC (integrated circuit) implementation of a Viterbi decoder. Then it presents a new decoding algorithm for convolutional codes, named Differential Trellis Decoding (DTD) algorithm. Chapter 12 presents a suboptimum reliability-based iterative decoding algorithm with a low-weight trellis search for the most likely codeword. This decoding algorithm provides a good trade-off between error performance and decoding complexity. All the decoding algorithms presented in Chapters 10 through 12 are devised to minimize word error probability. Chapter 13 presents decoding algorithms that minimize bit error probability and provide the corresponding soft (reliability) information at the output of the decoder. Decoding algorithms presented are the MAP (maximum a posteriori probability) decoding algorithm and the Soft-Output Viterbi Algorithm (SOVA) algorithm. Finally, the minimization of bit error probability in trellis-based MLD is discussed.

Application of TURBO-AE to Flutter Prediction: Aeroelastic Code Development

NASA Technical Reports Server (NTRS)

Hoyniak, Daniel; Simons, Todd A.; Stefko, George (Technical Monitor)

2001-01-01

The TURBO-AE program has been evaluated by comparing the obtained results to cascade rig data and to prediction made from various in-house programs. A high-speed fan cascade, a turbine cascade, a turbine cascade and a fan geometry that shower flutter in torsion mode were analyzed. The steady predictions for the high-speed fan cascade showed the TURBO-AE predictions to match in-house codes. However, the predictions did not match the measured blade surface data. Other researchers also reported similar disagreement with these data set. Unsteady runs for the fan configuration were not successful using TURBO-AE .

Bounded-Angle Iterative Decoding of LDPC Codes

NASA Technical Reports Server (NTRS)

Dolinar, Samuel; Andrews, Kenneth; Pollara, Fabrizio; Divsalar, Dariush

2009-01-01

Bounded-angle iterative decoding is a modified version of conventional iterative decoding, conceived as a means of reducing undetected-error rates for short low-density parity-check (LDPC) codes. For a given code, bounded-angle iterative decoding can be implemented by means of a simple modification of the decoder algorithm, without redesigning the code. Bounded-angle iterative decoding is based on a representation of received words and code words as vectors in an n-dimensional Euclidean space (where n is an integer).

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.

Preprocessor that Enables the Use of GridProTM Grids for Unsteady Reynolds-Averaged Navier-Stokes Code TURBO

NASA Technical Reports Server (NTRS)

Shyam, Vikram

2010-01-01

A preprocessor for the Computational Fluid Dynamics (CFD) code TURBO has been developed and tested. The preprocessor converts grids produced by GridPro (Program Development Company (PDC)) into a format readable by TURBO and generates the necessary input files associated with the grid. The preprocessor also generates information that enables the user to decide how to allocate the computational load in a multiple block per processor scenario.

Multi-stage decoding of multi-level modulation codes

NASA Technical Reports Server (NTRS)

Lin, Shu; Kasami, Tadao; Costello, Daniel J., Jr.

1991-01-01

Various types of multi-stage decoding for multi-level modulation codes are investigated. It is shown that if the component codes of a multi-level modulation code and types of decoding at various stages are chosen properly, high spectral efficiency and large coding gain can be achieved with reduced decoding complexity. Particularly, it is shown that the difference in performance between the suboptimum multi-stage soft-decision maximum likelihood decoding of a modulation code and the single-stage optimum soft-decision decoding of the code is very small, only a fraction of dB loss in signal to noise ratio at a bit error rate (BER) of 10(exp -6).

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; An Iterative Decoding Algorithm for Linear Block Codes Based on a Low-Weight Trellis Search

NASA Technical Reports Server (NTRS)

Lin, Shu; Fossorier, Marc

1998-01-01

For long linear block codes, maximum likelihood decoding based on full code trellises would be very hard to implement if not impossible. In this case, we may wish to trade error performance for the reduction in decoding complexity. Sub-optimum soft-decision decoding of a linear block code based on a low-weight sub-trellis can be devised to provide an effective trade-off between error performance and decoding complexity. This chapter presents such a suboptimal decoding algorithm for linear block codes. This decoding algorithm is iterative in nature and based on an optimality test. It has the following important features: (1) a simple method to generate a sequence of candidate code-words, one at a time, for test; (2) a sufficient condition for testing a candidate code-word for optimality; and (3) a low-weight sub-trellis search for finding the most likely (ML) code-word.

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.

On decoding of multi-level MPSK modulation codes

NASA Technical Reports Server (NTRS)

Lin, Shu; Gupta, Alok Kumar

1990-01-01

The decoding problem of multi-level block modulation codes is investigated. The hardware design of soft-decision Viterbi decoder for some short length 8-PSK block modulation codes is presented. An effective way to reduce the hardware complexity of the decoder by reducing the branch metric and path metric, using a non-uniform floating-point to integer mapping scheme, is proposed and discussed. The simulation results of the design are presented. The multi-stage decoding (MSD) of multi-level modulation codes is also investigated. The cases of soft-decision and hard-decision MSD are considered and their performance are evaluated for several codes of different lengths and different minimum squared Euclidean distances. It is shown that the soft-decision MSD reduces the decoding complexity drastically and it is suboptimum. The hard-decision MSD further simplifies the decoding while still maintaining a reasonable coding gain over the uncoded system, if the component codes are chosen properly. Finally, some basic 3-level 8-PSK modulation codes using BCH codes as component codes are constructed and their coding gains are found for hard decision multistage decoding.

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.

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.

Enhanced decoding for the Galileo low-gain antenna mission: Viterbi redecoding with four decoding stages

NASA Technical Reports Server (NTRS)

Dolinar, S.; Belongie, M.

1995-01-01

The Galileo low-gain antenna mission will be supported by a coding system that uses a (14,1/4) inner convolutional code concatenated with Reed-Solomon codes of four different redundancies. Decoding for this code is designed to proceed in four distinct stages of Viterbi decoding followed by Reed-Solomon decoding. In each successive stage, the Reed-Solomon decoder only tries to decode the highest redundancy codewords not yet decoded in previous stages, and the Viterbi decoder redecodes its data utilizing the known symbols from previously decoded Reed-Solomon codewords. A previous article analyzed a two-stage decoding option that was not selected by Galileo. The present article analyzes the four-stage decoding scheme and derives the near-optimum set of redundancies selected for use by Galileo. The performance improvements relative to one- and two-stage decoding systems are evaluated.

A long constraint length VLSI Viterbi decoder for the DSN

NASA Technical Reports Server (NTRS)

Statman, J. I.; Zimmerman, G.; Pollara, F.; Collins, O.

1988-01-01

A Viterbi decoder, capable of decoding convolutional codes with constraint lengths up to 15, is under development for the Deep Space Network (DSN). The objective is to complete a prototype of this decoder by late 1990, and demonstrate its performance using the (15, 1/4) encoder in Galileo. The decoder is expected to provide 1 to 2 dB improvement in bit SNR, compared to the present (7, 1/2) code and existing Maximum Likelihood Convolutional Decoder (MCD). The decoder will be fully programmable for any code up to constraint length 15, and code rate 1/2 to 1/6. The decoder architecture and top-level design are described.

Development of an Aeroelastic Code Based on an Euler/Navier-Stokes Aerodynamic Solver

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Srivastava, Rakesh; Keith, Theo G., Jr.; Stefko, George L.; Janus, Mark J.

1996-01-01

This paper describes the development of an aeroelastic code (TURBO-AE) based on an Euler/Navier-Stokes unsteady aerodynamic analysis. A brief review of the relevant research in the area of propulsion aeroelasticity is presented. The paper briefly describes the original Euler/Navier-Stokes code (TURBO) and then details the development of the aeroelastic extensions. The aeroelastic formulation is described. The modeling of the dynamics of the blade using a modal approach is detailed, along with the grid deformation approach used to model the elastic deformation of the blade. The work-per-cycle approach used to evaluate aeroelastic stability is described. Representative results used to verify the code are presented. The paper concludes with an evaluation of the development thus far, and some plans for further development and validation of the TURBO-AE code.

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3

NASA Technical Reports Server (NTRS)

Lin, Shu

1998-01-01

Decoding algorithms based on the trellis representation of a code (block or convolutional) drastically reduce decoding complexity. The best known and most commonly used trellis-based decoding algorithm is the Viterbi algorithm. It is a maximum likelihood decoding algorithm. Convolutional codes with the Viterbi decoding have been widely used for error control in digital communications over the last two decades. This chapter is concerned with the application of the Viterbi decoding algorithm to linear block codes. First, the Viterbi algorithm is presented. Then, optimum sectionalization of a trellis to minimize the computational complexity of a Viterbi decoder is discussed and an algorithm is presented. Some design issues for IC (integrated circuit) implementation of a Viterbi decoder are considered and discussed. Finally, a new decoding algorithm based on the principle of compare-select-add is presented. This new algorithm can be applied to both block and convolutional codes and is more efficient than the conventional Viterbi algorithm based on the add-compare-select principle. This algorithm is particularly efficient for rate 1/n antipodal convolutional codes and their high-rate punctured codes. It reduces computational complexity by one-third compared with the Viterbi algorithm.

Recent advances in coding theory for near error-free communications

NASA Technical Reports Server (NTRS)

Cheung, K.-M.; Deutsch, L. J.; Dolinar, S. J.; Mceliece, R. J.; Pollara, F.; Shahshahani, M.; Swanson, L.

1991-01-01

Channel and source coding theories are discussed. The following subject areas are covered: large constraint length convolutional codes (the Galileo code); decoder design (the big Viterbi decoder); Voyager's and Galileo's data compression scheme; current research in data compression for images; neural networks for soft decoding; neural networks for source decoding; finite-state codes; and fractals for data compression.

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.

Real-time minimal-bit-error probability decoding of convolutional codes

NASA Technical Reports Server (NTRS)

Lee, L.-N.

1974-01-01

A recursive procedure is derived for decoding of rate R = 1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit, subject to the constraint that the decoding delay be limited to Delta branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A real-time, i.e., fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications, such as in the inner coding system for concatenated coding.

Real-time minimal bit error probability decoding of convolutional codes

NASA Technical Reports Server (NTRS)

Lee, L. N.

1973-01-01

A recursive procedure is derived for decoding of rate R=1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit subject to the constraint that the decoding delay be limited to Delta branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A real-time, i.e. fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications such as in the inner coding system for concatenated coding.

Achievable Information Rates for Coded Modulation With Hard Decision Decoding for Coherent Fiber-Optic Systems

NASA Astrophysics Data System (ADS)

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

2017-12-01

We analyze the achievable information rates (AIRs) for coded modulation schemes with QAM constellations with both bit-wise and symbol-wise decoders, corresponding to the case where a binary code is used in combination with a higher-order modulation using the bit-interleaved coded modulation (BICM) paradigm and to the case where a nonbinary code over a field matched to the constellation size is used, respectively. In particular, we consider hard decision decoding, which is the preferable option for fiber-optic communication systems where decoding complexity is a concern. Recently, Liga \\emph{et al.} analyzed the AIRs for bit-wise and symbol-wise decoders considering what the authors called \\emph{hard decision decoder} which, however, exploits \\emph{soft information} of the transition probabilities of discrete-input discrete-output channel resulting from the hard detection. As such, the complexity of the decoder is essentially the same as the complexity of a soft decision decoder. In this paper, we analyze instead the AIRs for the standard hard decision decoder, commonly used in practice, where the decoding is based on the Hamming distance metric. We show that if standard hard decision decoding is used, bit-wise decoders yield significantly higher AIRs than symbol-wise decoders. As a result, contrary to the conclusion by Liga \\emph{et al.}, binary decoders together with the BICM paradigm are preferable for spectrally-efficient fiber-optic systems. We also design binary and nonbinary staircase codes and show that, in agreement with the AIRs, binary codes yield better performance.

Bandwidth efficient coding for satellite communications

NASA Technical Reports Server (NTRS)

Lin, Shu; Costello, Daniel J., Jr.; Miller, Warner H.; Morakis, James C.; Poland, William B., Jr.

1992-01-01

An error control coding scheme was devised to achieve large coding gain and high reliability by using coded modulation with reduced decoding complexity. To achieve a 3 to 5 dB coding gain and moderate reliability, the decoding complexity is quite modest. In fact, to achieve a 3 dB coding gain, the decoding complexity is quite simple, no matter whether trellis coded modulation or block coded modulation is used. However, to achieve coding gains exceeding 5 dB, the decoding complexity increases drastically, and the implementation of the decoder becomes very expensive and unpractical. The use is proposed of coded modulation in conjunction with concatenated (or cascaded) coding. A good short bandwidth efficient modulation code is used as the inner code and relatively powerful Reed-Solomon code is used as the outer code. With properly chosen inner and outer codes, a concatenated coded modulation scheme not only can achieve large coding gains and high reliability with good bandwidth efficiency but also can be practically implemented. This combination of coded modulation and concatenated coding really offers a way of achieving the best of three worlds, reliability and coding gain, bandwidth efficiency, and decoding complexity.

Advanced Subsonic Technology (AST) Area of Interest (AOI) 6: Develop and Validate Aeroelastic Codes for Turbomachinery

NASA Technical Reports Server (NTRS)

Gardner, Kevin D.; Liu, Jong-Shang; Murthy, Durbha V.; Kruse, Marlin J.; James, Darrell

1999-01-01

AlliedSignal Engines, in cooperation with NASA GRC (National Aeronautics and Space Administration Glenn Research Center), completed an evaluation of recently-developed aeroelastic computer codes using test cases from the AlliedSignal Engines fan blisk and turbine databases. Test data included strain gage, performance, and steady-state pressure information obtained for conditions where synchronous or flutter vibratory conditions were found to occur. Aeroelastic codes evaluated included quasi 3-D UNSFLO (MIT Developed/AE Modified, Quasi 3-D Aeroelastic Computer Code), 2-D FREPS (NASA-Developed Forced Response Prediction System Aeroelastic Computer Code), and 3-D TURBO-AE (NASA/Mississippi State University Developed 3-D Aeroelastic Computer Code). Unsteady pressure predictions for the turbine test case were used to evaluate the forced response prediction capabilities of each of the three aeroelastic codes. Additionally, one of the fan flutter cases was evaluated using TURBO-AE. The UNSFLO and FREPS evaluation predictions showed good agreement with the experimental test data trends, but quantitative improvements are needed. UNSFLO over-predicted turbine blade response reductions, while FREPS under-predicted them. The inviscid TURBO-AE turbine analysis predicted no discernible blade response reduction, indicating the necessity of including viscous effects for this test case. For the TURBO-AE fan blisk test case, significant effort was expended getting the viscous version of the code to give converged steady flow solutions for the transonic flow conditions. Once converged, the steady solutions provided an excellent match with test data and the calibrated DAWES (AlliedSignal 3-D Viscous Steady Flow CFD Solver). However, efforts expended establishing quality steady-state solutions prevented exercising the unsteady portion of the TURBO-AE code during the present program. AlliedSignal recommends that unsteady pressure measurement data be obtained for both test cases examined for use in aeroelastic code validation.

Singer product apertures-A coded aperture system with a fast decoding algorithm

NASA Astrophysics Data System (ADS)

Byard, Kevin; Shutler, Paul M. E.

2017-06-01

A new type of coded aperture configuration that enables fast decoding of the coded aperture shadowgram data is presented. Based on the products of incidence vectors generated from the Singer difference sets, we call these Singer product apertures. For a range of aperture dimensions, we compare experimentally the performance of three decoding methods: standard decoding, induction decoding and direct vector decoding. In all cases the induction and direct vector methods are several orders of magnitude faster than the standard method, with direct vector decoding being significantly faster than induction decoding. For apertures of the same dimensions the increase in speed offered by direct vector decoding over induction decoding is better for lower throughput apertures.

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.

A Scalable Architecture of a Structured LDPC Decoder

NASA Technical Reports Server (NTRS)

Lee, Jason Kwok-San; Lee, Benjamin; Thorpe, Jeremy; Andrews, Kenneth; Dolinar, Sam; Hamkins, Jon

2004-01-01

We present a scalable decoding architecture for a certain class of structured LDPC codes. The codes are designed using a small (n,r) protograph that is replicated Z times to produce a decoding graph for a (Z x n, Z x r) code. Using this architecture, we have implemented a decoder for a (4096,2048) LDPC code on a Xilinx Virtex-II 2000 FPGA, and achieved decoding speeds of 31 Mbps with 10 fixed iterations. The implemented message-passing algorithm uses an optimized 3-bit non-uniform quantizer that operates with 0.2dB implementation loss relative to a floating point decoder.

Complementary Reliability-Based Decodings of Binary Linear Block Codes

NASA Technical Reports Server (NTRS)

Fossorier, Marc P. C.; Lin, Shu

1997-01-01

This correspondence presents a hybrid reliability-based decoding algorithm which combines the reprocessing method based on the most reliable basis and a generalized Chase-type algebraic decoder based on the least reliable positions. It is shown that reprocessing with a simple additional algebraic decoding effort achieves significant coding gain. For long codes, the order of reprocessing required to achieve asymptotic optimum error performance is reduced by approximately 1/3. This significantly reduces the computational complexity, especially for long codes. Also, a more efficient criterion for stopping the decoding process is derived based on the knowledge of the algebraic decoding solution.

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.

Polar Coding with CRC-Aided List Decoding

DTIC Science & Technology

2015-08-01

TECHNICAL REPORT 2087 August 2015 Polar Coding with CRC-Aided List Decoding David Wasserman Approved...list decoding . RESULTS Our simulation results show that polar coding can produce results very similar to the FEC used in the Digital Video...standard. RECOMMENDATIONS In any application for which the DVB-S2 FEC is considered, polar coding with CRC-aided list decod - ing with N = 65536

Enhanced decoding for the Galileo S-band mission

NASA Technical Reports Server (NTRS)

Dolinar, S.; Belongie, M.

1993-01-01

A coding system under consideration for the Galileo S-band low-gain antenna mission is a concatenated system using a variable redundancy Reed-Solomon outer code and a (14,1/4) convolutional inner code. The 8-bit Reed-Solomon symbols are interleaved to depth 8, and the eight 255-symbol codewords in each interleaved block have redundancies 64, 20, 20, 20, 64, 20, 20, and 20, respectively (or equivalently, the codewords have 191, 235, 235, 235, 191, 235, 235, and 235 8-bit information symbols, respectively). This concatenated code is to be decoded by an enhanced decoder that utilizes a maximum likelihood (Viterbi) convolutional decoder; a Reed Solomon decoder capable of processing erasures; an algorithm for declaring erasures in undecoded codewords based on known erroneous symbols in neighboring decodable words; a second Viterbi decoding operation (redecoding) constrained to follow only paths consistent with the known symbols from previously decodable Reed-Solomon codewords; and a second Reed-Solomon decoding operation using the output from the Viterbi redecoder and additional erasure declarations to the extent possible. It is estimated that this code and decoder can achieve a decoded bit error rate of 1 x 10(exp 7) at a concatenated code signal-to-noise ratio of 0.76 dB. By comparison, a threshold of 1.17 dB is required for a baseline coding system consisting of the same (14,1/4) convolutional code, a (255,223) Reed-Solomon code with constant redundancy 32 also interleaved to depth 8, a one-pass Viterbi decoder, and a Reed Solomon decoder incapable of declaring or utilizing erasures. The relative gain of the enhanced system is thus 0.41 dB. It is predicted from analysis based on an assumption of infinite interleaving that the coding gain could be further improved by approximately 0.2 dB if four stages of Viterbi decoding and four levels of Reed-Solomon redundancy are permitted. Confirmation of this effect and specification of the optimum four-level redundancy profile for depth-8 interleaving is currently being done.

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.

Maximum likelihood decoding analysis of accumulate-repeat-accumulate codes

NASA Technical Reports Server (NTRS)

Abbasfar, A.; Divsalar, D.; Yao, K.

2004-01-01

In this paper, the performance of the repeat-accumulate codes with (ML) decoding are analyzed and compared to random codes by very tight bounds. Some simple codes are shown that perform very close to Shannon limit with maximum likelihood decoding.

Coding for reliable satellite communications

NASA Technical Reports Server (NTRS)

Lin, S.

1984-01-01

Several error control coding techniques for reliable satellite communications were investigated to find algorithms for fast decoding of Reed-Solomon codes in terms of dual basis. The decoding of the (255,223) Reed-Solomon code, which is used as the outer code in the concatenated TDRSS decoder, was of particular concern.

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; The Map and Related Decoding Algirithms

NASA Technical Reports Server (NTRS)

Lin, Shu; Fossorier, Marc

1998-01-01

In a coded communication system with equiprobable signaling, MLD minimizes the word error probability and delivers the most likely codeword associated with the corresponding received sequence. This decoding has two drawbacks. First, minimization of the word error probability is not equivalent to minimization of the bit error probability. Therefore, MLD becomes suboptimum with respect to the bit error probability. Second, MLD delivers a hard-decision estimate of the received sequence, so that information is lost between the input and output of the ML decoder. This information is important in coded schemes where the decoded sequence is further processed, such as concatenated coding schemes, multi-stage and iterative decoding schemes. In this chapter, we first present a decoding algorithm which both minimizes bit error probability, and provides the corresponding soft information at the output of the decoder. This algorithm is referred to as the MAP (maximum aposteriori probability) decoding algorithm.

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.

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.

Sequential Syndrome Decoding of Convolutional Codes

NASA Technical Reports Server (NTRS)

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

1984-01-01

The algebraic structure of convolutional codes are reviewed and sequential syndrome decoding is applied to those codes. These concepts are then used to realize by example actual sequential decoding, using the stack algorithm. The Fano metric for use in sequential decoding is modified so that it can be utilized to sequentially find the minimum weight error sequence.

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.

Concatenated coding systems employing a unit-memory convolutional code and a byte-oriented decoding algorithm

NASA Technical Reports Server (NTRS)

Lee, L.-N.

1977-01-01

Concatenated coding systems utilizing a convolutional code as the inner code and a Reed-Solomon code as the outer code are considered. In order to obtain very reliable communications over a very noisy channel with relatively modest coding complexity, it is proposed to concatenate a byte-oriented unit-memory convolutional code with an RS outer code whose symbol size is one byte. It is further proposed to utilize a real-time minimal-byte-error probability decoding algorithm, together with feedback from the outer decoder, in the decoder for the inner convolutional code. The performance of the proposed concatenated coding system is studied, and the improvement over conventional concatenated systems due to each additional feature is isolated.

Concatenated coding systems employing a unit-memory convolutional code and a byte-oriented decoding algorithm

NASA Technical Reports Server (NTRS)

Lee, L. N.

1976-01-01

Concatenated coding systems utilizing a convolutional code as the inner code and a Reed-Solomon code as the outer code are considered. In order to obtain very reliable communications over a very noisy channel with relatively small coding complexity, it is proposed to concatenate a byte oriented unit memory convolutional code with an RS outer code whose symbol size is one byte. It is further proposed to utilize a real time minimal byte error probability decoding algorithm, together with feedback from the outer decoder, in the decoder for the inner convolutional code. The performance of the proposed concatenated coding system is studied, and the improvement over conventional concatenated systems due to each additional feature is isolated.

LDPC-based iterative joint source-channel decoding for JPEG2000.

PubMed

Pu, Lingling; Wu, Zhenyu; Bilgin, Ali; Marcellin, Michael W; Vasic, Bane

2007-02-01

A framework is proposed for iterative joint source-channel decoding of JPEG2000 codestreams. At the encoder, JPEG2000 is used to perform source coding with certain error-resilience (ER) modes, and LDPC codes are used to perform channel coding. During decoding, the source decoder uses the ER modes to identify corrupt sections of the codestream and provides this information to the channel decoder. Decoding is carried out jointly in an iterative fashion. Experimental results indicate that the proposed method requires fewer iterations and improves overall system performance.

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.

Belief propagation decoding of quantum channels by passing quantum messages

NASA Astrophysics Data System (ADS)

Renes, Joseph M.

2017-07-01

The belief propagation (BP) algorithm is a powerful tool in a wide range of disciplines from statistical physics to machine learning to computational biology, and is ubiquitous in decoding classical error-correcting codes. The algorithm works by passing messages between nodes of the factor graph associated with the code and enables efficient decoding of the channel, in some cases even up to the Shannon capacity. Here we construct the first BP algorithm which passes quantum messages on the factor graph and is capable of decoding the classical-quantum channel with pure state outputs. This gives explicit decoding circuits whose number of gates is quadratic in the code length. We also show that this decoder can be modified to work with polar codes for the pure state channel and as part of a decoder for transmitting quantum information over the amplitude damping channel. These represent the first explicit capacity-achieving decoders for non-Pauli channels.

Tail Biting Trellis Representation of Codes: Decoding and Construction

NASA Technical Reports Server (NTRS)

Shao. Rose Y.; Lin, Shu; Fossorier, Marc

1999-01-01

This paper presents two new iterative algorithms for decoding linear codes based on their tail biting trellises, one is unidirectional and the other is bidirectional. Both algorithms are computationally efficient and achieves virtually optimum error performance with a small number of decoding iterations. They outperform all the previous suboptimal decoding algorithms. The bidirectional algorithm also reduces decoding delay. Also presented in the paper is a method for constructing tail biting trellises for linear block codes.

Application of a Design Space Exploration Tool to Enhance Interleaver Generation

DTIC Science & Technology

2009-06-24

2], originally dedicated to channel coding, are being currently reused in a large set of the whole digital communication systems (e.g. equalization... originally target interface synthesis, is shown to be also suited to the interleaver design space exploration. Our design flow can take as input...slice turbo codes,” in Proc. 3rd Int. Symp. Turbo Codes, Related Topics, Brest , 2003, pp. 343–346. [11] IEEE 802.15.3a, WPAN High Rate Alternative [12

A low-complexity and high performance concatenated coding scheme for high-speed satellite communications

NASA Technical Reports Server (NTRS)

Lin, Shu; Rhee, Dojun; Rajpal, Sandeep

1993-01-01

This report presents a low-complexity and high performance concatenated coding scheme for high-speed satellite communications. In this proposed scheme, the NASA Standard Reed-Solomon (RS) code over GF(2(exp 8) is used as the outer code and the second-order Reed-Muller (RM) code of Hamming distance 8 is used as the inner code. The RM inner code has a very simple trellis structure and is decoded with the soft-decision Viterbi decoding algorithm. It is shown that the proposed concatenated coding scheme achieves an error performance which is comparable to that of the NASA TDRS concatenated coding scheme in which the NASA Standard rate-1/2 convolutional code of constraint length 7 and d sub free = 10 is used as the inner code. However, the proposed RM inner code has much smaller decoding complexity, less decoding delay, and much higher decoding speed. Consequently, the proposed concatenated coding scheme is suitable for reliable high-speed satellite communications, and it may be considered as an alternate coding scheme for the NASA TDRS system.

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.

Multi-level trellis coded modulation and multi-stage decoding

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.; Wu, Jiantian; Lin, Shu

1990-01-01

Several constructions for multi-level trellis codes are presented and many codes with better performance than previously known codes are found. These codes provide a flexible trade-off between coding gain, decoding complexity, and decoding delay. New multi-level trellis coded modulation schemes using generalized set partitioning methods are developed for Quadrature Amplitude Modulation (QAM) and Phase Shift Keying (PSK) signal sets. New rotationally invariant multi-level trellis codes which can be combined with differential encoding to resolve phase ambiguity are presented.

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.

Deep Learning Methods for Improved Decoding of Linear Codes

NASA Astrophysics Data System (ADS)

Nachmani, Eliya; Marciano, Elad; Lugosch, Loren; Gross, Warren J.; Burshtein, David; Be'ery, Yair

2018-02-01

The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder, despite the large example space. Similar improvements are obtained for the min-sum algorithm. It is also shown that tying the parameters of the decoders across iterations, so as to form a recurrent neural network architecture, can be implemented with comparable results. The advantage is that significantly less parameters are required. We also introduce a recurrent neural decoder architecture based on the method of successive relaxation. Improvements over standard belief propagation are also observed on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the neural belief propagation decoder can be used to improve the performance, or alternatively reduce the computational complexity, of a close to optimal decoder of short BCH codes.

Unsteady Full Annulus Simulations of a Transonic Axial Compressor Stage

NASA Technical Reports Server (NTRS)

Herrick, Gregory P.; Hathaway, Michael D.; Chen, Jen-Ping

2009-01-01

Two recent research endeavors in turbomachinery at NASA Glenn Research Center have focused on compression system stall inception and compression system aerothermodynamic performance. Physical experiment and computational research are ongoing in support of these research objectives. TURBO, an unsteady, three-dimensional, Navier-Stokes computational fluid dynamics code commissioned and developed by NASA, has been utilized, enhanced, and validated in support of these endeavors. In the research which follows, TURBO is shown to accurately capture compression system flow range-from choke to stall inception-and also to accurately calculate fundamental aerothermodynamic performance parameters. Rigorous full-annulus calculations are performed to validate TURBO s ability to simulate the unstable, unsteady, chaotic stall inception process; as part of these efforts, full-annulus calculations are also performed at a condition approaching choke to further document TURBO s capabilities to compute aerothermodynamic performance data and support a NASA code assessment effort.

Parallel Unsteady Turbopump Simulations for Liquid Rocket Engines

NASA Technical Reports Server (NTRS)

Kiris, Cetin C.; Kwak, Dochan; Chan, William

2000-01-01

This paper reports the progress being made towards complete turbo-pump simulation capability for liquid rocket engines. Space Shuttle Main Engine (SSME) turbo-pump impeller is used as a test case for the performance evaluation of the MPI and hybrid MPI/Open-MP versions of the INS3D code. Then, a computational model of a turbo-pump has been developed for the shuttle upgrade program. Relative motion of the grid system for rotor-stator interaction was obtained by employing overset grid techniques. Time-accuracy of the scheme has been evaluated by using simple test cases. Unsteady computations for SSME turbo-pump, which contains 136 zones with 35 Million grid points, are currently underway on Origin 2000 systems at NASA Ames Research Center. Results from time-accurate simulations with moving boundary capability, and the performance of the parallel versions of the code will be presented in the final paper.

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.

The Limits of Coding with Joint Constraints on Detected and Undetected Error Rates

NASA Technical Reports Server (NTRS)

Dolinar, Sam; Andrews, Kenneth; Pollara, Fabrizio; Divsalar, Dariush

2008-01-01

We develop a remarkably tight upper bound on the performance of a parameterized family of bounded angle maximum-likelihood (BA-ML) incomplete decoders. The new bound for this class of incomplete decoders is calculated from the code's weight enumerator, and is an extension of Poltyrev-type bounds developed for complete ML decoders. This bound can also be applied to bound the average performance of random code ensembles in terms of an ensemble average weight enumerator. We also formulate conditions defining a parameterized family of optimal incomplete decoders, defined to minimize both the total codeword error probability and the undetected error probability for any fixed capability of the decoder to detect errors. We illustrate the gap between optimal and BA-ML incomplete decoding via simulation of a small code.

The VLSI design of an error-trellis syndrome decoder for certain convolutional codes

NASA Technical Reports Server (NTRS)

Reed, I. S.; Jensen, J. M.; Hsu, I.-S.; Truong, T. K.

1986-01-01

A recursive algorithm using the error-trellis decoding technique is developed to decode convolutional codes (CCs). An example, illustrating the very large scale integration (VLSI) architecture of such a decode, is given for a dual-K CC. It is demonstrated that such a decoder can be realized readily on a single chip with metal-nitride-oxide-semiconductor technology.

The VLSI design of error-trellis syndrome decoding for convolutional codes

NASA Technical Reports Server (NTRS)

Reed, I. S.; Jensen, J. M.; Truong, T. K.; Hsu, I. S.

1985-01-01

A recursive algorithm using the error-trellis decoding technique is developed to decode convolutional codes (CCs). An example, illustrating the very large scale integration (VLSI) architecture of such a decode, is given for a dual-K CC. It is demonstrated that such a decoder can be realized readily on a single chip with metal-nitride-oxide-semiconductor technology.

Progress of High Efficiency Centrifugal Compressor Simulations Using TURBO

NASA Technical Reports Server (NTRS)

Kulkarni, Sameer; Beach, Timothy A.

2017-01-01

Three-dimensional, time-accurate, and phase-lagged computational fluid dynamics (CFD) simulations of the High Efficiency Centrifugal Compressor (HECC) stage were generated using the TURBO solver. Changes to the TURBO Parallel Version 4 source code were made in order to properly model the no-slip boundary condition along the spinning hub region for centrifugal impellers. A startup procedure was developed to generate a converged flow field in TURBO. This procedure initialized computations on a coarsened mesh generated by the Turbomachinery Gridding System (TGS) and relied on a method of systematically increasing wheel speed and backpressure. Baseline design-speed TURBO results generally overpredicted total pressure ratio, adiabatic efficiency, and the choking flow rate of the HECC stage as compared with the design-intent CFD results of Code Leo. Including diffuser fillet geometry in the TURBO computation resulted in a 0.6 percent reduction in the choking flow rate and led to a better match with design-intent CFD. Diffuser fillets reduced annulus cross-sectional area but also reduced corner separation, and thus blockage, in the diffuser passage. It was found that the TURBO computations are somewhat insensitive to inlet total pressure changing from the TURBO default inlet pressure of 14.7 pounds per square inch (101.35 kilopascals) down to 11.0 pounds per square inch (75.83 kilopascals), the inlet pressure of the component test. Off-design tip clearance was modeled in TURBO in two computations: one in which the blade tip geometry was trimmed by 12 mils (0.3048 millimeters), and another in which the hub flow path was moved to reflect a 12-mil axial shift in the impeller hub, creating a step at the hub. The one-dimensional results of these two computations indicate non-negligible differences between the two modeling approaches.

National Aerospace Leadership Initiative - Phase I

DTIC Science & Technology

2008-09-30

Devised and validated CFD code for operation of a micro-channel heat exchanger. The work was published at the 2008 AIAA Annual Meeting and Exposition...and (3) preparation to implement this algorithm in TURBO. Heat Transfer Capability In the short and medium term, the following plan has been adopted...to provide heat transfer capability to the TURBO code: • Incorporation of a constant wall temperature boundary condition. This capability will be

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.

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.

Development of an Aeroelastic Analysis Including a Viscous Flow Model

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Bakhle, Milind A.

2001-01-01

Under this grant, Version 4 of the three-dimensional Navier-Stokes aeroelastic code (TURBO-AE) has been developed and verified. The TURBO-AE Version 4 aeroelastic code allows flutter calculations for a fan, compressor, or turbine blade row. This code models a vibrating three-dimensional bladed disk configuration and the associated unsteady flow (including shocks, and viscous effects) to calculate the aeroelastic instability using a work-per-cycle approach. Phase-lagged (time-shift) periodic boundary conditions are used to model the phase lag between adjacent vibrating blades. The direct-store approach is used for this purpose to reduce the computational domain to a single interblade passage. A disk storage option, implemented using direct access files, is available to reduce the large memory requirements of the direct-store approach. Other researchers have implemented 3D inlet/exit boundary conditions based on eigen-analysis. Appendix A: Aeroelastic calculations based on three-dimensional euler analysis. Appendix B: Unsteady aerodynamic modeling of blade vibration using the turbo-V3.1 code.

Maximum-likelihood soft-decision decoding of block codes using the A* algorithm

NASA Technical Reports Server (NTRS)

Ekroot, L.; Dolinar, S.

1994-01-01

The A* algorithm finds the path in a finite depth binary tree that optimizes a function. Here, it is applied to maximum-likelihood soft-decision decoding of block codes where the function optimized over the codewords is the likelihood function of the received sequence given each codeword. The algorithm considers codewords one bit at a time, making use of the most reliable received symbols first and pursuing only the partially expanded codewords that might be maximally likely. A version of the A* algorithm for maximum-likelihood decoding of block codes has been implemented for block codes up to 64 bits in length. The efficiency of this algorithm makes simulations of codes up to length 64 feasible. This article details the implementation currently in use, compares the decoding complexity with that of exhaustive search and Viterbi decoding algorithms, and presents performance curves obtained with this implementation of the A* algorithm for several codes.

On the error probability of general tree and trellis codes with applications to sequential decoding

NASA Technical Reports Server (NTRS)

Johannesson, R.

1973-01-01

An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random binary tree codes is derived and shown to be independent of the length of the tree. An upper bound on the average error probability for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n is derived which separates the effects of the tail length T and the memory length M of the code. It is shown that the bound is independent of the length L of the information sequence. This implication is investigated by computer simulations of sequential decoding utilizing the stack algorithm. These simulations confirm the implication and further suggest an empirical formula for the true undetected decoding error probability with sequential decoding.

Viterbi decoding for satellite and space communication.

NASA Technical Reports Server (NTRS)

Heller, J. A.; Jacobs, I. M.

1971-01-01

Convolutional coding and Viterbi decoding, along with binary phase-shift keyed modulation, is presented as an efficient system for reliable communication on power limited satellite and space channels. Performance results, obtained theoretically and through computer simulation, are given for optimum short constraint length codes for a range of code constraint lengths and code rates. System efficiency is compared for hard receiver quantization and 4 and 8 level soft quantization. The effects on performance of varying of certain parameters relevant to decoder complexity and cost are examined. Quantitative performance degradation due to imperfect carrier phase coherence is evaluated and compared to that of an uncoded system. As an example of decoder performance versus complexity, a recently implemented 2-Mbit/sec constraint length 7 Viterbi decoder is discussed. Finally a comparison is made between Viterbi and sequential decoding in terms of suitability to various system requirements.

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.

Numerical and analytical bounds on threshold error rates for hypergraph-product codes

NASA Astrophysics Data System (ADS)

Kovalev, Alexey A.; Prabhakar, Sanjay; Dumer, Ilya; Pryadko, Leonid P.

2018-06-01

We study analytically and numerically decoding properties of finite-rate hypergraph-product quantum low density parity-check codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several nontrivial lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models and a minimum-weight decoding threshold of approximately 7 % .

Low Power LDPC Code Decoder Architecture Based on Intermediate Message Compression Technique

NASA Astrophysics Data System (ADS)

Shimizu, Kazunori; Togawa, Nozomu; Ikenaga, Takeshi; Goto, Satoshi

Reducing the power dissipation for LDPC code decoder is a major challenging task to apply it to the practical digital communication systems. In this paper, we propose a low power LDPC code decoder architecture based on an intermediate message-compression technique which features as follows: (i) An intermediate message compression technique enables the decoder to reduce the required memory capacity and write power dissipation. (ii) A clock gated shift register based intermediate message memory architecture enables the decoder to decompress the compressed messages in a single clock cycle while reducing the read power dissipation. The combination of the above two techniques enables the decoder to reduce the power dissipation while keeping the decoding throughput. The simulation results show that the proposed architecture improves the power efficiency up to 52% and 18% compared to that of the decoder based on the overlapped schedule and the rapid convergence schedule without the proposed techniques respectively.

The fast decoding of Reed-Solomon codes using number theoretic transforms

NASA Technical Reports Server (NTRS)

Reed, I. S.; Welch, L. R.; Truong, T. K.

1976-01-01

It is shown that Reed-Solomon (RS) codes can be encoded and decoded by using a fast Fourier transform (FFT) algorithm over finite fields. The arithmetic utilized to perform these transforms requires only integer additions, circular shifts and a minimum number of integer multiplications. The computing time of this transform encoder-decoder for RS codes is less than the time of the standard method for RS codes. More generally, the field GF(q) is also considered, where q is a prime of the form K x 2 to the nth power + 1 and K and n are integers. GF(q) can be used to decode very long RS codes by an efficient FFT algorithm with an improvement in the number of symbols. It is shown that a radix-8 FFT algorithm over GF(q squared) can be utilized to encode and decode very long RS codes with a large number of symbols. For eight symbols in GF(q squared), this transform over GF(q squared) can be made simpler than any other known number theoretic transform with a similar capability. Of special interest is the decoding of a 16-tuple RS code with four errors.

Coding and decoding in a point-to-point communication using the polarization of the light beam.

PubMed

Kavehvash, Z; Massoumian, F

2008-05-10

A new technique for coding and decoding of optical signals through the use of polarization is described. In this technique the concept of coding is translated to polarization. In other words, coding is done in such a way that each code represents a unique polarization. This is done by implementing a binary pattern on a spatial light modulator in such a way that the reflected light has the required polarization. Decoding is done by the detection of the received beam's polarization. By linking the concept of coding to polarization we can use each of these concepts in measuring the other one, attaining some gains. In this paper the construction of a simple point-to-point communication where coding and decoding is done through polarization will be discussed.

