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IEEE International Conference on Communication Systems (ICCS)

作者： Sibel, Jean-Christophe Reynal, Sylvain Declercq, David Univ Cergy Pontoise ENSEA ETIS CNRSINRIAUMR 8051 Cergy Pontoise France Univ Cergy Pontoise CNRS UMR 8051 ETIS ENSEA Cergy Pontoise France

ISBN: (纸本)9781467320542;9781467320528

The Belief Propagation (BP) is an inference algorithm used to estimate marginal probability distributions for any Markov Random Field (MRF). In the realm of Low-Density Parity-Check (LDPC) codes that can be represented by MRF called Tanner graphs, the BP is used as a decoding algorithm to estimate the states of bits sent through a noisy channel. Known to be optimal when the Tanner graph is a tree, the BP suffers from suboptimality when the Tanner graph has a loop-like topology. Furthermore, combinations of loops, namely the trapping sets, are particularly harmful for the decoding. To circumvent this problem were proposed other algorithms, like the Generalized Belief Propagation (GBP) that comes from statistical physics. This algorithm allows to absorb topological structures inside new nodes called regions. An advantage is that the resulting graph, the region graph, is not unique then according to its construction this region graph is a media for the GBP that can provide more accurate estimates than the BP. In this paper, we propose novel constructions of the region graph for the famous Tanner code of length N = 155 by making use of the trapping sets as basis for the regions.

关键词： trapping sets Belief propagation Line graph noisy channel Inference algorithms Probability distribution decoding algorithm

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A quadratic Welch-Berlekamp algorithm to decode generalized Gabidulin codes, and some variants

A quadratic Welch-Berlekamp algorithm to decode generalized ...

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IEEE International Symposium on Information Theory (ISIT)

作者： Robert, Gwezheneg Univ Rennes 1 IRMAR Rennes France

ISBN: (纸本)9781509018062

Gabidulin codes are Maximum Rank Distance (MRD) codes. They have been recently generalized to cyclic Galois extension fields. The unique decoding problem is equivalent to the linear reconstruction problem. The aim of this article is the study of an algorithm to solve this reconstruction problem. We prove that the output of our algorithm is a solution of the reconstruction problem. Then we give some variants. We also establish that (one of the variant of) the algorithm is quadratic.

关键词： Gabidulin codes rank metric skew polynomials decoding algorithm

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decoding color codes by projection onto surface codes

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Physical Review A 2014年第1期89卷 012317-012317页

作者： Nicolas Delfosse []INRIA Saclay & LIX école Polytechnique 91128 Palaiseau France

We propose a general strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes. Applying this idea to a family of hexagonal color codes, with the perfect matching decoding algorithm for the three corresponding surface codes, we find a phase error threshold of approximately 8.7%. Finally, our approach enables us to establish a general lower bound on the error threshold of a family of color codes depending on the threshold of the three corresponding surface codes. These results are based on a chain complex interpretation of surface codes and color codes.

关键词： codes projection surface COLOR ENCODING Codes decoding algorithm

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Distributed source coding in wireless sensor networks using LDPC coding: The entire Slepian-Wolf rate region

Distributed source coding in wireless sensor networks using ...

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IEEE Wireless Communications and Networking Conference

作者： Sartipi, M Fekri, F Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

ISBN: (纸本)0780389662

In this paper, we propose a scheme for distributed source coding that achieves any arbitrary rate on the Slepian-Wolf rate region using a single systematic LDPC code. This method is based on sending a fraction of the information bits along with a fraction of parity bits generated by the LDPC code. First, we study the problem of distributed source coding of two correlated sources at the symmetric rate. We propose to use non-uniform LDPC codes for this application. Then, we generalize our approach to any arbitrary rate on the Slepian-Wolf rate region. The detailed construction of this scheme is investigated. We illustrate that the design procedure for the LDPC code simplifies to the design of rate-adaptive LDPC codes that need unequal error protection. It is shown that the performance of distributed source coding at any arbitrary rate is almost the same as that of asymmetric rates. Because of the proposed decoding algorithm, each of the sources is decoded independently (only part of the information bits are being exchanged between the decoders). Therefore, this approach does not suffer from the problems of heavily damaged or propagation of the errors. This method can be easily applied to joint source-channel coding.

