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 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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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

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.

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.

Fast QC-LDPC code for free space optical communication

NASA Astrophysics Data System (ADS)

Wang, Jin; Zhang, Qi; Udeh, Chinonso Paschal; Wu, Rangzhong

2017-02-01

Free Space Optical (FSO) Communication systems use the atmosphere as a propagation medium. Hence the atmospheric turbulence effects lead to multiplicative noise related with signal intensity. In order to suppress the signal fading induced by multiplicative noise, we propose a fast Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) code for FSO Communication systems. As a linear block code based on sparse matrix, the performances of QC-LDPC is extremely near to the Shannon limit. Currently, the studies on LDPC code in FSO Communications is mainly focused on Gauss-channel and Rayleigh-channel, respectively. In this study, the LDPC code design over atmospheric turbulence channel which is nether Gauss-channel nor Rayleigh-channel is closer to the practical situation. Based on the characteristics of atmospheric channel, which is modeled as logarithmic-normal distribution and K-distribution, we designed a special QC-LDPC code, and deduced the log-likelihood ratio (LLR). An irregular QC-LDPC code for fast coding, of which the rates are variable, is proposed in this paper. The proposed code achieves excellent performance of LDPC codes and can present the characteristics of high efficiency in low rate, stable in high rate and less number of iteration. The result of belief propagation (BP) decoding shows that the bit error rate (BER) obviously reduced as the Signal-to-Noise Ratio (SNR) increased. Therefore, the LDPC channel coding technology can effectively improve the performance of FSO. At the same time, the BER, after decoding reduces with the increase of SNR arbitrarily, and not having error limitation platform phenomenon with error rate slowing down.

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.

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.

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.

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

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

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

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.

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.

LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication.

PubMed

Djordjevic, Ivan B; Arabaci, Murat

2010-11-22

An orbital angular momentum (OAM) based LDPC-coded modulation scheme suitable for use in FSO communication is proposed. We demonstrate that the proposed scheme can operate under strong atmospheric turbulence regime and enable 100 Gb/s optical transmission while employing 10 Gb/s components. Both binary and nonbinary LDPC-coded OAM modulations are studied. In addition to providing better BER performance, the nonbinary LDPC-coded modulation reduces overall decoder complexity and latency. The nonbinary LDPC-coded OAM modulation provides a net coding gain of 9.3 dB at the BER of 10(-8). The maximum-ratio combining scheme outperforms the corresponding equal-gain combining scheme by almost 2.5 dB.

A novel construction scheme of QC-LDPC codes based on the RU algorithm for optical transmission systems

NASA Astrophysics Data System (ADS)

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

2016-03-01

A novel lower-complexity construction scheme of quasi-cyclic low-density parity-check (QC-LDPC) codes for optical transmission systems is proposed based on the structure of the parity-check matrix for the Richardson-Urbanke (RU) algorithm. Furthermore, a novel irregular QC-LDPC(4 288, 4 020) code with high code-rate of 0.937 is constructed by this novel construction scheme. The simulation analyses show that the net coding gain ( NCG) of the novel irregular QC-LDPC(4 288,4 020) code is respectively 2.08 dB, 1.25 dB and 0.29 dB more than those of the classic RS(255, 239) code, the LDPC(32 640, 30 592) code and the irregular QC-LDPC(3 843, 3 603) code at the bit error rate ( BER) of 10-6. The irregular QC-LDPC(4 288, 4 020) code has the lower encoding/decoding complexity compared with the LDPC(32 640, 30 592) code and the irregular QC-LDPC(3 843, 3 603) code. The proposed novel QC-LDPC(4 288, 4 020) code can be more suitable for the increasing development requirements of high-speed optical transmission systems.

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.

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.

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.

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.

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.

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.

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.

Maximum likelihood decoding analysis of Accumulate-Repeat-Accumulate Codes

NASA Technical Reports Server (NTRS)

Abbasfar, Aliazam; Divsalar, Dariush; Yao, Kung

2004-01-01

Repeat-Accumulate (RA) codes are the simplest turbo-like codes that achieve good performance. However, they cannot compete with Turbo codes or low-density parity check codes (LDPC) as far as performance is concerned. The Accumulate Repeat Accumulate (ARA) codes, as a subclass of LDPC codes, are obtained by adding a pre-coder in front of RA codes with puncturing where an accumulator is chosen as a precoder. These codes not only are very simple, but also achieve excellent performance with iterative decoding. In this paper, the performance of these codes with (ML) decoding are analyzed and compared to random codes by very tight bounds. The weight distribution of some simple ARA codes is obtained, and through existing tightest bounds we have shown the ML SNR threshold of ARA codes approaches very closely to the performance of random codes. We have shown that the use of precoder improves the SNR threshold but interleaving gain remains unchanged with respect to RA code with puncturing.

Protograph LDPC Codes for the Erasure Channel

NASA Technical Reports Server (NTRS)

Pollara, Fabrizio; Dolinar, Samuel J.; Divsalar, Dariush

2006-01-01

This viewgraph presentation reviews the use of protograph Low Density Parity Check (LDPC) codes for erasure channels. A protograph is a Tanner graph with a relatively small number of nodes. A "copy-and-permute" operation can be applied to the protograph to obtain larger derived graphs of various sizes. For very high code rates and short block sizes, a low asymptotic threshold criterion is not the best approach to designing LDPC codes. Simple protographs with much regularity and low maximum node degrees appear to be the best choices Quantized-rateless protograph LDPC codes can be built by careful design of the protograph such that multiple puncturing patterns will still permit message passing decoding to proceed

The application of LDPC code in MIMO-OFDM system

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

RETRACTED — PMD mitigation through interleaving LDPC codes with polarization scramblers

NASA Astrophysics Data System (ADS)

Han, Dahai; Chen, Haoran; Xi, Lixia

2012-11-01

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

PMD mitigation through interleaving LDPC codes with polarization scramblers

NASA Astrophysics Data System (ADS)

Han, Dahai; Chen, Haoran; Xi, Lixia

2013-09-01

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

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.

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

NASA Astrophysics Data System (ADS)

Andriamanalimanana, Bruno R.

2004-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Structured Low-Density Parity-Check Codes with Bandwidth Efficient Modulation

NASA Technical Reports Server (NTRS)

Cheng, Michael K.; Divsalar, Dariush; Duy, Stephanie

2009-01-01

In this work, we study the performance of structured Low-Density Parity-Check (LDPC) Codes together with bandwidth efficient modulations. We consider protograph-based LDPC codes that facilitate high-speed hardware implementations and have minimum distances that grow linearly with block sizes. We cover various higher- order modulations such as 8-PSK, 16-APSK, and 16-QAM. During demodulation, a demapper transforms the received in-phase and quadrature samples into reliability information that feeds the binary LDPC decoder. We will compare various low-complexity demappers and provide simulation results for assorted coded-modulation combinations on the additive white Gaussian noise and independent Rayleigh fading channels.

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.

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.

Information-reduced Carrier Synchronization of Iterative Decoded BPSK and QPSK using Soft Decision (Extrinsic) Feedback

NASA Technical Reports Server (NTRS)

Simon, Marvin; Valles, Esteban; Jones, Christopher

2008-01-01

This paper addresses the carrier-phase estimation problem under low SNR conditions as are typical of turbo- and LDPC-coded applications. In previous publications by the first author, closed-loop carrier synchronization schemes for error-correction coded BPSK and QPSK modulation were proposed that were based on feeding back hard data decisions at the input of the loop, the purpose being to remove the modulation prior to attempting to track the carrier phase as opposed to the more conventional decision-feedback schemes that incorporate such feedback inside the loop. In this paper, we consider an alternative approach wherein the extrinsic soft information from the iterative decoder of turbo or LDPC codes is instead used as the feedback.

Cooperative optimization and their application in LDPC codes

NASA Astrophysics Data System (ADS)

Chen, Ke; Rong, Jian; Zhong, Xiaochun

2008-10-01

Cooperative optimization is a new way for finding global optima of complicated functions of many variables. The proposed algorithm is a class of message passing algorithms and has solid theory foundations. It can achieve good coding gains over the sum-product algorithm for LDPC codes. For (6561, 4096) LDPC codes, the proposed algorithm can achieve 2.0 dB gains over the sum-product algorithm at BER of 4×10-7. The decoding complexity of the proposed algorithm is lower than the sum-product algorithm can do; furthermore, the former can achieve much lower error floor than the latter can do after the Eb / No is higher than 1.8 dB.

45 Gb/s low complexity optical front-end for soft-decision LDPC decoders.

PubMed

Sakib, Meer Nazmus; Moayedi, Monireh; Gross, Warren J; Liboiron-Ladouceur, Odile

2012-07-30

In this paper a low complexity and energy efficient 45 Gb/s soft-decision optical front-end to be used with soft-decision low-density parity-check (LDPC) decoders is demonstrated. The results show that the optical front-end exhibits a net coding gain of 7.06 and 9.62 dB for post forward error correction bit error rate of 10(-7) and 10(-12) for long block length LDPC(32768,26803) code. The performance over a hard decision front-end is 1.9 dB for this code. It is shown that the soft-decision circuit can also be used as a 2-bit flash type analog-to-digital converter (ADC), in conjunction with equalization schemes. At bit rate of 15 Gb/s using RS(255,239), LDPC(672,336), (672, 504), (672, 588), and (1440, 1344) used with a 6-tap finite impulse response (FIR) equalizer will result in optical power savings of 3, 5, 7, 9.5 and 10.5 dB, respectively. The 2-bit flash ADC consumes only 2.71 W at 32 GSamples/s. At 45 GSamples/s the power consumption is estimated to be 4.95 W.

Accumulate Repeat Accumulate Coded Modulation

NASA Technical Reports Server (NTRS)

Abbasfar, Aliazam; Divsalar, Dariush; Yao, Kung

2004-01-01

In this paper we propose an innovative coded modulation scheme called 'Accumulate Repeat Accumulate Coded Modulation' (ARA coded modulation). This class of codes can be viewed as serial turbo-like codes, or as a subclass of Low Density Parity Check (LDPC) codes that are combined with high level modulation. Thus at the decoder belief propagation can be used for iterative decoding of ARA coded modulation on a graph, provided a demapper transforms the received in-phase and quadrature samples to reliability of the bits.

Encoders for block-circulant LDPC codes

NASA Technical Reports Server (NTRS)

Andrews, Kenneth; Dolinar, Sam; Thorpe, Jeremy

2005-01-01

In this paper, we present two encoding methods for block-circulant LDPC codes. The first is an iterative encoding method based on the erasure decoding algorithm, and the computations required are well organized due to the block-circulant structure of the parity check matrix. The second method uses block-circulant generator matrices, and the encoders are very similar to those for recursive convolutional codes. Some encoders of the second type have been implemented in a small Field Programmable Gate Array (FPGA) and operate at 100 Msymbols/second.

Study regarding the density evolution of messages and the characteristic functions associated of a LDPC code

NASA Astrophysics Data System (ADS)

Drăghici, S.; Proştean, O.; Răduca, E.; Haţiegan, C.; Hălălae, I.; Pădureanu, I.; Nedeloni, M.; (Barboni Haţiegan, L.

2017-01-01

In this paper a method with which a set of characteristic functions are associated to a LDPC code is shown and also functions that represent the evolution density of messages that go along the edges of a Tanner graph. Graphic representations of the density evolution are shown respectively the study and simulation of likelihood threshold that render asymptotic boundaries between which there are decodable codes were made using MathCad V14 software.

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.

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

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.

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.

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.

Fixed-point Design of the Lattice-reduction-aided Iterative Detection and Decoding Receiver for Coded MIMO Systems

DTIC Science & Technology

2011-01-01

reliability, e.g., Turbo Codes [2] and Low Density Parity Check ( LDPC ) codes [3]. The challenge to apply both MIMO and ECC into wireless systems is on...REPORT Fixed-point Design of theLattice-reduction-aided Iterative Detection andDecoding Receiver for Coded MIMO Systems 14. ABSTRACT 16. SECURITY...illustrates the performance of coded LR aided detectors. 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND SUBTITLE 13. SUPPLEMENTARY NOTES The views, opinions

Comparison of soft-input-soft-output detection methods for dual-polarized quadrature duobinary system

NASA Astrophysics Data System (ADS)

Chang, Chun; Huang, Benxiong; Xu, Zhengguang; Li, Bin; Zhao, Nan

2018-02-01

Three soft-input-soft-output (SISO) detection methods for dual-polarized quadrature duobinary (DP-QDB), including maximum-logarithmic-maximum-a-posteriori-probability-algorithm (Max-log-MAP)-based detection, soft-output-Viterbi-algorithm (SOVA)-based detection, and a proposed SISO detection, which can all be combined with SISO decoding, are presented. The three detection methods are investigated at 128 Gb/s in five-channel wavelength-division-multiplexing uncoded and low-density-parity-check (LDPC) coded DP-QDB systems by simulations. Max-log-MAP-based detection needs the returning-to-initial-states (RTIS) process despite having the best performance. When the LDPC code with a code rate of 0.83 is used, the detecting-and-decoding scheme with the SISO detection does not need RTIS and has better bit error rate (BER) performance than the scheme with SOVA-based detection. The former can reduce the optical signal-to-noise ratio (OSNR) requirement (at BER=10-5) by 2.56 dB relative to the latter. The application of the SISO iterative detection in LDPC-coded DP-QDB systems makes a good trade-off between requirements on transmission efficiency, OSNR requirement, and transmission distance, compared with the other two SISO methods.

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 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 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.

Scalable video transmission over Rayleigh fading channels using LDPC codes

NASA Astrophysics Data System (ADS)

Bansal, Manu; Kondi, Lisimachos P.

2005-03-01

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

Statistical mechanics of broadcast channels using low-density parity-check codes.

PubMed

Nakamura, Kazutaka; Kabashima, Yoshiyuki; Morelos-Zaragoza, Robert; Saad, David

2003-03-01

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a degraded broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple time sharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based time sharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the time sharing limit.

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.