Adaptive software-defined coded modulation for ultra-high-speed optical transport

NASA Astrophysics Data System (ADS)

Djordjevic, Ivan B.; Zhang, Yequn

2013-10-01

In optically-routed networks, different wavelength channels carrying the traffic to different destinations can have quite different optical signal-to-noise ratios (OSNRs) and signal is differently impacted by various channel impairments. Regardless of the data destination, an optical transport system (OTS) must provide the target bit-error rate (BER) performance. To provide target BER regardless of the data destination we adjust the forward error correction (FEC) strength. Depending on the information obtained from the monitoring channels, we select the appropriate code rate matching to the OSNR range that current channel OSNR falls into. To avoid frame synchronization issues, we keep the codeword length fixed independent of the FEC code being employed. The common denominator is the employment of quasi-cyclic (QC-) LDPC codes in FEC. For high-speed implementation, low-complexity LDPC decoding algorithms are needed, and some of them will be described in this invited paper. Instead of conventional QAM based modulation schemes, we employ the signal constellations obtained by optimum signal constellation design (OSCD) algorithm. To improve the spectral efficiency, we perform the simultaneous rate adaptation and signal constellation size selection so that the product of number of bits per symbol × code rate is closest to the channel capacity. Further, we describe the advantages of using 4D signaling instead of polarization-division multiplexed (PDM) QAM, by using the 4D MAP detection, combined with LDPC coding, in a turbo equalization fashion. Finally, to solve the problems related to the limited bandwidth of information infrastructure, high energy consumption, and heterogeneity of optical networks, we describe an adaptive energy-efficient hybrid coded-modulation scheme, which in addition to amplitude, phase, and polarization state employs the spatial modes as additional basis functions for multidimensional coded-modulation.

Coset Codes Viewed as Terminated Convolutional Codes

NASA Technical Reports Server (NTRS)

Fossorier, Marc P. C.; Lin, Shu

1996-01-01

In this paper, coset codes are considered as terminated convolutional codes. Based on this approach, three new general results are presented. First, it is shown that the iterative squaring construction can equivalently be defined from a convolutional code whose trellis terminates. This convolutional code determines a simple encoder for the coset code considered, and the state and branch labelings of the associated trellis diagram become straightforward. Also, from the generator matrix of the code in its convolutional code form, much information about the trade-off between the state connectivity and complexity at each section, and the parallel structure of the trellis, is directly available. Based on this generator matrix, it is shown that the parallel branches in the trellis diagram of the convolutional code represent the same coset code C(sub 1), of smaller dimension and shorter length. Utilizing this fact, a two-stage optimum trellis decoding method is devised. The first stage decodes C(sub 1), while the second stage decodes the associated convolutional code, using the branch metrics delivered by stage 1. Finally, a bidirectional decoding of each received block starting at both ends is presented. If about the same number of computations is required, this approach remains very attractive from a practical point of view as it roughly doubles the decoding speed. This fact is particularly interesting whenever the second half of the trellis is the mirror image of the first half, since the same decoder can be implemented for both parts.

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.

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.

Reed-Solomon decoder

NASA Technical Reports Server (NTRS)

Lahmeyer, Charles R. (Inventor)

1987-01-01

A Reed-Solomon decoder with dedicated hardware for five sequential algorithms was designed with overall pipelining by memory swapping between input, processing and output memories, and internal pipelining through the five algorithms. The code definition used in decoding is specified by a keyword received with each block of data so that a number of different code formats may be decoded by the same hardware.

Evaluation of large girth LDPC codes for PMD compensation by turbo equalization.

PubMed

Minkov, Lyubomir L; Djordjevic, Ivan B; Xu, Lei; Wang, Ting; Kueppers, Franko

2008-08-18

Large-girth quasi-cyclic LDPC codes have been experimentally evaluated for use in PMD compensation by turbo equalization for a 10 Gb/s NRZ optical transmission system, and observing one sample per bit. Net effective coding gain improvement for girth-10, rate 0.906 code of length 11936 over maximum a posteriori probability (MAP) detector for differential group delay of 125 ps is 6.25 dB at BER of 10(-6). Girth-10 LDPC code of rate 0.8 outperforms the girth-10 code of rate 0.906 by 2.75 dB, and provides the net effective coding gain improvement of 9 dB at the same BER. It is experimentally determined that girth-10 LDPC codes of length around 15000 approach channel capacity limit within 1.25 dB.

Signal-processing theory for the TurboRogue receiver

NASA Technical Reports Server (NTRS)

Thomas, J. B.

1995-01-01

Signal-processing theory for the TurboRogue receiver is presented. The signal form is traced from its formation at the GPS satellite, to the receiver antenna, and then through the various stages of the receiver, including extraction of phase and delay. The analysis treats the effects of ionosphere, troposphere, signal quantization, receiver components, and system noise, covering processing in both the 'code mode' when the P code is not encrypted and in the 'P-codeless mode' when the P code is encrypted. As a possible future improvement to the current analog front end, an example of a highly digital front end is analyzed.

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.

Self-Configuration and Localization in Ad Hoc Wireless Sensor Networks

DTIC Science & Technology

2010-08-31

Goddard I. SUMMARY OF CONTRIBUTIONS We explored the error mechanisms of iterative decoding of low-density parity-check ( LDPC ) codes . This work has resulted...important problems in the area of channel coding , as their unpredictable behavior has impeded the deployment of LDPC codes in many real-world applications. We...tree-based decoders of LDPC codes , including the extrinsic tree decoder, and an investigation into their performance and bounding capabilities [5], [6

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.

Bit Error Probability for Maximum Likelihood Decoding of Linear Block Codes

NASA Technical Reports Server (NTRS)

Lin, Shu; Fossorier, Marc P. C.; Rhee, Dojun

1996-01-01

In this paper, the bit error probability P(sub b) for maximum likelihood decoding of binary linear codes is investigated. The contribution of each information bit to P(sub b) is considered. For randomly generated codes, it is shown that the conventional approximation at high SNR P(sub b) is approximately equal to (d(sub H)/N)P(sub s), where P(sub s) represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P(sub b) when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for decoding methods which require a generator matrix with a particular structure such as trellis decoding or algebraic-based soft decision decoding, equivalent schemes that reduce the bit error probability are discussed.

PSEUDO-CODEWORD LANDSCAPE

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

CHERTKOV, MICHAEL; STEPANOV, MIKHAIL

2007-01-10

The authors discuss performance of Low-Density-Parity-Check (LDPC) codes decoded by Linear Programming (LP) decoding at moderate and large Signal-to-Noise-Ratios (SNR). Frame-Error-Rate (FER) dependence on SNR and the noise space landscape of the coding/decoding scheme are analyzed by a combination of the previously introduced instanton/pseudo-codeword-search method and a new 'dendro' trick. To reduce complexity of the LP decoding for a code with high-degree checks, {ge} 5, they introduce its dendro-LDPC counterpart, that is the code performing identifically to the original one under Maximum-A-Posteriori (MAP) decoding but having reduced (down to three) check connectivity degree. Analyzing number of popular LDPC codes andmore » their dendro versions performing over the Additive-White-Gaussian-Noise (AWGN) channel, they observed two qualitatively different regimes: (i) error-floor sets early, at relatively low SNR, and (ii) FER decays with SNR increase faster at moderate SNR than at the largest SNR. They explain these regimes in terms of the pseudo-codeword spectra of the codes.« less

"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

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.

Low complexity Reed-Solomon-based low-density parity-check design for software defined optical transmission system based on adaptive puncturing decoding algorithm

NASA Astrophysics Data System (ADS)

Pan, Xiaolong; Liu, Bo; Zheng, Jianglong; Tian, Qinghua

2016-08-01

We propose and demonstrate a low complexity Reed-Solomon-based low-density parity-check (RS-LDPC) code with adaptive puncturing decoding algorithm for elastic optical transmission system. Partial received codes and the relevant column in parity-check matrix can be punctured to reduce the calculation complexity by adaptive parity-check matrix during decoding process. The results show that the complexity of the proposed decoding algorithm is reduced by 30% compared with the regular RS-LDPC system. The optimized code rate of the RS-LDPC code can be obtained after five times iteration.

High-dimensional structured light coding/decoding for free-space optical communications free of obstructions.

PubMed

Du, Jing; Wang, Jian

2015-11-01

Bessel beams carrying orbital angular momentum (OAM) with helical phase fronts exp(ilφ)(l=0;±1;±2;…), where φ is the azimuthal angle and l corresponds to the topological number, are orthogonal with each other. This feature of Bessel beams provides a new dimension to code/decode data information on the OAM state of light, and the theoretical infinity of topological number enables possible high-dimensional structured light coding/decoding for free-space optical communications. Moreover, Bessel beams are nondiffracting beams having the ability to recover by themselves in the face of obstructions, which is important for free-space optical communications relying on line-of-sight operation. By utilizing the OAM and nondiffracting characteristics of Bessel beams, we experimentally demonstrate 12 m distance obstruction-free optical m-ary coding/decoding using visible Bessel beams in a free-space optical communication system. We also study the bit error rate (BER) performance of hexadecimal and 32-ary coding/decoding based on Bessel beams with different topological numbers. After receiving 500 symbols at the receiver side, a zero BER of hexadecimal coding/decoding is observed when the obstruction is placed along the propagation path of light.

Robust Nonlinear Neural Codes

NASA Astrophysics Data System (ADS)

Yang, Qianli; Pitkow, Xaq

2015-03-01

Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.

Mapping visual stimuli to perceptual decisions via sparse decoding of mesoscopic neural activity.

PubMed

Sajda, Paul

2010-01-01

In this talk I will describe our work investigating sparse decoding of neural activity, given a realistic mapping of the visual scene to neuronal spike trains generated by a model of primary visual cortex (V1). We use a linear decoder which imposes sparsity via an L1 norm. The decoder can be viewed as a decoding neuron (linear summation followed by a sigmoidal nonlinearity) in which there are relatively few non-zero synaptic weights. We find: (1) the best decoding performance is for a representation that is sparse in both space and time, (2) decoding of a temporal code results in better performance than a rate code and is also a better fit to the psychophysical data, (3) the number of neurons required for decoding increases monotonically as signal-to-noise in the stimulus decreases, with as little as 1% of the neurons required for decoding at the highest signal-to-noise levels, and (4) sparse decoding results in a more accurate decoding of the stimulus and is a better fit to psychophysical performance than a distributed decoding, for example one imposed by an L2 norm. We conclude that sparse coding is well-justified from a decoding perspective in that it results in a minimum number of neurons and maximum accuracy when sparse representations can be decoded from the neural dynamics.

Implementation of control point form of algebraic grid-generation technique

NASA Technical Reports Server (NTRS)

Choo, Yung K.; Miller, David P.; Reno, Charles J.

1991-01-01

The control point form (CPF) provides explicit control of physical grid shape and grid spacing through the movement of the control points. The control point array, called a control net, is a space grid type arrangement of locations in physical space with an index for each direction. As an algebraic method CPF is efficient and works well with interactive computer graphics. A family of menu-driven, interactive grid-generation computer codes (TURBO) is being developed by using CPF. Key features of TurboI (a TURBO member) are discussed and typical results are presented. TurboI runs on any IRIS 4D series workstation.

Multiple-Symbol Noncoherent Decoding of Uncoded and Convolutionally Codes Continous Phase Modulation

NASA Technical Reports Server (NTRS)

Divsalar, D.; Raphaeli, D.

2000-01-01

Recently, a method for combined noncoherent detection and decoding of trellis-codes (noncoherent coded modulation) has been proposed, which can practically approach the performance of coherent detection.

Approximate maximum likelihood decoding of block codes

NASA Technical Reports Server (NTRS)

Greenberger, H. J.

1979-01-01

Approximate maximum likelihood decoding algorithms, based upon selecting a small set of candidate code words with the aid of the estimated probability of error of each received symbol, can give performance close to optimum with a reasonable amount of computation. By combining the best features of various algorithms and taking care to perform each step as efficiently as possible, a decoding scheme was developed which can decode codes which have better performance than those presently in use and yet not require an unreasonable amount of computation. The discussion of the details and tradeoffs of presently known efficient optimum and near optimum decoding algorithms leads, naturally, to the one which embodies the best features of all of them.

Rate-Compatible Protograph LDPC Codes

NASA Technical Reports Server (NTRS)

Nguyen, Thuy V. (Inventor); Nosratinia, Aria (Inventor); Divsalar, Dariush (Inventor)

2014-01-01

Digital communication coding methods resulting in rate-compatible low density parity-check (LDPC) codes built from protographs. Described digital coding methods start with a desired code rate and a selection of the numbers of variable nodes and check nodes to be used in the protograph. Constraints are set to satisfy a linear minimum distance growth property for the protograph. All possible edges in the graph are searched for the minimum iterative decoding threshold and the protograph with the lowest iterative decoding threshold is selected. Protographs designed in this manner are used in decode and forward relay channels.

Method of Error Floor Mitigation in Low-Density Parity-Check Codes

NASA Technical Reports Server (NTRS)

Hamkins, Jon (Inventor)

2014-01-01

A digital communication decoding method for low-density parity-check coded messages. The decoding method decodes the low-density parity-check coded messages within a bipartite graph having check nodes and variable nodes. Messages from check nodes are partially hard limited, so that every message which would otherwise have a magnitude at or above a certain level is re-assigned to a maximum magnitude.

Architecture for time or transform domain decoding of reed-solomon codes

NASA Technical Reports Server (NTRS)

Hsu, In-Shek (Inventor); Truong, Trieu-Kie (Inventor); Deutsch, Leslie J. (Inventor); Shao, Howard M. (Inventor)

1989-01-01

Two pipeline (255,233) RS decoders, one a time domain decoder and the other a transform domain decoder, use the same first part to develop an errata locator polynomial .tau.(x), and an errata evaluator polynominal A(x). Both the time domain decoder and transform domain decoder have a modified GCD that uses an input multiplexer and an output demultiplexer to reduce the number of GCD cells required. The time domain decoder uses a Chien search and polynomial evaluator on the GCD outputs .tau.(x) and A(x), for the final decoding steps, while the transform domain decoder uses a transform error pattern algorithm operating on .tau.(x) and the initial syndrome computation S(x), followed by an inverse transform algorithm in sequence for the final decoding steps prior to adding the received RS coded message to produce a decoded output message.

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.

Modulation and coding for satellite and space communications

NASA Technical Reports Server (NTRS)

Yuen, Joseph H.; Simon, Marvin K.; Pollara, Fabrizio; Divsalar, Dariush; Miller, Warner H.; Morakis, James C.; Ryan, Carl R.

1990-01-01

Several modulation and coding advances supported by NASA are summarized. To support long-constraint-length convolutional code, a VLSI maximum-likelihood decoder, utilizing parallel processing techniques, which is being developed to decode convolutional codes of constraint length 15 and a code rate as low as 1/6 is discussed. A VLSI high-speed 8-b Reed-Solomon decoder which is being developed for advanced tracking and data relay satellite (ATDRS) applications is discussed. A 300-Mb/s modem with continuous phase modulation (CPM) and codings which is being developed for ATDRS is discussed. Trellis-coded modulation (TCM) techniques are discussed for satellite-based mobile communication applications.

Soft-decision decoding techniques for linear block codes and their error performance analysis

NASA Technical Reports Server (NTRS)

Lin, Shu

1996-01-01

The first paper presents a new minimum-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The second paper derives an upper bound on the probability of block error for multilevel concatenated codes (MLCC). The bound evaluates difference in performance for different decompositions of some codes. The third paper investigates the bit error probability code for maximum likelihood decoding of binary linear codes. The fourth and final paper included in this report is concerns itself with the construction of multilevel concatenated block modulation codes using a multilevel concatenation scheme for the frequency non-selective Rayleigh fading channel.

Validation of Heat Transfer and Film Cooling Capabilities of the 3-D RANS Code TURBO

NASA Technical Reports Server (NTRS)

Shyam, Vikram; Ameri, Ali; Chen, Jen-Ping

2010-01-01

The capabilities of the 3-D unsteady RANS code TURBO have been extended to include heat transfer and film cooling applications. The results of simulations performed with the modified code are compared to experiment and to theory, where applicable. Wilcox s k-turbulence model has been implemented to close the RANS equations. Two simulations are conducted: (1) flow over a flat plate and (2) flow over an adiabatic flat plate cooled by one hole inclined at 35 to the free stream. For (1) agreement with theory is found to be excellent for heat transfer, represented by local Nusselt number, and quite good for momentum, as represented by the local skin friction coefficient. This report compares the local skin friction coefficients and Nusselt numbers on a flat plate obtained using Wilcox's k-model with the theory of Blasius. The study looks at laminar and turbulent flows over an adiabatic flat plate and over an isothermal flat plate for two different wall temperatures. It is shown that TURBO is able to accurately predict heat transfer on a flat plate. For (2) TURBO shows good qualitative agreement with film cooling experiments performed on a flat plate with one cooling hole. Quantitatively, film effectiveness is under predicted downstream of the hole.

Method and apparatus for data decoding and processing

DOEpatents

Hunter, Timothy M.; Levy, Arthur J.

1992-01-01

A system and technique is disclosed for automatically controlling the decoding and digitizaiton of an analog tape. The system includes the use of a tape data format which includes a plurality of digital codes recorded on the analog tape in a predetermined proximity to a period of recorded analog data. The codes associated with each period of analog data include digital identification codes prior to the analog data, a start of data code coincident with the analog data recording, and an end of data code subsequent to the associated period of recorded analog data. The formatted tape is decoded in a processing and digitization system which includes an analog tape player coupled to a digitizer to transmit analog information from the recorded tape over at least one channel to the digitizer. At the same time, the tape player is coupled to a decoder and interface system which detects and decodes the digital codes on the tape corresponding to each period of recorded analog data and controls tape movement and digitizer initiation in response to preprogramed modes. A host computer is also coupled to the decoder and interface system and the digitizer and programmed to initiate specific modes of data decoding through the decoder and interface system including the automatic compilation and storage of digital identification information and digitized data for the period of recorded analog data corresponding to the digital identification data, compilation and storage of selected digitized data representing periods of recorded analog data, and compilation of digital identification information related to each of the periods of recorded analog data.

A reduced complexity highly power/bandwidth efficient coded FQPSK system with iterative decoding

NASA Technical Reports Server (NTRS)

Simon, M. K.; Divsalar, D.

2001-01-01

Based on a representation of FQPSK as a trellis-coded modulation, this paper investigates the potential improvement in power efficiency obtained from the application of simple outer codes to form a concatenated coding arrangement with iterative decoding.

Investigation of the Use of Erasures in a Concatenated Coding Scheme

NASA Technical Reports Server (NTRS)

Kwatra, S. C.; Marriott, Philip J.

1997-01-01

A new method for declaring erasures in a concatenated coding scheme is investigated. This method is used with the rate 1/2 K = 7 convolutional code and the (255, 223) Reed Solomon code. Errors and erasures Reed Solomon decoding is used. The erasure method proposed uses a soft output Viterbi algorithm and information provided by decoded Reed Solomon codewords in a deinterleaving frame. The results show that a gain of 0.3 dB is possible using a minimum amount of decoding trials.

Separable concatenated codes with iterative map decoding for Rician fading channels

NASA Technical Reports Server (NTRS)

Lodge, J. H.; Young, R. J.

1993-01-01

Very efficient signalling in radio channels requires the design of very powerful codes having special structure suitable for practical decoding schemes. In this paper, powerful codes are obtained by combining comparatively simple convolutional codes to form multi-tiered 'separable' convolutional codes. The decoding of these codes, using separable symbol-by-symbol maximum a posteriori (MAP) 'filters', is described. It is known that this approach yields impressive results in non-fading additive white Gaussian noise channels. Interleaving is an inherent part of the code construction, and consequently, these codes are well suited for fading channel communications. Here, simulation results for communications over Rician fading channels are presented to support this claim.

Comparison of rate one-half, equivalent constraint length 24, binary convolutional codes for use with sequential decoding on the deep-space channel

NASA Technical Reports Server (NTRS)

Massey, J. L.

1976-01-01

Virtually all previously-suggested rate 1/2 binary convolutional codes with KE = 24 are compared. Their distance properties are given; and their performance, both in computation and in error probability, with sequential decoding on the deep-space channel is determined by simulation. Recommendations are made both for the choice of a specific KE = 24 code as well as for codes to be included in future coding standards for the deep-space channel. A new result given in this report is a method for determining the statistical significance of error probability data when the error probability is so small that it is not feasible to perform enough decoding simulations to obtain more than a very small number of decoding errors.

Feature reconstruction of LFP signals based on PLSR in the neural information decoding study.

PubMed

Yonghui Dong; Zhigang Shang; Mengmeng Li; Xinyu Liu; Hong Wan

2017-07-01

To solve the problems of Signal-to-Noise Ratio (SNR) and multicollinearity when the Local Field Potential (LFP) signals is used for the decoding of animal motion intention, a feature reconstruction of LFP signals based on partial least squares regression (PLSR) in the neural information decoding study is proposed in this paper. Firstly, the feature information of LFP coding band is extracted based on wavelet transform. Then the PLSR model is constructed by the extracted LFP coding features. According to the multicollinearity characteristics among the coding features, several latent variables which contribute greatly to the steering behavior are obtained, and the new LFP coding features are reconstructed. Finally, the K-Nearest Neighbor (KNN) method is used to classify the reconstructed coding features to verify the decoding performance. The results show that the proposed method can achieve the highest accuracy compared to the other three methods and the decoding effect of the proposed method is robust.

Good Trellises for IC Implementation of Viterbi Decoders for Linear Block Codes

NASA Technical Reports Server (NTRS)

Moorthy, Hari T.; Lin, Shu; Uehara, Gregory T.

1997-01-01

This paper investigates trellis structures of linear block codes for the integrated circuit (IC) implementation of Viterbi decoders capable of achieving high decoding speed while satisfying a constraint on the structural complexity of the trellis in terms of the maximum number of states at any particular depth. Only uniform sectionalizations of the code trellis diagram are considered. An upper-bound on the number of parallel and structurally identical (or isomorphic) subtrellises in a proper trellis for a code without exceeding the maximum state complexity of the minimal trellis of the code is first derived. Parallel structures of trellises with various section lengths for binary BCH and Reed-Muller (RM) codes of lengths 32 and 64 are analyzed. Next, the complexity of IC implementation of a Viterbi decoder based on an L-section trellis diagram for a code is investigated. A structural property of a Viterbi decoder called add-compare-select (ACS)-connectivity which is related to state connectivity is introduced. This parameter affects the complexity of wire-routing (interconnections within the IC). The effect of five parameters namely: (1) effective computational complexity; (2) complexity of the ACS-circuit; (3) traceback complexity; (4) ACS-connectivity; and (5) branch complexity of a trellis diagram on the very large scale integration (VISI) complexity of a Viterbi decoder is investigated. It is shown that an IC implementation of a Viterbi decoder based on a nonminimal trellis requires less area and is capable of operation at higher speed than one based on the minimal trellis when the commonly used ACS-array architecture is considered.

Good trellises for IC implementation of viterbi decoders for linear block codes

NASA Technical Reports Server (NTRS)

Lin, Shu; Moorthy, Hari T.; Uehara, Gregory T.

1996-01-01

This paper investigates trellis structures of linear block codes for the IC (integrated circuit) implementation of Viterbi decoders capable of achieving high decoding speed while satisfying a constraint on the structural complexity of the trellis in terms of the maximum number of states at any particular depth. Only uniform sectionalizations of the code trellis diagram are considered. An upper bound on the number of parallel and structurally identical (or isomorphic) subtrellises in a proper trellis for a code without exceeding the maximum state complexity of the minimal trellis of the code is first derived. Parallel structures of trellises with various section lengths for binary BCH and Reed-Muller (RM) codes of lengths 32 and 64 are analyzed. Next, the complexity of IC implementation of a Viterbi decoder based on an L-section trellis diagram for a code is investigated. A structural property of a Viterbi decoder called ACS-connectivity which is related to state connectivity is introduced. This parameter affects the complexity of wire-routing (interconnections within the IC). The effect of five parameters namely: (1) effective computational complexity; (2) complexity of the ACS-circuit; (3) traceback complexity; (4) ACS-connectivity; and (5) branch complexity of a trellis diagram on the VLSI complexity of a Viterbi decoder is investigated. It is shown that an IC implementation of a Viterbi decoder based on a non-minimal trellis requires less area and is capable of operation at higher speed than one based on the minimal trellis when the commonly used ACS-array architecture is considered.

Decoding DNA labels by melting curve analysis using real-time PCR.

PubMed

Balog, József A; Fehér, Liliána Z; Puskás, László G

2017-12-01

Synthetic DNA has been used as an authentication code for a diverse number of applications. However, existing decoding approaches are based on either DNA sequencing or the determination of DNA length variations. Here, we present a simple alternative protocol for labeling different objects using a small number of short DNA sequences that differ in their melting points. Code amplification and decoding can be done in two steps using quantitative PCR (qPCR). To obtain a DNA barcode with high complexity, we defined 8 template groups, each having 4 different DNA templates, yielding 158 (>2.5 billion) combinations of different individual melting temperature (Tm) values and corresponding ID codes. The reproducibility and specificity of the decoding was confirmed by using the most complex template mixture, which had 32 different products in 8 groups with different Tm values. The industrial applicability of our protocol was also demonstrated by labeling a drone with an oil-based paint containing a predefined DNA code, which was then successfully decoded. The method presented here consists of a simple code system based on a small number of synthetic DNA sequences and a cost-effective, rapid decoding protocol using a few qPCR reactions, enabling a wide range of authentication applications.

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.

Coding performance of the Probe-Orbiter-Earth communication link

NASA Technical Reports Server (NTRS)

Divsalar, D.; Dolinar, S.; Pollara, F.

1993-01-01

The coding performance of the Probe-Orbiter-Earth communication link is analyzed and compared for several cases. It is assumed that the coding system consists of a convolutional code at the Probe, a quantizer and another convolutional code at the Orbiter, and two cascaded Viterbi decoders or a combined decoder on the ground.

Bounds on Block Error Probability for Multilevel Concatenated Codes

NASA Technical Reports Server (NTRS)

Lin, Shu; Moorthy, Hari T.; Stojanovic, Diana

1996-01-01

Maximum likelihood decoding of long block codes is not feasable due to large complexity. Some classes of codes are shown to be decomposable into multilevel concatenated codes (MLCC). For these codes, multistage decoding provides good trade-off between performance and complexity. In this paper, we derive an upper bound on the probability of block error for MLCC. We use this bound to evaluate difference in performance for different decompositions of some codes. Examples given show that a significant reduction in complexity can be achieved when increasing number of stages of decoding. Resulting performance degradation varies for different decompositions. A guideline is given for finding good m-level decompositions.

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.

A study of digital holographic filters generation. Phase 2: Digital data communication system, volume 1

NASA Technical Reports Server (NTRS)

Ingels, F. M.; Mo, C. D.

1978-01-01

An empirical study of the performance of the Viterbi decoders in bursty channels was carried out and an improved algebraic decoder for nonsystematic codes was developed. The hybrid algorithm was simulated for the (2,1), k = 7 code on a computer using 20 channels having various error statistics, ranging from pure random error to pure bursty channels. The hybrid system outperformed both the algebraic and the Viterbi decoders in every case, except the 1% random error channel where the Viterbi decoder had one bit less decoding error.

The NASA Spacecraft Transponding Modem

NASA Technical Reports Server (NTRS)

Berner, Jeff B.; Kayalar, Selahattin; Perret, Jonathan D.

2000-01-01

A new deep space transponder is being developed by the Jet Propulsion Laboratory for NASA. The Spacecraft Transponding Modem (STM) implements the standard transponder functions and the channel service functions that have previously resided in spacecraft Command/Data Subsystems. The STM uses custom ASICs, MMICs, and MCMs to reduce the active device parts count to 70, mass to I kg, and volume to 524 cc. The first STMs will be flown on missions launching in the 2003 time frame. The STM tracks an X-band uplink signal and provides both X-band and Ka-band downlinks, either coherent or non-coherent with the uplink. A NASA standard Command Detector Unit is integrated into the STM, along with a codeblock processor and a hardware command decoder. The decoded command codeblocks are output to the spacecraft command/data subsystem. Virtual Channel 0 (VC-0) (hardware) commands are processed and output as critical controller (CRC) commands. Downlink telemetry is received from the spacecraft data subsystem as telemetry frames. The STM provides the following downlink coding options: the standard CCSDS (7-1/2) convolutional coding, ReedSolomon coding with interleave depths one and five, (15-1/6) convolutional coding, and Turbo coding with rates 1/3 and 1/6. The downlink symbol rates can be linearly ramped to match the G/T curve of the receiving station, providing up to a 1 dB increase in data return. Data rates range from 5 bits per second (bps) to 24 Mbps, with three modulation modes provided: modulated subcarrier (3 different frequencies provided), biphase-L modulated direct on carrier, and Offset QPSK. Also, the capability to generate one of four non-harmonically related telemetry beacon tones is provided, to allow for a simple spacecraft status monitoring scheme for cruise phases of missions. Three ranging modes are provided: standard turn around ranging, regenerative pseudo-noise (PN) ranging, and Differential One-way Ranging (DOR) tones. The regenerative ranging provides the capability of increasing the ground received ranging SNR by up to 30 dB. Two different avionics interfaces to the command/data subsystem's data bus are provided: a MIL STD 1553B bus or an industry standard PCI interface. Digital interfaces provide the capability to control antenna selection (e.g., switching between high gain and low gain antennas) and antenna pointing (for future steered Ka-band antennas).

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

Non-tables look-up search algorithm for efficient H.264/AVC context-based adaptive variable length coding decoding

NASA Astrophysics Data System (ADS)

Han, Yishi; Luo, Zhixiao; Wang, Jianhua; Min, Zhixuan; Qin, Xinyu; Sun, Yunlong

2014-09-01

In general, context-based adaptive variable length coding (CAVLC) decoding in H.264/AVC standard requires frequent access to the unstructured variable length coding tables (VLCTs) and significant memory accesses are consumed. Heavy memory accesses will cause high power consumption and time delays, which are serious problems for applications in portable multimedia devices. We propose a method for high-efficiency CAVLC decoding by using a program instead of all the VLCTs. The decoded codeword from VLCTs can be obtained without any table look-up and memory access. The experimental results show that the proposed algorithm achieves 100% memory access saving and 40% decoding time saving without degrading video quality. Additionally, the proposed algorithm shows a better performance compared with conventional CAVLC decoding, such as table look-up by sequential search, table look-up by binary search, Moon's method, and Kim's method.

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes. Part 3; A Recursive Maximum Likelihood Decoding

NASA Technical Reports Server (NTRS)

Lin, Shu; Fossorier, Marc

1998-01-01

The Viterbi algorithm is indeed a very simple and efficient method of implementing the maximum likelihood decoding. However, if we take advantage of the structural properties in a trellis section, other efficient trellis-based decoding algorithms can be devised. Recently, an efficient trellis-based recursive maximum likelihood decoding (RMLD) algorithm for linear block codes has been proposed. This algorithm is more efficient than the conventional Viterbi algorithm in both computation and hardware requirements. Most importantly, the implementation of this algorithm does not require the construction of the entire code trellis, only some special one-section trellises of relatively small state and branch complexities are needed for constructing path (or branch) metric tables recursively. At the end, there is only one table which contains only the most likely code-word and its metric for a given received sequence r = (r(sub 1), r(sub 2),...,r(sub n)). This algorithm basically uses the divide and conquer strategy. Furthermore, it allows parallel/pipeline processing of received sequences to speed up decoding.

Soft-Input Soft-Output Modules for the Construction and Distributed Iterative Decoding of Code Networks

NASA Technical Reports Server (NTRS)

Benedetto, S.; Divsalar, D.; Montorsi, G.; Pollara, F.

1998-01-01

Soft-input soft-output building blocks (modules) are presented to construct and iteratively decode in a distributed fashion code networks, a new concept that includes, and generalizes, various forms of concatenated coding schemes.

Theoretical and experimental studies of turbo product code with time diversity in free space optical communication.

PubMed

Han, Yaoqiang; Dang, Anhong; Ren, Yongxiong; Tang, Junxiong; Guo, Hong

2010-12-20

In free space optical communication (FSOC) systems, channel fading caused by atmospheric turbulence degrades the system performance seriously. However, channel coding combined with diversity techniques can be exploited to mitigate channel fading. In this paper, based on the experimental study of the channel fading effects, we propose to use turbo product code (TPC) as the channel coding scheme, which features good resistance to burst errors and no error floor. However, only channel coding cannot cope with burst errors caused by channel fading, interleaving is also used. We investigate the efficiency of interleaving for different interleaving depths, and then the optimum interleaving depth for TPC is also determined. Finally, an experimental study of TPC with interleaving is demonstrated, and we show that TPC with interleaving can significantly mitigate channel fading in FSOC systems.

On the reduced-complexity of LDPC decoders for ultra-high-speed optical transmission.

PubMed

Djordjevic, Ivan B; Xu, Lei; Wang, Ting

2010-10-25

We propose two reduced-complexity (RC) LDPC decoders, which can be used in combination with large-girth LDPC codes to enable ultra-high-speed serial optical transmission. We show that optimally attenuated RC min-sum sum algorithm performs only 0.46 dB (at BER of 10(-9)) worse than conventional sum-product algorithm, while having lower storage memory requirements and much lower latency. We further study the use of RC LDPC decoding algorithms in multilevel coded modulation with coherent detection and show that with RC decoding algorithms we can achieve the net coding gain larger than 11 dB at BERs below 10(-9).

Optimal operation of turbo blowers serially connected using inlet vanes

NASA Astrophysics Data System (ADS)

Jang, Choon-Man

2011-03-01

Optimal operation of the turbo blowers having an inlet vane has been studied to understand the blowers' operating performance. To analyze three-dimensional flow field in the turbo blowers serially connected, general analysis code, CFX, is introduced in the present work. SST turbulence model is employed to estimate the eddy viscosity. Throughout the numerical analysis, it is found that the flow rates of the turbo blowers can be controlled at the vane angle between 90 (full open condition) degrees and 60 degrees effectively, because pressure loss rapidly increases below 60 degree of a vane angle. Efficiency also has almost the same values from 90 degrees to 60 degrees of a vane angle. It is noted that the distorted inlet velocity generated in the small vane angle makes performance deterioration of the turbo blowers due to the local leading edge separation and the following non-uniform blade loading.

Soft decoding a self-dual (48, 24; 12) code

NASA Technical Reports Server (NTRS)

Solomon, G.

1993-01-01

A self-dual (48,24;12) code comes from restricting a binary cyclic (63,18;36) code to a 6 x 7 matrix, adding an eighth all-zero column, and then adjoining six dimensions to this extended 6 x 8 matrix. These six dimensions are generated by linear combinations of row permutations of a 6 x 8 matrix of weight 12, whose sums of rows and columns add to one. A soft decoding using these properties and approximating maximum likelihood is presented here. This is preliminary to a possible soft decoding of the box (72,36;15) code that promises a 7.7-dB theoretical coding under maximum likelihood.

LDPC Codes--Structural Analysis and Decoding Techniques

ERIC Educational Resources Information Center

Zhang, Xiaojie

2012-01-01

Low-density parity-check (LDPC) codes have been the focus of much research over the past decade thanks to their near Shannon limit performance and to their efficient message-passing (MP) decoding algorithms. However, the error floor phenomenon observed in MP decoding, which manifests itself as an abrupt change in the slope of the error-rate curve,…

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.

Hybrid and concatenated coding applications.

NASA Technical Reports Server (NTRS)

Hofman, L. B.; Odenwalder, J. P.

1972-01-01

Results of a study to evaluate the performance and implementation complexity of a concatenated and a hybrid coding system for moderate-speed deep-space applications. It is shown that with a total complexity of less than three times that of the basic Viterbi decoder, concatenated coding improves a constraint length 8 rate 1/3 Viterbi decoding system by 1.1 and 2.6 dB at bit error probabilities of 0.0001 and one hundred millionth, respectively. With a somewhat greater total complexity, the hybrid coding system is shown to obtain a 0.9-dB computational performance improvement over the basic rate 1/3 sequential decoding system. Although substantial, these complexities are much less than those required to achieve the same performances with more complex Viterbi or sequential decoder systems.

Architecture and implementation considerations of a high-speed Viterbi decoder for a Reed-Muller subcode

NASA Technical Reports Server (NTRS)

Lin, Shu (Principal Investigator); Uehara, Gregory T.; Nakamura, Eric; Chu, Cecilia W. P.

1996-01-01

The (64, 40, 8) subcode of the third-order Reed-Muller (RM) code for high-speed satellite communications is proposed. The RM subcode can be used either alone or as an inner code of a concatenated coding system with the NASA standard (255, 233, 33) Reed-Solomon (RS) code as the outer code to achieve high performance (or low bit-error rate) with reduced decoding complexity. It can also be used as a component code in a multilevel bandwidth efficient coded modulation system to achieve reliable bandwidth efficient data transmission. The progress made toward achieving the goal of implementing a decoder system based upon this code is summarized. The development of the integrated circuit prototype sub-trellis IC, particularly focusing on the design methodology, is addressed.

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.

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 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.

Iterative demodulation and decoding of coded non-square QAM

NASA Technical Reports Server (NTRS)

Li, L.; Divsalar, D.; Dolinar, S.

2003-01-01

Simulation results show that, with iterative demodulation and decoding, coded NS-8QAM performs 0.5 dB better than standard 8QAM and 0.7 dB better than 8PSK at BER= 10(sup -5), when the FEC code is the (15, 11) Hamming code concatenated with a rate-1 accumulator code, while coded NS-32QAM performs 0.25 dB better than standard 32QAM.

Soft-Decision Decoding of Binary Linear Block Codes Based on an Iterative Search Algorithm

NASA Technical Reports Server (NTRS)

Lin, Shu; Kasami, Tadao; Moorthy, H. T.

1997-01-01

This correspondence presents a suboptimum soft-decision decoding scheme for binary linear block codes based on an iterative search algorithm. The scheme uses an algebraic decoder to iteratively generate a sequence of candidate codewords one at a time using a set of test error patterns that are constructed based on the reliability information of the received symbols. When a candidate codeword is generated, it is tested based on an optimality condition. If it satisfies the optimality condition, then it is the most likely (ML) codeword and the decoding stops. If it fails the optimality test, a search for the ML codeword is conducted in a region which contains the ML codeword. The search region is determined by the current candidate codeword and the reliability of the received symbols. The search is conducted through a purged trellis diagram for the given code using the Viterbi algorithm. If the search fails to find the ML codeword, a new candidate is generated using a new test error pattern, and the optimality test and search are renewed. The process of testing and search continues until either the MEL codeword is found or all the test error patterns are exhausted and the decoding process is terminated. Numerical results show that the proposed decoding scheme achieves either practically optimal performance or a performance only a fraction of a decibel away from the optimal maximum-likelihood decoding with a significant reduction in decoding complexity compared with the Viterbi decoding based on the full trellis diagram of the codes.

Low-density parity-check codes for volume holographic memory systems.

PubMed

Pishro-Nik, Hossein; Rahnavard, Nazanin; Ha, Jeongseok; Fekri, Faramarz; Adibi, Ali

2003-02-10

We investigate the application of low-density parity-check (LDPC) codes in volume holographic memory (VHM) systems. We show that a carefully designed irregular LDPC code has a very good performance in VHM systems. We optimize high-rate LDPC codes for the nonuniform error pattern in holographic memories to reduce the bit error rate extensively. The prior knowledge of noise distribution is used for designing as well as decoding the LDPC codes. We show that these codes have a superior performance to that of Reed-Solomon (RS) codes and regular LDPC counterparts. Our simulation shows that we can increase the maximum storage capacity of holographic memories by more than 50 percent if we use irregular LDPC codes with soft-decision decoding instead of conventionally employed RS codes with hard-decision decoding. The performance of these LDPC codes is close to the information theoretic capacity.

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.

The algebraic decoding of the (41, 21, 9) quadratic residue code

NASA Technical Reports Server (NTRS)

Reed, Irving S.; Truong, T. K.; Chen, Xuemin; Yin, Xiaowei

1992-01-01

A new algebraic approach for decoding the quadratic residue (QR) codes, in particular the (41, 21, 9) QR code is presented. The key ideas behind this decoding technique are a systematic application of the Sylvester resultant method to the Newton identities associated with the code syndromes to find the error-locator polynomial, and next a method for determining error locations by solving certain quadratic, cubic and quartic equations over GF(2 exp m) in a new way which uses Zech's logarithms for the arithmetic. The algorithms developed here are suitable for implementation in a programmable microprocessor or special-purpose VLSI chip. It is expected that the algebraic methods developed here can apply generally to other codes such as the BCH and Reed-Solomon codes.

Phobos lander coding system: Software and analysis

NASA Technical Reports Server (NTRS)

Cheung, K.-M.; Pollara, F.

1988-01-01

The software developed for the decoding system used in the telemetry link of the Phobos Lander mission is described. Encoders and decoders are provided to cover the three possible telemetry configurations. The software can be used to decode actual data or to simulate the performance of the telemetry system. The theoretical properties of the codes chosen for this mission are analyzed and discussed.

Hamming and Accumulator Codes Concatenated with MPSK or QAM

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Dolinar, Samuel

2009-01-01

In a proposed coding-and-modulation scheme, a high-rate binary data stream would be processed as follows: 1. The input bit stream would be demultiplexed into multiple bit streams. 2. The multiple bit streams would be processed simultaneously into a high-rate outer Hamming code that would comprise multiple short constituent Hamming codes a distinct constituent Hamming code for each stream. 3. The streams would be interleaved. The interleaver would have a block structure that would facilitate parallelization for high-speed decoding. 4. The interleaved streams would be further processed simultaneously into an inner two-state, rate-1 accumulator code that would comprise multiple constituent accumulator codes - a distinct accumulator code for each stream. 5. The resulting bit streams would be mapped into symbols to be transmitted by use of a higher-order modulation - for example, M-ary phase-shift keying (MPSK) or quadrature amplitude modulation (QAM). The novelty of the scheme lies in the concatenation of the multiple-constituent Hamming and accumulator codes and the corresponding parallel architectures of the encoder and decoder circuitry (see figure) needed to process the multiple bit streams simultaneously. As in the cases of other parallel-processing schemes, one advantage of this scheme is that the overall data rate could be much greater than the data rate of each encoder and decoder stream and, hence, the encoder and decoder could handle data at an overall rate beyond the capability of the individual encoder and decoder circuits.

Optimal patch code design via device characterization

NASA Astrophysics Data System (ADS)

Wu, Wencheng; Dalal, Edul N.

2012-01-01

In many color measurement applications, such as those for color calibration and profiling, "patch code" has been used successfully for job identification and automation to reduce operator errors. A patch code is similar to a barcode, but is intended primarily for use in measurement devices that cannot read barcodes due to limited spatial resolution, such as spectrophotometers. There is an inherent tradeoff between decoding robustness and the number of code levels available for encoding. Previous methods have attempted to address this tradeoff, but those solutions have been sub-optimal. In this paper, we propose a method to design optimal patch codes via device characterization. The tradeoff between decoding robustness and the number of available code levels is optimized in terms of printing and measurement efforts, and decoding robustness against noises from the printing and measurement devices. Effort is drastically reduced relative to previous methods because print-and-measure is minimized through modeling and the use of existing printer profiles. Decoding robustness is improved by distributing the code levels in CIE Lab space rather than in CMYK space.

More on the decoder error probability for Reed-Solomon codes

NASA Technical Reports Server (NTRS)

Cheung, K.-M.

1987-01-01

The decoder error probability for Reed-Solomon codes (more generally, linear maximum distance separable codes) is examined. McEliece and Swanson offered an upper bound on P sub E (u), the decoder error probability given that u symbol errors occurs. This upper bound is slightly greater than Q, the probability that a completely random error pattern will cause decoder error. By using a combinatoric technique, the principle of inclusion and exclusion, an exact formula for P sub E (u) is derived. The P sub e (u) for the (255, 223) Reed-Solomon Code used by NASA, and for the (31,15) Reed-Solomon code (JTIDS code), are calculated using the exact formula, and the P sub E (u)'s are observed to approach the Q's of the codes rapidly as u gets larger. An upper bound for the expression is derived, and is shown to decrease nearly exponentially as u increases. This proves analytically that P sub E (u) indeed approaches Q as u becomes large, and some laws of large numbers come into play.

Integrated Performance of Next Generation High Data Rate Receiver and AR4JA LDPC Codec for Space Communications

NASA Technical Reports Server (NTRS)

Cheng, Michael K.; Lyubarev, Mark; Nakashima, Michael A.; Andrews, Kenneth S.; Lee, Dennis

2008-01-01

Low-density parity-check (LDPC) codes are the state-of-the-art in forward error correction (FEC) technology that exhibits capacity approaching performance. The Jet Propulsion Laboratory (JPL) has designed a family of LDPC codes that are similar in structure and therefore, leads to a single decoder implementation. The Accumulate-Repeat-by-4-Jagged- Accumulate (AR4JA) code design offers a family of codes with rates 1/2, 2/3, 4/5 and lengths 1024, 4096, 16384 information bits. Performance is less than one dB from capacity for all combinations.Integrating a stand-alone LDPC decoder with a commercial-off-the-shelf (COTS) receiver faces additional challenges than building a single receiver-decoder unit from scratch. In this work, we outline the issues and show that these additional challenges can be over-come by simple solutions. To demonstrate that an LDPC decoder can be made to work seamlessly with a COTS receiver, we interface an AR4JA LDPC decoder developed on a field-programmable gate array (FPGA) with a modern high data rate receiver and mea- sure the combined receiver-decoder performance. Through optimizations that include an improved frame synchronizer and different soft-symbol scaling algorithms, we show that a combined implementation loss of less than one dB is possible and therefore, most of the coding gain evidence in theory can also be obtained in practice. Our techniques can benefit any modem that utilizes an advanced FEC code.

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.

High-throughput GPU-based LDPC decoding

NASA Astrophysics Data System (ADS)

Chang, Yang-Lang; Chang, Cheng-Chun; Huang, Min-Yu; Huang, Bormin

2010-08-01

Low-density parity-check (LDPC) code is a linear block code known to approach the Shannon limit via the iterative sum-product algorithm. LDPC codes have been adopted in most current communication systems such as DVB-S2, WiMAX, WI-FI and 10GBASE-T. LDPC for the needs of reliable and flexible communication links for a wide variety of communication standards and configurations have inspired the demand for high-performance and flexibility computing. Accordingly, finding a fast and reconfigurable developing platform for designing the high-throughput LDPC decoder has become important especially for rapidly changing communication standards and configurations. In this paper, a new graphic-processing-unit (GPU) LDPC decoding platform with the asynchronous data transfer is proposed to realize this practical implementation. Experimental results showed that the proposed GPU-based decoder achieved 271x speedup compared to its CPU-based counterpart. It can serve as a high-throughput LDPC decoder.

Exploring Hill Ciphers with Graphing Calculators.

ERIC Educational Resources Information Center

St. John, Dennis

1998-01-01

Explains how to code and decode messages using Hill ciphers which combine matrix multiplication and modular arithmetic. Discusses how a graphing calculator can facilitate the matrix and modular arithmetic used in the coding and decoding procedures. (ASK)

A Dual Coding Theoretical Model of Decoding in Reading: Subsuming the LaBerge and Samuels Model

ERIC Educational Resources Information Center

Sadoski, Mark; McTigue, Erin M.; Paivio, Allan

2012-01-01

In this article we present a detailed Dual Coding Theory (DCT) model of decoding. The DCT model reinterprets and subsumes The LaBerge and Samuels (1974) model of the reading process which has served well to account for decoding behaviors and the processes that underlie them. However, the LaBerge and Samuels model has had little to say about…

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.

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.

Entanglement-assisted quantum quasicyclic low-density parity-check codes

NASA Astrophysics Data System (ADS)

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

2009-03-01

We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasicyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Skor-Steane construction do not need to satisfy the dual-containing property as long as preshared entanglement is available to both sender and receiver. We can use this to avoid the many four cycles which typically arise in dual-containing LDPC codes. The advantage of such quantum codes comes from the use of efficient decoding algorithms such as sum-product algorithm (SPA). It is well known that in the SPA, cycles of length 4 make successive decoding iterations highly correlated and hence limit the decoding performance. We show the principle of constructing quantum QC-LDPC codes which require only small amounts of initial shared entanglement.

Two-terminal video coding.

PubMed

Yang, Yang; Stanković, Vladimir; Xiong, Zixiang; Zhao, Wei

2009-03-01

Following recent works on the rate region of the quadratic Gaussian two-terminal source coding problem and limit-approaching code designs, this paper examines multiterminal source coding of two correlated, i.e., stereo, video sequences to save the sum rate over independent coding of both sequences. Two multiterminal video coding schemes are proposed. In the first scheme, the left sequence of the stereo pair is coded by H.264/AVC and used at the joint decoder to facilitate Wyner-Ziv coding of the right video sequence. The first I-frame of the right sequence is successively coded by H.264/AVC Intracoding and Wyner-Ziv coding. An efficient stereo matching algorithm based on loopy belief propagation is then adopted at the decoder to produce pixel-level disparity maps between the corresponding frames of the two decoded video sequences on the fly. Based on the disparity maps, side information for both motion vectors and motion-compensated residual frames of the right sequence are generated at the decoder before Wyner-Ziv encoding. In the second scheme, source splitting is employed on top of classic and Wyner-Ziv coding for compression of both I-frames to allow flexible rate allocation between the two sequences. Experiments with both schemes on stereo video sequences using H.264/AVC, LDPC codes for Slepian-Wolf coding of the motion vectors, and scalar quantization in conjunction with LDPC codes for Wyner-Ziv coding of the residual coefficients give a slightly lower sum rate than separate H.264/AVC coding of both sequences at the same video quality.

An efficient decoding for low density parity check codes

NASA Astrophysics Data System (ADS)

Zhao, Ling; Zhang, Xiaolin; Zhu, Manjie

2009-12-01

Low density parity check (LDPC) codes are a class of forward-error-correction codes. They are among the best-known codes capable of achieving low bit error rates (BER) approaching Shannon's capacity limit. Recently, LDPC codes have been adopted by the European Digital Video Broadcasting (DVB-S2) standard, and have also been proposed for the emerging IEEE 802.16 fixed and mobile broadband wireless-access standard. The consultative committee for space data system (CCSDS) has also recommended using LDPC codes in the deep space communications and near-earth communications. It is obvious that LDPC codes will be widely used in wired and wireless communication, magnetic recording, optical networking, DVB, and other fields in the near future. Efficient hardware implementation of LDPC codes is of great interest since LDPC codes are being considered for a wide range of applications. This paper presents an efficient partially parallel decoder architecture suited for quasi-cyclic (QC) LDPC codes using Belief propagation algorithm for decoding. Algorithmic transformation and architectural level optimization are incorporated to reduce the critical path. First, analyze the check matrix of LDPC code, to find out the relationship between the row weight and the column weight. And then, the sharing level of the check node updating units (CNU) and the variable node updating units (VNU) are determined according to the relationship. After that, rearrange the CNU and the VNU, and divide them into several smaller parts, with the help of some assistant logic circuit, these smaller parts can be grouped into CNU during the check node update processing and grouped into VNU during the variable node update processing. These smaller parts are called node update kernel units (NKU) and the assistant logic circuit are called node update auxiliary unit (NAU). With NAUs' help, the two steps of iteration operation are completed by NKUs, which brings in great hardware resource reduction. Meanwhile, efficient techniques have been developed to reduce the computation delay of the node processing units and to minimize hardware overhead for parallel processing. This method may be applied not only to regular LDPC codes, but also to the irregular ones. Based on the proposed architectures, a (7493, 6096) irregular QC-LDPC code decoder is described using verilog hardware design language and implemented on Altera field programmable gate array (FPGA) StratixII EP2S130. The implementation results show that over 20% of logic core size can be saved than conventional partially parallel decoder architectures without any performance degradation. If the decoding clock is 100MHz, the proposed decoder can achieve a maximum (source data) decoding throughput of 133 Mb/s at 18 iterations.

Direct migration motion estimation and mode decision to decoder for a low-complexity decoder Wyner-Ziv video coding

NASA Astrophysics Data System (ADS)

Lei, Ted Chih-Wei; Tseng, Fan-Shuo

2017-07-01

This paper addresses the problem of high-computational complexity decoding in traditional Wyner-Ziv video coding (WZVC). The key focus is the migration of two traditionally high-computationally complex encoder algorithms, namely motion estimation and mode decision. In order to reduce the computational burden in this process, the proposed architecture adopts the partial boundary matching algorithm and four flexible types of block mode decision at the decoder. This approach does away with the need for motion estimation and mode decision at the encoder. The experimental results show that the proposed padding block-based WZVC not only decreases decoder complexity to approximately one hundredth that of the state-of-the-art DISCOVER decoding but also outperforms DISCOVER codec by up to 3 to 4 dB.

Linearized Aeroelastic Solver Applied to the Flutter Prediction of Real Configurations

NASA Technical Reports Server (NTRS)

Reddy, Tondapu S.; Bakhle, Milind A.

2004-01-01

A fast-running unsteady aerodynamics code, LINFLUX, was previously developed for predicting turbomachinery flutter. This linearized code, based on a frequency domain method, models the effects of steady blade loading through a nonlinear steady flow field. The LINFLUX code, which is 6 to 7 times faster than the corresponding nonlinear time domain code, is suitable for use in the initial design phase. Earlier, this code was verified through application to a research fan, and it was shown that the predictions of work per cycle and flutter compared well with those from a nonlinear time-marching aeroelastic code, TURBO-AE. Now, the LINFLUX code has been applied to real configurations: fans developed under the Energy Efficient Engine (E-cubed) Program and the Quiet Aircraft Technology (QAT) project. The LINFLUX code starts with a steady nonlinear aerodynamic flow field and solves the unsteady linearized Euler equations to calculate the unsteady aerodynamic forces on the turbomachinery blades. First, a steady aerodynamic solution is computed for given operating conditions using the nonlinear unsteady aerodynamic code TURBO-AE. A blade vibration analysis is done to determine the frequencies and mode shapes of the vibrating blades, and an interface code is used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor is used to interpolate the mode shapes from the structural dynamics mesh onto the computational fluid dynamics mesh. Then, LINFLUX is used to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. Finally, a post-processor uses the unsteady pressures to calculate the generalized aerodynamic forces, eigenvalues, an esponse amplitudes. The eigenvalues determine the flutter frequency and damping. Results of flutter calculations from the LINFLUX code are presented for (1) the E-cubed fan developed under the E-cubed program and (2) the Quiet High Speed Fan (QHSF) developed under the Quiet Aircraft Technology project. The results are compared with those obtained from the TURBO-AE code. A graph of the work done per vibration cycle for the first vibration mode of the E-cubed fan is shown. It can be seen that the LINFLUX results show a very good comparison with TURBO-AE results over the entire range of interblade phase angle. The work done per vibration cycle for the first vibration mode of the QHSF fan is shown. Once again, the LINFLUX results compare very well with the results from the TURBOAE code.

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.

High-Speed Soft-Decision Decoding of Two Reed-Muller Codes

NASA Technical Reports Server (NTRS)

Lin, Shu; Uehara, Gregory T.

1996-01-01

In his research, we have proposed the (64, 40, 8) subcode of the third-order Reed-Muller (RM) code to NASA for high-speed satellite communications. This RM subcode can be used either alone or as an inner code of a concatenated coding system with the NASA standard (255, 233, 33) Reed-Solomon (RS) code as the outer code to achieve high performance (or low bit-error rate) with reduced decoding complexity. It can also be used as a component code in a multilevel bandwidth efficient coded modulation system to achieve reliable bandwidth efficient data transmission. This report will summarize the key progress we have made toward achieving our eventual goal of implementing a decoder system based upon this code. In the first phase of study, we investigated the complexities of various sectionalized trellis diagrams for the proposed (64, 40, 8) RNI subcode. We found a specific 8-trellis diagram for this code which requires the least decoding complexity with a high possibility of achieving a decoding speed of 600 M bits per second (Mbps). The combination of a large number of states and a hi ch data rate will be made possible due to the utilization of a high degree of parallelism throughout the architecture. This trellis diagram will be presented and briefly described. In the second phase of study which was carried out through the past year, we investigated circuit architectures to determine the feasibility of VLSI implementation of a high-speed Viterbi decoder based on this 8-section trellis diagram. We began to examine specific design and implementation approaches to implement a fully custom integrated circuit (IC) which will be a key building block for a decoder system implementation. The key results will be presented in this report. This report will be divided into three primary sections. First, we will briefly describe the system block diagram in which the proposed decoder is assumed to be operating and present some of the key architectural approaches being used to implement the system at high speed. Second, we will describe details of the 8-trellis diagram we found to best meet the trade-offs between chip and overall system complexity. The chosen approach implements the trellis for the (64, 40, 8) RM subcode with 32 independent sub-trellises. And third, we will describe results of our feasibility study on the implementation of such an IC chip in CMOS technology to implement one of these sub-trellises.

High-Speed Soft-Decision Decoding of Two Reed-Muller Codes

NASA Technical Reports Server (NTRS)

Lin, Shu; Uehara, Gregory T.

1996-01-01

In this research, we have proposed the (64, 40, 8) subcode of the third-order Reed-Muller (RM) code to NASA for high-speed satellite communications. This RM subcode can be used either alone or as an inner code of a concatenated coding system with the NASA standard (255, 233, 33) Reed-Solomon (RS) code as the outer code to achieve high performance (or low bit-error rate) with reduced decoding complexity. It can also be used as a component code in a multilevel bandwidth efficient coded modulation system to achieve reliable bandwidth efficient data transmission. This report will summarize the key progress we have made toward achieving our eventual goal of implementing, a decoder system based upon this code. In the first phase of study, we investigated the complexities of various sectionalized trellis diagrams for the proposed (64, 40, 8) RM subcode. We found a specific 8-trellis diagram for this code which requires the least decoding complexity with a high possibility of achieving a decoding speed of 600 M bits per second (Mbps). The combination of a large number of states and a high data rate will be made possible due to the utilization of a high degree of parallelism throughout the architecture. This trellis diagram will be presented and briefly described. In the second phase of study, which was carried out through the past year, we investigated circuit architectures to determine the feasibility of VLSI implementation of a high-speed Viterbi decoder based on this 8-section trellis diagram. We began to examine specific design and implementation approaches to implement a fully custom integrated circuit (IC) which will be a key building block for a decoder system implementation. The key results will be presented in this report. This report will be divided into three primary sections. First, we will briefly describe the system block diagram in which the proposed decoder is assumed to be operating, and present some of the key architectural approaches being used to implement the system at high speed. Second, we will describe details of the 8-trellis diagram we found to best meet the trade-offs between chip and overall system complexity. The chosen approach implements the trellis for the (64, 40, 8) RM subcode with 32 independent sub-trellises. And third, we will describe results of our feasibility study on the implementation of such an IC chip in CMOS technology to implement one of these sub-trellises.

Distributed Coding/Decoding Complexity in Video Sensor Networks

PubMed Central

Cordeiro, Paulo J.; Assunção, Pedro

2012-01-01

Video Sensor Networks (VSNs) are recent communication infrastructures used to capture and transmit dense visual information from an application context. In such large scale environments which include video coding, transmission and display/storage, there are several open problems to overcome in practical implementations. This paper addresses the most relevant challenges posed by VSNs, namely stringent bandwidth usage and processing time/power constraints. In particular, the paper proposes a novel VSN architecture where large sets of visual sensors with embedded processors are used for compression and transmission of coded streams to gateways, which in turn transrate the incoming streams and adapt them to the variable complexity requirements of both the sensor encoders and end-user decoder terminals. Such gateways provide real-time transcoding functionalities for bandwidth adaptation and coding/decoding complexity distribution by transferring the most complex video encoding/decoding tasks to the transcoding gateway at the expense of a limited increase in bit rate. Then, a method to reduce the decoding complexity, suitable for system-on-chip implementation, is proposed to operate at the transcoding gateway whenever decoders with constrained resources are targeted. The results show that the proposed method achieves good performance and its inclusion into the VSN infrastructure provides an additional level of complexity control functionality. PMID:22736972

Distributed coding/decoding complexity in video sensor networks.

PubMed

Cordeiro, Paulo J; Assunção, Pedro

2012-01-01

Video Sensor Networks (VSNs) are recent communication infrastructures used to capture and transmit dense visual information from an application context. In such large scale environments which include video coding, transmission and display/storage, there are several open problems to overcome in practical implementations. This paper addresses the most relevant challenges posed by VSNs, namely stringent bandwidth usage and processing time/power constraints. In particular, the paper proposes a novel VSN architecture where large sets of visual sensors with embedded processors are used for compression and transmission of coded streams to gateways, which in turn transrate the incoming streams and adapt them to the variable complexity requirements of both the sensor encoders and end-user decoder terminals. Such gateways provide real-time transcoding functionalities for bandwidth adaptation and coding/decoding complexity distribution by transferring the most complex video encoding/decoding tasks to the transcoding gateway at the expense of a limited increase in bit rate. Then, a method to reduce the decoding complexity, suitable for system-on-chip implementation, is proposed to operate at the transcoding gateway whenever decoders with constrained resources are targeted. The results show that the proposed method achieves good performance and its inclusion into the VSN infrastructure provides an additional level of complexity control functionality.

Robust pattern decoding in shape-coded structured light

NASA Astrophysics Data System (ADS)

Tang, Suming; Zhang, Xu; Song, Zhan; Song, Lifang; Zeng, Hai

2017-09-01

Decoding is a challenging and complex problem in a coded structured light system. In this paper, a robust pattern decoding method is proposed for the shape-coded structured light in which the pattern is designed as grid shape with embedded geometrical shapes. In our decoding method, advancements are made at three steps. First, a multi-template feature detection algorithm is introduced to detect the feature point which is the intersection of each two orthogonal grid-lines. Second, pattern element identification is modelled as a supervised classification problem and the deep neural network technique is applied for the accurate classification of pattern elements. Before that, a training dataset is established, which contains a mass of pattern elements with various blurring and distortions. Third, an error correction mechanism based on epipolar constraint, coplanarity constraint and topological constraint is presented to reduce the false matches. In the experiments, several complex objects including human hand are chosen to test the accuracy and robustness of the proposed method. The experimental results show that our decoding method not only has high decoding accuracy, but also owns strong robustness to surface color and complex textures.

Quantum image coding with a reference-frame-independent scheme

NASA Astrophysics Data System (ADS)

Chapeau-Blondeau, François; Belin, Etienne

2016-07-01

For binary images, or bit planes of non-binary images, we investigate the possibility of a quantum coding decodable by a receiver in the absence of reference frames shared with the emitter. Direct image coding with one qubit per pixel and non-aligned frames leads to decoding errors equivalent to a quantum bit-flip noise increasing with the misalignment. We show the feasibility of frame-invariant coding by using for each pixel a qubit pair prepared in one of two controlled entangled states. With just one common axis shared between the emitter and receiver, exact decoding for each pixel can be obtained by means of two two-outcome projective measurements operating separately on each qubit of the pair. With strictly no alignment information between the emitter and receiver, exact decoding can be obtained by means of a two-outcome projective measurement operating jointly on the qubit pair. In addition, the frame-invariant coding is shown much more resistant to quantum bit-flip noise compared to the direct non-invariant coding. For a cost per pixel of two (entangled) qubits instead of one, complete frame-invariant image coding and enhanced noise resistance are thus obtained.

Trellis coded multilevel DPSK system with doppler correction for mobile satellite channels

NASA Technical Reports Server (NTRS)

Divsalar, Dariush (Inventor); Simon, Marvin K. (Inventor)

1991-01-01

A trellis coded multilevel differential phase shift keyed mobile communication system. The system of the present invention includes a trellis encoder for translating input signals into trellis codes; a differential encoder for differentially encoding the trellis coded signals; a transmitter for transmitting the differentially encoded trellis coded signals; a receiver for receiving the transmitted signals; a differential demodulator for demodulating the received differentially encoded trellis coded signals; and a trellis decoder for decoding the differentially demodulated signals.

Quiet High Speed Fan (QHSF) Flutter Calculations Using the TURBO Code

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Srivastava, Rakesh; Keith, Theo G., Jr.; Min, James B.; Mehmed, Oral

2006-01-01

A scale model of the NASA/Honeywell Engines Quiet High Speed Fan (QHSF) encountered flutter wind tunnel testing. This report documents aeroelastic calculations done for the QHSF scale model using the blade vibration capability of the TURBO code. Calculations at design speed were used to quantify the effect of numerical parameters on the aerodynamic damping predictions. This numerical study allowed the selection of appropriate values of these parameters, and also allowed an assessment of the variability in the calculated aerodynamic damping. Calculations were also done at 90 percent of design speed. The predicted trends in aerodynamic damping corresponded to those observed during testing.

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.

A Synchronization Algorithm and Implementation for High-Speed Block Codes Applications. Part 4

NASA Technical Reports Server (NTRS)

Lin, Shu; Zhang, Yu; Nakamura, Eric B.; Uehara, Gregory T.

1998-01-01

Block codes have trellis structures and decoders amenable to high speed CMOS VLSI implementation. For a given CMOS technology, these structures enable operating speeds higher than those achievable using convolutional codes for only modest reductions in coding gain. As a result, block codes have tremendous potential for satellite trunk and other future high-speed communication applications. This paper describes a new approach for implementation of the synchronization function for block codes. The approach utilizes the output of the Viterbi decoder and therefore employs the strength of the decoder. Its operation requires no knowledge of the signal-to-noise ratio of the received signal, has a simple implementation, adds no overhead to the transmitted data, and has been shown to be effective in simulation for received SNR greater than 2 dB.

New Syndrome Decoding Techniques for the (n, K) Convolutional Codes

NASA Technical Reports Server (NTRS)

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

1983-01-01

This paper presents a new syndrome decoding algorithm for the (n,k) convolutional codes (CC) which differs completely from an earlier syndrome decoding algorithm of Schalkwijk and Vinck. The new algorithm is based on the general solution of the syndrome equation, a linear Diophantine equation for the error polynomial vector E(D). The set of Diophantine solutions is a coset of the CC. In this error coset a recursive, Viterbi-like algorithm is developed to find the minimum weight error vector (circumflex)E(D). An example, illustrating the new decoding algorithm, is given for the binary nonsystemmatic (3,1)CC.

Simplified Syndrome Decoding of (n, 1) Convolutional Codes

NASA Technical Reports Server (NTRS)

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

1983-01-01

A new syndrome decoding algorithm for the (n, 1) convolutional codes (CC) that is different and simpler than the previous syndrome decoding algorithm of Schalkwijk and Vinck is presented. The new algorithm uses the general solution of the polynomial linear Diophantine equation for the error polynomial vector E(D). This set of Diophantine solutions is a coset of the CC space. A recursive or Viterbi-like algorithm is developed to find the minimum weight error vector cirumflex E(D) in this error coset. An example illustrating the new decoding algorithm is given for the binary nonsymmetric (2,1)CC.

Adaptive Distributed Video Coding with Correlation Estimation using Expectation Propagation

PubMed Central

Cui, Lijuan; Wang, Shuang; Jiang, Xiaoqian; Cheng, Samuel

2013-01-01

Distributed video coding (DVC) is rapidly increasing in popularity by the way of shifting the complexity from encoder to decoder, whereas no compression performance degrades, at least in theory. In contrast with conventional video codecs, the inter-frame correlation in DVC is explored at decoder based on the received syndromes of Wyner-Ziv (WZ) frame and side information (SI) frame generated from other frames available only at decoder. However, the ultimate decoding performances of DVC are based on the assumption that the perfect knowledge of correlation statistic between WZ and SI frames should be available at decoder. Therefore, the ability of obtaining a good statistical correlation estimate is becoming increasingly important in practical DVC implementations. Generally, the existing correlation estimation methods in DVC can be classified into two main types: pre-estimation where estimation starts before decoding and on-the-fly (OTF) estimation where estimation can be refined iteratively during decoding. As potential changes between frames might be unpredictable or dynamical, OTF estimation methods usually outperforms pre-estimation techniques with the cost of increased decoding complexity (e.g., sampling methods). In this paper, we propose a low complexity adaptive DVC scheme using expectation propagation (EP), where correlation estimation is performed OTF as it is carried out jointly with decoding of the factor graph-based DVC code. Among different approximate inference methods, EP generally offers better tradeoff between accuracy and complexity. Experimental results show that our proposed scheme outperforms the benchmark state-of-the-art DISCOVER codec and other cases without correlation tracking, and achieves comparable decoding performance but with significantly low complexity comparing with sampling method. PMID:23750314

Adaptive distributed video coding with correlation estimation using expectation propagation

NASA Astrophysics Data System (ADS)

Cui, Lijuan; Wang, Shuang; Jiang, Xiaoqian; Cheng, Samuel

2012-10-01

Distributed video coding (DVC) is rapidly increasing in popularity by the way of shifting the complexity from encoder to decoder, whereas no compression performance degrades, at least in theory. In contrast with conventional video codecs, the inter-frame correlation in DVC is explored at decoder based on the received syndromes of Wyner-Ziv (WZ) frame and side information (SI) frame generated from other frames available only at decoder. However, the ultimate decoding performances of DVC are based on the assumption that the perfect knowledge of correlation statistic between WZ and SI frames should be available at decoder. Therefore, the ability of obtaining a good statistical correlation estimate is becoming increasingly important in practical DVC implementations. Generally, the existing correlation estimation methods in DVC can be classified into two main types: pre-estimation where estimation starts before decoding and on-the-fly (OTF) estimation where estimation can be refined iteratively during decoding. As potential changes between frames might be unpredictable or dynamical, OTF estimation methods usually outperforms pre-estimation techniques with the cost of increased decoding complexity (e.g., sampling methods). In this paper, we propose a low complexity adaptive DVC scheme using expectation propagation (EP), where correlation estimation is performed OTF as it is carried out jointly with decoding of the factor graph-based DVC code. Among different approximate inference methods, EP generally offers better tradeoff between accuracy and complexity. Experimental results show that our proposed scheme outperforms the benchmark state-of-the-art DISCOVER codec and other cases without correlation tracking, and achieves comparable decoding performance but with significantly low complexity comparing with sampling method.

Adaptive Distributed Video Coding with Correlation Estimation using Expectation Propagation.

PubMed

Cui, Lijuan; Wang, Shuang; Jiang, Xiaoqian; Cheng, Samuel

2012-10-15

Distributed video coding (DVC) is rapidly increasing in popularity by the way of shifting the complexity from encoder to decoder, whereas no compression performance degrades, at least in theory. In contrast with conventional video codecs, the inter-frame correlation in DVC is explored at decoder based on the received syndromes of Wyner-Ziv (WZ) frame and side information (SI) frame generated from other frames available only at decoder. However, the ultimate decoding performances of DVC are based on the assumption that the perfect knowledge of correlation statistic between WZ and SI frames should be available at decoder. Therefore, the ability of obtaining a good statistical correlation estimate is becoming increasingly important in practical DVC implementations. Generally, the existing correlation estimation methods in DVC can be classified into two main types: pre-estimation where estimation starts before decoding and on-the-fly (OTF) estimation where estimation can be refined iteratively during decoding. As potential changes between frames might be unpredictable or dynamical, OTF estimation methods usually outperforms pre-estimation techniques with the cost of increased decoding complexity (e.g., sampling methods). In this paper, we propose a low complexity adaptive DVC scheme using expectation propagation (EP), where correlation estimation is performed OTF as it is carried out jointly with decoding of the factor graph-based DVC code. Among different approximate inference methods, EP generally offers better tradeoff between accuracy and complexity. Experimental results show that our proposed scheme outperforms the benchmark state-of-the-art DISCOVER codec and other cases without correlation tracking, and achieves comparable decoding performance but with significantly low complexity comparing with sampling method.

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.

Performance Evaluation of LDPC Coding and Iterative Decoding System in BPM R/W Channel Affected by Head Field Gradient, Media SFD and Demagnetization Field

NASA Astrophysics Data System (ADS)

Nakamura, Yasuaki; Okamoto, Yoshihiro; Osawa, Hisashi; Aoi, Hajime; Muraoka, Hiroaki

We evaluate the performance of the write-margin for the low-density parity-check (LDPC) coding and iterative decoding system in the bit-patterned media (BPM) R/W channel affected by the write-head field gradient, the media switching field distribution (SFD), the demagnetization field from adjacent islands and the island position deviation. It is clarified that the LDPC coding and iterative decoding system in R/W channel using BPM at 3 Tbit/inch2 has a write-margin of about 20%.

Surveying multidisciplinary aspects in real-time distributed coding for Wireless Sensor Networks.

PubMed

Braccini, Carlo; Davoli, Franco; Marchese, Mario; Mongelli, Maurizio

2015-01-27

Wireless Sensor Networks (WSNs), where a multiplicity of sensors observe a physical phenomenon and transmit their measurements to one or more sinks, pertain to the class of multi-terminal source and channel coding problems of Information Theory. In this category, "real-time" coding is often encountered for WSNs, referring to the problem of finding the minimum distortion (according to a given measure), under transmission power constraints, attainable by encoding and decoding functions, with stringent limits on delay and complexity. On the other hand, the Decision Theory approach seeks to determine the optimal coding/decoding strategies or some of their structural properties. Since encoder(s) and decoder(s) possess different information, though sharing a common goal, the setting here is that of Team Decision Theory. A more pragmatic vision rooted in Signal Processing consists of fixing the form of the coding strategies (e.g., to linear functions) and, consequently, finding the corresponding optimal decoding strategies and the achievable distortion, generally by applying parametric optimization techniques. All approaches have a long history of past investigations and recent results. The goal of the present paper is to provide the taxonomy of the various formulations, a survey of the vast related literature, examples from the authors' own research, and some highlights on the inter-play of the different theories.

Coordinated design of coding and modulation systems

NASA Technical Reports Server (NTRS)

Massey, J. L.; Ancheta, T.; Johannesson, R.; Lauer, G.; Lee, L.

1976-01-01

The joint optimization of the coding and modulation systems employed in telemetry systems was investigated. Emphasis was placed on formulating inner and outer coding standards used by the Goddard Spaceflight Center. Convolutional codes were found that are nearly optimum for use with Viterbi decoding in the inner coding of concatenated coding systems. A convolutional code, the unit-memory code, was discovered and is ideal for inner system usage because of its byte-oriented structure. Simulations of sequential decoding on the deep-space channel were carried out to compare directly various convolutional codes that are proposed for use in deep-space systems.

Investigations on the sensitivity of the computer code TURBO-2D

NASA Astrophysics Data System (ADS)

Amon, B.

1994-12-01

The two-dimensional computer model TURBO-2D for the calculation of two-phase flow was used to calculate the cold injection of fuel into a model chamber. Investigations of the influence of the input parameter on its sensitivity relative to the obtained results were made. In addition to that calculations were performed and compared using experimental injection pressure data and corresponding averaged injection parameter.

A Numerical Investigation of Turbine Noise Source Hierarchy and Its Acoustic Transmission Characteristics: Proof-of-Concept Progress

NASA Technical Reports Server (NTRS)

VanZante, Dale; Envia, Edmane

2008-01-01

A CFD-based simulation of single-stage turbine was done using the TURBO code to assess its viability for determining acoustic transmission through blade rows. Temporal and spectral analysis of the unsteady pressure data from the numerical simulations showed the allowable Tyler-Sofrin modes that are consistent with expectations. This indicated that high-fidelity acoustic transmission calculations are feasible with TURBO.

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.

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.

D-DSC: Decoding Delay-based Distributed Source Coding for Internet of Sensing Things

PubMed Central

Akan, Ozgur B.

2018-01-01

Spatial correlation between densely deployed sensor nodes in a wireless sensor network (WSN) can be exploited to reduce the power consumption through a proper source coding mechanism such as distributed source coding (DSC). In this paper, we propose the Decoding Delay-based Distributed Source Coding (D-DSC) to improve the energy efficiency of the classical DSC by employing the decoding delay concept which enables the use of the maximum correlated portion of sensor samples during the event estimation. In D-DSC, network is partitioned into clusters, where the clusterheads communicate their uncompressed samples carrying the side information, and the cluster members send their compressed samples. Sink performs joint decoding of the compressed and uncompressed samples and then reconstructs the event signal using the decoded sensor readings. Based on the observed degree of the correlation among sensor samples, the sink dynamically updates and broadcasts the varying compression rates back to the sensor nodes. Simulation results for the performance evaluation reveal that D-DSC can achieve reliable and energy-efficient event communication and estimation for practical signal detection/estimation applications having massive number of sensors towards the realization of Internet of Sensing Things (IoST). PMID:29538405

D-DSC: Decoding Delay-based Distributed Source Coding for Internet of Sensing Things.

PubMed

Aktas, Metin; Kuscu, Murat; Dinc, Ergin; Akan, Ozgur B

2018-01-01

Spatial correlation between densely deployed sensor nodes in a wireless sensor network (WSN) can be exploited to reduce the power consumption through a proper source coding mechanism such as distributed source coding (DSC). In this paper, we propose the Decoding Delay-based Distributed Source Coding (D-DSC) to improve the energy efficiency of the classical DSC by employing the decoding delay concept which enables the use of the maximum correlated portion of sensor samples during the event estimation. In D-DSC, network is partitioned into clusters, where the clusterheads communicate their uncompressed samples carrying the side information, and the cluster members send their compressed samples. Sink performs joint decoding of the compressed and uncompressed samples and then reconstructs the event signal using the decoded sensor readings. Based on the observed degree of the correlation among sensor samples, the sink dynamically updates and broadcasts the varying compression rates back to the sensor nodes. Simulation results for the performance evaluation reveal that D-DSC can achieve reliable and energy-efficient event communication and estimation for practical signal detection/estimation applications having massive number of sensors towards the realization of Internet of Sensing Things (IoST).

Error floor behavior study of LDPC codes for concatenated codes design

NASA Astrophysics Data System (ADS)

Chen, Weigang; Yin, Liuguo; Lu, Jianhua

2007-11-01

Error floor behavior of low-density parity-check (LDPC) codes using quantized decoding algorithms is statistically studied with experimental results on a hardware evaluation platform. The results present the distribution of the residual errors after decoding failure and reveal that the number of residual error bits in a codeword is usually very small using quantized sum-product (SP) algorithm. Therefore, LDPC code may serve as the inner code in a concatenated coding system with a high code rate outer code and thus an ultra low error floor can be achieved. This conclusion is also verified by the experimental results.

Concatenated coding for low date rate space communications.

NASA Technical Reports Server (NTRS)

Chen, C. H.

1972-01-01

In deep space communications with distant planets, the data rate as well as the operating SNR may be very low. To maintain the error rate also at a very low level, it is necessary to use a sophisticated coding system (longer code) without excessive decoding complexity. The concatenated coding has been shown to meet such requirements in that the error rate decreases exponentially with the overall length of the code while the decoder complexity increases only algebraically. Three methods of concatenating an inner code with an outer code are considered. Performance comparison of the three concatenated codes is made.

Evaluation of three coding schemes designed for improved data communication

NASA Technical Reports Server (NTRS)

Snelsire, R. W.

1974-01-01

Three coding schemes designed for improved data communication are evaluated. Four block codes are evaluated relative to a quality function, which is a function of both the amount of data rejected and the error rate. The Viterbi maximum likelihood decoding algorithm as a decoding procedure is reviewed. This evaluation is obtained by simulating the system on a digital computer. Short constraint length rate 1/2 quick-look codes are studied, and their performance is compared to general nonsystematic codes.

New syndrome decoder for (n, 1) convolutional codes

NASA Technical Reports Server (NTRS)

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

1983-01-01

The letter presents a new syndrome decoding algorithm for the (n, 1) convolutional codes (CC) that is different and simpler than the previous syndrome decoding algorithm of Schalkwijk and Vinck. The new technique uses the general solution of the polynomial linear Diophantine equation for the error polynomial vector E(D). A recursive, Viterbi-like, algorithm is developed to find the minimum weight error vector E(D). An example is given for the binary nonsystematic (2, 1) CC.