High-efficiency reconciliation for continuous variable quantum key distribution

NASA Astrophysics Data System (ADS)

Bai, Zengliang; Yang, Shenshen; Li, Yongmin

2017-04-01

Quantum key distribution (QKD) is the most mature application of quantum information technology. Information reconciliation is a crucial step in QKD and significantly affects the final secret key rates shared between two legitimate parties. We analyze and compare various construction methods of low-density parity-check (LDPC) codes and design high-performance irregular LDPC codes with a block length of 106. Starting from these good codes and exploiting the slice reconciliation technique based on multilevel coding and multistage decoding, we realize high-efficiency Gaussian key reconciliation with efficiency higher than 95% for signal-to-noise ratios above 1. Our demonstrated method can be readily applied in continuous variable QKD.

Short-Block Protograph-Based LDPC Codes

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Dolinar, Samuel; Jones, Christopher

2010-01-01

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

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

Error Correction using Quantum Quasi-Cyclic Low-Density Parity-Check(LDPC) Codes

NASA Astrophysics Data System (ADS)

Jing, Lin; Brun, Todd; Quantum Research Team

Quasi-cyclic LDPC codes can approach the Shannon capacity and have efficient decoders. Manabu Hagiwara et al., 2007 presented a method to calculate parity check matrices with high girth. Two distinct, orthogonal matrices Hc and Hd are used. Using submatrices obtained from Hc and Hd by deleting rows, we can alter the code rate. The submatrix of Hc is used to correct Pauli X errors, and the submatrix of Hd to correct Pauli Z errors. We simulated this system for depolarizing noise on USC's High Performance Computing Cluster, and obtained the block error rate (BER) as a function of the error weight and code rate. From the rates of uncorrectable errors under different error weights we can extrapolate the BER to any small error probability. Our results show that this code family can perform reasonably well even at high code rates, thus considerably reducing the overhead compared to concatenated and surface codes. This makes these codes promising as storage blocks in fault-tolerant quantum computation. Error Correction using Quantum Quasi-Cyclic Low-Density Parity-Check(LDPC) Codes.

Nonlinear Demodulation and Channel Coding in EBPSK Scheme

PubMed Central

Chen, Xianqing; Wu, Lenan

2012-01-01

The extended binary phase shift keying (EBPSK) is an efficient modulation technique, and a special impacting filter (SIF) is used in its demodulator to improve the bit error rate (BER) performance. However, the conventional threshold decision cannot achieve the optimum performance, and the SIF brings more difficulty in obtaining the posterior probability for LDPC decoding. In this paper, we concentrate not only on reducing the BER of demodulation, but also on providing accurate posterior probability estimates (PPEs). A new approach for the nonlinear demodulation based on the support vector machine (SVM) classifier is introduced. The SVM method which selects only a few sampling points from the filter output was used for getting PPEs. The simulation results show that the accurate posterior probability can be obtained with this method and the BER performance can be improved significantly by applying LDPC codes. Moreover, we analyzed the effect of getting the posterior probability with different methods and different sampling rates. We show that there are more advantages of the SVM method under bad condition and it is less sensitive to the sampling rate than other methods. Thus, SVM is an effective method for EBPSK demodulation and getting posterior probability for LDPC decoding. PMID:23213281

Nonlinear demodulation and channel coding in EBPSK scheme.

PubMed

Chen, Xianqing; Wu, Lenan

2012-01-01

The extended binary phase shift keying (EBPSK) is an efficient modulation technique, and a special impacting filter (SIF) is used in its demodulator to improve the bit error rate (BER) performance. However, the conventional threshold decision cannot achieve the optimum performance, and the SIF brings more difficulty in obtaining the posterior probability for LDPC decoding. In this paper, we concentrate not only on reducing the BER of demodulation, but also on providing accurate posterior probability estimates (PPEs). A new approach for the nonlinear demodulation based on the support vector machine (SVM) classifier is introduced. The SVM method which selects only a few sampling points from the filter output was used for getting PPEs. The simulation results show that the accurate posterior probability can be obtained with this method and the BER performance can be improved significantly by applying LDPC codes. Moreover, we analyzed the effect of getting the posterior probability with different methods and different sampling rates. We show that there are more advantages of the SVM method under bad condition and it is less sensitive to the sampling rate than other methods. Thus, SVM is an effective method for EBPSK demodulation and getting posterior probability for LDPC decoding.

Information rates of probabilistically shaped coded modulation for a multi-span fiber-optic communication system with 64QAM

NASA Astrophysics Data System (ADS)

Fehenberger, Tobias

2018-02-01

This paper studies probabilistic shaping in a multi-span wavelength-division multiplexing optical fiber system with 64-ary quadrature amplitude modulation (QAM) input. In split-step fiber simulations and via an enhanced Gaussian noise model, three figures of merit are investigated, which are signal-to-noise ratio (SNR), achievable information rate (AIR) for capacity-achieving forward error correction (FEC) with bit-metric decoding, and the information rate achieved with low-density parity-check (LDPC) FEC. For the considered system parameters and different shaped input distributions, shaping is found to decrease the SNR by 0.3 dB yet simultaneously increases the AIR by up to 0.4 bit per 4D-symbol. The information rates of LDPC-coded modulation with shaped 64QAM input are improved by up to 0.74 bit per 4D-symbol, which is larger than the shaping gain when considering AIRs. This increase is attributed to the reduced coding gap of the higher-rate code that is used for decoding the nonuniform QAM input.

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.

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

PubMed

Djordjevic, Ivan B; Wang, Ting

2014-07-14

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

A rate-compatible family of protograph-based LDPC codes built by expurgation and lengthening

NASA Technical Reports Server (NTRS)

Dolinar, Sam

2005-01-01

We construct a protograph-based rate-compatible family of low-density parity-check codes that cover a very wide range of rates from 1/2 to 16/17, perform within about 0.5 dB of their capacity limits for all rates, and can be decoded conveniently and efficiently with a common hardware implementation.

The serial message-passing schedule for LDPC decoding algorithms

NASA Astrophysics Data System (ADS)

Liu, Mingshan; Liu, Shanshan; Zhou, Yuan; Jiang, Xue

2015-12-01

The conventional message-passing schedule for LDPC decoding algorithms is the so-called flooding schedule. It has the disadvantage that the updated messages cannot be used until next iteration, thus reducing the convergence speed . In this case, the Layered Decoding algorithm (LBP) based on serial message-passing schedule is proposed. In this paper the decoding principle of LBP algorithm is briefly introduced, and then proposed its two improved algorithms, the grouped serial decoding algorithm (Grouped LBP) and the semi-serial decoding algorithm .They can improve LBP algorithm's decoding speed while maintaining a good decoding performance.

Joint Carrier-Phase Synchronization and LDPC Decoding

NASA Technical Reports Server (NTRS)

Simon, Marvin; Valles, Esteban

2009-01-01

A method has been proposed to increase the degree of synchronization of a radio receiver with the phase of a suppressed carrier signal modulated with a binary- phase-shift-keying (BPSK) or quaternary- phase-shift-keying (QPSK) signal representing a low-density parity-check (LDPC) code. This method is an extended version of the method described in Using LDPC Code Constraints to Aid Recovery of Symbol Timing (NPO-43112), NASA Tech Briefs, Vol. 32, No. 10 (October 2008), page 54. Both methods and the receiver architectures in which they 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. The proposed method calls for the use of what is known in the art as soft decision feedback to remove the modulation from a replica of the incoming signal prior to feeding this replica to a phase-locked loop (PLL) or other carrier-tracking stage in the receiver. Soft decision feedback refers to suitably processed versions of intermediate results of iterative computations involved in the LDPC decoding process. Unlike a related prior method in which hard decision feedback (the final sequence of decoded symbols) is used to remove the modulation, the proposed method does not require estimation of the decoder error probability. In a basic digital implementation of the proposed method, the incoming signal (having carrier phase theta theta (sub c) plus noise would first be converted to inphase (I) and quadrature (Q) baseband signals by mixing it with I and Q signals at the carrier frequency [wc/(2 pi)] generated by a local oscillator. The resulting demodulated signals would be processed through one-symbol-period integrate and- dump filters, the outputs of which would be sampled and held, then multiplied by a soft-decision version of the baseband modulated signal. The resulting I and Q products consist of terms proportional to the cosine and sine of the carrier phase cc as well as correlated noise components. These products would be fed as inputs to a digital PLL that would include a number-controlled oscillator (NCO), which provides an estimate of the carrier phase, theta(sub c).

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.

Future capabilities for the Deep Space Network

NASA Technical Reports Server (NTRS)

Berner, J. B.; Bryant, S. H.; Andrews, K. S.

2004-01-01

This paper will look at three new capabilities that are in different stages of development. First, turbo decoding, which provides improved telemetry performance for data rates up to about 1 Mbps, will be discussed. Next, pseudo-noise ranging will be presented. Pseudo-noise ranging has several advantages over the current sequential ranging, anmely easier operations, improved performance, and the capability to be used in a regenerative implementation on a spacecraft. Finally, Low Density Parity Check decoding will be discussed. LDPC codes can provide performance that matches or slightly exceed turbo codes, but are designed for use in the 10 Mbps range.

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.

Performance analysis of LDPC codes on OOK terahertz wireless channels

NASA Astrophysics Data System (ADS)

Chun, Liu; Chang, Wang; Jun-Cheng, Cao

2016-02-01

Atmospheric absorption, scattering, and scintillation are the major causes to deteriorate the transmission quality of terahertz (THz) wireless communications. An error control coding scheme based on low density parity check (LDPC) codes with soft decision decoding algorithm is proposed to improve the bit-error-rate (BER) performance of an on-off keying (OOK) modulated THz signal through atmospheric channel. The THz wave propagation characteristics and channel model in atmosphere is set up. Numerical simulations validate the great performance of LDPC codes against the atmospheric fading and demonstrate the huge potential in future ultra-high speed beyond Gbps THz communications. Project supported by the National Key Basic Research Program of China (Grant No. 2014CB339803), the National High Technology Research and Development Program of China (Grant No. 2011AA010205), the National Natural Science Foundation of China (Grant Nos. 61131006, 61321492, and 61204135), the Major National Development Project of Scientific Instrument and Equipment (Grant No. 2011YQ150021), the National Science and Technology Major Project (Grant No. 2011ZX02707), the International Collaboration and Innovation Program on High Mobility Materials Engineering of the Chinese Academy of Sciences, and the Shanghai Municipal Commission of Science and Technology (Grant No. 14530711300).

Rate-Compatible LDPC Codes with Linear Minimum Distance

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Jones, Christopher; Dolinar, Samuel

2009-01-01

A recently developed method of constructing protograph-based low-density parity-check (LDPC) codes provides for low iterative decoding thresholds and minimum distances proportional to block sizes, and can be used for various code rates. A code constructed by this method can have either fixed input block size or fixed output block size and, in either case, provides rate compatibility. The method comprises two submethods: one for fixed input block size and one for fixed output block size. The first mentioned submethod is useful for applications in which there are requirements for rate-compatible codes that have fixed input block sizes. These are codes in which only the numbers of parity bits are allowed to vary. The fixed-output-blocksize submethod is useful for applications in which framing constraints are imposed on the physical layers of affected communication systems. An example of such a system is one that conforms to one of many new wireless-communication standards that involve the use of orthogonal frequency-division modulation

System on a Chip Real-Time Emulation (SOCRE)

DTIC Science & Technology

2006-09-01

code ) i Table of Contents Preface...emulation platform included LDPC decoders, A/V and radio applications Port BEE flow to Emulation Platforms, SOC Technologies One of the key tasks of the...Once the design has been described within Simulink, the designer runs the BEE design flow within Matlab using the bee_xps interface. At this point

Improving soft FEC performance for higher-order modulations via optimized bit channel mappings.

PubMed

Häger, Christian; Amat, Alexandre Graell I; Brännström, Fredrik; Alvarado, Alex; Agrell, Erik

2014-06-16

Soft forward error correction with higher-order modulations is often implemented in practice via the pragmatic bit-interleaved coded modulation paradigm, where a single binary code is mapped to a nonbinary modulation. In this paper, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed fiber-optical system without optical inline dispersion compensation. Our focus is on protograph-based low-density parity-check (LDPC) codes which allow for an efficient hardware implementation, suitable for high-speed optical communications. The optimization is applied to the AR4JA protograph family, and further extended to protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full field simulations via the split-step Fourier method are used to verify the analysis. The results show performance gains of up to 0.25 dB, which translate into a possible extension of the transmission reach by roughly up to 8%, without significantly increasing the system complexity.

A Low-Complexity and High-Performance 2D Look-Up Table for LDPC Hardware Implementation

NASA Astrophysics Data System (ADS)

Chen, Jung-Chieh; Yang, Po-Hui; Lain, Jenn-Kaie; Chung, Tzu-Wen

In this paper, we propose a low-complexity, high-efficiency two-dimensional look-up table (2D LUT) for carrying out the sum-product algorithm in the decoding of low-density parity-check (LDPC) codes. Instead of employing adders for the core operation when updating check node messages, in the proposed scheme, the main term and correction factor of the core operation are successfully merged into a compact 2D LUT. Simulation results indicate that the proposed 2D LUT not only attains close-to-optimal bit error rate performance but also enjoys a low complexity advantage that is suitable for hardware implementation.

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).

High performance reconciliation for continuous-variable quantum key distribution with LDPC code

NASA Astrophysics Data System (ADS)

Lin, Dakai; Huang, Duan; Huang, Peng; Peng, Jinye; Zeng, Guihua

2015-03-01

Reconciliation is a significant procedure in a continuous-variable quantum key distribution (CV-QKD) system. It is employed to extract secure secret key from the resulted string through quantum channel between two users. However, the efficiency and the speed of previous reconciliation algorithms are low. These problems limit the secure communication distance and the secure key rate of CV-QKD systems. In this paper, we proposed a high-speed reconciliation algorithm through employing a well-structured decoding scheme based on low density parity-check (LDPC) code. The complexity of the proposed algorithm is reduced obviously. By using a graphics processing unit (GPU) device, our method may reach a reconciliation speed of 25 Mb/s for a CV-QKD system, which is currently the highest level and paves the way to high-speed CV-QKD.

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.

Accumulate-Repeat-Accumulate-Accumulate Codes

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Dolinar, Samuel; Thorpe, Jeremy

2007-01-01

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

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).

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

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

Adaptive channel estimation for soft decision decoding over non-Gaussian optical channel

NASA Astrophysics Data System (ADS)

Xiang, Jing-song; Miao, Tao-tao; Huang, Sheng; Liu, Huan-lin

2016-10-01

An adaptive priori likelihood ratio (LLR) estimation method is proposed over non-Gaussian channel in the intensity modulation/direct detection (IM/DD) optical communication systems. Using the nonparametric histogram and the weighted least square linear fitting in the tail regions, the LLR is estimated and used for the soft decision decoding of the low-density parity-check (LDPC) codes. This method can adapt well to the three main kinds of intensity modulation/direct detection (IM/DD) optical channel, i.e., the chi-square channel, the Webb-Gaussian channel and the additive white Gaussian noise (AWGN) channel. The performance penalty of channel estimation is neglected.

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.

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.

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.

A novel concatenated code based on the improved SCG-LDPC code for optical transmission systems

NASA Astrophysics Data System (ADS)

Yuan, Jian-guo; Xie, Ya; Wang, Lin; Huang, Sheng; Wang, Yong

2013-01-01

Based on the optimization and improvement for the construction method of systematically constructed Gallager (SCG) (4, k) code, a novel SCG low density parity check (SCG-LDPC)(3969, 3720) code to be suitable for optical transmission systems is constructed. The novel SCG-LDPC (6561,6240) code with code rate of 95.1% is constructed by increasing the length of SCG-LDPC (3969,3720) code, and in a way, the code rate of LDPC codes can better meet the high requirements of optical transmission systems. And then the novel concatenated code is constructed by concatenating SCG-LDPC(6561,6240) code and BCH(127,120) code with code rate of 94.5%. The simulation results and analyses show that the net coding gain (NCG) of BCH(127,120)+SCG-LDPC(6561,6240) concatenated code is respectively 2.28 dB and 0.48 dB more than those of the classic RS(255,239) code and SCG-LDPC(6561,6240) code at the bit error rate (BER) of 10-7.

Performance of Low-Density Parity-Check Coded Modulation

NASA Technical Reports Server (NTRS)

Hamkins, Jon

2010-01-01

This paper reports the simulated performance of each of the nine accumulate-repeat-4-jagged-accumulate (AR4JA) low-density parity-check (LDPC) codes [3] when used in conjunction with binary phase-shift-keying (BPSK), quadrature PSK (QPSK), 8-PSK, 16-ary amplitude PSK (16- APSK), and 32-APSK.We also report the performance under various mappings of bits to modulation symbols, 16-APSK and 32-APSK ring scalings, log-likelihood ratio (LLR) approximations, and decoder variations. One of the simple and well-performing LLR approximations can be expressed in a general equation that applies to all of the modulation types.

Capacity achieving nonbinary LDPC coded non-uniform shaping modulation for adaptive optical communications.

PubMed

Lin, Changyu; Zou, Ding; Liu, Tao; Djordjevic, Ivan B

2016-08-08

A mutual information inspired nonbinary coded modulation design with non-uniform shaping is proposed. Instead of traditional power of two signal constellation sizes, we design 5-QAM, 7-QAM and 9-QAM constellations, which can be used in adaptive optical networks. The non-uniform shaping and LDPC code rate are jointly considered in the design, which results in a better performance scheme for the same SNR values. The matched nonbinary (NB) LDPC code is used for this scheme, which further improves the coding gain and the overall performance. We analyze both coding performance and system SNR performance. We show that the proposed NB LDPC-coded 9-QAM has more than 2dB gain in symbol SNR compared to traditional LDPC-coded star-8-QAM. On the other hand, the proposed NB LDPC-coded 5-QAM and 7-QAM have even better performance than LDPC-coded QPSK.

Evaluation of four-dimensional nonbinary LDPC-coded modulation for next-generation long-haul optical transport networks.

PubMed

Zhang, Yequn; Arabaci, Murat; Djordjevic, Ivan B

2012-04-09

Leveraging the advanced coherent optical communication technologies, this paper explores the feasibility of using four-dimensional (4D) nonbinary LDPC-coded modulation (4D-NB-LDPC-CM) schemes for long-haul transmission in future optical transport networks. In contrast to our previous works on 4D-NB-LDPC-CM which considered amplified spontaneous emission (ASE) noise as the dominant impairment, this paper undertakes transmission in a more realistic optical fiber transmission environment, taking into account impairments due to dispersion effects, nonlinear phase noise, Kerr nonlinearities, and stimulated Raman scattering in addition to ASE noise. We first reveal the advantages of using 4D modulation formats in LDPC-coded modulation instead of conventional two-dimensional (2D) modulation formats used with polarization-division multiplexing (PDM). Then we demonstrate that 4D LDPC-coded modulation schemes with nonbinary LDPC component codes significantly outperform not only their conventional PDM-2D counterparts but also the corresponding 4D bit-interleaved LDPC-coded modulation (4D-BI-LDPC-CM) schemes, which employ binary LDPC codes as component codes. We also show that the transmission reach improvement offered by the 4D-NB-LDPC-CM over 4D-BI-LDPC-CM increases as the underlying constellation size and hence the spectral efficiency of transmission increases. Our results suggest that 4D-NB-LDPC-CM can be an excellent candidate for long-haul transmission in next-generation optical networks.

High-Throughput Bit-Serial LDPC Decoder LSI Based on Multiple-Valued Asynchronous Interleaving

NASA Astrophysics Data System (ADS)

Onizawa, Naoya; Hanyu, Takahiro; Gaudet, Vincent C.

This paper presents a high-throughput bit-serial low-density parity-check (LDPC) decoder that uses an asynchronous interleaver. Since consecutive log-likelihood message values on the interleaver are similar, node computations are continuously performed by using the most recently arrived messages without significantly affecting bit-error rate (BER) performance. In the asynchronous interleaver, each message's arrival rate is based on the delay due to the wire length, so that the decoding throughput is not restricted by the worst-case latency, which results in a higher average rate of computation. Moreover, the use of a multiple-valued data representation makes it possible to multiplex control signals and data from mutual nodes, thus minimizing the number of handshaking steps in the asynchronous interleaver and eliminating the clock signal entirely. As a result, the decoding throughput becomes 1.3 times faster than that of a bit-serial synchronous decoder under a 90nm CMOS technology, at a comparable BER.

Ensemble Weight Enumerators for Protograph LDPC Codes

NASA Technical Reports Server (NTRS)

Divsalar, Dariush

2006-01-01

Recently LDPC codes with projected graph, or protograph structures have been proposed. In this paper, finite length ensemble weight enumerators for LDPC codes with protograph structures are obtained. Asymptotic results are derived as the block size goes to infinity. In particular we are interested in obtaining ensemble average weight enumerators for protograph LDPC codes which have minimum distance that grows linearly with block size. As with irregular ensembles, linear minimum distance property is sensitive to the proportion of degree-2 variable nodes. In this paper the derived results on ensemble weight enumerators show that linear minimum distance condition on degree distribution of unstructured irregular LDPC codes is a sufficient but not a necessary condition for protograph LDPC codes.

Design of ACM system based on non-greedy punctured LDPC codes

NASA Astrophysics Data System (ADS)

Lu, Zijun; Jiang, Zihong; Zhou, Lin; He, Yucheng

2017-08-01

In this paper, an adaptive coded modulation (ACM) scheme based on rate-compatible LDPC (RC-LDPC) codes was designed. The RC-LDPC codes were constructed by a non-greedy puncturing method which showed good performance in high code rate region. Moreover, the incremental redundancy scheme of LDPC-based ACM system over AWGN channel was proposed. By this scheme, code rates vary from 2/3 to 5/6 and the complication of the ACM system is lowered. Simulations show that more and more obvious coding gain can be obtained by the proposed ACM system with higher throughput.

FPGA-based rate-adaptive LDPC-coded modulation for the next generation of optical communication systems.

PubMed

Zou, Ding; Djordjevic, Ivan B

2016-09-05

In this paper, we propose a rate-adaptive FEC scheme based on LDPC codes together with its software reconfigurable unified FPGA architecture. By FPGA emulation, we demonstrate that the proposed class of rate-adaptive LDPC codes based on shortening with an overhead from 25% to 42.9% provides a coding gain ranging from 13.08 dB to 14.28 dB at a post-FEC BER of 10^-15 for BPSK transmission. In addition, the proposed rate-adaptive LDPC coding combined with higher-order modulations have been demonstrated including QPSK, 8-QAM, 16-QAM, 32-QAM, and 64-QAM, which covers a wide range of signal-to-noise ratios. Furthermore, we apply the unequal error protection by employing different LDPC codes on different bits in 16-QAM and 64-QAM, which results in additional 0.5dB gain compared to conventional LDPC coded modulation with the same code rate of corresponding LDPC code.

LDPC coded OFDM over the atmospheric turbulence channel.

PubMed

Djordjevic, Ivan B; Vasic, Bane; Neifeld, Mark A

2007-05-14

Low-density parity-check (LDPC) coded optical orthogonal frequency division multiplexing (OFDM) is shown to significantly outperform LDPC coded on-off keying (OOK) over the atmospheric turbulence channel in terms of both coding gain and spectral efficiency. In the regime of strong turbulence at a bit-error rate of 10(-5), the coding gain improvement of the LDPC coded single-side band unclipped-OFDM system with 64 sub-carriers is larger than the coding gain of the LDPC coded OOK system by 20.2 dB for quadrature-phase-shift keying (QPSK) and by 23.4 dB for binary-phase-shift keying (BPSK).

Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks.

PubMed

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

2010-02-01

In order to achieve high-speed transmission over optical transport networks (OTNs) and maximize its throughput, we propose using a rate-adaptive polarization-multiplexed coded multilevel modulation with coherent detection based on component non-binary quasi-cyclic (QC) LDPC codes. Compared to prior-art bit-interleaved LDPC-coded modulation (BI-LDPC-CM) scheme, the proposed non-binary LDPC-coded modulation (NB-LDPC-CM) scheme not only reduces latency due to symbol- instead of bit-level processing but also provides either impressive reduction in computational complexity or striking improvements in coding gain depending on the constellation size. As the paper presents, compared to its prior-art binary counterpart, the proposed NB-LDPC-CM scheme addresses the needs of future OTNs, which are achieving the target BER performance and providing maximum possible throughput both over the entire lifetime of the OTN, better.

High performance and cost effective CO-OFDM system aided by polar code.

PubMed

Liu, Ling; Xiao, Shilin; Fang, Jiafei; Zhang, Lu; Zhang, Yunhao; Bi, Meihua; Hu, Weisheng

2017-02-06

A novel polar coded coherent optical orthogonal frequency division multiplexing (CO-OFDM) system is proposed and demonstrated through experiment for the first time. The principle of a polar coded CO-OFDM signal is illustrated theoretically and the suitable polar decoding method is discussed. Results show that the polar coded CO-OFDM signal achieves a net coding gain (NCG) of more than 10 dB at bit error rate (BER) of 10^-3 over 25-Gb/s 480-km transmission in comparison with conventional CO-OFDM. Also, compared to the 25-Gb/s low-density parity-check (LDPC) coded CO-OFDM 160-km system, the polar code provides a NCG of 0.88 dB @BER = 10^-3. Moreover, the polar code can relieve the laser linewidth requirement massively to get a more cost-effective CO-OFDM system.

On the photonic implementation of universal quantum gates, bell states preparation circuit and quantum LDPC encoders and decoders based on directional couplers and HNLF.

PubMed

Djordjevic, Ivan B

2010-04-12

The Bell states preparation circuit is a basic circuit required in quantum teleportation. We describe how to implement it in all-fiber technology. The basic building blocks for its implementation are directional couplers and highly nonlinear optical fiber (HNLF). Because the quantum information processing is based on delicate superposition states, it is sensitive to quantum errors. In order to enable fault-tolerant quantum computing the use of quantum error correction is unavoidable. We show how to implement in all-fiber technology encoders and decoders for sparse-graph quantum codes, and provide an illustrative example to demonstrate this implementation. We also show that arbitrary set of universal quantum gates can be implemented based on directional couplers and HNLFs.

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

Construction of a new regular LDPC code for optical transmission systems

NASA Astrophysics Data System (ADS)

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

2013-05-01

A novel construction method of the check matrix for the regular low density parity check (LDPC) code is proposed. The novel regular systematically constructed Gallager (SCG)-LDPC(3969,3720) code with the code rate of 93.7% and the redundancy of 6.69% is constructed. The simulation results show that the net coding gain (NCG) and the distance from the Shannon limit of the novel SCG-LDPC(3969,3720) code can respectively be improved by about 1.93 dB and 0.98 dB at the bit error rate (BER) of 10-8, compared with those of the classic RS(255,239) code in ITU-T G.975 recommendation and the LDPC(32640,30592) code in ITU-T G.975.1 recommendation with the same code rate of 93.7% and the same redundancy of 6.69%. Therefore, the proposed novel regular SCG-LDPC(3969,3720) code has excellent performance, and is more suitable for high-speed long-haul optical transmission systems.

Construction method of QC-LDPC codes based on multiplicative group of finite field in optical communication

NASA Astrophysics Data System (ADS)

Huang, Sheng; Ao, Xiang; Li, Yuan-yuan; Zhang, Rui

2016-09-01

In order to meet the needs of high-speed development of optical communication system, a construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes based on multiplicative group of finite field is proposed. The Tanner graph of parity check matrix of the code constructed by this method has no cycle of length 4, and it can make sure that the obtained code can get a good distance property. Simulation results show that when the bit error rate ( BER) is 10-6, in the same simulation environment, the net coding gain ( NCG) of the proposed QC-LDPC(3 780, 3 540) code with the code rate of 93.7% in this paper is improved by 2.18 dB and 1.6 dB respectively compared with those of the RS(255, 239) code in ITU-T G.975 and the LDPC(3 2640, 3 0592) code in ITU-T G.975.1. In addition, the NCG of the proposed QC-LDPC(3 780, 3 540) code is respectively 0.2 dB and 0.4 dB higher compared with those of the SG-QC-LDPC(3 780, 3 540) code based on the two different subgroups in finite field and the AS-QC-LDPC(3 780, 3 540) code based on the two arbitrary sets of a finite field. Thus, the proposed QC-LDPC(3 780, 3 540) code in this paper can be well applied in optical communication systems.