Rate adaptive multilevel coded modulation with high coding gain in intensity modulation direct detection optical communication

NASA Astrophysics Data System (ADS)

Xiao, Fei; Liu, Bo; Zhang, Lijia; Xin, Xiangjun; Zhang, Qi; Tian, Qinghua; Tian, Feng; Wang, Yongjun; Rao, Lan; Ullah, Rahat; Zhao, Feng; Li, Deng'ao

2018-02-01

A rate-adaptive multilevel coded modulation (RA-MLC) scheme based on fixed code length and a corresponding decoding scheme is proposed. RA-MLC scheme combines the multilevel coded and modulation technology with the binary linear block code at the transmitter. Bits division, coding, optional interleaving, and modulation are carried out by the preset rule, then transmitted through standard single mode fiber span equal to 100 km. The receiver improves the accuracy of decoding by means of soft information passing through different layers, which enhances the performance. Simulations are carried out in an intensity modulation-direct detection optical communication system using MATLAB®. Results show that the RA-MLC scheme can achieve bit error rate of 1E-5 when optical signal-to-noise ratio is 20.7 dB. It also reduced the number of decoders by 72% and realized 22 rate adaptation without significantly increasing the computing time. The coding gain is increased by 7.3 dB at BER=1E-3.

Convolutional encoding of self-dual codes

NASA Technical Reports Server (NTRS)

Solomon, G.

1994-01-01

There exist almost complete convolutional encodings of self-dual codes, i.e., block codes of rate 1/2 with weights w, w = 0 mod 4. The codes are of length 8m with the convolutional portion of length 8m-2 and the nonsystematic information of length 4m-1. The last two bits are parity checks on the two (4m-1) length parity sequences. The final information bit complements one of the extended parity sequences of length 4m. Solomon and van Tilborg have developed algorithms to generate these for the Quadratic Residue (QR) Codes of lengths 48 and beyond. For these codes and reasonable constraint lengths, there are sequential decodings for both hard and soft decisions. There are also possible Viterbi-type decodings that may be simple, as in a convolutional encoding/decoding of the extended Golay Code. In addition, the previously found constraint length K = 9 for the QR (48, 24;12) Code is lowered here to K = 8.

Coherent direct sequence optical code multiple access encoding-decoding efficiency versus wavelength detuning.

PubMed

Pastor, D; Amaya, W; García-Olcina, R; Sales, S

2007-07-01

We present a simple theoretical model of and the experimental verification for vanishing of the autocorrelation peak due to wavelength detuning on the coding-decoding process of coherent direct sequence optical code multiple access systems based on a superstructured fiber Bragg grating. Moreover, the detuning vanishing effect has been explored to take advantage of this effect and to provide an additional degree of multiplexing and/or optical code tuning.

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.

Prioritized LT Codes

NASA Technical Reports Server (NTRS)

Woo, Simon S.; Cheng, Michael K.

2011-01-01

The original Luby Transform (LT) coding scheme is extended to account for data transmissions where some information symbols in a message block are more important than others. Prioritized LT codes provide unequal error protection (UEP) of data on an erasure channel by modifying the original LT encoder. The prioritized algorithm improves high-priority data protection without penalizing low-priority data recovery. Moreover, low-latency decoding is also obtained for high-priority data due to fast encoding. Prioritized LT codes only require a slight change in the original encoding algorithm, and no changes at all at the decoder. Hence, with a small complexity increase in the LT encoder, an improved UEP and low-decoding latency performance for high-priority data can be achieved. LT encoding partitions a data stream into fixed-sized message blocks each with a constant number of information symbols. To generate a code symbol from the information symbols in a message, the Robust-Soliton probability distribution is first applied in order to determine the number of information symbols to be used to compute the code symbol. Then, the specific information symbols are chosen uniform randomly from the message block. Finally, the selected information symbols are XORed to form the code symbol. The Prioritized LT code construction includes an additional restriction that code symbols formed by a relatively small number of XORed information symbols select some of these information symbols from the pool of high-priority data. Once high-priority data are fully covered, encoding continues with the conventional LT approach where code symbols are generated by selecting information symbols from the entire message block including all different priorities. Therefore, if code symbols derived from high-priority data experience an unusual high number of erasures, Prioritized LT codes can still reliably recover both high- and low-priority data. This hybrid approach decides not only "how to encode" but also "what to encode" to achieve UEP. Another advantage of the priority encoding process is that the majority of high-priority data can be decoded sooner since only a small number of code symbols are required to reconstruct high-priority data. This approach increases the likelihood that high-priority data is decoded first over low-priority data. The Prioritized LT code scheme achieves an improvement in high-priority data decoding performance as well as overall information recovery without penalizing the decoding of low-priority data, assuming high-priority data is no more than half of a message block. The cost is in the additional complexity required in the encoder. If extra computation resource is available at the transmitter, image, voice, and video transmission quality in terrestrial and space communications can benefit from accurate use of redundancy in protecting data with varying priorities.

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.

NASA Tech Briefs, March 2005

NASA Technical Reports Server (NTRS)

2005-01-01

Topics covered include: Scheme for Entering Binary Data Into a Quantum Computer; Encryption for Remote Control via Internet or Intranet; Coupled Receiver/Decoders for Low-Rate Turbo Codes; Processing GPS Occultation Data To Characterize Atmosphere; Displacing Unpredictable Nulls in Antenna Radiation Patterns; Integrated Pointing and Signal Detector for Optical Receiver; Adaptive Thresholding and Parameter Estimation for PPM; Data-Driven Software Framework for Web-Based ISS Telescience; Software for Secondary-School Learning About Robotics; Fuzzy Logic Engine; Telephone-Directory Program; Simulating a Direction-Finder Search for an ELT; Formulating Precursors for Coating Metals and Ceramics; Making Macroscopic Assemblies of Aligned Carbon Nanotubes; Ball Bearings Equipped for In Situ Lubrication on Demand; Synthetic Bursae for Robots; Robot Forearm and Dexterous Hand; Making a Metal-Lined Composite-Overwrapped Pressure Vessel; Ex Vivo Growth of Bioengineered Ligaments and Other Tissues; Stroboscopic Goggles for Reduction of Motion Sickness; Articulating Support for Horizontal Resistive Exercise; Modified Penning-Malmberg Trap for Storing Antiprotons; Tumbleweed Rovers; Two-Photon Fluorescence Microscope for Microgravity Research; Biased Randomized Algorithm for Fast Model-Based Diagnosis; Fast Algorithms for Model-Based Diagnosis; Simulations of Evaporating Multicomponent Fuel Drops; Formation Flying of Tethered and Nontethered Spacecraft; and Two Methods for Efficient Solution of the Hitting- Set Problem.

On the error statistics of Viterbi decoding and the performance of concatenated codes

NASA Technical Reports Server (NTRS)

Miller, R. L.; Deutsch, L. J.; Butman, S. A.

1981-01-01

Computer simulation results are presented on the performance of convolutional codes of constraint lengths 7 and 10 concatenated with the (255, 223) Reed-Solomon code (a proposed NASA standard). These results indicate that as much as 0.8 dB can be gained by concatenating this Reed-Solomon code with a (10, 1/3) convolutional code, instead of the (7, 1/2) code currently used by the DSN. A mathematical model of Viterbi decoder burst-error statistics is developed and is validated through additional computer simulations.

New syndrome decoding techniques for the (n, k) convolutional codes

NASA Technical Reports Server (NTRS)

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

1984-01-01

This paper presents a new syndrome decoding algorithm for the (n, k) convolutional codes (CC) which differs completely from an earlier syndrome decoding algorithm of Schalkwijk and Vinck. The new algorithm is based on the general solution of the syndrome equation, a linear Diophantine equation for the error polynomial vector E(D). The set of Diophantine solutions is a coset of the CC. In this error coset a recursive, Viterbi-like algorithm is developed to find the minimum weight error vector (circumflex)E(D). An example, illustrating the new decoding algorithm, is given for the binary nonsystemmatic (3, 1)CC. Previously announced in STAR as N83-34964

Synchronization Control for a Class of Discrete-Time Dynamical Networks With Packet Dropouts: A Coding-Decoding-Based Approach.

PubMed

Wang, Licheng; Wang, Zidong; Han, Qing-Long; Wei, Guoliang

2017-09-06

The synchronization control problem is investigated for a class of discrete-time dynamical networks with packet dropouts via a coding-decoding-based approach. The data is transmitted through digital communication channels and only the sequence of finite coded signals is sent to the controller. A series of mutually independent Bernoulli distributed random variables is utilized to model the packet dropout phenomenon occurring in the transmissions of coded signals. The purpose of the addressed synchronization control problem is to design a suitable coding-decoding procedure for each node, based on which an efficient decoder-based control protocol is developed to guarantee that the closed-loop network achieves the desired synchronization performance. By applying a modified uniform quantization approach and the Kronecker product technique, criteria for ensuring the detectability of the dynamical network are established by means of the size of the coding alphabet, the coding period and the probability information of packet dropouts. Subsequently, by resorting to the input-to-state stability theory, the desired controller parameter is obtained in terms of the solutions to a certain set of inequality constraints which can be solved effectively via available software packages. Finally, two simulation examples are provided to demonstrate the effectiveness of the obtained results.

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.

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.

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.

Time-Dependent Simulation of Incompressible Flow in a Turbopump Using Overset Grid Approach

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan

2001-01-01

This paper reports the progress being made towards complete unsteady turbopump simulation capability by using overset grid systems. A computational model of a turbo-pump impeller is used as a test case for the performance evaluation of the MPI, hybrid MPI/Open-MP, and MLP versions of the INS3D code. Relative motion of the grid system for rotor-stator interaction was obtained by employing overset grid techniques. Unsteady computations for a turbo-pump, which contains 114 zones with 34.3 Million grid points, are performed on Origin 2000 systems at NASA Ames Research Center. The approach taken for these simulations, and the performance of the parallel versions of the code are presented.

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.

Phonological Coding in Good and Poor Readers.

ERIC Educational Resources Information Center

Briggs, Pamela; Underwood, Geoffrey

1982-01-01

A set of four experiments investigates the relationship between phonological coding and reading ability, using a picture-word interference task and a decoding task. Results with regard to both adults and children suggest that while poor readers possess weak decoding skills, good and poor readers show equivalent evidence of direct semantic and…

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.

Product code optimization for determinate state LDPC decoding in robust image transmission.

PubMed

Thomos, Nikolaos; Boulgouris, Nikolaos V; Strintzis, Michael G

2006-08-01

We propose a novel scheme for error-resilient image transmission. The proposed scheme employs a product coder consisting of low-density parity check (LDPC) codes and Reed-Solomon codes in order to deal effectively with bit errors. The efficiency of the proposed scheme is based on the exploitation of determinate symbols in Tanner graph decoding of LDPC codes and a novel product code optimization technique based on error estimation. Experimental evaluation demonstrates the superiority of the proposed system in comparison to recent state-of-the-art techniques for image transmission.

Multiple-access relaying with network coding: iterative network/channel decoding with imperfect CSI

NASA Astrophysics Data System (ADS)

Vu, Xuan-Thang; Renzo, Marco Di; Duhamel, Pierre

2013-12-01

In this paper, we study the performance of the four-node multiple-access relay channel with binary Network Coding (NC) in various Rayleigh fading scenarios. In particular, two relay protocols, decode-and-forward (DF) and demodulate-and-forward (DMF) are considered. In the first case, channel decoding is performed at the relay before NC and forwarding. In the second case, only demodulation is performed at the relay. The contributions of the paper are as follows: (1) two joint network/channel decoding (JNCD) algorithms, which take into account possible decoding error at the relay, are developed in both DF and DMF relay protocols; (2) both perfect channel state information (CSI) and imperfect CSI at receivers are studied. In addition, we propose a practical method to forward the relays error characterization to the destination (quantization of the BER). This results in a fully practical scheme. (3) We show by simulation that the number of pilot symbols only affects the coding gain but not the diversity order, and that quantization accuracy affects both coding gain and diversity order. Moreover, when compared with the recent results using DMF protocol, our proposed DF protocol algorithm shows an improvement of 4 dB in fully interleaved Rayleigh fading channels and 0.7 dB in block Rayleigh fading channels.

Reliability and throughput issues for optical wireless and RF wireless systems

NASA Astrophysics Data System (ADS)

Yu, Meng

The fast development of wireless communication technologies has two main trends. On one hand, in point-to-point communications, the demand for higher throughput called for the emergence of wireless broadband techniques including optical wireless (OW). One the other hand, wireless networks are becoming pervasive. New application of wireless networks ask for more flexible system infrastructures beyond the point-to-point prototype to achieve better performance. This dissertation investigates two topics on the reliability and throughput issues of new wireless technologies. The first topic is to study the capacity, and practical forward error control strategies for OW systems. We investigate the performance of OW systems under weak atmospheric turbulence. We first investigate the capacity and power allocation for multi-laser and multi-detector systems. Our results show that uniform power allocation is a practically optimal solution for paralleled channels. We also investigate the performance of Reed Solomon (RS) codes and turbo codes for OW systems. We present RS codes as good candidates for OW systems. The second topic targets user cooperation in wireless networks. We evaluate the relative merits of amplify-forward (AF) and decode-forward (DF) in practical scenarios. Both analysis and simulations show that the overall system performance is critically affected by the quality of the inter-user channel. Following this result, we investigate two schemes to improve the overall system performance. We first investigate the impact of the relay location on the overall system performance and determine the optimal location of relay. A best-selective single-relay 1 system is proposed and evaluated. Through the analysis of the average capacity and outage, we show that a small candidate pool of 3 to 5 relays suffices to reap most of the "geometric" gain available to a selective system. Second, we propose a new user cooperation scheme to provide an effective better inter-user channel. Most user cooperation protocols work in a time sharing manner, where a node forwards others' messages and sends its own message at different sections within a provisioned time slot. In the proposed scheme the two messages are encoded together in a single codework using network coding and transmitted in the given time slot. We also propose a general multiple-user cooperation framework. Under this framework, we show that network coding can achieve better diversity and provide effective better inter-user channels than time sharing. The last part of the dissertation focuses on multi-relay packet transmission. We propose an adaptive and distributive coding scheme for the relay nodes to adaptively cooperate and forward messages. The adaptive scheme shows performance gain over fixed schemes. Then we shift our viewpoint and represent the network as part of encoders and part of decoders.

Protograph based LDPC codes with minimum distance linearly growing with block size

NASA Technical Reports Server (NTRS)

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

2005-01-01

We propose several LDPC code constructions that simultaneously achieve good threshold and error floor performance. Minimum distance is shown to grow linearly with block size (similar to regular codes of variable degree at least 3) by considering ensemble average weight enumerators. Our constructions are based on projected graph, or protograph, structures that support high-speed decoder implementations. As with irregular ensembles, our constructions are sensitive to the proportion of degree-2 variable nodes. A code with too few such nodes tends to have an iterative decoding threshold that is far from the capacity threshold. A code with too many such nodes tends to not exhibit a minimum distance that grows linearly in block length. In this paper we also show that precoding can be used to lower the threshold of regular LDPC codes. The decoding thresholds of the proposed codes, which have linearly increasing minimum distance in block size, outperform that of regular LDPC codes. Furthermore, a family of low to high rate codes, with thresholds that adhere closely to their respective channel capacity thresholds, is presented. Simulation results for a few example codes show that the proposed codes have low error floors as well as good threshold SNFt performance.

Space communication system for compressed data with a concatenated Reed-Solomon-Viterbi coding channel

NASA Technical Reports Server (NTRS)

Rice, R. F.; Hilbert, E. E. (Inventor)

1976-01-01

A space communication system incorporating a concatenated Reed Solomon Viterbi coding channel is discussed for transmitting compressed and uncompressed data from a spacecraft to a data processing center on Earth. Imaging (and other) data are first compressed into source blocks which are then coded by a Reed Solomon coder and interleaver, followed by a convolutional encoder. The received data is first decoded by a Viterbi decoder, followed by a Reed Solomon decoder and deinterleaver. The output of the latter is then decompressed, based on the compression criteria used in compressing the data in the spacecraft. The decompressed data is processed to reconstruct an approximation of the original data-producing condition or images.

Class of near-perfect coded apertures

NASA Technical Reports Server (NTRS)

Cannon, T. M.; Fenimore, E. E.

1977-01-01

Coded aperture imaging of gamma ray sources has long promised an improvement in the sensitivity of various detector systems. The promise has remained largely unfulfilled, however, for either one of two reasons. First, the encoding/decoding method produces artifacts, which even in the absence of quantum noise, restrict the quality of the reconstructed image. This is true of most correlation-type methods. Second, if the decoding procedure is of the deconvolution variety, small terms in the transfer function of the aperture can lead to excessive noise in the reconstructed image. It is proposed to circumvent both of these problems by use of a uniformly redundant array (URA) as the coded aperture in conjunction with a special correlation decoding method.

Coding gains and error rates from the Big Viterbi Decoder

NASA Technical Reports Server (NTRS)

Onyszchuk, I. M.

1991-01-01

A prototype hardware Big Viterbi Decoder (BVD) was completed for an experiment with the Galileo Spacecraft. Searches for new convolutional codes, studies of Viterbi decoder hardware designs and architectures, mathematical formulations, and decompositions of the deBruijn graph into identical and hierarchical subgraphs, and very large scale integration (VLSI) chip design are just a few examples of tasks completed for this project. The BVD bit error rates (BER), measured from hardware and software simulations, are plotted as a function of bit signal to noise ratio E sub b/N sub 0 on the additive white Gaussian noise channel. Using the constraint length 15, rate 1/4, experimental convolutional code for the Galileo mission, the BVD gains 1.5 dB over the NASA standard (7,1/2) Maximum Likelihood Convolution Decoder (MCD) at a BER of 0.005. At this BER, the same gain results when the (255,233) NASA standard Reed-Solomon decoder is used, which yields a word error rate of 2.1 x 10(exp -8) and a BER of 1.4 x 10(exp -9). The (15, 1/6) code to be used by the Cometary Rendezvous Asteroid Flyby (CRAF)/Cassini Missions yields 1.7 dB of coding gain. These gains are measured with respect to symbols input to the BVD and increase with decreasing BER. Also, 8-bit input symbol quantization makes the BVD resistant to demodulated signal-level variations which may cause higher bandwidth than the NASA (7,1/2) code, these gains are offset by about 0.1 dB of expected additional receiver losses. Coding gains of several decibels are possible by compressing all spacecraft data.

Small Engine Technology (Set) Task 8 Aeroelastic Prediction Methods

NASA Technical Reports Server (NTRS)

Eick, Chris D.; Liu, Jong-Shang

1998-01-01

AlliedSignal Engines, in cooperation with NASA LeRC, completed an evaluation of recently developed aeroelastic computer codes using test cases from the AlliedSignal Engines fan blisk database. Test data for this task includes strain gage, light probe, performance, and steady-state pressure information obtained for conditions where synchronous or flutter vibratory conditions were found to occur. Aeroelastic codes evaluated include the quasi 3-D UNSFLO (developed at MIT and modified to include blade motion by AlliedSignal), the 2-D FREPS (developed by NASA LeRC), and the 3-D TURBO-AE (under development at NASA LeRC). Six test cases each where flutter and synchronous vibrations were found to occur were used for evaluation of UNSFLO and FREPS. In addition, one of the flutter cases was evaluated using TURBO-AE. The UNSFLO flutter evaluations were completed for 75 percent radial span and provided good agreement with the experimental test data. Synchronous evaluations were completed for UNSFLO but further enhancement needs to be added to the code before the unsteady pressures can be used to predict forced response vibratory stresses. The FREPS evaluations were hindered as the steady flow solver (SFLOW) was unable to converge to a solution for the transonic flow conditions in the fan blisk. This situation resulted in all FREPS test cases being attempted but no results were obtained during the present program. Currently, AlliedSignal is evaluating integrating FREPS with our existing steady flow solvers to bypass the SFLOW difficulties. ne TURBO-AE steady flow solution provided an excellent match with the AlliedSignal Engines calibrated DAWES 3-D viscous solver. Finally, the TURBO-AE unsteady analyses also matched experimental observations by predicting flutter for the single test case evaluated.

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.

User Manual for Beta Version of TURBO-GRD: A Software System for Interactive Two-Dimensional Boundary/ Field Grid Generation, Modification, and Refinement

NASA Technical Reports Server (NTRS)

Choo, Yung K.; Slater, John W.; Henderson, Todd L.; Bidwell, Colin S.; Braun, Donald C.; Chung, Joongkee

1998-01-01

TURBO-GRD is a software system for interactive two-dimensional boundary/field grid generation. modification, and refinement. Its features allow users to explicitly control grid quality locally and globally. The grid control can be achieved interactively by using control points that the user picks and moves on the workstation monitor or by direct stretching and refining. The techniques used in the code are the control point form of algebraic grid generation, a damped cubic spline for edge meshing and parametric mapping between physical and computational domains. It also performs elliptic grid smoothing and free-form boundary control for boundary geometry manipulation. Internal block boundaries are constructed and shaped by using Bezier curve. Because TURBO-GRD is a highly interactive code, users can read in an initial solution, display its solution contour in the background of the grid and control net, and exercise grid modification using the solution contour as a guide. This process can be called an interactive solution-adaptive grid generation.

Error control for reliable digital data transmission and storage systems

NASA Technical Reports Server (NTRS)

Costello, D. J., Jr.; Deng, R. H.

1985-01-01

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. In this paper we present some special decoding techniques for extended single-and-double-error-correcting RS codes which are capable of high speed operation. These techniques are designed to find the error locations and the error values directly from the syndrome without having to use the iterative alorithm to find the error locator polynomial. Two codes are considered: (1) a d sub min = 4 single-byte-error-correcting (SBEC), double-byte-error-detecting (DBED) RS code; and (2) a d sub min = 6 double-byte-error-correcting (DBEC), triple-byte-error-detecting (TBED) RS code.

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.

Circuit Design Approaches for Implementation of a Subtrellis IC for a Reed-Muller Subcode

NASA Technical Reports Server (NTRS)

Lin, Shu; Uehara, Gregory T.; Nakamura, Eric B.; Chu, Cecilia W. P.

1996-01-01

In his research, we have proposed the (64, 40, 8) subcode of the third-order Reed-Muller (RM) code to NASA for high-speed satellite communications. This RM subcode can be used either alone or as an inner code of a concatenated coding system with the NASA standard (255, 233, 33) Reed-Solomon (RS) code as the outer code to achieve high performance (or low bit-error rate) with reduced decoding complexity. It can also be used as a component code in a multilevel bandwidth efficient coded modulation system to achieve reliable bandwidth efficient data transmission. This report will summarize the key progress we have made toward achieving our eventual goal of implementing a decoder system based upon this code. In the first phase of study, we investigated the complexities of various sectionalized trellis diagrams for the proposed (64, 40, 8) RM subcode. We found a specific 8-trellis diagram for this code which requires the least decoding complexity with a high possibility of achieving a decoding speed of 600 M bits per second(Mbps). The combination of a large number of states and a high data rate will be made possible due to the utilization of a high degree of parallelism throughout the architecture. This trellis diagram will be presented and briefly described. In the second phase of study which was carried out through the past year, we investigated circuit architectures to determine the feasibility of VLSI implementation of a high- speed Viterbi decoder based on this 8-section trellis diagram. We began to examine specific design and implementation approaches to implement a fully custom integrated circuit (IC) which will be a key building block for a decoder system implementation. The key results will be presented in this report. This report will be divided into three primary sections. First, we will briefly describe the system block diagram in which the proposed decoder is assumed to be operating and present some of the key architectural approaches being used to implement the system at high speed. Second, we will describe details of the 8-trellis diagram we found to best meet the trade-offs between chip and overall system complexity. The chosen approach implements the trellis for the (64, 40, 8) RM subcode with 32 independent sub-trellises. And third, we will describe results of our feasibility study on the implementation of such an IC chip in CMOS technology to implement one of these subtrellises.

Circuit Design Approaches for Implementation of a Subtrellis IC for a Reed-Muller Subcode

NASA Technical Reports Server (NTRS)

Lin, Shu; Uehara, Gregory T.; Nakamura, Eric B.; Chu, Cecilia W. P.

1996-01-01

In this research, we have proposed the (64, 40, 8) subcode of the third-order Reed-Muller (RM) code to NASA for high-speed satellite communications. This RM subcode can be used either alone or as an inner code of a concatenated coding system with the NASA standard (255, 233, 33) Reed-Solomon (RS) code as the outer code to achieve high performance (or low bit-error rate) with reduced decoding complexity. It can also be used as a component code in a multilevel bandwidth efficient coded modulation system to achieve reliable bandwidth efficient data transmission. This report will summarize the key progress we have made toward achieving our eventual goal of implementing a decoder system based upon this code. In the first phase of study, we investigated the complexities of various sectionalized trellis diagrams for the proposed (64, 40, 8) RM subcode. We found a specific 8-trellis diagram for this code which requires the least decoding complexity with a high possibility of achieving a decoding speed of 600 M bits per second (Mbps). The combination of a large number of states and a high data rate will be made possible due to the utilization of a high degree of parallelism throughout the architecture. This trellis diagram will be presented and briefly described. In the second phase of study which was carried out through the past year, we investigated circuit architectures to determine the feasibility of VLSI implementation of a high-speed Viterbi decoder based on this 8-section trellis diagram. We began to examine specific design and implementation approaches to implement a fully custom integrated circuit (IC) which will be a key building block for a decoder system implementation. The key results will be presented in this report. This report will be divided into three primary sections. First, we will briefly describe the system block diagram in which the proposed decoder is assumed to be operating and present some of the key architectural approaches being used to implement the system at high speed. Second, we will describe details of the 8-trellis diagram we found to best meet the trade-offs between chip and overall system complexity. The chosen approach implements the trellis for the (64, 40, 8) RM subcode with 32 independent sub-trellises. And third, we will describe results of our feasibility study on the implementation of such an IC chip in CMOS technology to implement one of these subtrellises.

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.

A Systolic VLSI Design of a Pipeline Reed-solomon Decoder

NASA Technical Reports Server (NTRS)

Shao, H. M.; Truong, T. K.; Deutsch, L. J.; Yuen, J. H.; Reed, I. S.

1984-01-01

A pipeline structure of a transform decoder similar to a systolic array was developed to decode Reed-Solomon (RS) codes. An important ingredient of this design is a modified Euclidean algorithm for computing the error locator polynomial. The computation of inverse field elements is completely avoided in this modification of Euclid's algorithm. The new decoder is regular and simple, and naturally suitable for VLSI implementation.

A VLSI design of a pipeline Reed-Solomon decoder

NASA Technical Reports Server (NTRS)

Shao, H. M.; Truong, T. K.; Deutsch, L. J.; Yuen, J. H.; Reed, I. S.

1985-01-01

A pipeline structure of a transform decoder similar to a systolic array was developed to decode Reed-Solomon (RS) codes. An important ingredient of this design is a modified Euclidean algorithm for computing the error locator polynomial. The computation of inverse field elements is completely avoided in this modification of Euclid's algorithm. The new decoder is regular and simple, and naturally suitable for VLSI implementation.

Coding/decoding two-dimensional images with orbital angular momentum of light.

PubMed

Chu, Jiaqi; Li, Xuefeng; Smithwick, Quinn; Chu, Daping

2016-04-01

We investigate encoding and decoding of two-dimensional information using the orbital angular momentum (OAM) of light. Spiral phase plates and phase-only spatial light modulators are used in encoding and decoding of OAM states, respectively. We show that off-axis points and spatial variables encoded with a given OAM state can be recovered through decoding with the corresponding complimentary OAM state.

Protograph LDPC Codes Over Burst Erasure Channels

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Dolinar, Sam; Jones, Christopher

2006-01-01

In this paper we design high rate protograph based LDPC codes suitable for binary erasure channels. To simplify the encoder and decoder implementation for high data rate transmission, the structure of codes are based on protographs and circulants. These LDPC codes can improve data link and network layer protocols in support of communication networks. Two classes of codes were designed. One class is designed for large block sizes with an iterative decoding threshold that approaches capacity of binary erasure channels. The other class is designed for short block sizes based on maximizing minimum stopping set size. For high code rates and short blocks the second class outperforms the first class.

Hybrid Hard and Soft Decision Decoding of Reed-Solomon Codes for M-ary Frequency-Shift Keying

DTIC Science & Technology

2010-06-01

Reed-Solomon (RS) coding, Orthogonal signaling, Additive White Gaussian Noise (AWGN), Pulse-Noise Interference (PNI), coherent detection, noncoherent ...Coherent Demodulation of MFSK ....................................................10 2. Noncoherent Demodulation of MFSK...62 V. PERFORMANCE SIMULATION AND ANALYSIS OF MFSK WITH RS ENCODING, HYBRID HD SD DECODING, AND NONCOHERENT DEMODULATION IN AWGN

Frequency-Accommodating Manchester Decoder

NASA Technical Reports Server (NTRS)

Vasquez, Mario J.

1988-01-01

No adjustment necessary to cover a 10:1 frequency range. Decoding circuit converts biphase-level pulse-code modulation to nonreturn-to-zero (NRZ)-level pulse-code modulation plus clock signal. Circuit accommodates input data rate of 50 to 500 kb/s. Tracks gradual changes in rate automatically, eliminating need for extra circuits and manual switching to adjust to different rates.

Fast decoder for local quantum codes using Groebner basis

NASA Astrophysics Data System (ADS)

Haah, Jeongwan

2013-03-01

Based on arXiv:1204.1063. A local translation-invariant quantum code has a description in terms of Laurent polynomials. As an application of this observation, we present a fast decoding algorithm for translation-invariant local quantum codes in any spatial dimensions using the straightforward division algorithm for multivariate polynomials. The running time is O (n log n) on average, or O (n2 log n) on worst cases, where n is the number of physical qubits. The algorithm improves a subroutine of the renormalization-group decoder by Bravyi and Haah (arXiv:1112.3252) in the translation-invariant case. This work is supported in part by the Insitute for Quantum Information and Matter, an NSF Physics Frontier Center, and the Korea Foundation for Advanced Studies.

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.

LDPC decoder with a limited-precision FPGA-based floating-point multiplication coprocessor

NASA Astrophysics Data System (ADS)

Moberly, Raymond; O'Sullivan, Michael; Waheed, Khurram

2007-09-01

Implementing the sum-product algorithm, in an FPGA with an embedded processor, invites us to consider a tradeoff between computational precision and computational speed. The algorithm, known outside of the signal processing community as Pearl's belief propagation, is used for iterative soft-decision decoding of LDPC codes. We determined the feasibility of a coprocessor that will perform product computations. Our FPGA-based coprocessor (design) performs computer algebra with significantly less precision than the standard (e.g. integer, floating-point) operations of general purpose processors. Using synthesis, targeting a 3,168 LUT Xilinx FPGA, we show that key components of a decoder are feasible and that the full single-precision decoder could be constructed using a larger part. Soft-decision decoding by the iterative belief propagation algorithm is impacted both positively and negatively by a reduction in the precision of the computation. Reducing precision reduces the coding gain, but the limited-precision computation can operate faster. A proposed solution offers custom logic to perform computations with less precision, yet uses the floating-point format to interface with the software. Simulation results show the achievable coding gain. Synthesis results help theorize the the full capacity and performance of an FPGA-based coprocessor.

An Energy-Efficient Compressive Image Coding for Green Internet of Things (IoT).

PubMed

Li, Ran; Duan, Xiaomeng; Li, Xu; He, Wei; Li, Yanling

2018-04-17

Aimed at a low-energy consumption of Green Internet of Things (IoT), this paper presents an energy-efficient compressive image coding scheme, which provides compressive encoder and real-time decoder according to Compressive Sensing (CS) theory. The compressive encoder adaptively measures each image block based on the block-based gradient field, which models the distribution of block sparse degree, and the real-time decoder linearly reconstructs each image block through a projection matrix, which is learned by Minimum Mean Square Error (MMSE) criterion. Both the encoder and decoder have a low computational complexity, so that they only consume a small amount of energy. Experimental results show that the proposed scheme not only has a low encoding and decoding complexity when compared with traditional methods, but it also provides good objective and subjective reconstruction qualities. In particular, it presents better time-distortion performance than JPEG. Therefore, the proposed compressive image coding is a potential energy-efficient scheme for Green IoT.

Influence of incident angle on the decoding in laser polarization encoding guidance

NASA Astrophysics Data System (ADS)

Zhou, Muchun; Chen, Yanru; Zhao, Qi; Xin, Yu; Wen, Hongyuan

2009-07-01

Dynamic detection of polarization states is very important for laser polarization coding guidance systems. In this paper, a set of dynamic polarization decoding and detection system used in laser polarization coding guidance was designed. Detection process of the normal incident polarized light is analyzed with Jones Matrix; the system can effectively detect changes in polarization. Influence of non-normal incident light on performance of polarization decoding and detection system is studied; analysis showed that changes in incident angle will have a negative impact on measure results, the non-normal incident influence is mainly caused by second-order birefringence and polarization sensitivity effect generated in the phase delay and beam splitter prism. Combined with Fresnel formula, decoding errors of linearly polarized light, elliptically polarized light and circularly polarized light with different incident angles into the detector are calculated respectively, the results show that the decoding errors increase with increase of incident angle. Decoding errors have relations with geometry parameters, material refractive index of wave plate, polarization beam splitting prism. Decoding error can be reduced by using thin low-order wave-plate. Simulation of detection of polarized light with different incident angle confirmed the corresponding conclusions.

Sum of the Magnitude for Hard Decision Decoding Algorithm Based on Loop Update Detection

PubMed Central

Meng, Jiahui; Zhao, Danfeng; Tian, Hai; Zhang, Liang

2018-01-01

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. PMID:29342963

Rate-compatible protograph LDPC code families with linear minimum distance

NASA Technical Reports Server (NTRS)

Divsalar, Dariush (Inventor); Dolinar, Jr., Samuel J (Inventor); Jones, Christopher R. (Inventor)

2012-01-01

Digital communication coding methods are shown, which generate certain types of low-density parity-check (LDPC) codes built from protographs. A first method creates protographs having the linear minimum distance property and comprising at least one variable node with degree less than 3. A second method creates families of protographs of different rates, all having the linear minimum distance property, and structurally identical for all rates except for a rate-dependent designation of certain variable nodes as transmitted or non-transmitted. A third method creates families of protographs of different rates, all having the linear minimum distance property, and structurally identical for all rates except for a rate-dependent designation of the status of certain variable nodes as non-transmitted or set to zero. LDPC codes built from the protographs created by these methods can simultaneously have low error floors and low iterative decoding thresholds, and families of such codes of different rates can be decoded efficiently using a common decoding architecture.

Efficient Polar Coding of Quantum Information

NASA Astrophysics Data System (ADS)

Renes, Joseph M.; Dupuis, Frédéric; Renner, Renato

2012-08-01

Polar coding, introduced 2008 by Arıkan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the asymptotic limit of large block sizes. Here, we study the use of polar codes for the transmission of quantum information. Focusing on the case of qubit Pauli channels and qubit erasure channels, we use classical polar codes to construct a coding scheme that asymptotically achieves a net transmission rate equal to the coherent information using efficient encoding and decoding operations and code construction. Our codes generally require preshared entanglement between sender and receiver, but for channels with a sufficiently low noise level we demonstrate that the rate of preshared entanglement required is zero.

Parameter as a Switch Between Dynamical States of a Network in Population Decoding.

PubMed

Yu, Jiali; Mao, Hua; Yi, Zhang

2017-04-01

Population coding is a method to represent stimuli using the collective activities of a number of neurons. Nevertheless, it is difficult to extract information from these population codes with the noise inherent in neuronal responses. Moreover, it is a challenge to identify the right parameter of the decoding model, which plays a key role for convergence. To address the problem, a population decoding model is proposed for parameter selection. Our method successfully identified the key conditions for a nonzero continuous attractor. Both the theoretical analysis and the application studies demonstrate the correctness and effectiveness of this strategy.

DSN telemetry system performance with convolutionally coded data using operational maximum-likelihood convolutional decoders

NASA Technical Reports Server (NTRS)

Benjauthrit, B.; Mulhall, B.; Madsen, B. D.; Alberda, M. E.

1976-01-01

The DSN telemetry system performance with convolutionally coded data using the operational maximum-likelihood convolutional decoder (MCD) being implemented in the Network is described. Data rates from 80 bps to 115.2 kbps and both S- and X-band receivers are reported. The results of both one- and two-way radio losses are included.

Channel coding/decoding alternatives for compressed TV data on advanced planetary missions.

NASA Technical Reports Server (NTRS)

Rice, R. F.

1972-01-01

The compatibility of channel coding/decoding schemes with a specific TV compressor developed for advanced planetary missions is considered. Under certain conditions, it is shown that compressed data can be transmitted at approximately the same rate as uncompressed data without any loss in quality. Thus, the full gains of data compression can be achieved in real-time transmission.

Picture data compression coder using subband/transform coding with a Lempel-Ziv-based coder

NASA Technical Reports Server (NTRS)

Glover, Daniel R. (Inventor)

1995-01-01

Digital data coders/decoders are used extensively in video transmission. A digitally encoded video signal is separated into subbands. Separating the video into subbands allows transmission at low data rates. Once the data is separated into these subbands it can be coded and then decoded by statistical coders such as the Lempel-Ziv based coder.

Cognitive Training and Reading Remediation

ERIC Educational Resources Information Center

Mahapatra, Shamita

2015-01-01

Reading difficulties are experienced by children either because they fail to decode the words and thus are unable to comprehend the text or simply fail to comprehend the text even if they are able to decode the words and read them out. Failure in word decoding results from a failure in phonological coding of written information, whereas, reading…

Strategic and Tactical Decision-Making Under Uncertainty

DTIC Science & Technology

2006-01-03

message passing algorithms. In recent work we applied this method to the problem of joint decoding of a low-density parity-check ( LDPC ) code and a partial...Joint Decoding of LDPC Codes and Partial-Response Channels." IEEE Transactions on Communications. Vol. 54, No. 7, 1149-1153, 2006. P. Pakzad and V...Michael I. Jordan PAGES U U U SAPR 20 19b. TELEPHONE NUMBER (Include area code ) 510/642-3806 Standard Form 298 (Rev. 8/98) Prescribed by ANSI Std. Z39.18

Image authentication using distributed source coding.

PubMed

Lin, Yao-Chung; Varodayan, David; Girod, Bernd

2012-01-01

We present a novel approach using distributed source coding for image authentication. The key idea is to provide a Slepian-Wolf encoded quantized image projection as authentication data. This version can be correctly decoded with the help of an authentic image as side information. Distributed source coding provides the desired robustness against legitimate variations while detecting illegitimate modification. The decoder incorporating expectation maximization algorithms can authenticate images which have undergone contrast, brightness, and affine warping adjustments. Our authentication system also offers tampering localization by using the sum-product algorithm.

High data rate coding for the space station telemetry links.

NASA Technical Reports Server (NTRS)

Lumb, D. R.; Viterbi, A. J.

1971-01-01

Coding systems for high data rates were examined from the standpoint of potential application in space-station telemetry links. Approaches considered included convolutional codes with sequential, Viterbi, and cascaded-Viterbi decoding. It was concluded that a high-speed (40 Mbps) sequential decoding system best satisfies the requirements for the assumed growth potential and specified constraints. Trade-off studies leading to this conclusion are viewed, and some sequential (Fano) algorithm improvements are discussed, together with real-time simulation results.

Constructing LDPC Codes from Loop-Free Encoding Modules

NASA Technical Reports Server (NTRS)

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

2009-01-01

A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to channel capacity limits can be achieved for the codes of the type in question having low maximum variable node degrees. The decoding thresholds in these examples are lower than those of the best-known unstructured irregular LDPC codes constrained to have the same maximum node degrees. Furthermore, the present method enables the construction of codes of any desired rate with thresholds that stay uniformly close to their respective channel capacity thresholds.

Large-Constraint-Length, Fast Viterbi Decoder

NASA Technical Reports Server (NTRS)

Collins, O.; Dolinar, S.; Hsu, In-Shek; Pollara, F.; Olson, E.; Statman, J.; Zimmerman, G.

1990-01-01

Scheme for efficient interconnection makes VLSI design feasible. Concept for fast Viterbi decoder provides for processing of convolutional codes of constraint length K up to 15 and rates of 1/2 to 1/6. Fully parallel (but bit-serial) architecture developed for decoder of K = 7 implemented in single dedicated VLSI circuit chip. Contains six major functional blocks. VLSI circuits perform branch metric computations, add-compare-select operations, and then store decisions in traceback memory. Traceback processor reads appropriate memory locations and puts out decoded bits. Used as building block for decoders of larger K.

Preliminary Assessment of Turbomachinery Codes

NASA Technical Reports Server (NTRS)

Mazumder, Quamrul H.

2007-01-01

This report assesses different CFD codes developed and currently being used at Glenn Research Center to predict turbomachinery fluid flow and heat transfer behavior. This report will consider the following codes: APNASA, TURBO, GlennHT, H3D, and SWIFT. Each code will be described separately in the following section with their current modeling capabilities, level of validation, pre/post processing, and future development and validation requirements. This report addresses only previously published and validations of the codes. However, the codes have been further developed to extend the capabilities of the codes.

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.

Methods of alleviation of ionospheric scintillation effects on digital communications

NASA Technical Reports Server (NTRS)

Massey, J. L.

1974-01-01

The degradation of the performance of digital communication systems because of ionospheric scintillation effects can be reduced either by diversity techniques or by coding. The effectiveness of traditional space-diversity, frequency-diversity and time-diversity techniques is reviewed and design considerations isolated. Time-diversity signaling is then treated as an extremely simple form of coding. More advanced coding methods, such as diffuse threshold decoding and burst-trapping decoding, which appear attractive in combatting scintillation effects are discussed and design considerations noted. Finally, adaptive coding techniques appropriate when the general state of the channel is known are discussed.

Investigation of the Flow Physics Driving Stall-Side Flutter in Advanced Forward Swept Fan Designs

NASA Technical Reports Server (NTRS)

Sanders, Albert J.; Liu, Jong S.; Panovsky, Josef; Bakhle, Milind A.; Stefko, George; Srivastava, Rakesh

2003-01-01

Flutter-free operation of advanced transonic fan designs continues to be a challenging task for the designers of aircraft engines. In order to meet the demands of increased performance and lighter weight, these modern fan designs usually feature low-aspect ratio shroudless rotor blade designs that make the task of achieving adequate flutter margin even more challenging for the aeroelastician. This is especially true for advanced forward swept designs that encompass an entirely new design space compared to previous experience. Fortunately, advances in unsteady computational fluid dynamic (CFD) techniques over the past decade now provide an analysis capability that can be used to quantitatively assess the aeroelastic characteristics of these next generation fans during the design cycle. For aeroelastic applications, Mississippi State University and NASA Glenn Research Center have developed the CFD code TURBO-AE. This code is a time-accurate three-dimensional Euler/Navier-Stokes unsteady flow solver developed for axial-flow turbomachinery that can model multiple blade rows undergoing harmonic oscillations with arbitrary interblade phase angles, i.e., nodal diameter patterns. Details of the code can be found in Chen et al. (1993, 1994), Bakhle et al. (1997, 1998), and Srivastava et al. (1999). To assess aeroelastic stability, the work-per-cycle from TURBO-AE is converted to the critical damping ratio since this value is more physically meaningful, with both the unsteady normal pressure and viscous shear forces included in the work-per-cycle calculation. If the total damping (aerodynamic plus mechanical) is negative, then the blade is unstable since it extracts energy from the flow field over the vibration cycle. TURBO-AE is an integral part of an aeroelastic design system being developed at Honeywell Engines, Systems & Services for flutter and forced response predictions, with test cases from development rig and engine tests being used to validate its predictive capability. A recent experimental program (Sanders et al., 2002) was aimed at providing the necessary unsteady aerodynamic and vibratory response data needed to validate TURBO-AE for fan flutter predictions. A comparison of numerical TURBO-AE simulations with the benchmark flutter data is given in Sanders et al. (2003), with the data used to guide the validation of the code and define best practices for performing accurate unsteady simulations. The agreement between the analyses and the predictions was quite remarkable, demonstrating the ability of the analysis to accurately model the unsteady flow processes driving stall-side flutter.

A novel decoding algorithm based on the hierarchical reliable strategy for SCG-LDPC codes in optical communications

NASA Astrophysics Data System (ADS)

Yuan, Jian-guo; Tong, Qing-zhen; Huang, Sheng; Wang, Yong

2013-11-01

An effective hierarchical reliable belief propagation (HRBP) decoding algorithm is proposed according to the structural characteristics of systematically constructed Gallager low-density parity-check (SCG-LDPC) codes. The novel decoding algorithm combines the layered iteration with the reliability judgment, and can greatly reduce the number of the variable nodes involved in the subsequent iteration process and accelerate the convergence rate. The result of simulation for SCG-LDPC(3969,3720) code shows that the novel HRBP decoding algorithm can greatly reduce the computing amount at the condition of ensuring the performance compared with the traditional belief propagation (BP) algorithm. The bit error rate (BER) of the HRBP algorithm is considerable at the threshold value of 15, but in the subsequent iteration process, the number of the variable nodes for the HRBP algorithm can be reduced by about 70% at the high signal-to-noise ratio (SNR) compared with the BP algorithm. When the threshold value is further increased, the HRBP algorithm will gradually degenerate into the layered-BP algorithm, but at the BER of 10-7 and the maximal iteration number of 30, the net coding gain (NCG) of the HRBP algorithm is 0.2 dB more than that of the BP algorithm, and the average iteration times can be reduced by about 40% at the high SNR. Therefore, the novel HRBP decoding algorithm is more suitable for optical communication systems.

Structured Light Based 3d Scanning for Specular Surface by the Combination of Gray Code and Phase Shifting

NASA Astrophysics Data System (ADS)

Zhang, Yujia; Yilmaz, Alper

2016-06-01

Surface reconstruction using coded structured light is considered one of the most reliable techniques for high-quality 3D scanning. With a calibrated projector-camera stereo system, a light pattern is projected onto the scene and imaged by the camera. Correspondences between projected and recovered patterns are computed in the decoding process, which is used to generate 3D point cloud of the surface. However, the indirect illumination effects on the surface, such as subsurface scattering and interreflections, will raise the difficulties in reconstruction. In this paper, we apply maximum min-SW gray code to reduce the indirect illumination effects of the specular surface. We also analysis the errors when comparing the maximum min-SW gray code and the conventional gray code, which justifies that the maximum min-SW gray code has significant superiority to reduce the indirect illumination effects. To achieve sub-pixel accuracy, we project high frequency sinusoidal patterns onto the scene simultaneously. But for specular surface, the high frequency patterns are susceptible to decoding errors. Incorrect decoding of high frequency patterns will result in a loss of depth resolution. Our method to resolve this problem is combining the low frequency maximum min-SW gray code and the high frequency phase shifting code, which achieves dense 3D reconstruction for specular surface. Our contributions include: (i) A complete setup of the structured light based 3D scanning system; (ii) A novel combination technique of the maximum min-SW gray code and phase shifting code. First, phase shifting decoding with sub-pixel accuracy. Then, the maximum min-SW gray code is used to resolve the ambiguity resolution. According to the experimental results and data analysis, our structured light based 3D scanning system enables high quality dense reconstruction of scenes with a small number of images. Qualitative and quantitative comparisons are performed to extract the advantages of our new combined coding method.

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.

Reading Disabilities and PASS Reading Enhancement Programme

ERIC Educational Resources Information Center

Mahapatra, Shamita

2016-01-01

Children experience difficulties in reading either because they fail to decode the words and thus are unable to comprehend the text or simply fail to comprehend the text even if they are able to decode the words and read them out. Failure in word decoding results from a failure in phonological coding of written information, whereas reading…

The Three Stages of Coding and Decoding in Listening Courses of College Japanese Specialty

ERIC Educational Resources Information Center

Yang, Fang

2008-01-01

The main focus of research papers on listening teaching published in recent years is the theoretical meanings of decoding on the training of listening comprehension ability. Although in many research papers the bottom-up approach and top-down approach, information processing mode theory, are applied to illustrate decoding and to emphasize the…

Complete Decoding and Reporting of Aviation Routine Weather Reports (METARs)

NASA Technical Reports Server (NTRS)

Lui, Man-Cheung Max

2014-01-01

Aviation Routine Weather Report (METAR) provides surface weather information at and around observation stations, including airport terminals. These weather observations are used by pilots for flight planning and by air traffic service providers for managing departure and arrival flights. The METARs are also an important source of weather data for Air Traffic Management (ATM) analysts and researchers at NASA and elsewhere. These researchers use METAR to correlate severe weather events with local or national air traffic actions that restrict air traffic, as one example. A METAR is made up of multiple groups of coded text, each with a specific standard coding format. These groups of coded text are located in two sections of a report: Body and Remarks. The coded text groups in a U.S. METAR are intended to follow the coding standards set by National Oceanic and Atmospheric Administration (NOAA). However, manual data entry and edits made by a human report observer may result in coded text elements that do not follow the standards, especially in the Remarks section. And contrary to the standards, some significant weather observations are noted only in the Remarks section and not in the Body section of the reports. While human readers can infer the intended meaning of non-standard coding of weather conditions, doing so with a computer program is far more challenging. However such programmatic pre-processing is necessary to enable efficient and faster database query when researchers need to perform any significant historical weather analysis. Therefore, to support such analysis, a computer algorithm was developed to identify groups of coded text anywhere in a report and to perform subsequent decoding in software. The algorithm considers common deviations from the standards and data entry mistakes made by observers. The implemented software code was tested to decode 12 million reports and the decoding process was able to completely interpret 99.93 of the reports. This document presents the deviations from the standards and the decoding algorithm. Storing all decoded data in a database allows users to quickly query a large amount of data and to perform data mining on the data. Users can specify complex query criteria not only on date or airport but also on weather condition. This document also describes the design of a database schema for storing the decoded data, and a Data Warehouse web application that allows users to perform reporting and analysis on the decoded data. Finally, this document presents a case study correlating dust storms reported in METARs from the Phoenix International airport with Ground Stops issued by Air Route Traffic Control Centers (ATCSCC). Blowing widespread dust is one of the weather conditions when dust storm occurs. By querying the database, 294 METARs were found to report blowing widespread dust at the Phoenix airport and 41 of them reported such condition only in the Remarks section of the reports. When METAR is a data source for an ATM research, it is important to include weather conditions not only from the Body section but also from the Remarks section of METARs.

An Off-Grid Turbo Channel Estimation Algorithm for Millimeter Wave Communications.

PubMed

Han, Lingyi; Peng, Yuexing; Wang, Peng; Li, Yonghui

2016-09-22

The bandwidth shortage has motivated the exploration of the millimeter wave (mmWave) frequency spectrum for future communication networks. To compensate for the severe propagation attenuation in the mmWave band, massive antenna arrays can be adopted at both the transmitter and receiver to provide large array gains via directional beamforming. To achieve such array gains, channel estimation (CE) with high resolution and low latency is of great importance for mmWave communications. However, classic super-resolution subspace CE methods such as multiple signal classification (MUSIC) and estimation of signal parameters via rotation invariant technique (ESPRIT) cannot be applied here due to RF chain constraints. In this paper, an enhanced CE algorithm is developed for the off-grid problem when quantizing the angles of mmWave channel in the spatial domain where off-grid problem refers to the scenario that angles do not lie on the quantization grids with high probability, and it results in power leakage and severe reduction of the CE performance. A new model is first proposed to formulate the off-grid problem. The new model divides the continuously-distributed angle into a quantized discrete grid part, referred to as the integral grid angle, and an offset part, termed fractional off-grid angle. Accordingly, an iterative off-grid turbo CE (IOTCE) algorithm is proposed to renew and upgrade the CE between the integral grid part and the fractional off-grid part under the Turbo principle. By fully exploiting the sparse structure of mmWave channels, the integral grid part is estimated by a soft-decoding based compressed sensing (CS) method called improved turbo compressed channel sensing (ITCCS). It iteratively updates the soft information between the linear minimum mean square error (LMMSE) estimator and the sparsity combiner. Monte Carlo simulations are presented to evaluate the performance of the proposed method, and the results show that it enhances the angle detection resolution greatly.

Enhanced 2/3 four-ary modulation code using soft-decision Viterbi decoding for four-level holographic data storage systems

NASA Astrophysics Data System (ADS)

Kong, Gyuyeol; Choi, Sooyong

2017-09-01

An enhanced 2/3 four-ary modulation code using soft-decision Viterbi decoding is proposed for four-level holographic data storage systems. While the previous four-ary modulation codes focus on preventing maximum two-dimensional intersymbol interference patterns, the proposed four-ary modulation code aims at maximizing the coding gains for better bit error rate performances. For achieving significant coding gains from the four-ary modulation codes, we design a new 2/3 four-ary modulation code in order to enlarge the free distance on the trellis through extensive simulation. The free distance of the proposed four-ary modulation code is extended from 1.21 to 2.04 compared with that of the conventional four-ary modulation code. The simulation result shows that the proposed four-ary modulation code has more than 1 dB gains compared with the conventional four-ary modulation code.

Design and implementation of a channel decoder with LDPC code

NASA Astrophysics Data System (ADS)

Hu, Diqing; Wang, Peng; Wang, Jianzong; Li, Tianquan

2008-12-01

Because Toshiba quit the competition, there is only one standard of blue-ray disc: BLU-RAY DISC, which satisfies the demands of high-density video programs. But almost all the patents are gotten by big companies such as Sony, Philips. As a result we must pay much for these patents when our productions use BD. As our own high-density optical disk storage system, Next-Generation Versatile Disc(NVD) which proposes a new data format and error correction code with independent intellectual property rights and high cost performance owns higher coding efficiency than DVD and 12GB which could meet the demands of playing the high-density video programs. In this paper, we develop Low-Density Parity-Check Codes (LDPC): a new channel encoding process and application scheme using Q-matrix based on LDPC encoding has application in NVD's channel decoder. And combined with the embedded system portable feature of SOPC system, we have completed all the decoding modules by FPGA. In the NVD experiment environment, tests are done. Though there are collisions between LDPC and Run-Length-Limited modulation codes (RLL) which are used in optical storage system frequently, the system is provided as a suitable solution. At the same time, it overcomes the defects of the instability and inextensibility, which occurred in the former decoding system of NVD--it was implemented by hardware.

DSN telemetry system performance using a maximum likelihood convolutional decoder

NASA Technical Reports Server (NTRS)

Benjauthrit, B.; Kemp, R. P.

1977-01-01

Results are described of telemetry system performance testing using DSN equipment and a Maximum Likelihood Convolutional Decoder (MCD) for code rates 1/2 and 1/3, constraint length 7 and special test software. The test results confirm the superiority of the rate 1/3 over that of the rate 1/2. The overall system performance losses determined at the output of the Symbol Synchronizer Assembly are less than 0.5 db for both code rates. Comparison of the performance is also made with existing mathematical models. Error statistics of the decoded data are examined. The MCD operational threshold is found to be about 1.96 db.

A novel design of optical CDMA system based on TCM and FFH

NASA Astrophysics Data System (ADS)

Fang, Jun-Bin; Xu, Zhi-Hai; Huang, Hong-bin; Zheng, Liming; Chen, Shun-er; Liu, Wei-ping

2005-02-01

For the application in Passive Optical Network (PON), a novel design of OCDMA system scheme is proposed in this paper. There are two key components included in this scheme: a new kind of OCDMA encoder/decoder system based on TCM and FFH and an improved Optical Line Terminal (OLT) receiving system with improved anti-interference performance by the use of Long Period Fiber Grating (LPFG). In the encoder/decoder system, Trellis Coded Modulation (TCM) encoder is applied in front of the FFH modulator. Original signal firstly is encoded through TCM encoder, and then the redundant code out of the TCM encoder will be mapped into one of the FFH modulation signal subsets for transmission. On the receiver (decoder) side, transmitting signal is demodulated through FFH and decoded by trellis decoder. Owing to the fact that high coding gain can be acquired by TCM without adding transmitting band and reducing transmitting speed, TCM is utilized to ameliorate bit error performance and reduce multi-user interference. In the OLT receiving system, EDFA and LPFG are placed in front of decoder to get excellent gain flatness on a large bandwidth, and Optical Hard Limiter (OHL) is also deployed to improve detection performance, through which the anti-interference performance of receiving system can be greatly enhanced. At the same time, some software is used to simulate the system performance for further analysis and authentication. The related work in this paper provides a valuable reference to the research.

Decoding communities in networks

NASA Astrophysics Data System (ADS)

Radicchi, Filippo

2018-02-01

According to a recent information-theoretical proposal, the problem of defining and identifying communities in networks can be interpreted as a classical communication task over a noisy channel: memberships of nodes are information bits erased by the channel, edges and nonedges in the network are parity bits introduced by the encoder but degraded through the channel, and a community identification algorithm is a decoder. The interpretation is perfectly equivalent to the one at the basis of well-known statistical inference algorithms for community detection. The only difference in the interpretation is that a noisy channel replaces a stochastic network model. However, the different perspective gives the opportunity to take advantage of the rich set of tools of coding theory to generate novel insights on the problem of community detection. In this paper, we illustrate two main applications of standard coding-theoretical methods to community detection. First, we leverage a state-of-the-art decoding technique to generate a family of quasioptimal community detection algorithms. Second and more important, we show that the Shannon's noisy-channel coding theorem can be invoked to establish a lower bound, here named as decodability bound, for the maximum amount of noise tolerable by an ideal decoder to achieve perfect detection of communities. When computed for well-established synthetic benchmarks, the decodability bound explains accurately the performance achieved by the best community detection algorithms existing on the market, telling us that only little room for their improvement is still potentially left.

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.

Decoding communities in networks.

PubMed

Radicchi, Filippo

2018-02-01

According to a recent information-theoretical proposal, the problem of defining and identifying communities in networks can be interpreted as a classical communication task over a noisy channel: memberships of nodes are information bits erased by the channel, edges and nonedges in the network are parity bits introduced by the encoder but degraded through the channel, and a community identification algorithm is a decoder. The interpretation is perfectly equivalent to the one at the basis of well-known statistical inference algorithms for community detection. The only difference in the interpretation is that a noisy channel replaces a stochastic network model. However, the different perspective gives the opportunity to take advantage of the rich set of tools of coding theory to generate novel insights on the problem of community detection. In this paper, we illustrate two main applications of standard coding-theoretical methods to community detection. First, we leverage a state-of-the-art decoding technique to generate a family of quasioptimal community detection algorithms. Second and more important, we show that the Shannon's noisy-channel coding theorem can be invoked to establish a lower bound, here named as decodability bound, for the maximum amount of noise tolerable by an ideal decoder to achieve perfect detection of communities. When computed for well-established synthetic benchmarks, the decodability bound explains accurately the performance achieved by the best community detection algorithms existing on the market, telling us that only little room for their improvement is still potentially left.

High-Speed, Low-Cost Workstation for Computation-Intensive Statistics. Phase 1

DTIC Science & Technology

1990-06-20

routine implementation and performance. 5 The two compiled versions given in the table were coded in an attempt to obtain an optimized compiled version...level statistics and linear algebra routines (BSAS and BLAS) that have been prototyped in this study. For each routine, both the C code ( Turbo C...OISTRIBUTION /AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Unlimited distribution 13. ABSTRACT (Maximum 200 words) High-performance and low-cost

Scalable L-infinite coding of meshes.

PubMed

Munteanu, Adrian; Cernea, Dan C; Alecu, Alin; Cornelis, Jan; Schelkens, Peter

2010-01-01

The paper investigates the novel concept of local-error control in mesh geometry encoding. In contrast to traditional mesh-coding systems that use the mean-square error as target distortion metric, this paper proposes a new L-infinite mesh-coding approach, for which the target distortion metric is the L-infinite distortion. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum error between the vertex positions in the original and decoded meshes is lower than a given upper bound. Furthermore, the proposed system achieves scalability in L-infinite sense, that is, any decoding of the input stream will correspond to a perfectly predictable L-infinite distortion upper bound. An instantiation of the proposed L-infinite-coding approach is demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this context, the advantages of scalable L-infinite coding over L-2-oriented coding are experimentally demonstrated. One concludes that the proposed L-infinite mesh-coding approach guarantees an upper bound on the local error in the decoded mesh, it enables a fast real-time implementation of the rate allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec.

Upper bounds on sequential decoding performance parameters

NASA Technical Reports Server (NTRS)

Jelinek, F.

1974-01-01

This paper presents the best obtainable random coding and expurgated upper bounds on the probabilities of undetectable error, of t-order failure (advance to depth t into an incorrect subset), and of likelihood rise in the incorrect subset, applicable to sequential decoding when the metric bias G is arbitrary. Upper bounds on the Pareto exponent are also presented. The G-values optimizing each of the parameters of interest are determined, and are shown to lie in intervals that in general have nonzero widths. The G-optimal expurgated bound on undetectable error is shown to agree with that for maximum likelihood decoding of convolutional codes, and that on failure agrees with the block code expurgated bound. Included are curves evaluating the bounds for interesting choices of G and SNR for a binary-input quantized-output Gaussian additive noise channel.

Universal Decoder for PPM of any Order

NASA Technical Reports Server (NTRS)

Moision, Bruce E.

2010-01-01

A recently developed algorithm for demodulation and decoding of a pulse-position- modulation (PPM) signal is suitable as a basis for designing a single hardware decoding apparatus to be capable of handling any PPM order. Hence, this algorithm offers advantages of greater flexibility and lower cost, in comparison with prior such algorithms, which necessitate the use of a distinct hardware implementation for each PPM order. In addition, in comparison with the prior algorithms, the present algorithm entails less complexity in decoding at large orders. An unavoidably lengthy presentation of background information, including definitions of terms, is prerequisite to a meaningful summary of this development. As an aid to understanding, the figure illustrates the relevant processes of coding, modulation, propagation, demodulation, and decoding. An M-ary PPM signal has M time slots per symbol period. A pulse (signifying 1) is transmitted during one of the time slots; no pulse (signifying 0) is transmitted during the other time slots. The information intended to be conveyed from the transmitting end to the receiving end of a radio or optical communication channel is a K-bit vector u. This vector is encoded by an (N,K) binary error-correcting code, producing an N-bit vector a. In turn, the vector a is subdivided into blocks of m = log2(M) bits and each such block is mapped to an M-ary PPM symbol. The resultant coding/modulation scheme can be regarded as equivalent to a nonlinear binary code. The binary vector of PPM symbols, x is transmitted over a Poisson channel, such that there is obtained, at the receiver, a Poisson-distributed photon count characterized by a mean background count nb during no-pulse time slots and a mean signal-plus-background count of ns+nb during a pulse time slot. In the receiver, demodulation of the signal is effected in an iterative soft decoding process that involves consideration of relationships among photon counts and conditional likelihoods of m-bit vectors of coded bits. Inasmuch as the likelihoods of all the m-bit vectors of coded bits mapping to the same PPM symbol are correlated, the best performance is obtained when the joint mbit conditional likelihoods are utilized. Unfortunately, the complexity of decoding, measured in the number of operations per bit, grows exponentially with m, and can thus become prohibitively expensive for large PPM orders. For a system required to handle multiple PPM orders, the cost is even higher because it is necessary to have separate decoding hardware for each order. This concludes the prerequisite background information. In the present algorithm, the decoding process as described above is modified by, among other things, introduction of an lbit marginalizer sub-algorithm. The term "l-bit marginalizer" signifies that instead of m-bit conditional likelihoods, the decoder computes l-bit conditional likelihoods, where l is fixed. Fixing l, regardless of the value of m, makes it possible to use a single hardware implementation for any PPM order. One could minimize the decoding complexity and obtain an especially simple design by fixing l at 1, but this would entail some loss of performance. An intermediate solution is to fix l at some value, greater than 1, that may be less than or greater than m. This solution makes it possible to obtain the desired flexibility to handle any PPM order while compromising between complexity and loss of performance.

A new LDPC decoding scheme for PDM-8QAM BICM coherent optical communication system

NASA Astrophysics Data System (ADS)

Liu, Yi; Zhang, Wen-bo; Xi, Li-xia; Tang, Xian-feng; Zhang, Xiao-guang

2015-11-01

A new log-likelihood ratio (LLR) message estimation method is proposed for polarization-division multiplexing eight quadrature amplitude modulation (PDM-8QAM) bit-interleaved coded modulation (BICM) optical communication system. The formulation of the posterior probability is theoretically analyzed, and the way to reduce the pre-decoding bit error rate ( BER) of the low density parity check (LDPC) decoder for PDM-8QAM constellations is presented. Simulation results show that it outperforms the traditional scheme, i.e., the new post-decoding BER is decreased down to 50% of that of the traditional post-decoding algorithm.

Research on coding and decoding method for digital levels.

PubMed

Tu, Li-fen; Zhong, Si-dong

2011-01-20

A new coding and decoding method for digital levels is proposed. It is based on an area-array CCD sensor and adopts mixed coding technology. By taking advantage of redundant information in a digital image signal, the contradiction that the field of view and image resolution restrict each other in a digital level measurement is overcome, and the geodetic leveling becomes easier. The experimental results demonstrate that the uncertainty of measurement is 1 mm when the measuring range is between 2 m and 100 m, which can meet practical needs.

Study of the OCDMA Transmission Characteristics in FSO-FTTH at Various Distances, Outdoor

NASA Astrophysics Data System (ADS)

Aldouri, Muthana Y.; Aljunid, S. A.; Fadhil, Hilal A.

2013-06-01

It is important to apply the field Programmable Gate Array (FPGA), and Optical Switch technology as an encoder and decoder for Spectral Amplitude Coding Optical Code Division Multiple Access (SAC-OCDMA) Free Space Optic Fiber to the Home (FSO-FTTH) transmitter and receiver system design. The encoder and decoder module will be using FPGA as a code generator, optical switch using as encode and decode of optical source. This module was tested by using the Modified Double Weight (MDW) code, which is selected as an excellent candidate because it had shown superior performance were by the total noise is reduced. It is also easy to construct and can reduce the number of filters required at a receiver by a newly proposed detection scheme known as AND Subtraction technique. MDW code is presented here to support Fiber-To-The-Home (FTTH) access network in Point-To-Multi-Point (P2MP) application. The conversion used a Mach-Zehnder interferometer (MZI) wavelength converter. The performances are characterized through BER and bit rate (BR), also, the received power at a variety of bit rates.

Literal readout of identification signals in Morse code

NASA Technical Reports Server (NTRS)

Meissner, C. W., Jr.

1969-01-01

Instrument, designed for mounting in aircraft instrument panels, decodes identification signals received in Morse from VOR or ILS transmitters as they are received and displays the literal equivalent. Without elaboration it cannot decode numbers.

Scan Line Difference Compression Algorithm Simulation Study.

DTIC Science & Technology

1985-08-01

introduced during the signal transmission process. ----------- SLDC Encoder------- I Image I IConditionedl IConditioned I LError Control I I Source I...I Error Control _____ _struction - Decoder I I Decoder I ----------- SLDC Decoder-------- Figure A-I. -- Overall Data Compression Process This...of noise or an effective channel coding subsystem providing the necessary error control . A- 2 ~~~~~~~~~ ..* : ~ -. . .- .** - .. . .** .* ... . . The

Low Density Parity Check Codes Based on Finite Geometries: A Rediscovery and More

NASA Technical Reports Server (NTRS)

Kou, Yu; Lin, Shu; Fossorier, Marc

1999-01-01

Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.

A new VLSI architecture for a single-chip-type Reed-Solomon decoder

NASA Technical Reports Server (NTRS)

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

1989-01-01

A new very large scale integration (VLSI) architecture for implementing Reed-Solomon (RS) decoders that can correct both errors and erasures is described. This new architecture implements a Reed-Solomon decoder by using replication of a single VLSI chip. It is anticipated that this single chip type RS decoder approach will save substantial development and production costs. It is estimated that reduction in cost by a factor of four is possible with this new architecture. Furthermore, this Reed-Solomon decoder is programmable between 8 bit and 10 bit symbol sizes. Therefore, both an 8 bit Consultative Committee for Space Data Systems (CCSDS) RS decoder and a 10 bit decoder are obtained at the same time, and when concatenated with a (15,1/6) Viterbi decoder, provide an additional 2.1-dB coding gain.

Performance of Low-Density Parity-Check Coded Modulation

NASA Astrophysics Data System (ADS)

Hamkins, J.

2011-02-01

This article presents the simulated performance of a family of nine AR4JA low-density parity-check (LDPC) codes when used with each of five modulations. In each case, the decoder inputs are codebit log-likelihood ratios computed from the received (noisy) modulation symbols using a general formula which applies to arbitrary modulations. Suboptimal soft-decision and hard-decision demodulators are also explored. Bit-interleaving and various mappings of bits to modulation symbols are considered. A number of subtle decoder algorithm details are shown to affect performance, especially in the error floor region. Among these are quantization dynamic range and step size, clipping degree-one variable nodes, "Jones clipping" of variable nodes, approximations of the min* function, and partial hard-limiting messages from check nodes. Using these decoder optimizations, all coded modulations simulated here are free of error floors down to codeword error rates below 10^{-6}. The purpose of generating this performance data is to aid system engineers in determining an appropriate code and modulation to use under specific power and bandwidth constraints, and to provide information needed to design a variable/adaptive coded modulation (VCM/ACM) system using the AR4JA codes. IPNPR Volume 42-185 Tagged File.txt

Teaching Decoding Strategies without Destroying Story.

ERIC Educational Resources Information Center

Kane, Sharon

1999-01-01

Argues that deep coding skills must and can be introduced, taught, practiced, and reinforced within contexts meaningful to students. Shows how teachers can provide these meaningful educational contexts within which decoding strategies make sense to emerging readers. (SR)

Automatic multi-banking of memory for microprocessors

NASA Technical Reports Server (NTRS)

Wiker, G. A. (Inventor)

1984-01-01

A microprocessor system is provided with added memories to expand its address spaces beyond its address word length capacity by using indirect addressing instructions of a type having a detectable operations code and dedicating designated address spaces of memory to each of the added memories, one space to a memory. By decoding each operations code of instructions read from main memory into a decoder to identify indirect addressing instructions of the specified type, and then decoding the address that follows in a decoder to determine which added memory is associated therewith, the associated added memory is selectively enabled through a unit while the main memory is disabled to permit the instruction to be executed on the location to which the effective address of the indirect address instruction points, either before the indirect address is read from main memory or afterwards, depending on how the system is arranged by a switch.

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.

Method and system for efficient video compression with low-complexity encoder

NASA Technical Reports Server (NTRS)

Chen, Jun (Inventor); He, Dake (Inventor); Sheinin, Vadim (Inventor); Jagmohan, Ashish (Inventor); Lu, Ligang (Inventor)

2012-01-01

Disclosed are a method and system for video compression, wherein the video encoder has low computational complexity and high compression efficiency. The disclosed system comprises a video encoder and a video decoder, wherein the method for encoding includes the steps of converting a source frame into a space-frequency representation; estimating conditional statistics of at least one vector of space-frequency coefficients; estimating encoding rates based on the said conditional statistics; and applying Slepian-Wolf codes with the said computed encoding rates. The preferred method for decoding includes the steps of; generating a side-information vector of frequency coefficients based on previously decoded source data, encoder statistics, and previous reconstructions of the source frequency vector; and performing Slepian-Wolf decoding of at least one source frequency vector based on the generated side-information, the Slepian-Wolf code bits and the encoder statistics.

Joint design of QC-LDPC codes for coded cooperation system with joint iterative decoding

NASA Astrophysics Data System (ADS)

Zhang, Shunwai; Yang, Fengfan; Tang, Lei; Ejaz, Saqib; Luo, Lin; Maharaj, B. T.

2016-03-01

In this paper, we investigate joint design of quasi-cyclic low-density-parity-check (QC-LDPC) codes for coded cooperation system with joint iterative decoding in the destination. First, QC-LDPC codes based on the base matrix and exponent matrix are introduced, and then we describe two types of girth-4 cycles in QC-LDPC codes employed by the source and relay. In the equivalent parity-check matrix corresponding to the jointly designed QC-LDPC codes employed by the source and relay, all girth-4 cycles including both type I and type II are cancelled. Theoretical analysis and numerical simulations show that the jointly designed QC-LDPC coded cooperation well combines cooperation gain and channel coding gain, and outperforms the coded non-cooperation under the same conditions. Furthermore, the bit error rate performance of the coded cooperation employing jointly designed QC-LDPC codes is better than those of random LDPC codes and separately designed QC-LDPC codes over AWGN channels.

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.

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.

Variable Coded Modulation software simulation

NASA Astrophysics Data System (ADS)

Sielicki, Thomas A.; Hamkins, Jon; Thorsen, Denise

This paper reports on the design and performance of a new Variable Coded Modulation (VCM) system. This VCM system comprises eight of NASA's recommended codes from the Consultative Committee for Space Data Systems (CCSDS) standards, including four turbo and four AR4JA/C2 low-density parity-check codes, together with six modulations types (BPSK, QPSK, 8-PSK, 16-APSK, 32-APSK, 64-APSK). The signaling protocol for the transmission mode is based on a CCSDS recommendation. The coded modulation may be dynamically chosen, block to block, to optimize throughput.

Protograph LDPC Codes with Node Degrees at Least 3

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Jones, Christopher

2006-01-01

In this paper we present protograph codes with a small number of degree-3 nodes and one high degree node. The iterative decoding threshold for proposed rate 1/2 codes are lower, by about 0.2 dB, than the best known irregular LDPC codes with degree at least 3. The main motivation is to gain linear minimum distance to achieve low error floor. Also to construct rate-compatible protograph-based LDPC codes for fixed block length that simultaneously achieves low iterative decoding threshold and linear minimum distance. We start with a rate 1/2 protograph LDPC code with degree-3 nodes and one high degree node. Higher rate codes are obtained by connecting check nodes with degree-2 non-transmitted nodes. This is equivalent to constraint combining in the protograph. The condition where all constraints are combined corresponds to the highest rate code. This constraint must be connected to nodes of degree at least three for the graph to have linear minimum distance. Thus having node degree at least 3 for rate 1/2 guarantees linear minimum distance property to be preserved for higher rates. Through examples we show that the iterative decoding threshold as low as 0.544 dB can be achieved for small protographs with node degrees at least three. A family of low- to high-rate codes with minimum distance linearly increasing in block size and with capacity-approaching performance thresholds is presented. FPGA simulation results for a few example codes show that the proposed codes perform as predicted.

Survey Of Lossless Image Coding Techniques

NASA Astrophysics Data System (ADS)

Melnychuck, Paul W.; Rabbani, Majid

1989-04-01

Many image transmission/storage applications requiring some form of data compression additionally require that the decoded image be an exact replica of the original. Lossless image coding algorithms meet this requirement by generating a decoded image that is numerically identical to the original. Several lossless coding techniques are modifications of well-known lossy schemes, whereas others are new. Traditional Markov-based models and newer arithmetic coding techniques are applied to predictive coding, bit plane processing, and lossy plus residual coding. Generally speaking, the compression ratio offered by these techniques are in the area of 1.6:1 to 3:1 for 8-bit pictorial images. Compression ratios for 12-bit radiological images approach 3:1, as these images have less detailed structure, and hence, their higher pel correlation leads to a greater removal of image redundancy.

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.

Coding and decoding for code division multiple user communication systems

NASA Technical Reports Server (NTRS)

Healy, T. J.

1985-01-01

A new algorithm is introduced which decodes code division multiple user communication signals. The algorithm makes use of the distinctive form or pattern of each signal to separate it from the composite signal created by the multiple users. Although the algorithm is presented in terms of frequency-hopped signals, the actual transmitter modulator can use any of the existing digital modulation techniques. The algorithm is applicable to error-free codes or to codes where controlled interference is permitted. It can be used when block synchronization is assumed, and in some cases when it is not. The paper also discusses briefly some of the codes which can be used in connection with the algorithm, and relates the algorithm to past studies which use other approaches to the same problem.

The "periodic table" of the genetic code: A new way to look at the code and the decoding process.

PubMed

Komar, Anton A

2016-01-01

Henri Grosjean and Eric Westhof recently presented an information-rich, alternative view of the genetic code, which takes into account current knowledge of the decoding process, including the complex nature of interactions between mRNA, tRNA and rRNA that take place during protein synthesis on the ribosome, and it also better reflects the evolution of the code. The new asymmetrical circular genetic code has a number of advantages over the traditional codon table and the previous circular diagrams (with a symmetrical/clockwise arrangement of the U, C, A, G bases). Most importantly, all sequence co-variances can be visualized and explained based on the internal logic of the thermodynamics of codon-anticodon interactions.

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.

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.

A good performance watermarking LDPC code used in high-speed optical fiber communication system

NASA Astrophysics Data System (ADS)

Zhang, Wenbo; Li, Chao; Zhang, Xiaoguang; Xi, Lixia; Tang, Xianfeng; He, Wenxue

2015-07-01

A watermarking LDPC code, which is a strategy designed to improve the performance of the traditional LDPC code, was introduced. By inserting some pre-defined watermarking bits into original LDPC code, we can obtain a more correct estimation about the noise level in the fiber channel. Then we use them to modify the probability distribution function (PDF) used in the initial process of belief propagation (BP) decoding algorithm. This algorithm was tested in a 128 Gb/s PDM-DQPSK optical communication system and results showed that the watermarking LDPC code had a better tolerances to polarization mode dispersion (PMD) and nonlinearity than that of traditional LDPC code. Also, by losing about 2.4% of redundancy for watermarking bits, the decoding efficiency of the watermarking LDPC code is about twice of the traditional one.

Advanced imaging communication system

NASA Technical Reports Server (NTRS)

Hilbert, E. E.; Rice, R. F.

1977-01-01

Key elements of system are imaging and nonimaging sensors, data compressor/decompressor, interleaved Reed-Solomon block coder, convolutional-encoded/Viterbi-decoded telemetry channel, and Reed-Solomon decoding. Data compression provides efficient representation of sensor data, and channel coding improves reliability of data transmission.

Simple scheme for encoding and decoding a qubit in unknown state for various topological codes

PubMed Central

Łodyga, Justyna; Mazurek, Paweł; Grudka, Andrzej; Horodecki, Michał

2015-01-01

We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and 3D Haah code. The protocol is local whenever in a given code the crossings between the logical operators consist of next neighbour pairs, which holds for the above codes. For subsystem code we also present scheme in a noisy case, where we allow for bit and phase-flip errors on qubits as well as state preparation and syndrome measurement errors. Similar scheme can be built for two other codes. We show that the fidelity of the protected qubit in the noisy scenario in a large code size limit is of , where p is a probability of error on a single qubit per time step. Regarding Haah code we provide noiseless scheme, leaving the noisy case as an open problem. PMID:25754905

BCH codes for large IC random-access memory systems

NASA Technical Reports Server (NTRS)

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

1983-01-01

In this report some shortened BCH codes for possible applications to large IC random-access memory systems are presented. These codes are given by their parity-check matrices. Encoding and decoding of these codes are discussed.

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.

Memory-efficient decoding of LDPC codes

NASA Technical Reports Server (NTRS)

Kwok-San Lee, Jason; Thorpe, Jeremy; Hawkins, Jon

2005-01-01

We present a low-complexity quantization scheme for the implementation of regular (3,6) LDPC codes. The quantization parameters are optimized to maximize the mutual information between the source and the quantized messages. Using this non-uniform quantized belief propagation algorithm, we have simulated that an optimized 3-bit quantizer operates with 0.2dB implementation loss relative to a floating point decoder, and an optimized 4-bit quantizer operates less than 0.1dB quantization loss.

16QAM transmission with 5.2 bits/s/Hz spectral efficiency over transoceanic distance.

PubMed

Zhang, H; Cai, J-X; Batshon, H G; Davidson, C R; Sun, Y; Mazurczyk, M; Foursa, D G; Pilipetskii, A; Mohs, G; Bergano, Neal S

2012-05-21

We transmit 160 x 100 G PDM RZ 16 QAM channels with 5.2 bits/s/Hz spectral efficiency over 6,860 km. There are more than 3 billion 16 QAM symbols, i.e., 12 billion bits, processed in total. Using coded modulation and iterative decoding between a MAP decoder and an LDPC based FEC all channels are decoded with no remaining errors.

Performance breakdown in optimal stimulus decoding

NASA Astrophysics Data System (ADS)

Kostal, Lubomir; Lansky, Petr; Pilarski, Stevan

2015-06-01

Objective. One of the primary goals of neuroscience is to understand how neurons encode and process information about their environment. The problem is often approached indirectly by examining the degree to which the neuronal response reflects the stimulus feature of interest. Approach. In this context, the methods of signal estimation and detection theory provide the theoretical limits on the decoding accuracy with which the stimulus can be identified. The Cramér-Rao lower bound on the decoding precision is widely used, since it can be evaluated easily once the mathematical model of the stimulus-response relationship is determined. However, little is known about the behavior of different decoding schemes with respect to the bound if the neuronal population size is limited. Main results. We show that under broad conditions the optimal decoding displays a threshold-like shift in performance in dependence on the population size. The onset of the threshold determines a critical range where a small increment in size, signal-to-noise ratio or observation time yields a dramatic gain in the decoding precision. Significance. We demonstrate the existence of such threshold regions in early auditory and olfactory information coding. We discuss the origin of the threshold effect and its impact on the design of effective coding approaches in terms of relevant population size.