Finite-connectivity spin-glass phase diagrams and low-density parity check codes.

PubMed

Migliorini, Gabriele; Saad, David

2006-02-01

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate , an RS critical transition point at while the critical RSB transition point is located at , to be compared with the corresponding Shannon bound . For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed.

FPGA implementation of concatenated non-binary QC-LDPC codes for high-speed optical transport.

PubMed

Zou, Ding; Djordjevic, Ivan B

2015-06-01

In this paper, we propose a soft-decision-based FEC scheme that is the concatenation of a non-binary LDPC code and hard-decision FEC code. The proposed NB-LDPC + RS with overhead of 27.06% provides a superior NCG of 11.9dB at a post-FEC BER of 10^-15. As a result, the proposed NB-LDPC codes represent the strong FEC candidate of soft-decision FEC for beyond 100Gb/s optical transmission systems.

Experimental research and comparison of LDPC and RS channel coding in ultraviolet communication systems.

PubMed

Wu, Menglong; Han, Dahai; Zhang, Xiang; Zhang, Feng; Zhang, Min; Yue, Guangxin

2014-03-10

We have implemented a modified Low-Density Parity-Check (LDPC) codec algorithm in ultraviolet (UV) communication system. Simulations are conducted with measured parameters to evaluate the LDPC-based UV system performance. Moreover, LDPC (960, 480) and RS (18, 10) are implemented and experimented via a non-line-of-sight (NLOS) UV test bed. The experimental results are in agreement with the simulation and suggest that based on the given power and 10(-3)bit error rate (BER), in comparison with an uncoded system, average communication distance increases 32% with RS code, while 78% with LDPC code.

A Golay complementary TS-based symbol synchronization scheme in variable rate LDPC-coded MB-OFDM UWBoF system

NASA Astrophysics Data System (ADS)

He, Jing; Wen, Xuejie; Chen, Ming; Chen, Lin

2015-09-01

In this paper, a Golay complementary training sequence (TS)-based symbol synchronization scheme is proposed and experimentally demonstrated in multiband orthogonal frequency division multiplexing (MB-OFDM) ultra-wideband over fiber (UWBoF) system with a variable rate low-density parity-check (LDPC) code. Meanwhile, the coding gain and spectral efficiency in the variable rate LDPC-coded MB-OFDM UWBoF system are investigated. By utilizing the non-periodic auto-correlation property of the Golay complementary pair, the start point of LDPC-coded MB-OFDM UWB signal can be estimated accurately. After 100 km standard single-mode fiber (SSMF) transmission, at the bit error rate of 1×10-3, the experimental results show that the short block length 64QAM-LDPC coding provides a coding gain of 4.5 dB, 3.8 dB and 2.9 dB for a code rate of 62.5%, 75% and 87.5%, respectively.

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

PubMed

Islam, Mohammad Rakibul; Han, Young Shin

2011-01-01

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

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

PubMed Central

Islam, Mohammad Rakibul; Han, Young Shin

2011-01-01

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

Low-Density Parity-Check (LDPC) Codes Constructed from Protographs

NASA Astrophysics Data System (ADS)

Thorpe, J.

2003-08-01

We introduce a new class of low-density parity-check (LDPC) codes constructed from a template called a protograph. The protograph serves as a blueprint for constructing LDPC codes of arbitrary size whose performance can be predicted by analyzing the protograph. We apply standard density evolution techniques to predict the performance of large protograph codes. Finally, we use a randomized search algorithm to find good protographs.

A Simulation Testbed for Adaptive Modulation and Coding in Airborne Telemetry

DTIC Science & Technology

2014-05-29

its modulation waveforms and LDPC for the FEC codes . It also uses several sets of published telemetry channel sounding data as its channel models...waveforms and LDPC for the FEC codes . It also uses several sets of published telemetry channel sounding data as its channel models. Within the context...check ( LDPC ) codes with tunable code rates, and both static and dynamic telemetry channel models are included. In an effort to maximize the

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Parallel Subspace Subcodes of Reed-Solomon Codes for Magnetic Recording Channels

ERIC Educational Resources Information Center

Wang, Han

2010-01-01

Read channel architectures based on a single low-density parity-check (LDPC) code are being considered for the next generation of hard disk drives. However, LDPC-only solutions suffer from the error floor problem, which may compromise reliability, if not handled properly. Concatenated architectures using an LDPC code plus a Reed-Solomon (RS) code…

Experimental study of non-binary LDPC coding for long-haul coherent optical QPSK transmissions.

PubMed

Zhang, Shaoliang; Arabaci, Murat; Yaman, Fatih; Djordjevic, Ivan B; Xu, Lei; Wang, Ting; Inada, Yoshihisa; Ogata, Takaaki; Aoki, Yasuhiro

2011-09-26

The performance of rate-0.8 4-ary LDPC code has been studied in a 50 GHz-spaced 40 Gb/s DWDM system with PDM-QPSK modulation. The net effective coding gain of 10 dB is obtained at BER of 10(-6). With the aid of time-interleaving polarization multiplexing and MAP detection, 10,560 km transmission over legacy dispersion managed fiber is achieved without any countable errors. The proposed nonbinary quasi-cyclic LDPC code achieves an uncoded BER threshold at 4×10(-2). Potential issues like phase ambiguity and coding length are also discussed when implementing LDPC in current coherent optical systems. © 2011 Optical Society of America

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.

Advanced GF(3²) nonbinary LDPC coded modulation with non-uniform 9-QAM outperforming star 8-QAM.

PubMed

Liu, Tao; Lin, Changyu; Djordjevic, Ivan B

2016-06-27

In this paper, we first describe a 9-symbol non-uniform signaling scheme based on Huffman code, in which different symbols are transmitted with different probabilities. By using the Huffman procedure, prefix code is designed to approach the optimal performance. Then, we introduce an algorithm to determine the optimal signal constellation sets for our proposed non-uniform scheme with the criterion of maximizing constellation figure of merit (CFM). The proposed nonuniform polarization multiplexed signaling 9-QAM scheme has the same spectral efficiency as the conventional 8-QAM. Additionally, we propose a specially designed GF(3²) nonbinary quasi-cyclic LDPC code for the coded modulation system based on the 9-QAM non-uniform scheme. Further, we study the efficiency of our proposed non-uniform 9-QAM, combined with nonbinary LDPC coding, and demonstrate by Monte Carlo simulation that the proposed GF(2³) nonbinary LDPC coded 9-QAM scheme outperforms nonbinary LDPC coded uniform 8-QAM by at least 0.8dB.

Coded Cooperation for Multiway Relaying in Wireless Sensor Networks †

PubMed Central

Si, Zhongwei; Ma, Junyang; Thobaben, Ragnar

2015-01-01

Wireless sensor networks have been considered as an enabling technology for constructing smart cities. One important feature of wireless sensor networks is that the sensor nodes collaborate in some manner for communications. In this manuscript, we focus on the model of multiway relaying with full data exchange where each user wants to transmit and receive data to and from all other users in the network. We derive the capacity region for this specific model and propose a coding strategy through coset encoding. To obtain good performance with practical codes, we choose spatially-coupled LDPC (SC-LDPC) codes for the coded cooperation. In particular, for the message broadcasting from the relay, we construct multi-edge-type (MET) SC-LDPC codes by repeatedly applying coset encoding. Due to the capacity-achieving property of the SC-LDPC codes, we prove that the capacity region can theoretically be achieved by the proposed MET SC-LDPC codes. Numerical results with finite node degrees are provided, which show that the achievable rates approach the boundary of the capacity region in both binary erasure channels and additive white Gaussian channels. PMID:26131675

Coded Cooperation for Multiway Relaying in Wireless Sensor Networks.

PubMed

Si, Zhongwei; Ma, Junyang; Thobaben, Ragnar

2015-06-29

Wireless sensor networks have been considered as an enabling technology for constructing smart cities. One important feature of wireless sensor networks is that the sensor nodes collaborate in some manner for communications. In this manuscript, we focus on the model of multiway relaying with full data exchange where each user wants to transmit and receive data to and from all other users in the network. We derive the capacity region for this specific model and propose a coding strategy through coset encoding. To obtain good performance with practical codes, we choose spatially-coupled LDPC (SC-LDPC) codes for the coded cooperation. In particular, for the message broadcasting from the relay, we construct multi-edge-type (MET) SC-LDPC codes by repeatedly applying coset encoding. Due to the capacity-achieving property of the SC-LDPC codes, we prove that the capacity region can theoretically be achieved by the proposed MET SC-LDPC codes. Numerical results with finite node degrees are provided, which show that the achievable rates approach the boundary of the capacity region in both binary erasure channels and additive white Gaussian channels.

Ultra high speed optical transmission using subcarrier-multiplexed four-dimensional LDPC-coded modulation.

PubMed

Batshon, Hussam G; Djordjevic, Ivan; Schmidt, Ted

2010-09-13

We propose a subcarrier-multiplexed four-dimensional LDPC bit-interleaved coded modulation scheme that is capable of achieving beyond 480 Gb/s single-channel transmission rate over optical channels. Subcarrier-multiplexed four-dimensional LDPC coded modulation scheme outperforms the corresponding dual polarization schemes by up to 4.6 dB in OSNR at BER 10(-8).

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.

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

NASA Astrophysics Data System (ADS)

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

2005-01-01

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

Bilayer Protograph Codes for Half-Duplex Relay Channels

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; VanNguyen, Thuy; Nosratinia, Aria

2013-01-01

Direct to Earth return links are limited by the size and power of lander devices. A standard alternative is provided by a two-hops return link: a proximity link (from lander to orbiter relay) and a deep-space link (from orbiter relay to Earth). Although direct to Earth return links are limited by the size and power of lander devices, using an additional link and a proposed coding for relay channels, one can obtain a more reliable signal. Although significant progress has been made in the relay coding problem, existing codes must be painstakingly optimized to match to a single set of channel conditions, many of them do not offer easy encoding, and most of them do not have structured design. A high-performing LDPC (low-density parity-check) code for the relay channel addresses simultaneously two important issues: a code structure that allows low encoding complexity, and a flexible rate-compatible code that allows matching to various channel conditions. Most of the previous high-performance LDPC codes for the relay channel are tightly optimized for a given channel quality, and are not easily adapted without extensive re-optimization for various channel conditions. This code for the relay channel combines structured design and easy encoding with rate compatibility to allow adaptation to the three links involved in the relay channel, and furthermore offers very good performance. The proposed code is constructed by synthesizing a bilayer structure with a pro to graph. In addition to the contribution to relay encoding, an improved family of protograph codes was produced for the point-to-point AWGN (additive white Gaussian noise) channel whose high-rate members enjoy thresholds that are within 0.07 dB of capacity. These LDPC relay codes address three important issues in an integrative manner: low encoding complexity, modular structure allowing for easy design, and rate compatibility so that the code can be easily matched to a variety of channel conditions without extensive re-optimization. The main problem of half-duplex relay coding can be reduced to the simultaneous design of two codes at two rates and two SNRs (signal-to-noise ratios), such that one is a subset of the other. This problem can be addressed by forceful optimization, but a clever method of addressing this problem is via the bilayer lengthened (BL) LDPC structure. This method uses a bilayer Tanner graph to make the two codes while using a concept of "parity forwarding" with subsequent successive decoding that removes the need to directly address the issue of uneven SNRs among the symbols of a given codeword. This method is attractive in that it addresses some of the main issues in the design of relay codes, but it does not by itself give rise to highly structured codes with simple encoding, nor does it give rate-compatible codes. The main contribution of this work is to construct a class of codes that simultaneously possess a bilayer parity- forwarding mechanism, while also benefiting from the properties of protograph codes having an easy encoding, a modular design, and being a rate-compatible code.

Constellation labeling optimization for bit-interleaved coded APSK

NASA Astrophysics Data System (ADS)

Xiang, Xingyu; Mo, Zijian; Wang, Zhonghai; Pham, Khanh; Blasch, Erik; Chen, Genshe

2016-05-01

This paper investigates the constellation and mapping optimization for amplitude phase shift keying (APSK) modulation, which is deployed in Digital Video Broadcasting Satellite - Second Generation (DVB-S2) and Digital Video Broadcasting - Satellite services to Handhelds (DVB-SH) broadcasting standards due to its merits of power and spectral efficiency together with the robustness against nonlinear distortion. The mapping optimization is performed for 32-APSK according to combined cost functions related to Euclidean distance and mutual information. A Binary switching algorithm and its modified version are used to minimize the cost function and the estimated error between the original and received data. The optimized constellation mapping is tested by combining DVB-S2 standard Low-Density Parity-Check (LDPC) codes in both Bit-Interleaved Coded Modulation (BICM) and BICM with iterative decoding (BICM-ID) systems. The simulated results validate the proposed constellation labeling optimization scheme which yields better performance against conventional 32-APSK constellation defined in DVB-S2 standard.

Simultaneous chromatic dispersion and PMD compensation by using coded-OFDM and girth-10 LDPC codes.

PubMed

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

2008-07-07

Low-density parity-check (LDPC)-coded orthogonal frequency division multiplexing (OFDM) is studied as an efficient coded modulation scheme suitable for simultaneous chromatic dispersion and polarization mode dispersion (PMD) compensation. We show that, for aggregate rate of 10 Gb/s, accumulated dispersion over 6500 km of SMF and differential group delay of 100 ps can be simultaneously compensated with penalty within 1.5 dB (with respect to the back-to-back configuration) when training sequence based channel estimation and girth-10 LDPC codes of rate 0.8 are employed.