Bitstream decoding processor for fast entropy decoding of variable length coding-based multiformat videos

NASA Astrophysics Data System (ADS)

Jo, Hyunho; Sim, Donggyu

2014-06-01

We present a bitstream decoding processor for entropy decoding of variable length coding-based multiformat videos. Since most of the computational complexity of entropy decoders comes from bitstream accesses and table look-up process, the developed bitstream processing unit (BsPU) has several designated instructions to access bitstreams and to minimize branch operations in the table look-up process. In addition, the instruction for bitstream access has the capability to remove emulation prevention bytes (EPBs) of H.264/AVC without initial delay, repeated memory accesses, and additional buffer. Experimental results show that the proposed method for EPB removal achieves a speed-up of 1.23 times compared to the conventional EPB removal method. In addition, the BsPU achieves speed-ups of 5.6 and 3.5 times in entropy decoding of H.264/AVC and MPEG-4 Visual bitstreams, respectively, compared to an existing processor without designated instructions and a new table mapping algorithm. The BsPU is implemented on a Xilinx Virtex5 LX330 field-programmable gate array. The MPEG-4 Visual (ASP, Level 5) and H.264/AVC (Main Profile, Level 4) are processed using the developed BsPU with a core clock speed of under 250 MHz in real time.

Performance breakdown in optimal stimulus decoding.

PubMed

Lubomir Kostal; Lansky, Petr; Pilarski, Stevan

2015-06-01

One of the primary goals of neuroscience is to understand how neurons encode and process information about their environment. The problem is often approached indirectly by examining the degree to which the neuronal response reflects the stimulus feature of interest. In this context, the methods of signal estimation and detection theory provide the theoretical limits on the decoding accuracy with which the stimulus can be identified. The Cramér-Rao lower bound on the decoding precision is widely used, since it can be evaluated easily once the mathematical model of the stimulus-response relationship is determined. However, little is known about the behavior of different decoding schemes with respect to the bound if the neuronal population size is limited. We show that under broad conditions the optimal decoding displays a threshold-like shift in performance in dependence on the population size. The onset of the threshold determines a critical range where a small increment in size, signal-to-noise ratio or observation time yields a dramatic gain in the decoding precision. We demonstrate the existence of such threshold regions in early auditory and olfactory information coding. We discuss the origin of the threshold effect and its impact on the design of effective coding approaches in terms of relevant population size.

Memory-efficient table look-up optimized algorithm for context-based adaptive variable length decoding in H.264/advanced video coding

NASA Astrophysics Data System (ADS)

Wang, Jianhua; Cheng, Lianglun; Wang, Tao; Peng, Xiaodong

2016-03-01

Table look-up operation plays a very important role during the decoding processing of context-based adaptive variable length decoding (CAVLD) in H.264/advanced video coding (AVC). However, frequent table look-up operation can result in big table memory access, and then lead to high table power consumption. Aiming to solve the problem of big table memory access of current methods, and then reduce high power consumption, a memory-efficient table look-up optimized algorithm is presented for CAVLD. The contribution of this paper lies that index search technology is introduced to reduce big memory access for table look-up, and then reduce high table power consumption. Specifically, in our schemes, we use index search technology to reduce memory access by reducing the searching and matching operations for code_word on the basis of taking advantage of the internal relationship among length of zero in code_prefix, value of code_suffix and code_lengh, thus saving the power consumption of table look-up. The experimental results show that our proposed table look-up algorithm based on index search can lower about 60% memory access consumption compared with table look-up by sequential search scheme, and then save much power consumption for CAVLD in H.264/AVC.

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.

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.

The trellis complexity of convolutional codes

NASA Technical Reports Server (NTRS)

Mceliece, R. J.; Lin, W.

1995-01-01

It has long been known that convolutional codes have a natural, regular trellis structure that facilitates the implementation of Viterbi's algorithm. It has gradually become apparent that linear block codes also have a natural, though not in general a regular, 'minimal' trellis structure, which allows them to be decoded with a Viterbi-like algorithm. In both cases, the complexity of the Viterbi decoding algorithm can be accurately estimated by the number of trellis edges per encoded bit. It would, therefore, appear that we are in a good position to make a fair comparison of the Viterbi decoding complexity of block and convolutional codes. Unfortunately, however, this comparison is somewhat muddled by the fact that some convolutional codes, the punctured convolutional codes, are known to have trellis representations that are significantly less complex than the conventional trellis. In other words, the conventional trellis representation for a convolutional code may not be the minimal trellis representation. Thus, ironically, at present we seem to know more about the minimal trellis representation for block than for convolutional codes. In this article, we provide a remedy, by developing a theory of minimal trellises for convolutional codes. (A similar theory has recently been given by Sidorenko and Zyablov). This allows us to make a direct performance-complexity comparison for block and convolutional codes. A by-product of our work is an algorithm for choosing, from among all generator matrices for a given convolutional code, what we call a trellis-minimal generator matrix, from which the minimal trellis for the code can be directly constructed. Another by-product is that, in the new theory, punctured convolutional codes no longer appear as a special class, but simply as high-rate convolutional codes whose trellis complexity is unexpectedly small.

Multiformat decoder for a DSP-based IP set-top box

NASA Astrophysics Data System (ADS)

Pescador, F.; Garrido, M. J.; Sanz, C.; Juárez, E.; Samper, D.; Antoniello, R.

2007-05-01

Internet Protocol Set-Top Boxes (IP STBs) based on single-processor architectures have been recently introduced in the market. In this paper, the implementation of an MPEG-4 SP/ASP video decoder for a multi-format IP STB based on a TMS320DM641 DSP is presented. An initial decoder for PC platform was fully tested and ported to the DSP. Using this code an optimization process was started achieving a 90% speedup. This process allows real-time MPEG-4 SP/ASP decoding. The MPEG-4 decoder has been integrated in an IP STB and tested in a real environment using DVD movies and TV channels with excellent results.

HEVC real-time decoding

NASA Astrophysics Data System (ADS)

Bross, Benjamin; Alvarez-Mesa, Mauricio; George, Valeri; Chi, Chi Ching; Mayer, Tobias; Juurlink, Ben; Schierl, Thomas

2013-09-01

The new High Efficiency Video Coding Standard (HEVC) was finalized in January 2013. Compared to its predecessor H.264 / MPEG4-AVC, this new international standard is able to reduce the bitrate by 50% for the same subjective video quality. This paper investigates decoder optimizations that are needed to achieve HEVC real-time software decoding on a mobile processor. It is shown that HEVC real-time decoding up to high definition video is feasible using instruction extensions of the processor while decoding 4K ultra high definition video in real-time requires additional parallel processing. For parallel processing, a picture-level parallel approach has been chosen because it is generic and does not require bitstreams with special indication.

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.

An adaptable binary entropy coder

NASA Technical Reports Server (NTRS)

Kiely, A.; Klimesh, M.

2001-01-01

We present a novel entropy coding technique which is based on recursive interleaving of variable-to-variable length binary source codes. We discuss code design and performance estimation methods, as well as practical encoding and decoding algorithms.

Optimum Code Rates for Noncoherent MFSK with Errors and Erasures Decoding over Rayleigh Fading Channels

NASA Technical Reports Server (NTRS)

Ritcey, Adina Matache James A.

1997-01-01

In this paper, we analyze the performance of a communication system employing M-ary frequency shift keying (FSK) modulation with errors-and-erasures decoding using Viterbi ratio threshold technique for erasure insertion, in Rayleigh fading and AWGN channels.

Construction of Protograph LDPC Codes with Linear Minimum Distance

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Dolinar, Sam; Jones, Christopher

2006-01-01

A construction method for protograph-based LDPC codes that simultaneously achieve low iterative decoding threshold and linear minimum distance is proposed. We start with a high-rate protograph LDPC code with variable node degrees of at least 3. Lower rate codes are obtained by splitting check nodes and connecting them by degree-2 nodes. This guarantees the linear minimum distance property for the lower-rate codes. Excluding checks connected to degree-1 nodes, we show that the number of degree-2 nodes should be at most one less than the number of checks for the protograph LDPC code to have linear minimum distance. Iterative decoding thresholds are obtained by using the reciprocal channel approximation. Thresholds are lowered by using either precoding or at least one very high-degree node in the base protograph. A family of high- to low-rate codes with minimum distance linearly increasing in block size and with capacity-approaching performance thresholds is presented. FPGA simulation results for a few example codes show that the proposed codes perform as predicted.

A Very Efficient Transfer Function Bounding Technique on Bit Error Rate for Viterbi Decoded, Rate 1/N Convolutional Codes

NASA Technical Reports Server (NTRS)

Lee, P. J.

1984-01-01

For rate 1/N convolutional codes, a recursive algorithm for finding the transfer function bound on bit error rate (BER) at the output of a Viterbi decoder is described. This technique is very fast and requires very little storage since all the unnecessary operations are eliminated. Using this technique, we find and plot bounds on the BER performance of known codes of rate 1/2 with K 18, rate 1/3 with K 14. When more than one reported code with the same parameter is known, we select the code that minimizes the required signal to noise ratio for a desired bit error rate of 0.000001. This criterion of determining goodness of a code had previously been found to be more useful than the maximum free distance criterion and was used in the code search procedures of very short constraint length codes. This very efficient technique can also be used for searches of longer constraint length codes.

Image transmission system using adaptive joint source and channel decoding

NASA Astrophysics Data System (ADS)

Liu, Weiliang; Daut, David G.

2005-03-01

In this paper, an adaptive joint source and channel decoding method is designed to accelerate the convergence of the iterative log-dimain sum-product decoding procedure of LDPC codes as well as to improve the reconstructed image quality. Error resilience modes are used in the JPEG2000 source codec, which makes it possible to provide useful source decoded information to the channel decoder. After each iteration, a tentative decoding is made and the channel decoded bits are then sent to the JPEG2000 decoder. Due to the error resilience modes, some bits are known to be either correct or in error. The positions of these bits are then fed back to the channel decoder. The log-likelihood ratios (LLR) of these bits are then modified by a weighting factor for the next iteration. By observing the statistics of the decoding procedure, the weighting factor is designed as a function of the channel condition. That is, for lower channel SNR, a larger factor is assigned, and vice versa. Results show that the proposed joint decoding methods can greatly reduce the number of iterations, and thereby reduce the decoding delay considerably. At the same time, this method always outperforms the non-source controlled decoding method up to 5dB in terms of PSNR for various reconstructed images.

New decoding methods of interleaved burst error-correcting codes

NASA Astrophysics Data System (ADS)

Nakano, Y.; Kasahara, M.; Namekawa, T.

1983-04-01

A probabilistic method of single burst error correction, using the syndrome correlation of subcodes which constitute the interleaved code, is presented. This method makes it possible to realize a high capability of burst error correction with less decoding delay. By generalizing this method it is possible to obtain probabilistic method of multiple (m-fold) burst error correction. After estimating the burst error positions using syndrome correlation of subcodes which are interleaved m-fold burst error detecting codes, this second method corrects erasure errors in each subcode and m-fold burst errors. The performance of these two methods is analyzed via computer simulation, and their effectiveness is demonstrated.

More About Vector Adaptive/Predictive Coding Of Speech

NASA Technical Reports Server (NTRS)

Jedrey, Thomas C.; Gersho, Allen

1992-01-01

Report presents additional information about digital speech-encoding and -decoding system described in "Vector Adaptive/Predictive Encoding of Speech" (NPO-17230). Summarizes development of vector adaptive/predictive coding (VAPC) system and describes basic functions of algorithm. Describes refinements introduced enabling receiver to cope with errors. VAPC algorithm implemented in integrated-circuit coding/decoding processors (codecs). VAPC and other codecs tested under variety of operating conditions. Tests designed to reveal effects of various background quiet and noisy environments and of poor telephone equipment. VAPC found competitive with and, in some respects, superior to other 4.8-kb/s codecs and other codecs of similar complexity.

110 °C range athermalization of wavefront coding infrared imaging systems

NASA Astrophysics Data System (ADS)

Feng, Bin; Shi, Zelin; Chang, Zheng; Liu, Haizheng; Zhao, Yaohong

2017-09-01

110 °C range athermalization is significant but difficult for designing infrared imaging systems. Our wavefront coding athermalized infrared imaging system adopts an optical phase mask with less manufacturing errors and a decoding method based on shrinkage function. The qualitative experiments prove that our wavefront coding athermalized infrared imaging system has three prominent merits: (1) working well over a temperature range of 110 °C; (2) extending the focal depth up to 15.2 times; (3) achieving a decoded image being approximate to its corresponding in-focus infrared image, with a mean structural similarity index (MSSIM) value greater than 0.85.

Convolutional code performance in planetary entry channels

NASA Technical Reports Server (NTRS)

Modestino, J. W.

1974-01-01

The planetary entry channel is modeled for communication purposes representing turbulent atmospheric scattering effects. The performance of short and long constraint length convolutional codes is investigated in conjunction with coherent BPSK modulation and Viterbi maximum likelihood decoding. Algorithms for sequential decoding are studied in terms of computation and/or storage requirements as a function of the fading channel parameters. The performance of the coded coherent BPSK system is compared with the coded incoherent MFSK system. Results indicate that: some degree of interleaving is required to combat time correlated fading of channel; only modest amounts of interleaving are required to approach performance of memoryless channel; additional propagational results are required on the phase perturbation process; and the incoherent MFSK system is superior when phase tracking errors are considered.

Method for Veterbi decoding of large constraint length convolutional codes

NASA Technical Reports Server (NTRS)

Hsu, In-Shek (Inventor); Truong, Trieu-Kie (Inventor); Reed, Irving S. (Inventor); Jing, Sun (Inventor)

1988-01-01

A new method of Viterbi decoding of convolutional codes lends itself to a pipline VLSI architecture using a single sequential processor to compute the path metrics in the Viterbi trellis. An array method is used to store the path information for NK intervals where N is a number, and K is constraint length. The selected path at the end of each NK interval is then selected from the last entry in the array. A trace-back method is used for returning to the beginning of the selected path back, i.e., to the first time unit of the interval NK to read out the stored branch metrics of the selected path which correspond to the message bits. The decoding decision made in this way is no longer maximum likelihood, but can be almost as good, provided that constraint length K in not too small. The advantage is that for a long message, it is not necessary to provide a large memory to store the trellis derived information until the end of the message to select the path that is to be decoded; the selection is made at the end of every NK time unit, thus decoding a long message in successive blocks.

Maximum likelihood decoding of Reed Solomon Codes

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

Sudan, M.

We present a randomized algorithm which takes as input n distinct points ((x{sub i}, y{sub i})){sup n}{sub i=1} from F x F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in at least t places (i.e., y{sub i} = f (x{sub i}) for at least t values of i), provided t = {Omega}({radical}nd). The running time is bounded by a polynomial in n. This immediately provides a maximum likelihoodmore » decoding algorithm for Reed Solomon Codes, which works in a setting with a larger number of errors than any previously known algorithm. To the best of our knowledge, this is the first efficient (i.e., polynomial time bounded) algorithm which provides some maximum likelihood decoding for any efficient (i.e., constant or even polynomial rate) code.« less

Coding for Single-Line Transmission

NASA Technical Reports Server (NTRS)

Madison, L. G.

1983-01-01

Digital transmission code combines data and clock signals into single waveform. MADCODE needs four standard integrated circuits in generator and converter plus five small discrete components. MADCODE allows simple coding and decoding for transmission of digital signals over single line.

Adaptive distributed source coding.

PubMed

Varodayan, David; Lin, Yao-Chung; Girod, Bernd

2012-05-01

We consider distributed source coding in the presence of hidden variables that parameterize the statistical dependence among sources. We derive the Slepian-Wolf bound and devise coding algorithms for a block-candidate model of this problem. The encoder sends, in addition to syndrome bits, a portion of the source to the decoder uncoded as doping bits. The decoder uses the sum-product algorithm to simultaneously recover the source symbols and the hidden statistical dependence variables. We also develop novel techniques based on density evolution (DE) to analyze the coding algorithms. We experimentally confirm that our DE analysis closely approximates practical performance. This result allows us to efficiently optimize parameters of the algorithms. In particular, we show that the system performs close to the Slepian-Wolf bound when an appropriate doping rate is selected. We then apply our coding and analysis techniques to a reduced-reference video quality monitoring system and show a bit rate saving of about 75% compared with fixed-length coding.

De-Coding Writing Assignments.

ERIC Educational Resources Information Center

Simon, Linda

1991-01-01

Argues that understanding assignments is the first step toward successful college writing. Urges instructors to support students by helping them to decode assignments. Breaks down instructions into individual tasks including (1) writing an essay, (2) examining an issue, (3) reviewing articles and books, and (4) focusing on some texts. Defines each…

Unsteady Flowfield in a High-Pressure Turbine Modeled by TURBO

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Mehmed, Oral

2003-01-01

Forced response, or resonant vibrations, in turbomachinery components can cause blades to crack or fail because of the large vibratory blade stresses and subsequent high-cycle fatigue. Forced-response vibrations occur when turbomachinery blades are subjected to periodic excitation at a frequency close to their natural frequency. Rotor blades in a turbine are constantly subjected to periodic excitations when they pass through the spatially nonuniform flowfield created by upstream vanes. Accurate numerical prediction of the unsteady aerodynamics phenomena that cause forced-response vibrations can lead to an improved understanding of the problem and offer potential approaches to reduce or eliminate specific forced-response problems. The objective of the current work was to validate an unsteady aerodynamics code (named TURBO) for the modeling of the unsteady blade row interactions that can cause forced response vibrations. The three-dimensional, unsteady, multi-blade-row, Reynolds-averaged Navier-Stokes turbomachinery code named TURBO was used to model a high-pressure turbine stage for which benchmark data were recently acquired under a NASA contract by researchers at the Ohio State University. The test article was an initial design for a high-pressure turbine stage that experienced forced-response vibrations which were eliminated by increasing the axial gap. The data, acquired in a short duration or shock tunnel test facility, included unsteady blade surface pressures and vibratory strains.

FPGA Implementation of Reed-Solomon Decoder for IEEE 802.16 WiMAX Systems using Simulink-Sysgen Design Environment

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

Bobrek, Miljko; Albright, Austin P

This paper presents FPGA implementation of the Reed-Solomon decoder for use in IEEE 802.16 WiMAX systems. The decoder is based on RS(255,239) code, and is additionally shortened and punctured according to the WiMAX specifications. Simulink model based on Sysgen library of Xilinx blocks was used for simulation and hardware implementation. At the end, simulation results and hardware implementation performances are presented.

Local statistics adaptive entropy coding method for the improvement of H.26L VLC coding

NASA Astrophysics Data System (ADS)

Yoo, Kook-yeol; Kim, Jong D.; Choi, Byung-Sun; Lee, Yung Lyul

2000-05-01

In this paper, we propose an adaptive entropy coding method to improve the VLC coding efficiency of H.26L TML-1 codec. First of all, we will show that the VLC coding presented in TML-1 does not satisfy the sibling property of entropy coding. Then, we will modify the coding method into the local statistics adaptive one to satisfy the property. The proposed method based on the local symbol statistics dynamically changes the mapping relationship between symbol and bit pattern in the VLC table according to sibling property. Note that the codewords in the VLC table of TML-1 codec is not changed. Since this changed mapping relationship also derived in the decoder side by using the decoded symbols, the proposed VLC coding method does not require any overhead information. The simulation results show that the proposed method gives about 30% and 37% reduction in average bit rate for MB type and CBP information, respectively.

Neuron selection based on deflection coefficient maximization for the neural decoding of dexterous finger movements.

PubMed

Kim, Yong-Hee; Thakor, Nitish V; Schieber, Marc H; Kim, Hyoung-Nam

2015-05-01

Future generations of brain-machine interface (BMI) will require more dexterous motion control such as hand and finger movements. Since a population of neurons in the primary motor cortex (M1) area is correlated with finger movements, neural activities recorded in M1 area are used to reconstruct an intended finger movement. In a BMI system, decoding discrete finger movements from a large number of input neurons does not guarantee a higher decoding accuracy in spite of the increase in computational burden. Hence, we hypothesize that selecting neurons important for coding dexterous flexion/extension of finger movements would improve the BMI performance. In this paper, two metrics are presented to quantitatively measure the importance of each neuron based on Bayes risk minimization and deflection coefficient maximization in a statistical decision problem. Since motor cortical neurons are active with movements of several different fingers, the proposed method is more suitable for a discrete decoding of flexion-extension finger movements than the previous methods for decoding reaching movements. In particular, the proposed metrics yielded high decoding accuracies across all subjects and also in the case of including six combined two-finger movements. While our data acquisition and analysis was done off-line and post processing, our results point to the significance of highly coding neurons in improving BMI performance.

Neuron Selection Based on Deflection Coefficient Maximization for the Neural Decoding of Dexterous Finger Movements

PubMed Central

Kim, Yong-Hee; Thakor, Nitish V.; Schieber, Marc H.; Kim, Hyoung-Nam

2015-01-01

Future generations of brain-machine interface (BMI) will require more dexterous motion control such as hand and finger movements. Since a population of neurons in the primary motor cortex (M1) area is correlated with finger movements, neural activities recorded in M1 area are used to reconstruct an intended finger movement. In a BMI system, decoding discrete finger movements from a large number of input neurons does not guarantee a higher decoding accuracy in spite of the increase in computational burden. Hence, we hypothesize that selecting neurons important for coding dexterous flexion/extension of finger movements would improve the BMI performance. In this paper, two metrics are presented to quantitatively measure the importance of each neuron based on Bayes risk minimization and deflection coefficient maximization in a statistical decision problem. Since motor cortical neurons are active with movements of several different fingers, the proposed method is more suitable for a discrete decoding of flexion-extension finger movements than the previous methods for decoding reaching movements. In particular, the proposed metrics yielded high decoding accuracies across all subjects and also in the case of including six combined two-finger movements. While our data acquisition and analysis was done off-line and post processing, our results point to the significance of highly coding neurons in improving BMI performance. PMID:25347884

Advancing Underwater Acoustic Communication for Autonomous Distributed Networks via Sparse Channel Sensing, Coding, and Navigation Support

DTIC Science & Technology

2011-09-30

channel interference mitigation for underwater acoustic MIMO - OFDM . 3) Turbo equalization for OFDM modulated physical layer network coding. 4) Blind CFO...Underwater Acoustic MIMO - OFDM . MIMO - OFDM has been actively studied for high data rate communications over the bandwidthlimited underwater acoustic...with the cochannel interference (CCI) due to parallel transmissions in MIMO - OFDM . Our proposed receiver has the following components: 1

Analysis of Optical CDMA Signal Transmission: Capacity Limits and Simulation Results

NASA Astrophysics Data System (ADS)

Garba, Aminata A.; Yim, Raymond M. H.; Bajcsy, Jan; Chen, Lawrence R.

2005-12-01

We present performance limits of the optical code-division multiple-access (OCDMA) networks. In particular, we evaluate the information-theoretical capacity of the OCDMA transmission when single-user detection (SUD) is used by the receiver. First, we model the OCDMA transmission as a discrete memoryless channel, evaluate its capacity when binary modulation is used in the interference-limited (noiseless) case, and extend this analysis to the case when additive white Gaussian noise (AWGN) is corrupting the received signals. Next, we analyze the benefits of using nonbinary signaling for increasing the throughput of optical CDMA transmission. It turns out that up to a fourfold increase in the network throughput can be achieved with practical numbers of modulation levels in comparison to the traditionally considered binary case. Finally, we present BER simulation results for channel coded binary and[InlineEquation not available: see fulltext.]-ary OCDMA transmission systems. In particular, we apply turbo codes concatenated with Reed-Solomon codes so that up to several hundred concurrent optical CDMA users can be supported at low target bit error rates. We observe that unlike conventional OCDMA systems, turbo-empowered OCDMA can allow overloading (more active users than is the length of the spreading sequences) with good bit error rate system performance.

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.

Pseudoinverse Decoding Process in Delay-Encoded Synthetic Transmit Aperture Imaging.

PubMed

Gong, Ping; Kolios, Michael C; Xu, Yuan

2016-09-01

Recently, we proposed a new method to improve the signal-to-noise ratio of the prebeamformed radio-frequency data in synthetic transmit aperture (STA) imaging: the delay-encoded STA (DE-STA) imaging. In the decoding process of DE-STA, the equivalent STA data were obtained by directly inverting the coding matrix. This is usually regarded as an ill-posed problem, especially under high noise levels. Pseudoinverse (PI) is usually used instead for seeking a more stable inversion process. In this paper, we apply singular value decomposition to the coding matrix to conduct the PI. Our numerical studies demonstrate that the singular values of the coding matrix have a special distribution, i.e., all the values are the same except for the first and last ones. We compare the PI in two cases: complete PI (CPI), where all the singular values are kept, and truncated PI (TPI), where the last and smallest singular value is ignored. The PI (both CPI and TPI) DE-STA processes are tested against noise with both numerical simulations and experiments. The CPI and TPI can restore the signals stably, and the noise mainly affects the prebeamformed signals corresponding to the first transmit channel. The difference in the overall enveloped beamformed image qualities between the CPI and TPI is negligible. Thus, it demonstrates that DE-STA is a relatively stable encoding and decoding technique. Also, according to the special distribution of the singular values of the coding matrix, we propose a new efficient decoding formula that is based on the conjugate transpose of the coding matrix. We also compare the computational complexity of the direct inverse and the new formula.

Optimum coding techniques for MST radars

NASA Technical Reports Server (NTRS)

Sulzer, M. P.; Woodman, R. F.

1986-01-01

The optimum coding technique for MST (mesosphere stratosphere troposphere) radars is that which gives the lowest possible sidelobes in practice and can be implemented without too much computing power. Coding techniques are described in Farley (1985). A technique mentioned briefly there but not fully developed and not in general use is discussed here. This is decoding by means of a filter which is not matched to the transmitted waveform, in order to reduce sidelobes below the level obtained with a matched filter. This is the first part of the technique discussed here; the second part consists of measuring the transmitted waveform and using it as the basis for the decoding filter, thus reducing errors due to imperfections in the transmitter. There are two limitations to this technique. The first is a small loss in signal to noise ratio (SNR), which usually is not significant. The second problem is related to incomplete information received at the lowest ranges. An appendix shows a technique for handling this problem. Finally, it is shown that the use of complementary codes on transmission and nonmatched decoding gives the lowest possible sidelobe level and the minimum loss in SNR due to mismatch.

Symposium on Signal and Image Processing English-Language Abstracts (12th) Held in Juan-Les-Pins, France on 12-16 June 1989

DTIC Science & Technology

1989-12-01

Neril1" (’)INFOCOM Dpt., via Eudossiana 18, 1-00184 Roma, Italy (2) CONTRAVES Italiana SpA. via Affile 102, 1-00139 Roma, Italy SUMMARY The paper...central processor. This makes the perception of the system less accurate and induces a loss in performance. Previous studies have considered the case...current practice. An inner code, often decoded using a weighted input, is concatenated with an outer code decoded without such a weighting . If

Securing information display by use of visual cryptography.

PubMed

Yamamoto, Hirotsugu; Hayasaki, Yoshio; Nishida, Nobuo

2003-09-01

We propose a secure display technique based on visual cryptography. The proposed technique ensures the security of visual information. The display employs a decoding mask based on visual cryptography. Without the decoding mask, the displayed information cannot be viewed. The viewing zone is limited by the decoding mask so that only one person can view the information. We have developed a set of encryption codes to maintain the designed viewing zone and have demonstrated a display that provides a limited viewing zone.

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.

Underwater Acoustic Propagation and Communications: A Coupled Research Program

DTIC Science & Technology

2015-06-15

coding technique suitable for both SIMO and MIMO systems. 4. an adaptive OFDM modulation technique, whereby the transmitter acts in response to...timate based adaptation for SIMO and MIMO systems in a interactive turbo-equalization framework were developed and analyzed. MIMO and SISO

Cross-Layer Design for Robust and Scalable Video Transmission in Dynamic Wireless Environment

DTIC Science & Technology

2011-02-01

code rate convolutional codes or prioritized Rate - Compatible Punctured ...34New rate - compatible punctured convolutional codes for Viterbi decoding," IEEE Trans. Communications, Volume 42, Issue 12, pp. 3073-3079, Dec...Quality of service RCPC Rate - compatible and punctured convolutional codes SNR Signal to noise

A Low-Complexity Euclidean Orthogonal LDPC Architecture for Low Power Applications.

PubMed

Revathy, M; Saravanan, R

2015-01-01

Low-density parity-check (LDPC) codes have been implemented in latest digital video broadcasting, broadband wireless access (WiMax), and fourth generation of wireless standards. In this paper, we have proposed a high efficient low-density parity-check code (LDPC) decoder architecture for low power applications. This study also considers the design and analysis of check node and variable node units and Euclidean orthogonal generator in LDPC decoder architecture. The Euclidean orthogonal generator is used to reduce the error rate of the proposed LDPC architecture, which can be incorporated between check and variable node architecture. This proposed decoder design is synthesized on Xilinx 9.2i platform and simulated using Modelsim, which is targeted to 45 nm devices. Synthesis report proves that the proposed architecture greatly reduces the power consumption and hardware utilizations on comparing with different conventional architectures.

Frame Synchronization Without Attached Sync Markers

NASA Technical Reports Server (NTRS)

Hamkins, Jon

2011-01-01

We describe a method to synchronize codeword frames without making use of attached synchronization markers (ASMs). Instead, the synchronizer identifies the code structure present in the received symbols, by operating the decoder for a handful of iterations at each possible symbol offset and forming an appropriate metric. This method is computationally more complex and doesn't perform as well as frame synchronizers that utilize an ASM; nevertheless, the new synchronizer acquires frame synchronization in about two seconds when using a 600 kbps software decoder, and would take about 15 milliseconds on prototype hardware. It also eliminates the need for the ASMs, which is an attractive feature for short uplink codes whose coding gain would be diminished by the overheard of ASM bits. The lack of ASMs also would simplify clock distribution for the AR4JA low-density parity-check (LDPC) codes and adds a small amount to the coding gain as well (up to 0.2 dB).

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.

A comparison of frame synchronization methods. [Deep Space Network

NASA Technical Reports Server (NTRS)

Swanson, L.

1982-01-01

Different methods are considered for frame synchronization of a concatenated block code/Viterbi link. Synchronization after Viterbi decoding, synchronization before Viterbi decoding based on hard-quantized channel symbols are all compared. For each scheme, the probability under certain conditions of true detection of sync within four 10,000 bit frames is tabulated.

Process-Based Remediation of Decoding in Gifted LD Students: Three Case Studies.

ERIC Educational Resources Information Center

Crawford, Shawn; Snart, Fern

1994-01-01

Three gifted males (ages 10-13) with deficits in successive coding participated in a process-based remedial program which combined global training on tasks requiring successive processing and tasks applying successive processing to decoding in reading, and which utilized verbal mediation. Differences in student improvement were related to entry…

A stimulus-dependent spike threshold is an optimal neural coder

PubMed Central

Jones, Douglas L.; Johnson, Erik C.; Ratnam, Rama

2015-01-01

A neural code based on sequences of spikes can consume a significant portion of the brain's energy budget. Thus, energy considerations would dictate that spiking activity be kept as low as possible. However, a high spike-rate improves the coding and representation of signals in spike trains, particularly in sensory systems. These are competing demands, and selective pressure has presumably worked to optimize coding by apportioning a minimum number of spikes so as to maximize coding fidelity. The mechanisms by which a neuron generates spikes while maintaining a fidelity criterion are not known. Here, we show that a signal-dependent neural threshold, similar to a dynamic or adapting threshold, optimizes the trade-off between spike generation (encoding) and fidelity (decoding). The threshold mimics a post-synaptic membrane (a low-pass filter) and serves as an internal decoder. Further, it sets the average firing rate (the energy constraint). The decoding process provides an internal copy of the coding error to the spike-generator which emits a spike when the error equals or exceeds a spike threshold. When optimized, the trade-off leads to a deterministic spike firing-rule that generates optimally timed spikes so as to maximize fidelity. The optimal coder is derived in closed-form in the limit of high spike-rates, when the signal can be approximated as a piece-wise constant signal. The predicted spike-times are close to those obtained experimentally in the primary electrosensory afferent neurons of weakly electric fish (Apteronotus leptorhynchus) and pyramidal neurons from the somatosensory cortex of the rat. We suggest that KCNQ/Kv7 channels (underlying the M-current) are good candidates for the decoder. They are widely coupled to metabolic processes and do not inactivate. We conclude that the neural threshold is optimized to generate an energy-efficient and high-fidelity neural code. PMID:26082710

Layered Wyner-Ziv video coding.

PubMed

Xu, Qian; Xiong, Zixiang

2006-12-01

Following recent theoretical works on successive Wyner-Ziv coding (WZC), we propose a practical layered Wyner-Ziv video coder using the DCT, nested scalar quantization, and irregular LDPC code based Slepian-Wolf coding (or lossless source coding with side information at the decoder). Our main novelty is to use the base layer of a standard scalable video coder (e.g., MPEG-4/H.26L FGS or H.263+) as the decoder side information and perform layered WZC for quality enhancement. Similar to FGS coding, there is no performance difference between layered and monolithic WZC when the enhancement bitstream is generated in our proposed coder. Using an H.26L coded version as the base layer, experiments indicate that WZC gives slightly worse performance than FGS coding when the channel (for both the base and enhancement layers) is noiseless. However, when the channel is noisy, extensive simulations of video transmission over wireless networks conforming to the CDMA2000 1X standard show that H.26L base layer coding plus Wyner-Ziv enhancement layer coding are more robust against channel errors than H.26L FGS coding. These results demonstrate that layered Wyner-Ziv video coding is a promising new technique for video streaming over wireless networks.

Optimal Codes for the Burst Erasure Channel

NASA Technical Reports Server (NTRS)

Hamkins, Jon

2010-01-01

Deep space communications over noisy channels lead to certain packets that are not decodable. These packets leave gaps, or bursts of erasures, in the data stream. Burst erasure correcting codes overcome this problem. These are forward erasure correcting codes that allow one to recover the missing gaps of data. Much of the recent work on this topic concentrated on Low-Density Parity-Check (LDPC) codes. These are more complicated to encode and decode than Single Parity Check (SPC) codes or Reed-Solomon (RS) codes, and so far have not been able to achieve the theoretical limit for burst erasure protection. A block interleaved maximum distance separable (MDS) code (e.g., an SPC or RS code) offers near-optimal burst erasure protection, in the sense that no other scheme of equal total transmission length and code rate could improve the guaranteed correctible burst erasure length by more than one symbol. The optimality does not depend on the length of the code, i.e., a short MDS code block interleaved to a given length would perform as well as a longer MDS code interleaved to the same overall length. As a result, this approach offers lower decoding complexity with better burst erasure protection compared to other recent designs for the burst erasure channel (e.g., LDPC codes). A limitation of the design is its lack of robustness to channels that have impairments other than burst erasures (e.g., additive white Gaussian noise), making its application best suited for correcting data erasures in layers above the physical layer. The efficiency of a burst erasure code is the length of its burst erasure correction capability divided by the theoretical upper limit on this length. The inefficiency is one minus the efficiency. The illustration compares the inefficiency of interleaved RS codes to Quasi-Cyclic (QC) LDPC codes, Euclidean Geometry (EG) LDPC codes, extended Irregular Repeat Accumulate (eIRA) codes, array codes, and random LDPC codes previously proposed for burst erasure protection. As can be seen, the simple interleaved RS codes have substantially lower inefficiency over a wide range of transmission lengths.

Real-time data compression of broadcast video signals

NASA Technical Reports Server (NTRS)

Shalkauser, Mary Jo W. (Inventor); Whyte, Wayne A., Jr. (Inventor); Barnes, Scott P. (Inventor)

1991-01-01

A non-adaptive predictor, a nonuniform quantizer, and a multi-level Huffman coder are incorporated into a differential pulse code modulation system for coding and decoding broadcast video signals in real time.

Carbon source-dependent expansion of the genetic code in bacteria

PubMed Central

Prat, Laure; Heinemann, Ilka U.; Aerni, Hans R.; Rinehart, Jesse; O’Donoghue, Patrick; Söll, Dieter

2012-01-01

Despite the fact that the genetic code is known to vary between organisms in rare cases, it is believed that in the lifetime of a single cell the code is stable. We found Acetohalobium arabaticum cells grown on pyruvate genetically encode 20 amino acids, but in the presence of trimethylamine (TMA), A. arabaticum dynamically expands its genetic code to 21 amino acids including pyrrolysine (Pyl). A. arabaticum is the only known organism that modulates the size of its genetic code in response to its environment and energy source. The gene cassette pylTSBCD, required to biosynthesize and genetically encode UAG codons as Pyl, is present in the genomes of 24 anaerobic archaea and bacteria. Unlike archaeal Pyl-decoding organisms that constitutively encode Pyl, we observed that A. arabaticum controls Pyl encoding by down-regulating transcription of the entire Pyl operon under growth conditions lacking TMA, to the point where no detectable Pyl-tRNAPyl is made in vivo. Pyl-decoding archaea adapted to an expanded genetic code by minimizing TAG codon frequency to typically ∼5% of ORFs, whereas Pyl-decoding bacteria (∼20% of ORFs contain in-frame TAGs) regulate Pyl-tRNAPyl formation and translation of UAG by transcriptional deactivation of genes in the Pyl operon. We further demonstrate that Pyl encoding occurs in a bacterium that naturally encodes the Pyl operon, and identified Pyl residues by mass spectrometry in A. arabaticum proteins including two methylamine methyltransferases. PMID:23185002

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…

Universal Noiseless Coding Subroutines

NASA Technical Reports Server (NTRS)

Schlutsmeyer, A. P.; Rice, R. F.

1986-01-01

Software package consists of FORTRAN subroutines that perform universal noiseless coding and decoding of integer and binary data strings. Purpose of this type of coding to achieve data compression in sense that coded data represents original data perfectly (noiselessly) while taking fewer bits to do so. Routines universal because they apply to virtually any "real-world" data source.

Flexible High Speed Codec (FHSC)

NASA Technical Reports Server (NTRS)

Segallis, G. P.; Wernlund, J. V.

1991-01-01

The ongoing NASA/Harris Flexible High Speed Codec (FHSC) program is described. The program objectives are to design and build an encoder decoder that allows operation in either burst or continuous modes at data rates of up to 300 megabits per second. The decoder handles both hard and soft decision decoding and can switch between modes on a burst by burst basis. Bandspreading is low since the code rate is greater than or equal to 7/8. The encoder and a hard decision decoder fit on a single application specific integrated circuit (ASIC) chip. A soft decision applique is implemented using 300 K emitter coupled logic (ECL) which can be easily translated to an ECL gate array.

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.

Performance of concatenated Reed-Solomon/Viterbi channel coding

NASA Technical Reports Server (NTRS)

Divsalar, D.; Yuen, J. H.

1982-01-01

The concatenated Reed-Solomon (RS)/Viterbi coding system is reviewed. The performance of the system is analyzed and results are derived with a new simple approach. A functional model for the input RS symbol error probability is presented. Based on this new functional model, we compute the performance of a concatenated system in terms of RS word error probability, output RS symbol error probability, bit error probability due to decoding failure, and bit error probability due to decoding error. Finally we analyze the effects of the noisy carrier reference and the slow fading on the system performance.

Distributed Coding of Compressively Sensed Sources

NASA Astrophysics Data System (ADS)

Goukhshtein, Maxim

In this work we propose a new method for compressing multiple correlated sources with a very low-complexity encoder in the presence of side information. Our approach uses ideas from compressed sensing and distributed source coding. At the encoder, syndromes of the quantized compressively sensed sources are generated and transmitted. The decoder uses side information to predict the compressed sources. The predictions are then used to recover the quantized measurements via a two-stage decoding process consisting of bitplane prediction and syndrome decoding. Finally, guided by the structure of the sources and the side information, the sources are reconstructed from the recovered measurements. As a motivating example, we consider the compression of multispectral images acquired on board satellites, where resources, such as computational power and memory, are scarce. Our experimental results exhibit a significant improvement in the rate-distortion trade-off when compared against approaches with similar encoder complexity.