Experimental demonstration of the transmission performance for LDPC-coded multiband OFDM ultra-wideband over fiber system

NASA Astrophysics Data System (ADS)

He, Jing; Wen, Xuejie; Chen, Ming; Chen, Lin; Su, Jinshu

2015-01-01

To improve the transmission performance of multiband orthogonal frequency division multiplexing (MB-OFDM) ultra-wideband (UWB) over optical fiber, a pre-coding scheme based on low-density parity-check (LDPC) is adopted and experimentally demonstrated in the intensity-modulation and direct-detection MB-OFDM UWB over fiber system. Meanwhile, a symbol synchronization and pilot-aided channel estimation scheme is implemented on the receiver of the MB-OFDM UWB over fiber system. The experimental results show that the LDPC pre-coding scheme can work effectively in the MB-OFDM UWB over fiber system. After 70 km standard single-mode fiber (SSMF) transmission, at the bit error rate of 1 × 10-3, the receiver sensitivities are improved about 4 dB when the LDPC code rate is 75%.

PMD compensation in fiber-optic communication systems with direct detection using LDPC-coded OFDM.

PubMed

Djordjevic, Ivan B

2007-04-02

The possibility of polarization-mode dispersion (PMD) compensation in fiber-optic communication systems with direct detection using a simple channel estimation technique and low-density parity-check (LDPC)-coded orthogonal frequency division multiplexing (OFDM) is demonstrated. It is shown that even for differential group delay (DGD) of 4/BW (BW is the OFDM signal bandwidth), the degradation due to the first-order PMD can be completely compensated for. Two classes of LDPC codes designed based on two different combinatorial objects (difference systems and product of combinatorial designs) suitable for use in PMD compensation are introduced.

DNA Barcoding through Quaternary LDPC Codes

PubMed Central

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

2015-01-01

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

DNA Barcoding through Quaternary LDPC Codes.

PubMed

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

2015-01-01

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

LDPC-coded MIMO optical communication over the atmospheric turbulence channel using Q-ary pulse-position modulation.

PubMed

Djordjevic, Ivan B

2007-08-06

We describe a coded power-efficient transmission scheme based on repetition MIMO principle suitable for communication over the atmospheric turbulence channel, and determine its channel capacity. The proposed scheme employs the Q-ary pulse-position modulation. We further study how to approach the channel capacity limits using low-density parity-check (LDPC) codes. Component LDPC codes are designed using the concept of pairwise-balanced designs. Contrary to the several recent publications, bit-error rates and channel capacities are reported assuming non-ideal photodetection. The atmospheric turbulence channel is modeled using the Gamma-Gamma distribution function due to Al-Habash et al. Excellent bit-error rate performance improvement, over uncoded case, is found.

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

NASA Astrophysics Data System (ADS)

Matsui, Chihiro; Kinoshita, Reika; Takeuchi, Ken

2018-04-01

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

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.

NASA Tech Briefs, April 2009

NASA Technical Reports Server (NTRS)

2009-01-01

Topics covered include: Direct-Solve Image-Based Wavefront Sensing; Use of UV Sources for Detection and Identification of Explosives; Using Fluorescent Viruses for Detecting Bacteria in Water; Gradiometer Using Middle Loops as Sensing Elements in a Low-Field SQUID MRI System; Volcano Monitor: Autonomous Triggering of In-Situ Sensors; Wireless Fluid-Level Sensors for Harsh Environments; Interference-Detection Module in a Digital Radar Receiver; Modal Vibration Analysis of Large Castings; Structural/Radiation-Shielding Epoxies; Integrated Multilayer Insulation; Apparatus for Screening Multiple Oxygen-Reduction Catalysts; Determining Aliasing in Isolated Signal Conditioning Modules; Composite Bipolar Plate for Unitized Fuel Cell/Electrolyzer Systems; Spectrum Analyzers Incorporating Tunable WGM Resonators; Quantum-Well Thermophotovoltaic Cells; Bounded-Angle Iterative Decoding of LDPC Codes; Conversion from Tree to Graph Representation of Requirements; Parallel Hybrid Vehicle Optimal Storage System; and Anaerobic Digestion in a Flooded Densified Leachbed.

FPGA-based LDPC-coded APSK for optical communication systems.

PubMed

Zou, Ding; Lin, Changyu; Djordjevic, Ivan B

2017-02-20

In this paper, with the aid of mutual information and generalized mutual information (GMI) capacity analyses, it is shown that the geometrically shaped APSK that mimics an optimal Gaussian distribution with equiprobable signaling together with the corresponding gray-mapping rules can approach the Shannon limit closer than conventional quadrature amplitude modulation (QAM) at certain range of FEC overhead for both 16-APSK and 64-APSK. The field programmable gate array (FPGA) based LDPC-coded APSK emulation is conducted on block interleaver-based and bit interleaver-based systems; the results verify a significant improvement in hardware efficient bit interleaver-based systems. In bit interleaver-based emulation, the LDPC-coded 64-APSK outperforms 64-QAM, in terms of symbol signal-to-noise ratio (SNR), by 0.1 dB, 0.2 dB, and 0.3 dB at spectral efficiencies of 4.8, 4.5, and 4.2 b/s/Hz, respectively. It is found by emulation that LDPC-coded 64-APSK for spectral efficiencies of 4.8, 4.5, and 4.2 b/s/Hz is 1.6 dB, 1.7 dB, and 2.2 dB away from the GMI capacity.

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.

Error Control Coding Techniques for Space and Satellite Communications

NASA Technical Reports Server (NTRS)

Lin, Shu

2000-01-01

This paper presents a concatenated turbo coding system in which a Reed-Solomom outer code is concatenated with a binary turbo inner code. In the proposed system, the outer code decoder and the inner turbo code decoder interact to achieve both good bit error and frame error performances. The outer code decoder helps the inner turbo code decoder to terminate its decoding iteration while the inner turbo code decoder provides soft-output information to the outer code decoder to carry out a reliability-based soft-decision decoding. In the case that the outer code decoding fails, the outer code decoder instructs the inner code decoder to continue its decoding iterations until the outer code decoding is successful or a preset maximum number of decoding iterations is reached. This interaction between outer and inner code decoders reduces decoding delay. Also presented in the paper are an effective criterion for stopping the iteration process of the inner code decoder and a new reliability-based decoding algorithm for nonbinary codes.

An Interactive Concatenated Turbo Coding System

NASA Technical Reports Server (NTRS)

Liu, Ye; Tang, Heng; Lin, Shu; Fossorier, Marc

1999-01-01

This paper presents a concatenated turbo coding system in which a Reed-Solomon outer code is concatenated with a binary turbo inner code. In the proposed system, the outer code decoder and the inner turbo code decoder interact to achieve both good bit error and frame error performances. The outer code decoder helps the inner turbo code decoder to terminate its decoding iteration while the inner turbo code decoder provides soft-output information to the outer code decoder to carry out a reliability-based soft- decision decoding. In the case that the outer code decoding fails, the outer code decoder instructs the inner code decoder to continue its decoding iterations until the outer code decoding is successful or a preset maximum number of decoding iterations is reached. This interaction between outer and inner code decoders reduces decoding delay. Also presented in the paper are an effective criterion for stopping the iteration process of the inner code decoder and a new reliability-based decoding algorithm for nonbinary codes.

Pilotless Frame Synchronization Using LDPC Code Constraints

NASA Technical Reports Server (NTRS)

Jones, Christopher; Vissasenor, John

2009-01-01

A method of pilotless frame synchronization has been devised for low- density parity-check (LDPC) codes. In pilotless frame synchronization , there are no pilot symbols; instead, the offset is estimated by ex ploiting selected aspects of the structure of the code. The advantag e of pilotless frame synchronization is that the bandwidth of the sig nal is reduced by an amount associated with elimination of the pilot symbols. The disadvantage is an increase in the amount of receiver data processing needed for frame synchronization.

Nonlinear detection for a high rate extended binary phase shift keying system.

PubMed

Chen, Xian-Qing; Wu, Le-Nan

2013-03-28

The algorithm and the results of a nonlinear detector using a machine learning technique called support vector machine (SVM) on an efficient modulation system with high data rate and low energy consumption is presented in this paper. Simulation results showed that the performance achieved by the SVM detector is comparable to that of a conventional threshold decision (TD) detector. The two detectors detect the received signals together with the special impacting filter (SIF) that can improve the energy utilization efficiency. However, unlike the TD detector, the SVM detector concentrates not only on reducing the BER of the detector, but also on providing accurate posterior probability estimates (PPEs), which can be used as soft-inputs of the LDPC decoder. The complexity of this detector is considered in this paper by using four features and simplifying the decision function. In addition, a bandwidth efficient transmission is analyzed with both SVM and TD detector. The SVM detector is more robust to sampling rate than TD detector. We find that the SVM is suitable for extended binary phase shift keying (EBPSK) signal detection and can provide accurate posterior probability for LDPC decoding.

Nonlinear Detection for a High Rate Extended Binary Phase Shift Keying System

PubMed Central

Chen, Xian-Qing; Wu, Le-Nan

2013-01-01

The algorithm and the results of a nonlinear detector using a machine learning technique called support vector machine (SVM) on an efficient modulation system with high data rate and low energy consumption is presented in this paper. Simulation results showed that the performance achieved by the SVM detector is comparable to that of a conventional threshold decision (TD) detector. The two detectors detect the received signals together with the special impacting filter (SIF) that can improve the energy utilization efficiency. However, unlike the TD detector, the SVM detector concentrates not only on reducing the BER of the detector, but also on providing accurate posterior probability estimates (PPEs), which can be used as soft-inputs of the LDPC decoder. The complexity of this detector is considered in this paper by using four features and simplifying the decision function. In addition, a bandwidth efficient transmission is analyzed with both SVM and TD detector. The SVM detector is more robust to sampling rate than TD detector. We find that the SVM is suitable for extended binary phase shift keying (EBPSK) signal detection and can provide accurate posterior probability for LDPC decoding. PMID:23539034

Received response based heuristic LDPC code for short-range non-line-of-sight ultraviolet communication.

PubMed

Qin, Heng; Zuo, Yong; Zhang, Dong; Li, Yinghui; Wu, Jian

2017-03-06

Through slight modification on typical photon multiplier tube (PMT) receiver output statistics, a generalized received response model considering both scattered propagation and random detection is presented to investigate the impact of inter-symbol interference (ISI) on link data rate of short-range non-line-of-sight (NLOS) ultraviolet communication. Good agreement with the experimental results by numerical simulation is shown. Based on the received response characteristics, a heuristic check matrix construction algorithm of low-density-parity-check (LDPC) code is further proposed to approach the data rate bound derived in a delayed sampling (DS) binary pulse position modulation (PPM) system. Compared to conventional LDPC coding methods, better bit error ratio (BER) below 1E-05 is achieved for short-range NLOS UVC systems operating at data rate of 2Mbps.

Characterization of LDPC-coded orbital angular momentum modes transmission and multiplexing over a 50-km fiber.

PubMed

Wang, Andong; Zhu, Long; Chen, Shi; Du, Cheng; Mo, Qi; Wang, Jian

2016-05-30

Mode-division multiplexing over fibers has attracted increasing attention over the last few years as a potential solution to further increase fiber transmission capacity. In this paper, we demonstrate the viability of orbital angular momentum (OAM) modes transmission over a 50-km few-mode fiber (FMF). By analyzing mode properties of eigen modes in an FMF, we study the inner mode group differential modal delay (DMD) in FMF, which may influence the transmission capacity in long-distance OAM modes transmission and multiplexing. To mitigate the impact of large inner mode group DMD in long-distance fiber-based OAM modes transmission, we use low-density parity-check (LDPC) codes to increase the system reliability. By evaluating the performance of LDPC-coded single OAM mode transmission over 50-km fiber, significant coding gains of >4 dB, 8 dB and 14 dB are demonstrated for 1-Gbaud, 2-Gbaud and 5-Gbaud quadrature phase-shift keying (QPSK) signals, respectively. Furthermore, in order to verify and compare the influence of DMD in long-distance fiber transmission, single OAM mode transmission over 10-km FMF is also demonstrated in the experiment. Finally, we experimentally demonstrate OAM multiplexing and transmission over a 50-km FMF using LDPC-coded 1-Gbaud QPSK signals to compensate the influence of mode crosstalk and DMD in the 50 km FMF.

On the performance of joint iterative detection and decoding in coherent optical channels with laser frequency fluctuations

NASA Astrophysics Data System (ADS)

Castrillón, Mario A.; Morero, Damián A.; Agazzi, Oscar E.; Hueda, Mario R.

2015-08-01

The joint iterative detection and decoding (JIDD) technique has been proposed by Barbieri et al. (2007) with the objective of compensating the time-varying phase noise and constant frequency offset experienced in satellite communication systems. The application of JIDD to optical coherent receivers in the presence of laser frequency fluctuations has not been reported in prior literature. Laser frequency fluctuations are caused by mechanical vibrations, power supply noise, and other mechanisms. They significantly degrade the performance of the carrier phase estimator in high-speed intradyne coherent optical receivers. This work investigates the performance of the JIDD algorithm in multi-gigabit optical coherent receivers. We present simulation results of bit error rate (BER) for non-differential polarization division multiplexing (PDM)-16QAM modulation in a 200 Gb/s coherent optical system that includes an LDPC code with 20% overhead and net coding gain of 11.3 dB at BER = 10-15. Our study shows that JIDD with a pilot rate ⩽ 5 % compensates for both laser phase noise and laser frequency fluctuation. Furthermore, since JIDD is used with non-differential modulation formats, we find that gains in excess of 1 dB can be achieved over existing solutions based on an explicit carrier phase estimator with differential modulation. The impact of the fiber nonlinearities in dense wavelength division multiplexing (DWDM) systems is also investigated. Our results demonstrate that JIDD is an excellent candidate for application in next generation high-speed optical coherent receivers.

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

PubMed

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

2010-08-02

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

LDPC product coding scheme with extrinsic information for bit patterned media recoding

NASA Astrophysics Data System (ADS)

Jeong, Seongkwon; Lee, Jaejin

2017-05-01

Since the density limit of the current perpendicular magnetic storage system will soon be reached, bit patterned media recording (BPMR) is a promising candidate for the next generation storage system to achieve an areal density beyond 1 Tb/in2. Each recording bit is stored in a fabricated magnetic island and the space between the magnetic islands is nonmagnetic in BPMR. To approach recording densities of 1 Tb/in2, the spacing of the magnetic islands must be less than 25 nm. Consequently, severe inter-symbol interference (ISI) and inter-track interference (ITI) occur. ITI and ISI degrade the performance of BPMR. In this paper, we propose a low-density parity check (LDPC) product coding scheme that exploits extrinsic information for BPMR. This scheme shows an improved bit error rate performance compared to that in which one LDPC code is used.