A Low-Complexity Euclidean Orthogonal LDPC Architecture for Low Power Applications

PubMed Central

Revathy, M.; Saravanan, R.

2015-01-01

Low-density parity-check (LDPC) codes have been implemented in latest digital video broadcasting, broadband wireless access (WiMax), and fourth generation of wireless standards. In this paper, we have proposed a high efficient low-density parity-check code (LDPC) decoder architecture for low power applications. This study also considers the design and analysis of check node and variable node units and Euclidean orthogonal generator in LDPC decoder architecture. The Euclidean orthogonal generator is used to reduce the error rate of the proposed LDPC architecture, which can be incorporated between check and variable node architecture. This proposed decoder design is synthesized on Xilinx 9.2i platform and simulated using Modelsim, which is targeted to 45 nm devices. Synthesis report proves that the proposed architecture greatly reduces the power consumption and hardware utilizations on comparing with different conventional architectures. PMID:26065017

Reward Motivation Enhances Task Coding in Frontoparietal Cortex

PubMed Central

Etzel, Joset A.; Cole, Michael W.; Zacks, Jeffrey M.; Kay, Kendrick N.; Braver, Todd S.

2016-01-01

Reward motivation often enhances task performance, but the neural mechanisms underlying such cognitive enhancement remain unclear. Here, we used a multivariate pattern analysis (MVPA) approach to test the hypothesis that motivation-related enhancement of cognitive control results from improved encoding and representation of task set information. Participants underwent two fMRI sessions of cued task switching, the first under baseline conditions, and the second with randomly intermixed reward incentive and no-incentive trials. Information about the upcoming task could be successfully decoded from cue-related activation patterns in a set of frontoparietal regions typically associated with task control. More critically, MVPA classifiers trained on the baseline session had significantly higher decoding accuracy on incentive than non-incentive trials, with decoding improvement mediating reward-related enhancement of behavioral performance. These results strongly support the hypothesis that reward motivation enhances cognitive control, by improving the discriminability of task-relevant information coded and maintained in frontoparietal brain regions. PMID:25601237

Decoding thalamic afferent input using microcircuit spiking activity

PubMed Central

Sederberg, Audrey J.; Palmer, Stephanie E.

2015-01-01

A behavioral response appropriate to a sensory stimulus depends on the collective activity of thousands of interconnected neurons. The majority of cortical connections arise from neighboring neurons, and thus understanding the cortical code requires characterizing information representation at the scale of the cortical microcircuit. Using two-photon calcium imaging, we densely sampled the thalamically evoked response of hundreds of neurons spanning multiple layers and columns in thalamocortical slices of mouse somatosensory cortex. We then used a biologically plausible decoder to characterize the representation of two distinct thalamic inputs, at the level of the microcircuit, to reveal those aspects of the activity pattern that are likely relevant to downstream neurons. Our data suggest a sparse code, distributed across lamina, in which a small population of cells carries stimulus-relevant information. Furthermore, we find that, within this subset of neurons, decoder performance improves when noise correlations are taken into account. PMID:25695647

Decoding thalamic afferent input using microcircuit spiking activity.

PubMed

Sederberg, Audrey J; Palmer, Stephanie E; MacLean, Jason N

2015-04-01

A behavioral response appropriate to a sensory stimulus depends on the collective activity of thousands of interconnected neurons. The majority of cortical connections arise from neighboring neurons, and thus understanding the cortical code requires characterizing information representation at the scale of the cortical microcircuit. Using two-photon calcium imaging, we densely sampled the thalamically evoked response of hundreds of neurons spanning multiple layers and columns in thalamocortical slices of mouse somatosensory cortex. We then used a biologically plausible decoder to characterize the representation of two distinct thalamic inputs, at the level of the microcircuit, to reveal those aspects of the activity pattern that are likely relevant to downstream neurons. Our data suggest a sparse code, distributed across lamina, in which a small population of cells carries stimulus-relevant information. Furthermore, we find that, within this subset of neurons, decoder performance improves when noise correlations are taken into account. Copyright © 2015 the American Physiological Society.

Integrated source and channel encoded digital communications system design study

NASA Technical Reports Server (NTRS)

Huth, G. K.

1974-01-01

Studies on the digital communication system for the direct communication links from ground to space shuttle and the links involving the Tracking and Data Relay Satellite (TDRS). Three main tasks were performed:(1) Channel encoding/decoding parameter optimization for forward and reverse TDRS links,(2)integration of command encoding/decoding and channel encoding/decoding; and (3) modulation coding interface study. The general communication environment is presented to provide the necessary background for the tasks and to provide an understanding of the implications of the results of the studies.

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

"Coding" and "Decoding": hypothesis for the regulatory mechanism involved in heparan sulfate biosynthesis.

PubMed

Zhang, Xu; Wang, Fengshan; Sheng, Juzheng

2016-06-16

Heparan sulfate (HS) is widely distributed in mammalian tissues in the form of HS proteoglycans, which play essential roles in various physiological and pathological processes. In contrast to the template-guided processes involved in the synthesis of DNA and proteins, HS biosynthesis is not believed to involve a template. However, it appears that the final structure of HS chains was strictly regulated. Herein, we report research based hypothesis that two major steps, namely "coding" and "decoding" steps, are involved in the biosynthesis of HS, which strictly regulate its chemical structure and biological activity. The "coding" process in this context is based on the distribution of sulfate moieties on the amino groups of the glucosamine residues in the HS chains. The sulfation of these amine groups is catalyzed by N-deacetylase/N-sulfotransferase, which has four isozymes. The composition and distribution of sulfate groups and iduronic acid residues on the glycan chains of HS are determined by several other modification enzymes, which can recognize these coding sequences (i.e., the "decoding" process). The degree and pattern of the sulfation and epimerization in the HS chains determines the extent of their interactions with several different protein factors, which further influences their biological activity. Copyright © 2016 Elsevier Ltd. All rights reserved.

Code-modulated visual evoked potentials using fast stimulus presentation and spatiotemporal beamformer decoding.

PubMed

Wittevrongel, Benjamin; Van Wolputte, Elia; Van Hulle, Marc M

2017-11-08

When encoding visual targets using various lagged versions of a pseudorandom binary sequence of luminance changes, the EEG signal recorded over the viewer's occipital pole exhibits so-called code-modulated visual evoked potentials (cVEPs), the phase lags of which can be tied to these targets. The cVEP paradigm has enjoyed interest in the brain-computer interfacing (BCI) community for the reported high information transfer rates (ITR, in bits/min). In this study, we introduce a novel decoding algorithm based on spatiotemporal beamforming, and show that this algorithm is able to accurately identify the gazed target. Especially for a small number of repetitions of the coding sequence, our beamforming approach significantly outperforms an optimised support vector machine (SVM)-based classifier, which is considered state-of-the-art in cVEP-based BCI. In addition to the traditional 60 Hz stimulus presentation rate for the coding sequence, we also explore the 120 Hz rate, and show that the latter enables faster communication, with a maximal median ITR of 172.87 bits/min. Finally, we also report on a transition effect in the EEG signal following the onset of the stimulus sequence, and recommend to exclude the first 150 ms of the trials from decoding when relying on a single presentation of the stimulus sequence.

Improved convolutional coding

NASA Technical Reports Server (NTRS)

Doland, G. D.

1970-01-01

Convolutional coding, used to upgrade digital data transmission under adverse signal conditions, has been improved by a method which ensures data transitions, permitting bit synchronizer operation at lower signal levels. Method also increases decoding ability by removing ambiguous condition.

Real-time SHVC software decoding with multi-threaded parallel processing

NASA Astrophysics Data System (ADS)

Gudumasu, Srinivas; He, Yuwen; Ye, Yan; He, Yong; Ryu, Eun-Seok; Dong, Jie; Xiu, Xiaoyu

2014-09-01

This paper proposes a parallel decoding framework for scalable HEVC (SHVC). Various optimization technologies are implemented on the basis of SHVC reference software SHM-2.0 to achieve real-time decoding speed for the two layer spatial scalability configuration. SHVC decoder complexity is analyzed with profiling information. The decoding process at each layer and the up-sampling process are designed in parallel and scheduled by a high level application task manager. Within each layer, multi-threaded decoding is applied to accelerate the layer decoding speed. Entropy decoding, reconstruction, and in-loop processing are pipeline designed with multiple threads based on groups of coding tree units (CTU). A group of CTUs is treated as a processing unit in each pipeline stage to achieve a better trade-off between parallelism and synchronization. Motion compensation, inverse quantization, and inverse transform modules are further optimized with SSE4 SIMD instructions. Simulations on a desktop with an Intel i7 processor 2600 running at 3.4 GHz show that the parallel SHVC software decoder is able to decode 1080p spatial 2x at up to 60 fps (frames per second) and 1080p spatial 1.5x at up to 50 fps for those bitstreams generated with SHVC common test conditions in the JCT-VC standardization group. The decoding performance at various bitrates with different optimization technologies and different numbers of threads are compared in terms of decoding speed and resource usage, including processor and memory.

An architecture of entropy decoder, inverse quantiser and predictor for multi-standard video decoding

NASA Astrophysics Data System (ADS)

Liu, Leibo; Chen, Yingjie; Yin, Shouyi; Lei, Hao; He, Guanghui; Wei, Shaojun

2014-07-01

A VLSI architecture for entropy decoder, inverse quantiser and predictor is proposed in this article. This architecture is used for decoding video streams of three standards on a single chip, i.e. H.264/AVC, AVS (China National Audio Video coding Standard) and MPEG2. The proposed scheme is called MPMP (Macro-block-Parallel based Multilevel Pipeline), which is intended to improve the decoding performance to satisfy the real-time requirements while maintaining a reasonable area and power consumption. Several techniques, such as slice level pipeline, MB (Macro-Block) level pipeline, MB level parallel, etc., are adopted. Input and output buffers for the inverse quantiser and predictor are shared by the decoding engines for H.264, AVS and MPEG2, therefore effectively reducing the implementation overhead. Simulation shows that decoding process consumes 512, 435 and 438 clock cycles per MB in H.264, AVS and MPEG2, respectively. Owing to the proposed techniques, the video decoder can support H.264 HP (High Profile) 1920 × 1088@30fps (frame per second) streams, AVS JP (Jizhun Profile) 1920 × 1088@41fps streams and MPEG2 MP (Main Profile) 1920 × 1088@39fps streams when exploiting a 200 MHz working frequency.

Low-delay predictive audio coding for the HIVITS HDTV codec

NASA Astrophysics Data System (ADS)

McParland, A. K.; Gilchrist, N. H. C.

1995-01-01

The status of work relating to predictive audio coding, as part of the European project on High Quality Video Telephone and HD(TV) Systems (HIVITS), is reported. The predictive coding algorithm is developed, along with six-channel audio coding and decoding hardware. Demonstrations of the audio codec operating in conjunction with the video codec, are given.

A novel bit-wise adaptable entropy coding technique

NASA Technical Reports Server (NTRS)

Kiely, A.; Klimesh, M.

2001-01-01

We present a novel entropy coding technique which is adaptable in that each bit to be encoded may have an associated probability esitmate which depends on previously encoded bits. The technique may have advantages over arithmetic coding. The technique can achieve arbitrarily small redundancy and admits a simple and fast decoder.

Computer algorithm for coding gain

NASA Technical Reports Server (NTRS)

Dodd, E. E.

1974-01-01

Development of a computer algorithm for coding gain for use in an automated communications link design system. Using an empirical formula which defines coding gain as used in space communications engineering, an algorithm is constructed on the basis of available performance data for nonsystematic convolutional encoding with soft-decision (eight-level) Viterbi decoding.

A novel coherent optical en/decoder for optical label processing of OCDM-based optical packets switching networks

NASA Astrophysics Data System (ADS)

Zhang, Chongfu; Qiu, Kun

2007-11-01

A coherent optical en/decoder based on photonic crystal (PhC) for optical code-division-multiple (OCDM)-based optical label (OCDM-OL) optical packets switching (OPS) networks is proposed in this paper. In this scheme, the optical pulse phase and time delay can be flexibly controlled by the photonic crystal phase shifter and delayer using the appropriate design of fabrication. In this design, the combination calculation of the impurity and normal period layers is applied, according to the PhC transmission matrix theorem. The design and theoretical analysis of the PhC-based optical coherent en/decoder is mainly focused. In addition, the performances of the PhC-based optical en/decoders are analyzed in detail. The reflection, the transmission, delay characteristic and the optical spectrum of pulse en/decoded are studied for the waves tuned in the photonic band-gap by the numerical calculation, taking into account 1-Dimension (1D) PhC. Theoretical analysis and numerical results show that optical pulse is achieved to properly phase modulation and time delay by the proposed scheme, optical label based on OCDM is rewrote successfully by new code for OCDM-based OPS (OCDM-OPS), and an over 8.5 dB ration of auto- and cross-correlation is gained, which demonstrates the applicability of true pulse phase modulation in a number of applications.

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).

Decoding the genome beyond sequencing: the new phase of genomic research.

PubMed

Heng, Henry H Q; Liu, Guo; Stevens, Joshua B; Bremer, Steven W; Ye, Karen J; Abdallah, Batoul Y; Horne, Steven D; Ye, Christine J

2011-10-01

While our understanding of gene-based biology has greatly improved, it is clear that the function of the genome and most diseases cannot be fully explained by genes and other regulatory elements. Genes and the genome represent distinct levels of genetic organization with their own coding systems; Genes code parts like protein and RNA, but the genome codes the structure of genetic networks, which are defined by the whole set of genes, chromosomes and their topological interactions within a cell. Accordingly, the genetic code of DNA offers limited understanding of genome functions. In this perspective, we introduce the genome theory which calls for the departure of gene-centric genomic research. To make this transition for the next phase of genomic research, it is essential to acknowledge the importance of new genome-based biological concepts and to establish new technology platforms to decode the genome beyond sequencing. Copyright © 2011 Elsevier Inc. All rights reserved.

3D scene reconstruction based on multi-view distributed video coding in the Zernike domain for mobile applications

NASA Astrophysics Data System (ADS)

Palma, V.; Carli, M.; Neri, A.

2011-02-01

In this paper a Multi-view Distributed Video Coding scheme for mobile applications is presented. Specifically a new fusion technique between temporal and spatial side information in Zernike Moments domain is proposed. Distributed video coding introduces a flexible architecture that enables the design of very low complex video encoders compared to its traditional counterparts. The main goal of our work is to generate at the decoder the side information that optimally blends temporal and interview data. Multi-view distributed coding performance strongly depends on the side information quality built at the decoder. At this aim for improving its quality a spatial view compensation/prediction in Zernike moments domain is applied. Spatial and temporal motion activity have been fused together to obtain the overall side-information. The proposed method has been evaluated by rate-distortion performances for different inter-view and temporal estimation quality conditions.

Properties of a certain stochastic dynamical system, channel polarization, and polar codes

NASA Astrophysics Data System (ADS)

Tanaka, Toshiyuki

2010-06-01

A new family of codes, called polar codes, has recently been proposed by Arikan. Polar codes are of theoretical importance because they are provably capacity achieving with low-complexity encoding and decoding. We first discuss basic properties of a certain stochastic dynamical system, on the basis of which properties of channel polarization and polar codes are reviewed, with emphasis on our recent results.

Coded excitation with spectrum inversion (CEXSI) for ultrasound array imaging.

PubMed

Wang, Yao; Metzger, Kurt; Stephens, Douglas N; Williams, Gregory; Brownlie, Scott; O'Donnell, Matthew

2003-07-01

In this paper, a scheme called coded excitation with spectrum inversion (CEXSI) is presented. An established optimal binary code whose spectrum has no nulls and possesses the least variation is encoded as a burst for transmission. Using this optimal code, the decoding filter can be derived directly from its inverse spectrum. Various transmission techniques can be used to improve energy coupling within the system pass-band. We demonstrate its potential to achieve excellent decoding with very low (< 80 dB) side-lobes. For a 2.6 micros code, an array element with a center frequency of 10 MHz and fractional bandwidth of 38%, range side-lobes of about 40 dB have been achieved experimentally with little compromise in range resolution. The signal-to-noise ratio (SNR) improvement also has been characterized at about 14 dB. Along with simulations and experimental data, we present a formulation of the scheme, according to which CEXSI can be extended to improve SNR in sparse array imaging in general.

Iterative decoding of SOVA and LDPC product code for bit-patterned media recoding

NASA Astrophysics Data System (ADS)

Jeong, Seongkwon; Lee, Jaejin

2018-05-01

The demand for high-density storage systems has increased due to the exponential growth of data. Bit-patterned media recording (BPMR) is one of the promising technologies to achieve the density of 1Tbit/in2 and higher. To increase the areal density in BPMR, the spacing between islands needs to be reduced, yet this aggravates inter-symbol interference and inter-track interference and degrades the bit error rate performance. In this paper, we propose a decision feedback scheme using low-density parity check (LDPC) product code for BPMR. This scheme can improve the decoding performance using an iterative approach with extrinsic information and log-likelihood ratio value between iterative soft output Viterbi algorithm and LDPC product code. Simulation results show that the proposed LDPC product code can offer 1.8dB and 2.3dB gains over the one LDPC code at the density of 2.5 and 3 Tb/in2, respectively, when bit error rate is 10-6.

A Fixed-Point Phase Lock Loop in a Software Defined Radio

DTIC Science & Technology

2002-09-01

code from a simulation model. This feature will allow easy implementation on an FPGA as C can be easily converted to VHDL , the language required...this is equivalent to the MATLAB code implementation in Appendix A. The PD takes the input signal 40 and multiplies it by the in-phase and...stop to 60 mph in 3.1 seconds (the fastest production car ever built is the Porsche Carrera twin turbo which was tested at 0-60 mph in 3.1 seconds

Efficiency turns the table on neural encoding, decoding and noise.

PubMed

Deneve, Sophie; Chalk, Matthew

2016-04-01

Sensory neurons are usually described with an encoding model, for example, a function that predicts their response from the sensory stimulus using a receptive field (RF) or a tuning curve. However, central to theories of sensory processing is the notion of 'efficient coding'. We argue here that efficient coding implies a completely different neural coding strategy. Instead of a fixed encoding model, neural populations would be described by a fixed decoding model (i.e. a model reconstructing the stimulus from the neural responses). Because the population solves a global optimization problem, individual neurons are variable, but not noisy, and have no truly invariant tuning curve or receptive field. We review recent experimental evidence and implications for neural noise correlations, robustness and adaptation. Copyright © 2016. Published by Elsevier Ltd.

An adaptive distributed data aggregation based on RCPC for wireless sensor networks

NASA Astrophysics Data System (ADS)

Hua, Guogang; Chen, Chang Wen

2006-05-01

One of the most important design issues in wireless sensor networks is energy efficiency. Data aggregation has significant impact on the energy efficiency of the wireless sensor networks. With massive deployment of sensor nodes and limited energy supply, data aggregation has been considered as an essential paradigm for data collection in sensor networks. Recently, distributed source coding has been demonstrated to possess several advantages in data aggregation for wireless sensor networks. Distributed source coding is able to encode sensor data with lower bit rate without direct communication among sensor nodes. To ensure reliable and high throughput transmission with the aggregated data, we proposed in this research a progressive transmission and decoding of Rate-Compatible Punctured Convolutional (RCPC) coded data aggregation with distributed source coding. Our proposed 1/2 RSC codes with Viterbi algorithm for distributed source coding are able to guarantee that, even without any correlation between the data, the decoder can always decode the data correctly without wasting energy. The proposed approach achieves two aspects in adaptive data aggregation for wireless sensor networks. First, the RCPC coding facilitates adaptive compression corresponding to the correlation of the sensor data. When the data correlation is high, higher compression ration can be achieved. Otherwise, lower compression ratio will be achieved. Second, the data aggregation is adaptively accumulated. There is no waste of energy in the transmission; even there is no correlation among the data, the energy consumed is at the same level as raw data collection. Experimental results have shown that the proposed distributed data aggregation based on RCPC is able to achieve high throughput and low energy consumption data collection for wireless sensor networks

Time-Shifted Boundary Conditions Used for Navier-Stokes Aeroelastic Solver

NASA Technical Reports Server (NTRS)

Srivastava, Rakesh

1999-01-01

Under the Advanced Subsonic Technology (AST) Program, an aeroelastic analysis code (TURBO-AE) based on Navier-Stokes equations is currently under development at NASA Lewis Research Center s Machine Dynamics Branch. For a blade row, aeroelastic instability can occur in any of the possible interblade phase angles (IBPA s). Analyzing small IBPA s is very computationally expensive because a large number of blade passages must be simulated. To reduce the computational cost of these analyses, we used time shifted, or phase-lagged, boundary conditions in the TURBO-AE code. These conditions can be used to reduce the computational domain to a single blade passage by requiring the boundary conditions across the passage to be lagged depending on the IBPA being analyzed. The time-shifted boundary conditions currently implemented are based on the direct-store method. This method requires large amounts of data to be stored over a period of the oscillation cycle. On CRAY computers this is not a major problem because solid-state devices can be used for fast input and output to read and write the data onto a disk instead of storing it in core memory.

LINFLUX-AE: A Turbomachinery Aeroelastic Code Based on a 3-D Linearized Euler Solver

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Bakhle, M. A.; Trudell, J. J.; Mehmed, O.; Stefko, G. L.

2004-01-01

This report describes the development and validation of LINFLUX-AE, a turbomachinery aeroelastic code based on the linearized unsteady 3-D Euler solver, LINFLUX. A helical fan with flat plate geometry is selected as the test case for numerical validation. The steady solution required by LINFLUX is obtained from the nonlinear Euler/Navier Stokes solver TURBO-AE. The report briefly describes the salient features of LINFLUX and the details of the aeroelastic extension. The aeroelastic formulation is based on a modal approach. An eigenvalue formulation is used for flutter analysis. The unsteady aerodynamic forces required for flutter are obtained by running LINFLUX for each mode, interblade phase angle and frequency of interest. The unsteady aerodynamic forces for forced response analysis are obtained from LINFLUX for the prescribed excitation, interblade phase angle, and frequency. The forced response amplitude is calculated from the modal summation of the generalized displacements. The unsteady pressures, work done per cycle, eigenvalues and forced response amplitudes obtained from LINFLUX are compared with those obtained from LINSUB, TURBO-AE, ASTROP2, and ANSYS.

New Bandwidth Efficient Parallel Concatenated Coding Schemes

NASA Technical Reports Server (NTRS)

Denedetto, S.; Divsalar, D.; Montorsi, G.; Pollara, F.

1996-01-01

We propose a new solution to parallel concatenation of trellis codes with multilevel amplitude/phase modulations and a suitable iterative decoding structure. Examples are given for throughputs 2 bits/sec/Hz with 8PSK and 16QAM signal constellations.

Complementary-encoding holographic associative memory using a photorefractive crystal

NASA Astrophysics Data System (ADS)

Yuan, ShiFu; Wu, Minxian; Yan, Yingbai; Jin, Guofan

1996-06-01

We present a holographic implementation of accurate associative memory with only one holographic memory system. In the implementation, the stored and test images are coded by using complementary-encoding method. The recalled complete image is also a coded image that can be decoded with a decoding mask to get an original image or its complement image. The experiment shows that the complementary encoding can efficiently increase the addressing accuracy in a simple way. Instead of the above complementary-encoding method, a scheme that uses complementary area-encoding method is also proposed for the holographic implementation of gray-level image associative memory with accurate addressing.

An LDPC Decoder Architecture for Wireless Sensor Network Applications

PubMed Central

Giancarlo Biroli, Andrea Dario; Martina, Maurizio; Masera, Guido

2012-01-01

The pervasive use of wireless sensors in a growing spectrum of human activities reinforces the need for devices with low energy dissipation. In this work, coded communication between a couple of wireless sensor devices is considered as a method to reduce the dissipated energy per transmitted bit with respect to uncoded communication. Different Low Density Parity Check (LDPC) codes are considered to this purpose and post layout results are shown for a low-area low-energy decoder, which offers percentage energy savings with respect to the uncoded solution in the range of 40%–80%, depending on considered environment, distance and bit error rate. PMID:22438724

An LDPC decoder architecture for wireless sensor network applications.

PubMed

Biroli, Andrea Dario Giancarlo; Martina, Maurizio; Masera, Guido

2012-01-01

The pervasive use of wireless sensors in a growing spectrum of human activities reinforces the need for devices with low energy dissipation. In this work, coded communication between a couple of wireless sensor devices is considered as a method to reduce the dissipated energy per transmitted bit with respect to uncoded communication. Different Low Density Parity Check (LDPC) codes are considered to this purpose and post layout results are shown for a low-area low-energy decoder, which offers percentage energy savings with respect to the uncoded solution in the range of 40%-80%, depending on considered environment, distance and bit error rate.

25 Tb/s transmission over 5,530 km using 16QAM at 5.2 b/s/Hz spectral efficiency.

PubMed

Cai, J-X; Batshon, H G; Zhang, H; Davidson, C R; Sun, Y; Mazurczyk, M; Foursa, D G; Sinkin, O; Pilipetskii, A; Mohs, G; Bergano, Neal S

2013-01-28

We transmit 250x100G PDM RZ-16QAM channels with 5.2 b/s/Hz spectral efficiency over 5,530 km using single-stage C-band EDFAs equalized to 40 nm. We use single parity check coded modulation and all channels are decoded with no errors after iterative decoding between a MAP decoder and an LDPC based FEC algorithm. We also observe that the optimum power spectral density is nearly independent of SE, signal baud rate or modulation format in a dispersion uncompensated system.

Secure information display with limited viewing zone by use of multi-color visual cryptography.

PubMed

Yamamoto, Hirotsugu; Hayasaki, Yoshio; Nishida, Nobuo

2004-04-05

We propose a display technique that ensures security of visual information by use of visual cryptography. A displayed image appears as a completely random pattern unless viewed through a decoding mask. The display has a limited viewing zone with the decoding mask. We have developed a multi-color encryption code set. Eight colors are represented in combinations of a displayed image composed of red, green, blue, and black subpixels and a decoding mask composed of transparent and opaque subpixels. Furthermore, we have demonstrated secure information display by use of an LCD panel.

Biosamples, genomics, and human rights: context and content of Iceland's Biobanks Act.

PubMed

Winickoff, D E

2001-01-01

In recent years, human DNA sampling and collection has accelerated without the development of enforceable rules protecting the human rights of donors. The need for regulation of biobanking is especially acute in Iceland, whose parliament has granted a for-profit corporation, deCODE Genetics, an exclusive license to create a centralized database of health records for studies on human genetic variation. Until recently, how deCODE Genetics would get genetic material for its genotypic-phenotypic database remained unclear. However, in May 2000, the Icelandic Parliament passed the Icelandic Biobanks Act, the world's earliest attempt to construct binding rules for the use of biobanks in scientific research. Unfortunately, Iceland has lost an opportunity for bringing clear and ethically sound standards to the use of human biological samples in deCODE's database and in other projects: the Biobanks Act has extended a notion of "presumed consent" from the use of medical records to the use of patients' biological samples; worse, the act has made it possible--perhaps likely--that a donor's wish to withdraw his/her sample will be ignored. Inadequacies in the Act's legislative process help account for these deficiencies in the protection of donor autonomy.

Coding and Comprehension in Skilled Reading and Implications for Reading Instruction.

ERIC Educational Resources Information Center

Perfetti, Charles A.; Lesgold, Alan M.

A view of skilled reading is suggested that emphasizes an intimate connection between coding and comprehension. It is suggested that skilled comprehension depends on a highly refined facility for generating and manipulating language codes, especially at the phonetic/articulatory level. The argument is developed that decoding expertise should be a…

Performance of convolutional codes on fading channels typical of planetary entry missions

NASA Technical Reports Server (NTRS)

Modestino, J. W.; Mui, S. Y.; Reale, T. J.

1974-01-01

The performance of convolutional codes in fading channels typical of the planetary entry channel is examined in detail. The signal fading is due primarily to turbulent atmospheric scattering of the RF signal transmitted from an entry probe through a planetary atmosphere. Short constraint length convolutional codes are considered in conjunction with binary phase-shift keyed modulation and Viterbi maximum likelihood decoding, and for longer constraint length codes sequential decoding utilizing both the Fano and Zigangirov-Jelinek (ZJ) algorithms are considered. Careful consideration is given to the modeling of the channel in terms of a few meaningful parameters which can be correlated closely with theoretical propagation studies. For short constraint length codes the bit error probability performance was investigated as a function of E sub b/N sub o parameterized by the fading channel parameters. For longer constraint length codes the effect was examined of the fading channel parameters on the computational requirements of both the Fano and ZJ algorithms. The effects of simple block interleaving in combatting the memory of the channel is explored, using the analytic approach or digital computer simulation.

A Three-Dimensional Parallel Time-Accurate Turbopump Simulation Procedure Using Overset Grid System

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Chan, William; Kwak, Dochan

2002-01-01

The objective of the current effort is to provide a computational framework for design and analysis of the entire fuel supply system of a liquid rocket engine, including high-fidelity unsteady turbopump flow analysis. This capability is needed to support the design of pump sub-systems for advanced space transportation vehicles that are likely to involve liquid propulsion systems. To date, computational tools for design/analysis of turbopump flows are based on relatively lower fidelity methods. An unsteady, three-dimensional viscous flow analysis tool involving stationary and rotational components for the entire turbopump assembly has not been available for real-world engineering applications. The present effort provides developers with information such as transient flow phenomena at start up, and nonuniform inflows, and will eventually impact on system vibration and structures. In the proposed paper, the progress toward the capability of complete simulation of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of the hybrid MPI/Open-MP and MLP versions of the INS3D code. CAD to solution auto-scripting capability is being developed for turbopump applications. The relative motion of the grid systems for the rotor-stator interaction was obtained using overset grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on Origin 3000 systems at NASA Ames Research Center. Results from these time-accurate simulations with moving boundary capability are presented along with the performance of parallel versions of the code.

Time-Dependent Simulations of Turbopump Flows

NASA Technical Reports Server (NTRS)

Kris, Cetin C.; Kwak, Dochan

2001-01-01

The objective of the current effort is to provide a computational framework for design and analysis of the entire fuel supply system of a liquid rocket engine, including high-fidelity unsteady turbopump flow analysis. This capability is needed to support the design of pump sub-systems for advanced space transportation vehicles that are likely to involve liquid propulsion systems. To date, computational tools for design/analysis of turbopump flows are based on relatively lower fidelity methods. An unsteady, three-dimensional viscous flow analysis tool involving stationary and rotational components for the entire turbopump assembly has not been available for real-world engineering applications. The present effort will provide developers with information such as transient flow phenomena at start up, impact of non-uniform inflows, system vibration and impact on the structure. In the proposed paper, the progress toward the capability of complete simulation of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of the hybrid MPI/Open-MP and MLP versions of the INS3D code. The relative motion of the grid systems for the rotor-stator interaction was obtained using overset grid techniques. Time-accuracy of the scheme has been evaluated with simple test cases. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on Origin 2000 systems at NASA Ames Research Center. Results from these time-accurate simulations with moving boundary capability will be presented along with the performance of parallel versions of the code.

Throughput Optimization Via Adaptive MIMO Communications

DTIC Science & Technology

2006-05-30

End-to-end matlab packet simulation platform. * Low density parity check code (LDPCC). * Field trials with Silvus DSP MIMO testbed. * High mobility...incorporate advanced LDPC (low density parity check) codes . Realizing that the power of LDPC codes come at the price of decoder complexity, we also...Channel Coding Binary Convolution Code or LDPC Packet Length 0 - 216-1, bytes Coding Rate 1/2, 2/3, 3/4, 5/6 MIMO Channel Training Length 0 - 4, symbols

Error control techniques for satellite and space communications

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.

1989-01-01

The performance of bandwidth efficient trellis codes on channels with phase jitter, or those disturbed by jamming and impulse noise is analyzed. An heuristic algorithm for construction of bandwidth efficient trellis codes with any constraint length up to about 30, any signal constellation, and any code rate was developed. Construction of good distance profile trellis codes for sequential decoding and comparison of random coding bounds of trellis coded modulation schemes are also discussed.

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.

De-coding Reading at Work: Workplace Reading Competencies.

ERIC Educational Resources Information Center

Searle, Jean

1998-01-01

Naturalistic observations and interviews with service workers found on-the-job reading was based on knowledge of codes and rules of practice and required problem-solving and metacognitive strategies. Workplace competencies should be considered within their social and cultural context. (SK)

Research on lossless compression of true color RGB image with low time and space complexity

NASA Astrophysics Data System (ADS)

Pan, ShuLin; Xie, ChengJun; Xu, Lin

2008-12-01

Eliminating correlated redundancy of space and energy by using a DWT lifting scheme and reducing the complexity of the image by using an algebraic transform among the RGB components. An improved Rice Coding algorithm, in which presents an enumerating DWT lifting scheme that fits any size images by image renormalization has been proposed in this paper. This algorithm has a coding and decoding process without backtracking for dealing with the pixels of an image. It support LOCO-I and it can also be applied to Coder / Decoder. Simulation analysis indicates that the proposed method can achieve a high image compression. Compare with Lossless-JPG, PNG(Microsoft), PNG(Rene), PNG(Photoshop), PNG(Anix PicViewer), PNG(ACDSee), PNG(Ulead photo Explorer), JPEG2000, PNG(KoDa Inc), SPIHT and JPEG-LS, the lossless image compression ratio improved 45%, 29%, 25%, 21%, 19%, 17%, 16%, 15%, 11%, 10.5%, 10% separately with 24 pieces of RGB image provided by KoDa Inc. Accessing the main memory in Pentium IV,CPU2.20GHZ and 256MRAM, the coding speed of the proposed coder can be increased about 21 times than the SPIHT and the efficiency of the performance can be increased 166% or so, the decoder's coding speed can be increased about 17 times than the SPIHT and the efficiency of the performance can be increased 128% or so.

Design and Implementation of Viterbi Decoder Using VHDL

NASA Astrophysics Data System (ADS)

Thakur, Akash; Chattopadhyay, Manju K.

2018-03-01

A digital design conversion of Viterbi decoder for ½ rate convolutional encoder with constraint length k = 3 is presented in this paper. The design is coded with the help of VHDL, simulated and synthesized using XILINX ISE 14.7. Synthesis results show a maximum frequency of operation for the design is 100.725 MHz. The requirement of memory is less as compared to conventional method.

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.

A CCIR-based prediction model for Earth-Space propagation

NASA Technical Reports Server (NTRS)

Zhang, Zengjun; Smith, Ernest K.

1991-01-01

At present there is no single 'best way' to predict propagation impairments to an Earth-Space path. However, there is an internationally accepted way, namely that given in the most recent version of CCIR Report 564 of Study Group 5. This paper treats a computer code conforming as far as possible to Report 564. It was prepared for an IBM PS/2 using a 386 chip and for Macintosh SE or Mach II. It is designed to be easy to write and read, easy to modify, fast, have strong graphic capability, contain adequate functions, have dialog capability and windows capability. Computer languages considered included the following: (1) Turbo BASIC, (2) Turbo PASCAL, (3) FORTRAN, (4) SMALL TALK, (5) C++, (6) MS SPREADSHEET, (7) MS Excel-Macro, (8) SIMSCRIPT II.5, and (9) WINGZ.

An automatic editing algorithm for GPS data

NASA Technical Reports Server (NTRS)

Blewitt, Geoffrey

1990-01-01

An algorithm has been developed to edit automatically Global Positioning System data such that outlier deletion, cycle slip identification, and correction are independent of clock instability, selective availability, receiver-satellite kinematics, and tropospheric conditions. This algorithm, called TurboEdit, operates on undifferenced, dual frequency carrier phase data, and requires the use of P code pseudorange data and a smoothly varying ionospheric electron content. TurboEdit was tested on the large data set from the CASA Uno experiment, which contained over 2500 cycle slips.Analyst intervention was required on 1 percent of the station-satellite passes, almost all of these problems being due to difficulties in extrapolating variations in the ionospheric delay. The algorithm is presently being adapted for real time data editing in the Rogue receiver for continuous monitoring applications.

Population coding and decoding in a neural field: a computational study.

PubMed

Wu, Si; Amari, Shun-Ichi; Nakahara, Hiroyuki

2002-05-01

This study uses a neural field model to investigate computational aspects of population coding and decoding when the stimulus is a single variable. A general prototype model for the encoding process is proposed, in which neural responses are correlated, with strength specified by a gaussian function of their difference in preferred stimuli. Based on the model, we study the effect of correlation on the Fisher information, compare the performances of three decoding methods that differ in the amount of encoding information being used, and investigate the implementation of the three methods by using a recurrent network. This study not only rediscovers main results in existing literatures in a unified way, but also reveals important new features, especially when the neural correlation is strong. As the neural correlation of firing becomes larger, the Fisher information decreases drastically. We confirm that as the width of correlation increases, the Fisher information saturates and no longer increases in proportion to the number of neurons. However, we prove that as the width increases further--wider than (sqrt)2 times the effective width of the turning function--the Fisher information increases again, and it increases without limit in proportion to the number of neurons. Furthermore, we clarify the asymptotic efficiency of the maximum likelihood inference (MLI) type of decoding methods for correlated neural signals. It shows that when the correlation covers a nonlocal range of population (excepting the uniform correlation and when the noise is extremely small), the MLI type of method, whose decoding error satisfies the Cauchy-type distribution, is not asymptotically efficient. This implies that the variance is no longer adequate to measure decoding accuracy.

Impact of jammer side information on the performance of anti-jam systems

NASA Astrophysics Data System (ADS)

Lim, Samuel

1992-03-01

The Chernoff bound parameter, D, provides a performance measure for all coded communication systems. D can be used to determine upper-bounds on bit error probabilities (BEPs) of Viterbi decoded convolutional codes. The impact on BEP bounds of channel measurements that provide additional side information can also be evaluated with D. This memo documents the results of a Chernoff bound parameter evaluation in optimum partial-band noise jamming (OPBNJ) for both BPSK and DPSK modulation schemes. Hard and soft quantized receivers, with and without jammer side information (JSI), were examined. The results of this analysis indicate that JSI does improve decoding performance. However, a knowledge of jammer presence alone achieves a performance level comparable to soft decision decoding with perfect JSI. Furthermore, performance degradation due to the lack of JSI can be compensated for by increasing the number of levels of quantization. Therefore, an anti-jam system without JSI can be made to perform almost as well as a system with JSI.

Shape-coded silica nanotubes for multiplexed bioassay: rapid and reliable magnetic decoding protocols

PubMed Central

He, Bo; Kim, Sung Kyoung; Son, Sang Jun; Lee, Sang Bok

2010-01-01

Aims The recent development of 1D barcode arrays has proved their capabilities to be applicable to highly multiplexed bioassays. This article introduces two magnetic decoding protocols for suspension arrays of shape-coded silica nanotubes to process multiplexed assays rapidly and easily, which will benefit the minimization and automation of the arrays. Methods In the first protocol, the magnetic nanocrystals are incorporated into the inner voids of barcoded silica nanotubes in order to give the nanotubes magnetic properties. The second protocol is performed by trapping the barcoded silica nanotubes onto streptavidin-modified magnetic beads. Results The rapid and easy decoding process was demonstrated by applying the above two protocols to multiplexed assays, resulting in high selectivity. Furthermore, the magnetic bead-trapped barcode nanotubes provided a great opportunity to exclude the use of dye molecules in multiplexed assays by using barcode nanotubes as signals. Conclusion The rapid and easy manipulation of encoded carriers using magnetic properties could be used to develop promising suspension arrays for portable bioassays. PMID:20025466

Real-time transmission of digital video using variable-length coding

NASA Technical Reports Server (NTRS)

Bizon, Thomas P.; Shalkhauser, Mary JO; Whyte, Wayne A., Jr.