Combining Ratio Estimation for Low Density Parity Check (LDPC) Coding

NASA Technical Reports Server (NTRS)

Mahmoud, Saad; Hi, Jianjun

2012-01-01

The Low Density Parity Check (LDPC) Code decoding algorithm make use of a scaled receive signal derived from maximizing the log-likelihood ratio of the received signal. The scaling factor (often called the combining ratio) in an AWGN channel is a ratio between signal amplitude and noise variance. Accurately estimating this ratio has shown as much as 0.6 dB decoding performance gain. This presentation briefly describes three methods for estimating the combining ratio: a Pilot-Guided estimation method, a Blind estimation method, and a Simulation-Based Look-Up table. The Pilot Guided Estimation method has shown that the maximum likelihood estimates of signal amplitude is the mean inner product of the received sequence and the known sequence, the attached synchronization marker (ASM) , and signal variance is the difference of the mean of the squared received sequence and the square of the signal amplitude. This method has the advantage of simplicity at the expense of latency since several frames worth of ASMs. The Blind estimation method s maximum likelihood estimator is the average of the product of the received signal with the hyperbolic tangent of the product combining ratio and the received signal. The root of this equation can be determined by an iterative binary search between 0 and 1 after normalizing the received sequence. This method has the benefit of requiring one frame of data to estimate the combining ratio which is good for faster changing channels compared to the previous method, however it is computationally expensive. The final method uses a look-up table based on prior simulated results to determine signal amplitude and noise variance. In this method the received mean signal strength is controlled to a constant soft decision value. The magnitude of the deviation is averaged over a predetermined number of samples. This value is referenced in a look up table to determine the combining ratio that prior simulation associated with the average magnitude of the deviation. This method is more complicated than the Pilot-Guided Method due to the gain control circuitry, but does not have the real-time computation complexity of the Blind Estimation method. Each of these methods can be used to provide an accurate estimation of the combining ratio, and the final selection of the estimation method depends on other design constraints.

PMD compensation in multilevel coded-modulation schemes with coherent detection using BLAST algorithm and iterative polarization cancellation.

PubMed

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

2008-09-15

We present two PMD compensation schemes suitable for use in multilevel (M>or=2) block-coded modulation schemes with coherent detection. The first scheme is based on a BLAST-type polarization-interference cancellation scheme, and the second scheme is based on iterative polarization cancellation. Both schemes use the LDPC codes as channel codes. The proposed PMD compensations schemes are evaluated by employing coded-OFDM and coherent detection. When used in combination with girth-10 LDPC codes those schemes outperform polarization-time coding based OFDM by 1 dB at BER of 10(-9), and provide two times higher spectral efficiency. The proposed schemes perform comparable and are able to compensate even 1200 ps of differential group delay with negligible penalty.

Statistical physics inspired energy-efficient coded-modulation for optical communications.

PubMed

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

2012-04-15

Because Shannon's entropy can be obtained by Stirling's approximation of thermodynamics entropy, the statistical physics energy minimization methods are directly applicable to the signal constellation design. We demonstrate that statistical physics inspired energy-efficient (EE) signal constellation designs, in combination with large-girth low-density parity-check (LDPC) codes, significantly outperform conventional LDPC-coded polarization-division multiplexed quadrature amplitude modulation schemes. We also describe an EE signal constellation design algorithm. Finally, we propose the discrete-time implementation of D-dimensional transceiver and corresponding EE polarization-division multiplexed system. © 2012 Optical Society of America

On the optimum signal constellation design for high-speed optical transport networks.

PubMed

Liu, Tao; Djordjevic, Ivan B

2012-08-27

In this paper, we first describe an optimum signal constellation design algorithm, which is optimum in MMSE-sense, called MMSE-OSCD, for channel capacity achieving source distribution. Secondly, we introduce a feedback channel capacity inspired optimum signal constellation design (FCC-OSCD) to further improve the performance of MMSE-OSCD, inspired by the fact that feedback channel capacity is higher than that of systems without feedback. The constellations obtained by FCC-OSCD are, however, OSNR dependent. The optimization is jointly performed together with regular quasi-cyclic low-density parity-check (LDPC) code design. Such obtained coded-modulation scheme, in combination with polarization-multiplexing, is suitable as both 400 Gb/s and multi-Tb/s optical transport enabling technology. Using large girth LDPC code, we demonstrate by Monte Carlo simulations that a 32-ary signal constellation, obtained by FCC-OSCD, outperforms previously proposed optimized 32-ary CIPQ signal constellation by 0.8 dB at BER of 10(-7). On the other hand, the LDPC-coded 16-ary FCC-OSCD outperforms 16-QAM by 1.15 dB at the same BER.

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.

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.

A code-aided carrier synchronization algorithm based on improved nonbinary low-density parity-check codes

NASA Astrophysics Data System (ADS)

Bai, Cheng-lin; Cheng, Zhi-hui

2016-09-01

In order to further improve the carrier synchronization estimation range and accuracy at low signal-to-noise ratio ( SNR), this paper proposes a code-aided carrier synchronization algorithm based on improved nonbinary low-density parity-check (NB-LDPC) codes to study the polarization-division-multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) system performance in the cases of quadrature phase shift keying (QPSK) and 16 quadrature amplitude modulation (16-QAM) modes. The simulation results indicate that this algorithm can enlarge frequency and phase offset estimation ranges and enhance accuracy of the system greatly, and the bit error rate ( BER) performance of the system is improved effectively compared with that of the system employing traditional NB-LDPC code-aided carrier synchronization algorithm.

Performance optimization of PM-16QAM transmission system enabled by real-time self-adaptive coding.

PubMed

Qu, Zhen; Li, Yao; Mo, Weiyang; Yang, Mingwei; Zhu, Shengxiang; Kilper, Daniel C; Djordjevic, Ivan B

2017-10-15

We experimentally demonstrate self-adaptive coded 5×100  Gb/s WDM polarization multiplexed 16 quadrature amplitude modulation transmission over a 100 km fiber link, which is enabled by a real-time control plane. The real-time optical signal-to-noise ratio (OSNR) is measured using an optical performance monitoring device. The OSNR measurement is processed and fed back using control plane logic and messaging to the transmitter side for code adaptation, where the binary data are adaptively encoded with three types of low-density parity-check (LDPC) codes with code rates of 0.8, 0.75, and 0.7 of large girth. The total code-adaptation latency is measured to be 2273 ms. Compared with transmission without adaptation, average net capacity improvements of 102%, 36%, and 7.5% are obtained, respectively, by adaptive LDPC coding.

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.

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.

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.

Efficacy analysis of LDPC coded APSK modulated differential space-time-frequency coded for wireless body area network using MB-pulsed OFDM UWB technology.

PubMed

Manimegalai, C T; Gauni, Sabitha; Kalimuthu, K

2017-12-04

Wireless body area network (WBAN) is a breakthrough technology in healthcare areas such as hospital and telemedicine. The human body has a complex mixture of different tissues. It is expected that the nature of propagation of electromagnetic signals is distinct in each of these tissues. This forms the base for the WBAN, which is different from other environments. In this paper, the knowledge of Ultra Wide Band (UWB) channel is explored in the WBAN (IEEE 802.15.6) system. The measurements of parameters in frequency range from 3.1-10.6 GHz are taken. The proposed system, transmits data up to 480 Mbps by using LDPC coded APSK Modulated Differential Space-Time-Frequency Coded MB-OFDM to increase the throughput and power efficiency.

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.

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.

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 objectives, meeting goals and overall NASA goals for the NASA Data Standards Working Group. The presentation includes information on the technical progress surrounding the objective, short LDPC codes, and the general results on the Pu-Pw tradeoff.

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.

Two-stage cross-talk mitigation in an orbital-angular-momentum-based free-space optical communication system.

PubMed

Qu, Zhen; Djordjevic, Ivan B

2017-08-15

We propose and experimentally demonstrate a two-stage cross-talk mitigation method in an orbital-angular-momentum (OAM)-based free-space optical communication system, which is enabled by combining spatial offset and low-density parity-check (LDPC) coded nonuniform signaling. Different from traditional OAM multiplexing, where the OAM modes are centrally aligned for copropagation, the adjacent OAM modes (OAM states 2 and -6 and OAM states -2 and 6) in our proposed scheme are spatially offset to mitigate the mode cross talk. Different from traditional rectangular modulation formats, which transmit equidistant signal points with uniform probability, the 5-quadrature amplitude modulation (5-QAM) and 9-QAM are introduced to relieve cross-talk-induced performance degradation. The 5-QAM and 9-QAM formats are based on the Huffman coding technique, which can potentially achieve great cross-talk tolerance by combining them with corresponding nonbinary LDPC codes. We demonstrate that cross talk can be reduced by 1.6 dB and 1 dB via spatial offset for OAM states ±2 and ±6, respectively. Compared to quadrature phase shift keying and 8-QAM formats, the LDPC-coded 5-QAM and 9-QAM are able to bring 1.1 dB and 5.4 dB performance improvements in the presence of atmospheric turbulence, respectively.

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.

An Efficient Downlink Scheduling Strategy Using Normal Graphs for Multiuser MIMO Wireless Systems

NASA Astrophysics Data System (ADS)

Chen, Jung-Chieh; Wu, Cheng-Hsuan; Lee, Yao-Nan; Wen, Chao-Kai

Inspired by the success of the low-density parity-check (LDPC) codes in the field of error-control coding, in this paper we propose transforming the downlink multiuser multiple-input multiple-output scheduling problem into an LDPC-like problem using the normal graph. Based on the normal graph framework, soft information, which indicates the probability that each user will be scheduled to transmit packets at the access point through a specified angle-frequency sub-channel, is exchanged among the local processors to iteratively optimize the multiuser transmission schedule. Computer simulations show that the proposed algorithm can efficiently schedule simultaneous multiuser transmission which then increases the overall channel utilization and reduces the average packet delay.

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.

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.

Soft-output decoding algorithms in iterative decoding of turbo codes

NASA Technical Reports Server (NTRS)

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

1996-01-01

In this article, we present two versions of a simplified maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplified a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed.

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.

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.

Serial turbo trellis coded modulation using a serially concatenated coder

NASA Technical Reports Server (NTRS)

Divsalar, Dariush (Inventor); Dolinar, Samuel J. (Inventor); Pollara, Fabrizio (Inventor)

2010-01-01

Serial concatenated trellis coded modulation (SCTCM) includes an outer coder, an interleaver, a recursive inner coder and a mapping element. The outer coder receives data to be coded and produces outer coded data. The interleaver permutes the outer coded data to produce interleaved data. The recursive inner coder codes the interleaved data to produce inner coded data. The mapping element maps the inner coded data to a symbol. The recursive inner coder has a structure which facilitates iterative decoding of the symbols at a decoder system. The recursive inner coder and the mapping element are selected to maximize the effective free Euclidean distance of a trellis coded modulator formed from the recursive inner coder and the mapping element. The decoder system includes a demodulation unit, an inner SISO (soft-input soft-output) decoder, a deinterleaver, an outer SISO decoder, and an interleaver.

Adaptive transmission based on multi-relay selection and rate-compatible LDPC codes

NASA Astrophysics Data System (ADS)

Su, Hualing; He, Yucheng; Zhou, Lin

2017-08-01

In order to adapt to the dynamical changeable channel condition and improve the transmissive reliability of the system, a cooperation system of rate-compatible low density parity check (RC-LDPC) codes combining with multi-relay selection protocol is proposed. In traditional relay selection protocol, only the channel state information (CSI) of source-relay and the CSI of relay-destination has been considered. The multi-relay selection protocol proposed by this paper takes the CSI between relays into extra account in order to obtain more chances of collabration. Additionally, the idea of hybrid automatic request retransmission (HARQ) and rate-compatible are introduced. Simulation results show that the transmissive reliability of the system can be significantly improved by the proposed protocol.

Optimal signal constellation design for ultra-high-speed optical transport in the presence of nonlinear phase noise.

PubMed

Liu, Tao; Djordjevic, Ivan B

2014-12-29

In this paper, we first describe an optimal signal constellation design algorithm suitable for the coherent optical channels dominated by the linear phase noise. Then, we modify this algorithm to be suitable for the nonlinear phase noise dominated channels. In optimization procedure, the proposed algorithm uses the cumulative log-likelihood function instead of the Euclidian distance. Further, an LDPC coded modulation scheme is proposed to be used in combination with signal constellations obtained by proposed algorithm. Monte Carlo simulations indicate that the LDPC-coded modulation schemes employing the new constellation sets, obtained by our new signal constellation design algorithm, outperform corresponding QAM constellations significantly in terms of transmission distance and have better nonlinearity tolerance.

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.

Secret information reconciliation based on punctured low-density parity-check codes for continuous-variable quantum key distribution

NASA Astrophysics Data System (ADS)

Jiang, Xue-Qin; Huang, Peng; Huang, Duan; Lin, Dakai; Zeng, Guihua

2017-02-01

Achieving information theoretic security with practical complexity is of great interest to continuous-variable quantum key distribution in the postprocessing procedure. In this paper, we propose a reconciliation scheme based on the punctured low-density parity-check (LDPC) codes. Compared to the well-known multidimensional reconciliation scheme, the present scheme has lower time complexity. Especially when the chosen punctured LDPC code achieves the Shannon capacity, the proposed reconciliation scheme can remove the information that has been leaked to an eavesdropper in the quantum transmission phase. Therefore, there is no information leaked to the eavesdropper after the reconciliation stage. This indicates that the privacy amplification algorithm of the postprocessing procedure is no more needed after the reconciliation process. These features lead to a higher secret key rate, optimal performance, and availability for the involved quantum key distribution scheme.

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.

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.

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.

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 % .

Error Control Coding Techniques for Space and Satellite Communications

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.; Takeshita, Oscar Y.; Cabral, Hermano A.; He, Jiali; White, Gregory S.

1997-01-01

Turbo coding using iterative SOVA decoding and M-ary differentially coherent or non-coherent modulation can provide an effective coding modulation solution: (1) Energy efficient with relatively simple SOVA decoding and small packet lengths, depending on BEP required; (2) Low number of decoding iterations required; and (3) Robustness in fading with channel interleaving.

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.

Joint Schemes for Physical Layer Security and Error Correction

ERIC Educational Resources Information Center

Adamo, Oluwayomi

2011-01-01

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

Encoders for block-circulant LDPC codes

NASA Technical Reports Server (NTRS)

Divsalar, Dariush (Inventor); Abbasfar, Aliazam (Inventor); Jones, Christopher R. (Inventor); Dolinar, Samuel J. (Inventor); Thorpe, Jeremy C. (Inventor); Andrews, Kenneth S. (Inventor); Yao, Kung (Inventor)

2009-01-01

Methods and apparatus to encode message input symbols in accordance with an accumulate-repeat-accumulate code with repetition three or four are disclosed. Block circulant matrices are used. A first method and apparatus make use of the block-circulant structure of the parity check matrix. A second method and apparatus use block-circulant generator matrices.

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.

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.

Design and performance investigation of LDPC-coded upstream transmission systems in IM/DD OFDM-PONs

NASA Astrophysics Data System (ADS)

Gong, Xiaoxue; Guo, Lei; Wu, Jingjing; Ning, Zhaolong

2016-12-01

In Intensity-Modulation Direct-Detection (IM/DD) Orthogonal Frequency Division Multiplexing Passive Optical Networks (OFDM-PONs), aside from Subcarrier-to-Subcarrier Intermixing Interferences (SSII) induced by square-law detection, the same laser frequency for data sending from Optical Network Units (ONUs) results in ONU-to-ONU Beating Interferences (OOBI) at the receiver. To mitigate those interferences, we design a Low-Density Parity Check (LDPC)-coded and spectrum-efficient upstream transmission system. A theoretical channel model is also derived, in order to analyze the detrimental factors influencing system performances. Simulation results demonstrate that the receiver sensitivity is improved 3.4 dB and 2.5 dB under QPSK and 8QAM, respectively, after 100 km Standard Single-Mode Fiber (SSMF) transmission. Furthermore, the spectrum efficiency can be improved by about 50%.

MIMO-OFDM System's Performance Using LDPC Codes for a Mobile Robot

NASA Astrophysics Data System (ADS)

Daoud, Omar; Alani, Omar

This work deals with the performance of a Sniffer Mobile Robot (SNFRbot)-based spatial multiplexed wireless Orthogonal Frequency Division Multiplexing (OFDM) transmission technology. The use of Multi-Input Multi-Output (MIMO)-OFDM technology increases the wireless transmission rate without increasing transmission power or bandwidth. A generic multilayer architecture of the SNFRbot is proposed with low power and low cost. Some experimental results are presented and show the efficiency of sniffing deadly gazes, sensing high temperatures and sending live videos of the monitored situation. Moreover, simulation results show the achieved performance by tackling the Peak-to-Average Power Ratio (PAPR) problem of the used technology using Low Density Parity Check (LDPC) codes; and the effect of combating the PAPR on the bit error rate (BER) and the signal to noise ratio (SNR) over a Doppler spread channel.

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.

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.

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.

"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

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.

Spinstand demonstration of areal density enhancement using two-dimensional magnetic recording (invited)

NASA Astrophysics Data System (ADS)

Lippman, Thomas; Brockie, Richard; Coker, Jon; Contreras, John; Galbraith, Rick; Garzon, Samir; Hanson, Weldon; Leong, Tom; Marley, Arley; Wood, Roger; Zakai, Rehan; Zolla, Howard; Duquette, Paul; Petrizzi, Joe

2015-05-01

Exponential growth of the areal density has driven the magnetic recording industry for almost sixty years. But now areal density growth is slowing down, suggesting that current technologies are reaching their fundamental limit. The next generation of recording technologies, namely, energy-assisted writing and bit-patterned media, remains just over the horizon. Two-Dimensional Magnetic Recording (TDMR) is a promising new approach, enabling continued areal density growth with only modest changes to the heads and recording electronics. We demonstrate a first generation implementation of TDMR by using a dual-element read sensor to improve the recovery of data encoded by a conventional low-density parity-check (LDPC) channel. The signals are combined with a 2D equalizer into a single modified waveform that is decoded by a standard LDPC channel. Our detection hardware can perform simultaneous measurement of the pre- and post-combined error rate information, allowing one set of measurements to assess the absolute areal density capability of the TDMR system as well as the gain over a conventional shingled magnetic recording system with identical components. We discuss areal density measurements using this hardware and demonstrate gains exceeding five percent based on experimental dual reader components.

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.

Error Control Coding Techniques for Space and Satellite Communications

NASA Technical Reports Server (NTRS)

Costello, Daniel J., Jr.; Cabral, Hermano A.; He, Jiali

1997-01-01

Bootstrap Hybrid Decoding (BHD) (Jelinek and Cocke, 1971) is a coding/decoding scheme that adds extra redundancy to a set of convolutionally encoded codewords and uses this redundancy to provide reliability information to a sequential decoder. Theoretical results indicate that bit error probability performance (BER) of BHD is close to that of Turbo-codes, without some of their drawbacks. In this report we study the use of the Multiple Stack Algorithm (MSA) (Chevillat and Costello, Jr., 1977) as the underlying sequential decoding algorithm in BHD, which makes possible an iterative version of BHD.

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.

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.

Optimizations of a Hardware Decoder for Deep-Space Optical Communications

NASA Technical Reports Server (NTRS)

Cheng, Michael K.; Nakashima, Michael A.; Moision, Bruce E.; Hamkins, Jon

2007-01-01

The National Aeronautics and Space Administration has developed a capacity approaching modulation and coding scheme that comprises a serial concatenation of an inner accumulate pulse-position modulation (PPM) and an outer convolutional code [or serially concatenated PPM (SCPPM)] for deep-space optical communications. Decoding of this code uses the turbo principle. However, due to the nonbinary property of SCPPM, a straightforward application of classical turbo decoding is very inefficient. Here, we present various optimizations applicable in hardware implementation of the SCPPM decoder. More specifically, we feature a Super Gamma computation to efficiently handle parallel trellis edges, a pipeline-friendly 'maxstar top-2' circuit that reduces the max-only approximation penalty, a low-latency cyclic redundancy check circuit for window-based decoders, and a high-speed algorithmic polynomial interleaver that leads to memory savings. Using the featured optimizations, we implement a 6.72 megabits-per-second (Mbps) SCPPM decoder on a single field-programmable gate array (FPGA). Compared to the current data rate of 256 kilobits per second from Mars, the SCPPM coded scheme represents a throughput increase of more than twenty-six fold. Extension to a 50-Mbps decoder on a board with multiple FPGAs follows naturally. We show through hardware simulations that the SCPPM coded system can operate within 1 dB of the Shannon capacity at nominal operating conditions.

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.

Measurement Techniques for Clock Jitter

NASA Technical Reports Server (NTRS)

Lansdowne, Chatwin; Schlesinger, Adam

2012-01-01

NASA is in the process of modernizing its communications infrastructure to accompany the development of a Crew Exploration Vehicle (CEV) to replace the shuttle. With this effort comes the opportunity to infuse more advanced coded modulation techniques, including low-density parity-check (LDPC) codes that offer greater coding gains than the current capability. However, in order to take full advantage of these codes, the ground segment receiver synchronization loops must be able to operate at a lower signal-to-noise ratio (SNR) than supported by equipment currently in use.

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.

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.

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.

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

Landsat Data Continuity Mission (LDCM) - Optimizing X-Band Usage

NASA Technical Reports Server (NTRS)

Garon, H. M.; Gal-Edd, J. S.; Dearth, K. W.; Sank, V. I.

2010-01-01

The NASA version of the low-density parity check (LDPC) 7/8-rate code, shortened to the dimensions of (8160, 7136), has been implemented as the forward error correction (FEC) schema for the Landsat Data Continuity Mission (LDCM). This is the first flight application of this code. In order to place a 440 Msps link within the 375 MHz wide X band we found it necessary to heavily bandpass filter the satellite transmitter output . Despite the significant amplitude and phase distortions that accompanied the spectral truncation, the mission required BER is maintained at < 10(exp -12) with less than 2 dB of implementation loss. We utilized a band-pass filter designed ostensibly to replicate the link distortions to demonstrate link design viability. The same filter was then used to optimize the adaptive equalizer in the receiver employed at the terminus of the downlink. The excellent results we obtained could be directly attributed to the implementation of the LDPC code and the amplitude and phase compensation provided in the receiver. Similar results were obtained with receivers from several vendors.

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.

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.

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.

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.

Quantum Kronecker sum-product low-density parity-check codes with finite rate

NASA Astrophysics Data System (ADS)

Kovalev, Alexey A.; Pryadko, Leonid P.

2013-07-01

We introduce an ansatz for quantum codes which gives the hypergraph-product (generalized toric) codes by Tillich and Zémor and generalized bicycle codes by MacKay as limiting cases. The construction allows for both the lower and the upper bounds on the minimum distance; they scale as a square root of the block length. Many thus defined codes have a finite rate and limited-weight stabilizer generators, an analog of classical low-density parity-check (LDPC) codes. Compared to the hypergraph-product codes, hyperbicycle codes generally have a wider range of parameters; in particular, they can have a higher rate while preserving the estimated error threshold.

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.

A Simulation Testbed for Adaptive Modulation and Coding in Airborne Telemetry (Brief)

DTIC Science & Technology

2014-10-01

SOQPSK 0.0085924 us 0.015231 kH2 10 1/2 20 Time Modulation/ Coding State ... .. . . D - 2/3 3/4 4/5 GTRI_B-‹#› MATLAB GUI Interface 8...802.11a) • Modulations: BPSK, QPSK, 16 QAM, 64 QAM • Cyclic Prefix Lengths • Number of Subcarriers • Coding • LDPC • Rates: 1/2, 2/3, 3/4, 4/5...and Coding in Airborne Telemetry (Brief) October 2014 DISTRIBUTION STATEMENT A. Approved for public release: distribution unlimited. Test

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.

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.

500  Gb/s free-space optical transmission over strong atmospheric turbulence channels.

PubMed

Qu, Zhen; Djordjevic, Ivan B

2016-07-15

We experimentally demonstrate a high-spectral-efficiency, large-capacity, featured free-space-optical (FSO) transmission system by using low-density, parity-check (LDPC) coded quadrature phase shift keying (QPSK) combined with orbital angular momentum (OAM) multiplexing. The strong atmospheric turbulence channel is emulated by two spatial light modulators on which four randomly generated azimuthal phase patterns yielding the Andrews spectrum are recorded. The validity of such an approach is verified by reproducing the intensity distribution and irradiance correlation function (ICF) from the full-scale simulator. Excellent agreement of experimental, numerical, and analytical results is found. To reduce the phase distortion induced by the turbulence emulator, the inexpensive wavefront sensorless adaptive optics (AO) is used. To deal with remaining channel impairments, a large-girth LDPC code is used. To further improve the aggregate data rate, the OAM multiplexing is combined with WDM, and 500 Gb/s optical transmission over the strong atmospheric turbulence channels is demonstrated.

A Novel Strategy Using Factor Graphs and the Sum-Product Algorithm for Satellite Broadcast Scheduling Problems

NASA Astrophysics Data System (ADS)

Chen, Jung-Chieh

This paper presents a low complexity algorithmic framework for finding a broadcasting schedule in a low-altitude satellite system, i. e., the satellite broadcast scheduling (SBS) problem, based on the recent modeling and computational methodology of factor graphs. Inspired by the huge success of the low density parity check (LDPC) codes in the field of error control coding, in this paper, we transform the SBS problem into an LDPC-like problem through a factor graph instead of using the conventional neural network approaches to solve the SBS problem. Based on a factor graph framework, the soft-information, describing the probability that each satellite will broadcast information to a terminal at a specific time slot, is exchanged among the local processing in the proposed framework via the sum-product algorithm to iteratively optimize the satellite broadcasting schedule. Numerical results show that the proposed approach not only can obtain optimal solution but also enjoys the low complexity suitable for integral-circuit implementation.

Optimum Boundaries of Signal-to-Noise Ratio for Adaptive Code Modulations

DTIC Science & Technology

2017-11-14

1510–1521, Feb. 2015. [2]. Pursley, M. B. and Royster, T. C., “Adaptive-rate nonbinary LDPC coding for frequency - hop communications ,” IEEE...and this can cause a very narrowband noise near the center frequency during USRP signal acquisition and generation. This can cause a high BER...Final Report APPROVED FOR PUBLIC RELEASE; DISTRIBUTION IS UNLIMITED. AIR FORCE RESEARCH LABORATORY Space Vehicles Directorate 3550 Aberdeen Ave

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.

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.

Research on Formation of Microsatellite Communication with Genetic Algorithm

PubMed Central

Wu, Guoqiang; Bai, Yuguang; Sun, Zhaowei

2013-01-01

For the formation of three microsatellites which fly in the same orbit and perform three-dimensional solid mapping for terra, this paper proposes an optimizing design method of space circular formation order based on improved generic algorithm and provides an intersatellite direct spread spectrum communication system. The calculating equation of LEO formation flying satellite intersatellite links is guided by the special requirements of formation-flying microsatellite intersatellite links, and the transmitter power is also confirmed throughout the simulation. The method of space circular formation order optimizing design based on improved generic algorithm is given, and it can keep formation order steady for a long time under various absorb impetus. The intersatellite direct spread spectrum communication system is also provided. It can be found that, when the distance is 1 km and the data rate is 1 Mbps, the input wave matches preferably with the output wave. And LDPC code can improve the communication performance. The correct capability of (512, 256) LDPC code is better than (2, 1, 7) convolution code, distinctively. The design system can satisfy the communication requirements of microsatellites. So, the presented method provides a significant theory foundation for formation-flying and intersatellite communication. PMID:24078796

Research on formation of microsatellite communication with genetic algorithm.