1993-01-01

Huffman coding is a variable-length lossless compression technique where data with a high probability of occurrence is represented with short codewords, while 'not-so-likely' data is assigned longer codewords. Compression is achieved when the high-probability levels occur so frequently that their benefit outweighs any penalty paid when a less likely input occurs. One instance where Huffman coding is extremely effective occurs when data is highly predictable and differential coding can be applied (as with a digital video signal). For that reason, it is desirable to apply this compression technique to digital video transmission; however, special care must be taken in order to implement a communication protocol utilizing Huffman coding. This paper addresses several of the issues relating to the real-time transmission of Huffman-coded digital video over a constant-rate serial channel. Topics discussed include data rate conversion (from variable to a fixed rate), efficient data buffering, channel coding, recovery from communication errors, decoder synchronization, and decoder architectures. A description of the hardware developed to execute Huffman coding and serial transmission is also included. Although this paper focuses on matters relating to Huffman-coded digital video, the techniques discussed can easily be generalized for a variety of applications which require transmission of variable-length data.

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.

Scalable Video Transmission Over Multi-Rate Multiple Access Channels

DTIC Science & Technology

2007-06-01

Rate - compatible punctured convolutional codes (RCPC codes ) and their ap- plications,” IEEE...source encoded using the MPEG-4 video codec. The source encoded bitstream is then channel encoded with Rate Compatible Punctured Convolutional (RCPC...Clark, and J. M. Geist, “ Punctured convolutional codes or rate (n-1)/n and simplified maximum likelihood decoding,” IEEE Transactions on

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.

On the reduced-complexity of LDPC decoders for beyond 400 Gb/s serial optical transmission

NASA Astrophysics Data System (ADS)

Djordjevic, Ivan B.; Xu, Lei; Wang, Ting

2010-12-01

Two reduced-complexity (RC) LDPC decoders are proposed, which can be used in combination with large-girth LDPC codes to enable beyond 400 Gb/s serial optical transmission. We show that optimally attenuated RC min-sum sum algorithm performs only 0.45 dB worse than conventional sum-product algorithm, while having lower storage memory requirements and much lower latency. We further evaluate the proposed algorithms for use in beyond 400 Gb/s serial optical transmission in combination with PolMUX 32-IPQ-based signal constellation and show that low BERs can be achieved for medium optical SNRs, while achieving the net coding gain above 11.4 dB.

Efficient random access high resolution region-of-interest (ROI) image retrieval using backward coding of wavelet trees (BCWT)

NASA Astrophysics Data System (ADS)

Corona, Enrique; Nutter, Brian; Mitra, Sunanda; Guo, Jiangling; Karp, Tanja

2008-03-01

Efficient retrieval of high quality Regions-Of-Interest (ROI) from high resolution medical images is essential for reliable interpretation and accurate diagnosis. Random access to high quality ROI from codestreams is becoming an essential feature in many still image compression applications, particularly in viewing diseased areas from large medical images. This feature is easier to implement in block based codecs because of the inherent spatial independency of the code blocks. This independency implies that the decoding order of the blocks is unimportant as long as the position for each is properly identified. In contrast, wavelet-tree based codecs naturally use some interdependency that exploits the decaying spectrum model of the wavelet coefficients. Thus one must keep track of the decoding order from level to level with such codecs. We have developed an innovative multi-rate image subband coding scheme using "Backward Coding of Wavelet Trees (BCWT)" which is fast, memory efficient, and resolution scalable. It offers far less complexity than many other existing codecs including both, wavelet-tree, and block based algorithms. The ROI feature in BCWT is implemented through a transcoder stage that generates a new BCWT codestream containing only the information associated with the user-defined ROI. This paper presents an efficient technique that locates a particular ROI within the BCWT coded domain, and decodes it back to the spatial domain. This technique allows better access and proper identification of pathologies in high resolution images since only a small fraction of the codestream is required to be transmitted and analyzed.

Frame synchronization for the Galileo code

NASA Technical Reports Server (NTRS)

Arnold, S.; Swanson, L.

1991-01-01

Results are reported on the performance of the Deep Space Network's frame synchronizer for the (15,1/4) convolutional code after Viterbi decoding. The threshold is found that optimizes the probability of acquiring true sync within four frames using a strategy that requires next frame verification.

Television News Without Pictures?

ERIC Educational Resources Information Center

Graber, Doris A.

1987-01-01

Describes "gestalt" coding procedures that concentrate on the meanings conveyed by audio-visual messages rather than on coding individual pictorial elements shown in a news story. Discusses the totality of meaning that results from the interaction of verbal and visual story elements, external settings, and the decoding proclivities of…

A thesaurus for a neural population code

PubMed Central

Ganmor, Elad; Segev, Ronen; Schneidman, Elad

2015-01-01

Information is carried in the brain by the joint spiking patterns of large groups of noisy, unreliable neurons. This noise limits the capacity of the neural code and determines how information can be transmitted and read-out. To accurately decode, the brain must overcome this noise and identify which patterns are semantically similar. We use models of network encoding noise to learn a thesaurus for populations of neurons in the vertebrate retina responding to artificial and natural videos, measuring the similarity between population responses to visual stimuli based on the information they carry. This thesaurus reveals that the code is organized in clusters of synonymous activity patterns that are similar in meaning but may differ considerably in their structure. This organization is highly reminiscent of the design of engineered codes. We suggest that the brain may use this structure and show how it allows accurate decoding of novel stimuli from novel spiking patterns. DOI: http://dx.doi.org/10.7554/eLife.06134.001 PMID:26347983

Pre-coding method and apparatus for multiple source or time-shifted single source data and corresponding inverse post-decoding method and apparatus

NASA Technical Reports Server (NTRS)

Yeh, Pen-Shu (Inventor)

1997-01-01

A pre-coding method and device for improving data compression performance by removing correlation between a first original data set and a second original data set, each having M members, respectively. The pre-coding method produces a compression-efficiency-enhancing double-difference data set. The method and device produce a double-difference data set, i.e., an adjacent-delta calculation performed on a cross-delta data set or a cross-delta calculation performed on two adjacent-delta data sets, from either one of (1) two adjacent spectral bands coming from two discrete sources, respectively, or (2) two time-shifted data sets coming from a single source. The resulting double-difference data set is then coded using either a distortionless data encoding scheme (entropy encoding) or a lossy data compression scheme. Also, a post-decoding method and device for recovering a second original data set having been represented by such a double-difference data set.

Pre-coding method and apparatus for multiple source or time-shifted single source data and corresponding inverse post-decoding method and apparatus

NASA Technical Reports Server (NTRS)

Yeh, Pen-Shu (Inventor)

1998-01-01

A pre-coding method and device for improving data compression performance by removing correlation between a first original data set and a second original data set, each having M members, respectively. The pre-coding method produces a compression-efficiency-enhancing double-difference data set. The method and device produce a double-difference data set, i.e., an adjacent-delta calculation performed on a cross-delta data set or a cross-delta calculation performed on two adjacent-delta data sets, from either one of (1) two adjacent spectral bands coming from two discrete sources, respectively, or (2) two time-shifted data sets coming from a single source. The resulting double-difference data set is then coded using either a distortionless data encoding scheme (entropy encoding) or a lossy data compression scheme. Also, a post-decoding method and device for recovering a second original data set having been represented by such a double-difference data set.

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.

Box codes of lengths 48 and 72

NASA Technical Reports Server (NTRS)

Solomon, G.; Jin, Y.

1993-01-01

A self-dual code length 48, dimension 24, with Hamming distance essentially equal to 12 is constructed here. There are only six code words of weight eight. All the other code words have weights that are multiples of four and have a minimum weight equal to 12. This code may be encoded systematically and arises from a strict binary representation of the (8,4;5) Reed-Solomon (RS) code over GF (64). The code may be considered as six interrelated (8,7;2) codes. The Mattson-Solomon representation of the cyclic decomposition of these codes and their parity sums are used to detect an odd number of errors in any of the six codes. These may then be used in a correction algorithm for hard or soft decision decoding. A (72,36;15) box code was constructed from a (63,35;8) cyclic code. The theoretical justification is presented herein. A second (72,36;15) code is constructed from an inner (63,27;16) Bose Chaudhuri Hocquenghem (BCH) code and expanded to length 72 using box code algorithms for extension. This code was simulated and verified to have a minimum distance of 15 with even weight words congruent to zero modulo four. The decoding for hard and soft decision is still more complex than the first code constructed above. Finally, an (8,4;5) RS code over GF (512) in the binary representation of the (72,36;15) box code gives rise to a (72,36;16*) code with nine words of weight eight, and all the rest have weights greater than or equal to 16.

Error control techniques for satellite and space communications

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.

1989-01-01

Two aspects of the work for NASA are examined: the construction of multi-dimensional phase modulation trellis codes and a performance analysis of these codes. A complete list is contained of all the best trellis codes for use with phase modulation. LxMPSK signal constellations are included for M = 4, 8, and 16 and L = 1, 2, 3, and 4. Spectral efficiencies range from 1 bit/channel symbol (equivalent to rate 1/2 coded QPSK) to 3.75 bits/channel symbol (equivalent to 15/16 coded 16-PSK). The parity check polynomials, rotational invariance properties, free distance, path multiplicities, and coding gains are given for all codes. These codes are considered to be the best candidates for implementation of a high speed decoder for satellite transmission. The design of a hardware decoder for one of these codes, viz., the 16-state 3x8-PSK code with free distance 4.0 and coding gain 3.75 dB is discussed. An exhaustive simulation study of the multi-dimensional phase modulation trellis codes is contained. This study was motivated by the fact that coding gains quoted for almost all codes found in literature are in fact only asymptotic coding gains, i.e., the coding gain at very high signal to noise ratios (SNRs) or very low BER. These asymptotic coding gains can be obtained directly from a knowledge of the free distance of the code. On the other hand, real coding gains at BERs in the range of 10(exp -2) to 10(exp -6), where these codes are most likely to operate in a concatenated system, must be done by simulation.

47 CFR 15.122 - Closed caption decoder requirements for digital television receivers and converter boxes.

Code of Federal Regulations, 2011 CFR

2011-10-01

... code 0×2D Lower-left border (⌊), G2 char code 0×7C G0 dash (-), char code 0×2D Horizontal border... (-), char code 0×2D Upper-left border (⌈), G2 char code 0×7F G0 dash (-), char code 0×2D (4) Support for..., if the character to the left of the embedded return is a hyphen, the embedded return should be...

47 CFR 15.122 - Closed caption decoder requirements for digital television receivers and converter boxes.

Code of Federal Regulations, 2010 CFR

2010-10-01

... code 0×2D Lower-left border (⌊), G2 char code 0×7C G0 dash (-), char code 0×2D Horizontal border... (-), char code 0×2D Upper-left border (⌈), G2 char code 0×7F G0 dash (-), char code 0×2D (4) Support for..., if the character to the left of the embedded return is a hyphen, the embedded return should be...

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.

Visual coding with a population of direction-selective neurons.

PubMed

Fiscella, Michele; Franke, Felix; Farrow, Karl; Müller, Jan; Roska, Botond; da Silveira, Rava Azeredo; Hierlemann, Andreas

2015-10-01

The brain decodes the visual scene from the action potentials of ∼20 retinal ganglion cell types. Among the retinal ganglion cells, direction-selective ganglion cells (DSGCs) encode motion direction. Several studies have focused on the encoding or decoding of motion direction by recording multiunit activity, mainly in the visual cortex. In this study, we simultaneously recorded from all four types of ON-OFF DSGCs of the rabbit retina using a microelectronics-based high-density microelectrode array (HDMEA) and decoded their concerted activity using probabilistic and linear decoders. Furthermore, we investigated how the modification of stimulus parameters (velocity, size, angle of moving object) and the use of different tuning curve fits influenced decoding precision. Finally, we simulated ON-OFF DSGC activity, based on real data, in order to understand how tuning curve widths and the angular distribution of the cells' preferred directions influence decoding performance. We found that probabilistic decoding strategies outperformed, on average, linear methods and that decoding precision was robust to changes in stimulus parameters such as velocity. The removal of noise correlations among cells, by random shuffling trials, caused a drop in decoding precision. Moreover, we found that tuning curves are broad in order to minimize large errors at the expense of a higher average error, and that the retinal direction-selective system would not substantially benefit, on average, from having more than four types of ON-OFF DSGCs or from a perfect alignment of the cells' preferred directions. Copyright © 2015 the American Physiological Society.

Visual coding with a population of direction-selective neurons

PubMed Central

Farrow, Karl; Müller, Jan; Roska, Botond; Azeredo da Silveira, Rava; Hierlemann, Andreas

2015-01-01

The brain decodes the visual scene from the action potentials of ∼20 retinal ganglion cell types. Among the retinal ganglion cells, direction-selective ganglion cells (DSGCs) encode motion direction. Several studies have focused on the encoding or decoding of motion direction by recording multiunit activity, mainly in the visual cortex. In this study, we simultaneously recorded from all four types of ON-OFF DSGCs of the rabbit retina using a microelectronics-based high-density microelectrode array (HDMEA) and decoded their concerted activity using probabilistic and linear decoders. Furthermore, we investigated how the modification of stimulus parameters (velocity, size, angle of moving object) and the use of different tuning curve fits influenced decoding precision. Finally, we simulated ON-OFF DSGC activity, based on real data, in order to understand how tuning curve widths and the angular distribution of the cells' preferred directions influence decoding performance. We found that probabilistic decoding strategies outperformed, on average, linear methods and that decoding precision was robust to changes in stimulus parameters such as velocity. The removal of noise correlations among cells, by random shuffling trials, caused a drop in decoding precision. Moreover, we found that tuning curves are broad in order to minimize large errors at the expense of a higher average error, and that the retinal direction-selective system would not substantially benefit, on average, from having more than four types of ON-OFF DSGCs or from a perfect alignment of the cells' preferred directions. PMID:26289471

Decoding the genome with an integrative analysis tool: combinatorial CRM Decoder.

PubMed

Kang, Keunsoo; Kim, Joomyeong; Chung, Jae Hoon; Lee, Daeyoup

2011-09-01

The identification of genome-wide cis-regulatory modules (CRMs) and characterization of their associated epigenetic features are fundamental steps toward the understanding of gene regulatory networks. Although integrative analysis of available genome-wide information can provide new biological insights, the lack of novel methodologies has become a major bottleneck. Here, we present a comprehensive analysis tool called combinatorial CRM decoder (CCD), which utilizes the publicly available information to identify and characterize genome-wide CRMs in a species of interest. CCD first defines a set of the epigenetic features which is significantly associated with a set of known CRMs as a code called 'trace code', and subsequently uses the trace code to pinpoint putative CRMs throughout the genome. Using 61 genome-wide data sets obtained from 17 independent mouse studies, CCD successfully catalogued ∼12 600 CRMs (five distinct classes) including polycomb repressive complex 2 target sites as well as imprinting control regions. Interestingly, we discovered that ∼4% of the identified CRMs belong to at least two different classes named 'multi-functional CRM', suggesting their functional importance for regulating spatiotemporal gene expression. From these examples, we show that CCD can be applied to any potential genome-wide datasets and therefore will shed light on unveiling genome-wide CRMs in various species.

Multidimensional Trellis Coded Phase Modulation Using a Multilevel Concatenation Approach. Part 2; Codes for AWGN and Fading Channels

NASA Technical Reports Server (NTRS)

Rajpal, Sandeep; Rhee, DoJun; Lin, Shu

1997-01-01

In this paper, we will use the construction technique proposed in to construct multidimensional trellis coded modulation (TCM) codes for both the additive white Gaussian noise (AWGN) and the fading channels. Analytical performance bounds and simulation results show that these codes perform very well and achieve significant coding gains over uncoded reference modulation systems. In addition, the proposed technique can be used to construct codes which have a performance/decoding complexity advantage over the codes listed in literature.

A VHDL Interface for Altera Design Files

DTIC Science & Technology

1990-01-01

this requirement dictated that all prototype products developed during this research would have to mirror standard VHDL code . In fact, the final... product would have to meet the 20 syntactic and semantic requirements of standard VHDL . The coding style used to create the transformation program was the...Transformed Decoder File ....................... 47 C. Supplemental VHDL Package Source Code ........... 54 Altpk.vhd .................................... 54 D

12 CFR 1016.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2013 CFR

2013-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... reporting agency, an account number or similar form of access number or access code for a consumer's credit... similar form of access number or access code: (1) To your agent or service provider solely in order to...

12 CFR 1016.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2014 CFR

2014-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... reporting agency, an account number or similar form of access number or access code for a consumer's credit... similar form of access number or access code: (1) To your agent or service provider solely in order to...

12 CFR 216.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2012 CFR

2012-01-01

... code in an encrypted form, as long as you do not provide the recipient with a means to decode the... than to a consumer reporting agency, an account number or similar form of access number or access code... account number or similar form of access number or access code: (1) To your agent or service provider...

16 CFR 313.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2013 CFR

2013-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... consumer reporting agency, an account number or similar form of access number or access code for a consumer... similar form of access number or access code: (1) To your agent or service provider solely in order to...

16 CFR 313.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2011 CFR

2011-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... consumer reporting agency, an account number or similar form of access number or access code for a consumer... similar form of access number or access code: (1) To your agent or service provider solely in order to...

12 CFR 216.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2014 CFR

2014-01-01

... code in an encrypted form, as long as you do not provide the recipient with a means to decode the... than to a consumer reporting agency, an account number or similar form of access number or access code... account number or similar form of access number or access code: (1) To your agent or service provider...

16 CFR 313.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2012 CFR

2012-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... consumer reporting agency, an account number or similar form of access number or access code for a consumer... similar form of access number or access code: (1) To your agent or service provider solely in order to...

12 CFR 216.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2013 CFR

2013-01-01

... code in an encrypted form, as long as you do not provide the recipient with a means to decode the... than to a consumer reporting agency, an account number or similar form of access number or access code... account number or similar form of access number or access code: (1) To your agent or service provider...

12 CFR 1016.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2012 CFR

2012-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... reporting agency, an account number or similar form of access number or access code for a consumer's credit... similar form of access number or access code: (1) To your agent or service provider solely in order to...

12 CFR 332.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2013 CFR

2013-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... consumer reporting agency, an account number or similar form of access number or access code for a consumer... similar form of access number or access code: (1) To your agent or service provider solely in order to...

12 CFR 332.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2011 CFR

2011-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... consumer reporting agency, an account number or similar form of access number or access code for a consumer... similar form of access number or access code: (1) To your agent or service provider solely in order to...

12 CFR 332.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2014 CFR

2014-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... consumer reporting agency, an account number or similar form of access number or access code for a consumer... similar form of access number or access code: (1) To your agent or service provider solely in order to...

12 CFR 216.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2011 CFR

2011-01-01

... code in an encrypted form, as long as you do not provide the recipient with a means to decode the... than to a consumer reporting agency, an account number or similar form of access number or access code... account number or similar form of access number or access code: (1) To your agent or service provider...

12 CFR 332.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2012 CFR

2012-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... consumer reporting agency, an account number or similar form of access number or access code for a consumer... similar form of access number or access code: (1) To your agent or service provider solely in order to...

16 CFR 313.12 - Limits on sharing account number information for marketing purposes.

Code of Federal Regulations, 2014 CFR

2014-01-01

... encrypted form, as long as you do not provide the recipient with a means to decode the number or code. (2... consumer reporting agency, an account number or similar form of access number or access code for a consumer... similar form of access number or access code: (1) To your agent or service provider solely in order to...

Evaluation of an electrocardiogram on QR code.

PubMed

Nakayama, Masaharu; Shimokawa, Hiroaki

2013-01-01

An electrocardiogram (ECG) is an indispensable tool to diagnose cardiac diseases, such as ischemic heart disease, myocarditis, arrhythmia, and cardiomyopathy. Since ECG patterns vary depend on patient status, it is also used to monitor patients during treatment and comparison with ECGs with previous results is important for accurate diagnosis. However, the comparison requires connection to ECG data server in a hospital and the availability of data connection among hospitals is limited. To improve the portability and availability of ECG data regardless of server connection, we here introduce conversion of ECG data into 2D barcodes as text data and decode of the QR code for drawing ECG with Google Chart API. Fourteen cardiologists and six general physicians evaluated the system using iPhone and iPad. Overall, they were satisfied with the system in usability and accuracy of decoded ECG compared to the original ECG. This new coding system may be useful in utilizing ECG data irrespective of server connections.

Optimal decoding in fading channels - A combined envelope, multiple differential and coherent detection approach

NASA Astrophysics Data System (ADS)

Makrakis, Dimitrios; Mathiopoulos, P. Takis

A maximum likelihood sequential decoder for the reception of digitally modulated signals with single or multiamplitude constellations transmitted over a multiplicative, nonselective fading channel is derived. It is shown that its structure consists of a combination of envelope, multiple differential, and coherent detectors. The outputs of each of these detectors are jointly processed by means of an algorithm. This algorithm is presented in a recursive form. The derivation of the new receiver is general enough to accommodate uncoded as well as coded (e.g., trellis-coded) schemes. Performance evaluation results for a reduced-complexity trellis-coded QPSK system have demonstrated that the proposed receiver dramatically reduces the error floors caused by fading. At Eb/N0 = 20 dB the new receiver structure results in bit-error-rate reductions of more than three orders of magnitude compared to a conventional Viterbi receiver, while being reasonably simple to implement.

Lithographically Encrypted Inverse Opals for Anti-Counterfeiting Applications.

PubMed

Heo, Yongjoon; Kang, Hyelim; Lee, Joon-Seok; Oh, You-Kwan; Kim, Shin-Hyun

2016-07-01

Colloidal photonic crystals possess inimitable optical properties of iridescent structural colors and unique spectral shape, which render them useful for security materials. This work reports a novel method to encrypt graphical and spectral codes in polymeric inverse opals to provide advanced security. To accomplish this, this study prepares lithographically featured micropatterns on the top surface of hydrophobic inverse opals, which serve as shadow masks against the surface modification of air cavities to achieve hydrophilicity. The resultant inverse opals allow rapid infiltration of aqueous solution into the hydrophilic cavities while retaining air in the hydrophobic cavities. Therefore, the structural color of inverse opals is regioselectively red-shifted, disclosing the encrypted graphical codes. The decoded inverse opals also deliver unique reflectance spectral codes originated from two distinct regions. The combinatorial code composed of graphical and optical codes is revealed only when the aqueous solution agreed in advance is used for decoding. In addition, the encrypted inverse opals are chemically stable, providing invariant codes with high reproducibility. In addition, high mechanical stability enables the transfer of the films onto any surfaces. This novel encryption technology will provide a new opportunity in a wide range of security applications. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A Three Dimensional Parallel Time Accurate Turbopump Simulation Procedure Using Overset Grid Systems

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Chan, William; Kwak, Dochan

2001-01-01

The objective of the current effort is to provide a computational framework for design and analysis of the entire fuel supply system of a liquid rocket engine, including high-fidelity unsteady turbopump flow analysis. This capability is needed to support the design of pump sub-systems for advanced space transportation vehicles that are likely to involve liquid propulsion systems. To date, computational tools for design/analysis of turbopump flows are based on relatively lower fidelity methods. An unsteady, three-dimensional viscous flow analysis tool involving stationary and rotational components for the entire turbopump assembly has not been available for real-world engineering applications. The present effort provides developers with information such as transient flow phenomena at start up, and non-uniform inflows, and will eventually impact on system vibration and structures. In the proposed paper, the progress toward the capability of complete simulation of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of the hybrid MPI/Open-MP and MLP versions of the INS3D code. CAD to solution auto-scripting capability is being developed for turbopump applications. The relative motion of the grid systems for the rotor-stator interaction was obtained using overset grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on Origin 3000 systems at NASA Ames Research Center. Results from these time-accurate simulations with moving boundary capability will be presented along with the performance of parallel versions of the code.

Global navigation satellite system receiver for weak signals under all dynamic conditions

NASA Astrophysics Data System (ADS)

Ziedan, Nesreen Ibrahim

The ability of the Global Navigation Satellite System (GNSS) receiver to work under weak signal and various dynamic conditions is required in some applications. For example, to provide a positioning capability in wireless devices, or orbit determination of Geostationary and high Earth orbit satellites. This dissertation develops Global Positioning System (GPS) receiver algorithms for such applications. Fifteen algorithms are developed for the GPS C/A signal. They cover all the receiver main functions, which include acquisition, fine acquisition, bit synchronization, code and carrier tracking, and navigation message decoding. They are integrated together, and they can be used in any software GPS receiver. They also can be modified to fit any other GPS or GNSS signals. The algorithms have new capabilities. The processing and memory requirements are considered in the design to allow the algorithms to fit the limited resources of some applications; they do not require any assisting information. Weak signals can be acquired in the presence of strong interfering signals and under high dynamic conditions. The fine acquisition, bit synchronization, and tracking algorithms are based on the Viterbi algorithm and Extended Kalman filter approaches. The tracking algorithms capabilities increase the time to lose lock. They have the ability to adaptively change the integration length and the code delay separation. More than one code delay separation can be used in the same time. Large tracking errors can be detected and then corrected by a re-initialization and an acquisition-like algorithms. Detecting the navigation message is needed to increase the coherent integration; decoding it is needed to calculate the navigation solution. The decoding algorithm utilizes the message structure to enable its decoding for signals with high Bit Error Rate. The algorithms are demonstrated using simulated GPS C/A code signals, and TCXO clocks. The results have shown the algorithms ability to reliably work with 15 dB-Hz signals and acceleration over 6 g.

Gamma-Ray Imaging Probes.

NASA Astrophysics Data System (ADS)

Wild, Walter James

1988-12-01

External nuclear medicine diagnostic imaging of early primary and metastatic lung cancer tumors is difficult due to the poor sensitivity and resolution of existing gamma cameras. Nonimaging counting detectors used for internal tumor detection give ambiguous results because distant background variations are difficult to discriminate from neighboring tumor sites. This suggests that an internal imaging nuclear medicine probe, particularly an esophageal probe, may be advantageously used to detect small tumors because of the ability to discriminate against background variations and the capability to get close to sites neighboring the esophagus. The design, theory of operation, preliminary bench tests, characterization of noise behavior and optimization of such an imaging probe is the central theme of this work. The central concept lies in the representation of the aperture shell by a sequence of binary digits. This, coupled with the mode of operation which is data encoding within an axial slice of space, leads to the fundamental imaging equation in which the coding operation is conveniently described by a circulant matrix operator. The coding/decoding process is a classic coded-aperture problem, and various estimators to achieve decoding are discussed. Some estimators require a priori information about the object (or object class) being imaged; the only unbiased estimator that does not impose this requirement is the simple inverse-matrix operator. The effects of noise on the estimate (or reconstruction) is discussed for general noise models and various codes/decoding operators. The choice of an optimal aperture for detector count times of clinical relevance is examined using a statistical class-separability formalism.

Optical control system for high-voltage terminals

DOEpatents

Bicek, John J.

1978-01-01

An optical control system for the control of devices in the terminal of an electrostatic accelerator includes a laser that is modulated by a series of preselected codes produced by an encoder. A photodiode receiver is placed in the laser beam at the high-voltage terminal of an electrostatic accelerator. A decoder connected to the photodiode decodes the signals to provide control impulses for a plurality of devices at the high voltage of the terminal.

Coding and decoding with adapting neurons: a population approach to the peri-stimulus time histogram.

PubMed

Naud, Richard; Gerstner, Wulfram

2012-01-01

The response of a neuron to a time-dependent stimulus, as measured in a Peri-Stimulus-Time-Histogram (PSTH), exhibits an intricate temporal structure that reflects potential temporal coding principles. Here we analyze the encoding and decoding of PSTHs for spiking neurons with arbitrary refractoriness and adaptation. As a modeling framework, we use the spike response model, also known as the generalized linear neuron model. Because of refractoriness, the effect of the most recent spike on the spiking probability a few milliseconds later is very strong. The influence of the last spike needs therefore to be described with high precision, while the rest of the neuronal spiking history merely introduces an average self-inhibition or adaptation that depends on the expected number of past spikes but not on the exact spike timings. Based on these insights, we derive a 'quasi-renewal equation' which is shown to yield an excellent description of the firing rate of adapting neurons. We explore the domain of validity of the quasi-renewal equation and compare it with other rate equations for populations of spiking neurons. The problem of decoding the stimulus from the population response (or PSTH) is addressed analogously. We find that for small levels of activity and weak adaptation, a simple accumulator of the past activity is sufficient to decode the original input, but when refractory effects become large decoding becomes a non-linear function of the past activity. The results presented here can be applied to the mean-field analysis of coupled neuron networks, but also to arbitrary point processes with negative self-interaction.

Phonetic radicals, not phonological coding systems, support orthographic learning via self-teaching in Chinese.

PubMed

Li, Luan; Wang, Hua-Chen; Castles, Anne; Hsieh, Miao-Ling; Marinus, Eva

2018-07-01

According to the self-teaching hypothesis (Share, 1995), phonological decoding is fundamental to acquiring orthographic representations of novel written words. However, phonological decoding is not straightforward in non-alphabetic scripts such as Chinese, where words are presented as characters. Here, we present the first study investigating the role of phonological decoding in orthographic learning in Chinese. We examined two possible types of phonological decoding: the use of phonetic radicals, an internal phonological aid, andthe use of Zhuyin, an external phonological coding system. Seventy-three Grade 2 children were taught the pronunciations and meanings of twelve novel compound characters over four days. They were then exposed to the written characters in short stories, and were assessed on their reading accuracy and on their subsequent orthographic learning via orthographic choice and spelling tasks. The novel characters were assigned three different types of pronunciation in relation to its phonetic radical - (1) a pronunciation that is identical to the phonetic radical in isolation; (2) a common alternative pronunciation associated with the phonetic radical when it appears in other characters; and (3) a pronunciation that is unrelated to the phonetic radical. The presence of Zhuyin was also manipulated. The children read the novel characters more accurately when phonological cues from the phonetic radicals were available and in the presence of Zhuyin. However, only the phonetic radicals facilitated orthographic learning. The findings provide the first empirical evidence of orthographic learning via self-teaching in Chinese, and reveal how phonological decoding functions to support learning in non-alphabetic writing systems. Copyright © 2018 Elsevier B.V. All rights reserved.

Design of convolutional tornado code

NASA Astrophysics Data System (ADS)

Zhou, Hui; Yang, Yao; Gao, Hongmin; Tan, Lu

2017-09-01

As a linear block code, the traditional tornado (tTN) code is inefficient in burst-erasure environment and its multi-level structure may lead to high encoding/decoding complexity. This paper presents a convolutional tornado (cTN) code which is able to improve the burst-erasure protection capability by applying the convolution property to the tTN code, and reduce computational complexity by abrogating the multi-level structure. The simulation results show that cTN code can provide a better packet loss protection performance with lower computation complexity than tTN code.

Error control techniques for satellite and space communications

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.

1993-01-01

The results included in the Ph.D. dissertation of Dr. Fu Quan Wang, who was supported by the grant as a Research Assistant from January 1989 through December 1992 are discussed. The sections contain a brief summary of the important aspects of this dissertation, which include: (1) erasurefree sequential decoding of trellis codes; (2) probabilistic construction of trellis codes; (3) construction of robustly good trellis codes; and (4) the separability of shaping and coding.

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.

Image statistics decoding for convolutional codes

NASA Technical Reports Server (NTRS)

Pitt, G. H., III; Swanson, L.; Yuen, J. H.

1987-01-01

It is a fact that adjacent pixels in a Voyager image are very similar in grey level. This fact can be used in conjunction with the Maximum-Likelihood Convolutional Decoder (MCD) to decrease the error rate when decoding a picture from Voyager. Implementing this idea would require no changes in the Voyager spacecraft and could be used as a backup to the current system without too much expenditure, so the feasibility of it and the possible gains for Voyager were investigated. Simulations have shown that the gain could be as much as 2 dB at certain error rates, and experiments with real data inspired new ideas on ways to get the most information possible out of the received symbol stream.

Coding/decoding and reversibility of droplet trains in microfluidic networks.

PubMed

Fuerstman, Michael J; Garstecki, Piotr; Whitesides, George M

2007-02-09

Droplets of one liquid suspended in a second, immiscible liquid move through a microfluidic device in which a channel splits into two branches that reconnect downstream. The droplets choose a path based on the number of droplets that occupy each branch. The interaction among droplets in the channels results in complex sequences of path selection. The linearity of the flow through the microchannels, however, ensures that the behavior of the system can be reversed. This reversibility makes it possible to encrypt and decrypt signals coded in the intervals between droplets. The encoding/decoding device is a functional microfluidic system that requires droplets to navigate a network in a precise manner without the use of valves, switches, or other means of external control.

Joint reconstruction of multiview compressed images.

PubMed

Thirumalai, Vijayaraghavan; Frossard, Pascal

2013-05-01

Distributed representation of correlated multiview images is an important problem that arises in vision sensor networks. This paper concentrates on the joint reconstruction problem where the distributively compressed images are decoded together in order to take benefit from the image correlation. We consider a scenario where the images captured at different viewpoints are encoded independently using common coding solutions (e.g., JPEG) with a balanced rate distribution among different cameras. A central decoder first estimates the inter-view image correlation from the independently compressed data. The joint reconstruction is then cast as a constrained convex optimization problem that reconstructs total-variation (TV) smooth images, which comply with the estimated correlation model. At the same time, we add constraints that force the reconstructed images to be as close as possible to their compressed versions. We show through experiments that the proposed joint reconstruction scheme outperforms independent reconstruction in terms of image quality, for a given target bit rate. In addition, the decoding performance of our algorithm compares advantageously to state-of-the-art distributed coding schemes based on motion learning and on the DISCOVER algorithm.

Reward Motivation Enhances Task Coding in Frontoparietal Cortex.

PubMed

Etzel, Joset A; Cole, Michael W; Zacks, Jeffrey M; Kay, Kendrick N; Braver, Todd S

2016-04-01

Reward motivation often enhances task performance, but the neural mechanisms underlying such cognitive enhancement remain unclear. Here, we used a multivariate pattern analysis (MVPA) approach to test the hypothesis that motivation-related enhancement of cognitive control results from improved encoding and representation of task set information. Participants underwent two fMRI sessions of cued task switching, the first under baseline conditions, and the second with randomly intermixed reward incentive and no-incentive trials. Information about the upcoming task could be successfully decoded from cue-related activation patterns in a set of frontoparietal regions typically associated with task control. More critically, MVPA classifiers trained on the baseline session had significantly higher decoding accuracy on incentive than non-incentive trials, with decoding improvement mediating reward-related enhancement of behavioral performance. These results strongly support the hypothesis that reward motivation enhances cognitive control, by improving the discriminability of task-relevant information coded and maintained in frontoparietal brain regions. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Mapping and Deciphering Neural Codes of NMDA Receptor-Dependent Fear Memory Engrams in the Hippocampus

PubMed Central

Tsien, Joe Z.

2013-01-01

Mapping and decoding brain activity patterns underlying learning and memory represents both great interest and immense challenge. At present, very little is known regarding many of the very basic questions regarding the neural codes of memory: are fear memories retrieved during the freezing state or non-freezing state of the animals? How do individual memory traces give arise to a holistic, real-time associative memory engram? How are memory codes regulated by synaptic plasticity? Here, by applying high-density electrode arrays and dimensionality-reduction decoding algorithms, we investigate hippocampal CA1 activity patterns of trace fear conditioning memory code in inducible NMDA receptor knockout mice and their control littermates. Our analyses showed that the conditioned tone (CS) and unconditioned foot-shock (US) can evoke hippocampal ensemble responses in control and mutant mice. Yet, temporal formats and contents of CA1 fear memory engrams differ significantly between the genotypes. The mutant mice with disabled NMDA receptor plasticity failed to generate CS-to-US or US-to-CS associative memory traces. Moreover, the mutant CA1 region lacked memory traces for “what at when” information that predicts the timing relationship between the conditioned tone and the foot shock. The degraded associative fear memory engram is further manifested in its lack of intertwined and alternating temporal association between CS and US memory traces that are characteristic to the holistic memory recall in the wild-type animals. Therefore, our study has decoded real-time memory contents, timing relationship between CS and US, and temporal organizing patterns of fear memory engrams and demonstrated how hippocampal memory codes are regulated by NMDA receptor synaptic plasticity. PMID:24302990

A cascaded coding scheme for error control

NASA Technical Reports Server (NTRS)

Shu, L.; Kasami, T.

1985-01-01

A cascade coding scheme for error control is investigated. The scheme employs a combination of hard and soft decisions in decoding. Error performance is analyzed. If the inner and outer codes are chosen properly, extremely high reliability can be attained even for a high channel bit-error-rate. Some example schemes are evaluated. They seem to be quite suitable for satellite down-link error control.

A cascaded coding scheme for error control

NASA Technical Reports Server (NTRS)

Kasami, T.; Lin, S.

1985-01-01

A cascaded coding scheme for error control was investigated. The scheme employs a combination of hard and soft decisions in decoding. Error performance is analyzed. If the inner and outer codes are chosen properly, extremely high reliability can be attained even for a high channel bit-error-rate. Some example schemes are studied which seem to be quite suitable for satellite down-link error control.

Telemetry coding study for the international magnetosphere explorers, mother/daughter and heliocentric missions. Volume 2: Final report

NASA Technical Reports Server (NTRS)

Cartier, D. E.

1973-01-01

A convolutional coding theory is given for the IME and the Heliocentric spacecraft. The amount of coding gain needed by the mission is determined. Recommendations are given for an encoder/decoder system to provide the gain along with an evaluation of the impact of the system on the space network in terms of costs and complexity.

Feasibility of video codec algorithms for software-only playback

NASA Astrophysics Data System (ADS)

Rodriguez, Arturo A.; Morse, Ken

1994-05-01

Software-only video codecs can provide good playback performance in desktop computers with a 486 or 68040 CPU running at 33 MHz without special hardware assistance. Typically, playback of compressed video can be categorized into three tasks: the actual decoding of the video stream, color conversion, and the transfer of decoded video data from system RAM to video RAM. By current standards, good playback performance is the decoding and display of video streams of 320 by 240 (or larger) compressed frames at 15 (or greater) frames-per- second. Software-only video codecs have evolved by modifying and tailoring existing compression methodologies to suit video playback in desktop computers. In this paper we examine the characteristics used to evaluate software-only video codec algorithms, namely: image fidelity (i.e., image quality), bandwidth (i.e., compression) ease-of-decoding (i.e., playback performance), memory consumption, compression to decompression asymmetry, scalability, and delay. We discuss the tradeoffs among these variables and the compromises that can be made to achieve low numerical complexity for software-only playback. Frame- differencing approaches are described since software-only video codecs typically employ them to enhance playback performance. To complement other papers that appear in this session of the Proceedings, we review methods derived from binary pattern image coding since these methods are amenable for software-only playback. In particular, we introduce a novel approach called pixel distribution image coding.

Advanced modulation technology development for earth station demodulator applications. Coded modulation system development

NASA Technical Reports Server (NTRS)

Miller, Susan P.; Kappes, J. Mark; Layer, David H.; Johnson, Peter N.

1990-01-01

A jointly optimized coded modulation system is described which was designed, built, and tested by COMSAT Laboratories for NASA LeRC which provides a bandwidth efficiency of 2 bits/s/Hz at an information rate of 160 Mbit/s. A high speed rate 8/9 encoder with a Viterbi decoder and an Octal PSK modem are used to achieve this. The BER performance is approximately 1 dB from the theoretically calculated value for this system at a BER of 5 E-7 under nominal conditions. The system operates in burst mode for downlink applications and tests have demonstrated very little degradation in performance with frequency and level offset. Unique word miss rate measurements were conducted which demonstrate reliable acquisition at low values of Eb/No. Codec self tests have verified the performance of this subsystem in a stand alone mode. The codec is capable of operation at a 200 Mbit/s information rate as demonstrated using a codec test set which introduces noise digitally. The measured performance is within 0.2 dB of the computer simulated predictions. A gate array implementation of the most time critical element of the high speed Viterbi decoder was completed. This gate array add-compare-select chip significantly reduces the power consumption and improves the manufacturability of the decoder. This chip has general application in the implementation of high speed Viterbi decoders.

New double-byte error-correcting codes for memory systems

NASA Technical Reports Server (NTRS)

Feng, Gui-Liang; Wu, Xinen; Rao, T. R. N.

1996-01-01

Error-correcting or error-detecting codes have been used in the computer industry to increase reliability, reduce service costs, and maintain data integrity. The single-byte error-correcting and double-byte error-detecting (SbEC-DbED) codes have been successfully used in computer memory subsystems. There are many methods to construct double-byte error-correcting (DBEC) codes. In the present paper we construct a class of double-byte error-correcting codes, which are more efficient than those known to be optimum, and a decoding procedure for our codes is also considered.