PubMed

Wu, Guoqiang; Bai, Yuguang; Sun, Zhaowei

2013-01-01

For the formation of three microsatellites which fly in the same orbit and perform three-dimensional solid mapping for terra, this paper proposes an optimizing design method of space circular formation order based on improved generic algorithm and provides an intersatellite direct spread spectrum communication system. The calculating equation of LEO formation flying satellite intersatellite links is guided by the special requirements of formation-flying microsatellite intersatellite links, and the transmitter power is also confirmed throughout the simulation. The method of space circular formation order optimizing design based on improved generic algorithm is given, and it can keep formation order steady for a long time under various absorb impetus. The intersatellite direct spread spectrum communication system is also provided. It can be found that, when the distance is 1 km and the data rate is 1 Mbps, the input wave matches preferably with the output wave. And LDPC code can improve the communication performance. The correct capability of (512, 256) LDPC code is better than (2, 1, 7) convolution code, distinctively. The design system can satisfy the communication requirements of microsatellites. So, the presented method provides a significant theory foundation for formation-flying and intersatellite communication.

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.

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.

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.

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.

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).

A software reconfigurable optical multiband UWB system utilizing a bit-loading combined with adaptive LDPC code rate scheme

NASA Astrophysics Data System (ADS)

He, Jing; Dai, Min; Chen, Qinghui; Deng, Rui; Xiang, Changqing; Chen, Lin

2017-07-01

In this paper, an effective bit-loading combined with adaptive LDPC code rate algorithm is proposed and investigated in software reconfigurable multiband UWB over fiber system. To compensate the power fading and chromatic dispersion for the high frequency of multiband OFDM UWB signal transmission over standard single mode fiber (SSMF), a Mach-Zehnder modulator (MZM) with negative chirp parameter is utilized. In addition, the negative power penalty of -1 dB for 128 QAM multiband OFDM UWB signal are measured at the hard-decision forward error correction (HD-FEC) limitation of 3.8 × 10-3 after 50 km SSMF transmission. The experimental results show that, compared to the fixed coding scheme with the code rate of 75%, the signal-to-noise (SNR) is improved by 2.79 dB for 128 QAM multiband OFDM UWB system after 100 km SSMF transmission using ALCR algorithm. Moreover, by employing bit-loading combined with ALCR algorithm, the bit error rate (BER) performance of system can be further promoted effectively. The simulation results present that, at the HD-FEC limitation, the value of Q factor is improved by 3.93 dB at the SNR of 19.5 dB over 100 km SSMF transmission, compared to the fixed modulation with uncoded scheme at the same spectrum efficiency (SE).

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.

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.

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.

Advanced error-prediction LDPC with temperature compensation for highly reliable SSDs

NASA Astrophysics Data System (ADS)

Tokutomi, Tsukasa; Tanakamaru, Shuhei; Iwasaki, Tomoko Ogura; Takeuchi, Ken

2015-09-01

To improve the reliability of NAND Flash memory based solid-state drives (SSDs), error-prediction LDPC (EP-LDPC) has been proposed for multi-level-cell (MLC) NAND Flash memory (Tanakamaru et al., 2012, 2013), which is effective for long retention times. However, EP-LDPC is not as effective for triple-level cell (TLC) NAND Flash memory, because TLC NAND Flash has higher error rates and is more sensitive to program-disturb error. Therefore, advanced error-prediction LDPC (AEP-LDPC) has been proposed for TLC NAND Flash memory (Tokutomi et al., 2014). AEP-LDPC can correct errors more accurately by precisely describing the error phenomena. In this paper, the effects of AEP-LDPC are investigated in a 2×nm TLC NAND Flash memory with temperature characterization. Compared with LDPC-with-BER-only, the SSD's data-retention time is increased by 3.4× and 9.5× at room-temperature (RT) and 85 °C, respectively. Similarly, the acceptable BER is increased by 1.8× and 2.3×, respectively. Moreover, AEP-LDPC can correct errors with pre-determined tables made at higher temperatures to shorten the measurement time before shipping. Furthermore, it is found that one table can cover behavior over a range of temperatures in AEP-LDPC. As a result, the total table size can be reduced to 777 kBytes, which makes this approach more practical.

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…

Sparsening Filter Design for Iterative Soft-Input Soft-Output Detectors

DTIC Science & Technology

2012-02-29

filter/detector structure. Since the BP detector itself is unaltered from [1], it can accommodate a system employing channel codes such as LDPC encoding...considered in [1], or can readily be extended to the MIMO case with, for example, space-time coding as in [2,8]. Since our focus is on the design of...simplex method of [15], since it was already available in Matlab , via the “fminsearch” function. 6 Cost surfaces To visualize the cost surfaces, consider

Low-Density Parity-Check Code Design Techniques to Simplify Encoding

NASA Astrophysics Data System (ADS)

Perez, J. M.; Andrews, K.

2007-11-01

This work describes a method for encoding low-density parity-check (LDPC) codes based on the accumulate-repeat-4-jagged-accumulate (AR4JA) scheme, using the low-density parity-check matrix H instead of the dense generator matrix G. The use of the H matrix to encode allows a significant reduction in memory consumption and provides the encoder design a great flexibility. Also described are new hardware-efficient codes, based on the same kind of protographs, which require less memory storage and area, allowing at the same time a reduction in the encoding delay.

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.

Investigation of Different Constituent Encoders in a Turbo-code Scheme for Reduced Decoder Complexity

NASA Technical Reports Server (NTRS)

Kwatra, S. C.

1998-01-01

A large number of papers have been published attempting to give some analytical basis for the performance of Turbo-codes. It has been shown that performance improves with increased interleaver length. Also procedures have been given to pick the best constituent recursive systematic convolutional codes (RSCC's). However testing by computer simulation is still required to verify these results. This thesis begins by describing the encoding and decoding schemes used. Next simulation results on several memory 4 RSCC's are shown. It is found that the best BER performance at low E(sub b)/N(sub o) is not given by the RSCC's that were found using the analytic techniques given so far. Next the results are given from simulations using a smaller memory RSCC for one of the constituent encoders. Significant reduction in decoding complexity is obtained with minimal loss in performance. Simulation results are then given for a rate 1/3 Turbo-code with the result that this code performed as well as a rate 1/2 Turbo-code as measured by the distance from their respective Shannon limits. Finally the results of simulations where an inaccurate noise variance measurement was used are given. From this it was observed that Turbo-decoding is fairly stable with regard to noise variance measurement.

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.

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.

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.

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.

Irreducible normalizer operators and thresholds for degenerate quantum codes with sublinear distances

NASA Astrophysics Data System (ADS)

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

2015-03-01

We construct a lower (existence) bound for the threshold of scalable quantum computation which is applicable to all stabilizer codes, including degenerate quantum codes with sublinear distance scaling. The threshold is based on enumerating irreducible operators in the normalizer of the code, i.e., those that cannot be decomposed into a product of two such operators with non-overlapping support. For quantum LDPC codes with logarithmic or power-law distances, we get threshold values which are parametrically better than the existing analytical bound based on percolation. The new bound also gives a finite threshold when applied to other families of degenerate quantum codes, e.g., the concatenated codes. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.

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.

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.

Protograph-Based Raptor-Like Codes

NASA Technical Reports Server (NTRS)

Divsalar, Dariush; Chen, Tsung-Yi; Wang, Jiadong; Wesel, Richard D.

2014-01-01

Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of pointto- point memoryless channels. The analytic and empirical results indicate that at short blocklength regime, practical rate-compatible punctured convolutional (RCPC) codes achieve low latency with the use of noiseless feedback. In 3GPP, standard rate-compatible turbo codes (RCPT) did not outperform the convolutional codes in the short blocklength regime. The reason is the convolutional codes for low number of states can be decoded optimally using Viterbi decoder. Despite excellent performance of convolutional codes at very short blocklengths, the strength of convolutional codes does not scale with the blocklength for a fixed number of states in its trellis.

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.

Low-complexity video encoding method for wireless image transmission in capsule endoscope.

PubMed

Takizawa, Kenichi; Hamaguchi, Kiyoshi

2010-01-01

This paper presents a low-complexity video encoding method applicable for wireless image transmission in capsule endoscopes. This encoding method is based on Wyner-Ziv theory, in which side information available at a transmitter is treated as side information at its receiver. Therefore complex processes in video encoding, such as estimation of the motion vector, are moved to the receiver side, which has a larger-capacity battery. As a result, the encoding process is only to decimate coded original data through channel coding. We provide a performance evaluation for a low-density parity check (LDPC) coding method in the AWGN channel.

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…

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Modified hybrid subcarrier/amplitude/ phase/polarization LDPC-coded modulation for 400 Gb/s optical transmission and beyond.

PubMed

Batshon, Hussam G; Djordjevic, Ivan; Xu, Lei; Wang, Ting

2010-06-21

In this paper, we present a modified coded hybrid subcarrier/ amplitude/phase/polarization (H-SAPP) modulation scheme as a technique capable of achieving beyond 400 Gb/s single-channel transmission over optical channels. The modified H-SAPP scheme profits from the available resources in addition to geometry to increase the bandwidth efficiency of the transmission system, and so increases the aggregate rate of the system. In this report we present the modified H-SAPP scheme and focus on an example that allows 11 bits/Symbol that can achieve 440 Gb/s transmission using components of 50 Giga Symbol/s (GS/s).

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.

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.

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…

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

Turbo Trellis Coded Modulation With Iterative Decoding for Mobile Satellite Communications

NASA Technical Reports Server (NTRS)

Divsalar, D.; Pollara, F.

1997-01-01

In this paper, analytical bounds on the performance of parallel concatenation of two codes, known as turbo codes, and serial concatenation of two codes over fading channels are obtained. Based on this analysis, design criteria for the selection of component trellis codes for MPSK modulation, and a suitable bit-by-bit iterative decoding structure are proposed. Examples are given for throughput of 2 bits/sec/Hz with 8PSK modulation. The parallel concatenation example uses two rate 4/5 8-state convolutional codes with two interleavers. The convolutional codes' outputs are then mapped to two 8PSK modulations. The serial concatenated code example uses an 8-state outer code with rate 4/5 and a 4-state inner trellis code with 5 inputs and 2 x 8PSK outputs per trellis branch. Based on the above mentioned design criteria for fading channels, a method to obtain he structure of the trellis code with maximum diversity is proposed. Simulation results are given for AWGN and an independent Rayleigh fading channel with perfect Channel State Information (CSI).

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.

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.

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.

Design space exploration of high throughput finite field multipliers for channel coding on Xilinx FPGAs

NASA Astrophysics Data System (ADS)

de Schryver, C.; Weithoffer, S.; Wasenmüller, U.; Wehn, N.

2012-09-01

Channel coding is a standard technique in all wireless communication systems. In addition to the typically employed methods like convolutional coding, turbo coding or low density parity check (LDPC) coding, algebraic codes are used in many cases. For example, outer BCH coding is applied in the DVB-S2 standard for satellite TV broadcasting. A key operation for BCH and the related Reed-Solomon codes are multiplications in finite fields (Galois Fields), where extension fields of prime fields are used. A lot of architectures for multiplications in finite fields have been published over the last decades. This paper examines four different multiplier architectures in detail that offer the potential for very high throughputs. We investigate the implementation performance of these multipliers on FPGA technology in the context of channel coding. We study the efficiency of the multipliers with respect to area, frequency and throughput, as well as configurability and scalability. The implementation data of the fully verified circuits are provided for a Xilinx Virtex-4 device after place and route.

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.

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

Inter-track interference mitigation with two-dimensional variable equalizer for bit patterned media recording

NASA Astrophysics Data System (ADS)

Wang, Yao; Vijaya Kumar, B. V. K.

2017-05-01

The increased track density in bit patterned media recording (BPMR) causes increased inter-track interference (ITI), which degrades the bit error rate (BER) performance. In order to mitigate the effect of the ITI, signals from multiple tracks can be equalized by a 2D equalizer with 1D target. Usually, the 2D fixed equalizer coefficients are obtained by using a pseudo-random bit sequence (PRBS) for training. In this study, a 2D variable equalizer is proposed, where various sets of 2D equalizer coefficients are predetermined and stored for different ITI patterns besides the usual PRBS training. For data detection, as the ITI patterns are unknown in the first global iteration, the main and adjacent tracks are equalized with the conventional 2D fixed equalizer, detected with Bahl-Cocke-Jelinek-Raviv (BCJR) detector and decoded with low-density parity-check (LDPC) decoder. Then using the estimated bit information from main and adjacent tracks, the ITI pattern for each island of the main track can be estimated and the corresponding 2D variable equalizers are used to better equalize the bits on the main track. This process is executed iteratively by feeding back the main track information. Simulation results indicate that for both single-track and two-track detection, the proposed 2D variable equalizer can achieve better BER and frame error rate (FER) compared to that with the 2D fixed equalizer.

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

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.

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.

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.

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.

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

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.

"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.

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.

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.

High-Performance CCSDS AOS Protocol Implementation in FPGA

NASA Technical Reports Server (NTRS)

Clare, Loren P.; Torgerson, Jordan L.; Pang, Jackson

2010-01-01

The Consultative Committee for Space Data Systems (CCSDS) Advanced Orbiting Systems (AOS) space data link protocol provides a framing layer between channel coding such as LDPC (low-density parity-check) and higher-layer link multiplexing protocols such as CCSDS Encapsulation Service, which is described in the following article. Recent advancement in RF modem technology has allowed multi-megabit transmission over space links. With this increase in data rate, the CCSDS AOS protocol implementation needs to be optimized to both reduce energy consumption and operate at a high rate.

SCaN Network Ground Station Receiver Performance for Future Service Support

NASA Technical Reports Server (NTRS)

Estabrook, Polly; Lee, Dennis; Cheng, Michael; Lau, Chi-Wung

2012-01-01

Objectives: Examine the impact of providing the newly standardized CCSDS Low Density Parity Check (LDPC) codes to the SCaN return data service on the SCaN SN and DSN ground stations receivers: SN Current Receiver: Integrated Receiver (IR). DSN Current Receiver: Downlink Telemetry and Tracking (DTT) Receiver. Early Commercial-Off-The-Shelf (COTS) prototype of the SN User Service Subsystem Component Replacement (USS CR) Narrow Band Receiver. Motivate discussion of general issues of ground station hardware design to enable simple and cheap modifications for support of future services.

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

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.