关键词： decoding parity check codes source coding variable rate codes wireless sensor networks Slepian-Wolf rate region decoding algorithm distributed source coding nonuniform LDPC codes rate-adaptive LDPC codes symmetric rate correlated sources systematic LDPC

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LDPC Decoder Based on Markov Chain Monte Carlo Method 14

LDPC Decoder Based on Markov Chain Monte Carlo Method

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14th IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)

作者： Jin, Jiejun Liang, Xiao Xu, Yunhao Zhang, Zaichen You, Xiaohu Zhang, Chuan Southeast Univ Lab Efficient Architectures Digital Commun & Sign Nanjing Jiangsu Peoples R China Southeast Univ Natl Mobile Commun Res Lab Nanjing Jiangsu Peoples R China Southeast Univ Chien Shiung Wu Coll Nanjing Jiangsu Peoples R China Southeast Univ Quantum Informat Ctr Nanjing Jiangsu Peoples R China

ISBN: (纸本)9781538682401

Low-density parity check (LDPC) codes have attracted the attention of a large number of researchers with its near-Shannon performance and easy implementation features. As a data coding scheme under the 5G scenario, how to achieve efficient encoding/decoding for LDPC codes has become one of the important research topics. Under this condition, this paper 1) proposes a novel decoding algorithm for LDPC codes using the Markov Chain Monte Carlo (MCMC) method and 2) introduces two improved versions, MCMC-S and MCMC-L, which achieve better results. Simulation figures show that the improved methods outperform the traditional belief propagation (BP) decoding method in relatively short codes by more than 1 dB at the bit error rate (BER) of 10. Very large scale integration (VLSI) architecture of the proposed method is also given in this paper.

关键词： LDPC codes decoding algorithm Markov Chain Monte Carlo (MCMC) method VLSI

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decoding OF MATRIX-PRODUCT CODES

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JOURNAL OF ALGEBRA AND ITS APPLICATIONS 2013年第4期12卷 1250185-1250185页

作者： Hernando, Fernando Ruano, Diego Univ Jaume 1 Dept Math Castellon De La Plana 12071 Spain Aalborg Univ Dept Math Sci DK-9220 Aalborg Denmark

We propose a decoding algorithm for the (u vertical bar u + v)-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two diffe... 详细信息

关键词： Linear codes matrix-product codes decoding algorithm minimum distance

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Hierarchical Constrained Coding for Floating-Gate to Floating-Gate Coupling Mitigation in Flash Memory

Hierarchical Constrained Coding for Floating-Gate to Floatin...

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54th Annual IEEE Global Telecommunications Conference (GLOBECOM)

作者： Motwani, Ravi Intel Corp NVM Solut Grp Santa Clara CA 95051 USA

ISBN: (纸本)9781424492688

Flash memory comprises of grid of cells arranged in a rectangular lattice. A cell is a floating gate and the information is stored as charge in these floating gates. A multi-level-cell (MLC) stores more than one bit per cell. Programming of a cell in NAND Flash is attained by Fowler-Nordhiem tunneling till the ideal programmed voltage is attained. However, due to programming time constraints, some tolerance is accepted and the actual programmed voltage is allowed to be within some range of the ideal value. The read level is a random variable with some distribution around the mean programming level. Errors occur during reads because of overlaps of the level distributions. If the raw bit error rate has to be kept low, the distributions must be narrow. One of the impairment which broadens the distributions is the capacitive coupling between neighboring cells. This phenomenon called as inter-cell-interference due to floating-gate to floating-gate coupling can be from mild to extreme. To combat this effect, constrained coding is a possible solution. Constrained coding entails forbidding certain adjacent-cell charge-level combinations. There can be various types of constrained codes, one type of constrained codes assumes that level information is available while decoding all pages [1]. However, due to read latency requirements, level information may not be available while reading all pages. In this paper, constrained codes are proposed which do not need level information while decoding all pages and hence the average read latency is reduced. Error propagation is a crucial degrading factor for constrained decoding and the codes proposed are robust to channel noise. A new decoding algorithm which keeps synchronization which is crucial to contain error propagation is also proposed.

关键词： decoding Encoding Flash memory Indexes Maximum likelihood estimation Noise measurement Synchronization capacitive coupling decoding algorithm error propagation flash memories flash memory floating-gate coupling mitigation hierarchical constrained coding hot-electron injection intercell-interference multilevel-cell neighboring cells programming time constraints rectangular lattice

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A QC-LDPC code based digital signature algorithm

A QC-LDPC code based digital signature algorithm

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International Conference on Networking and Network Applications (NaNA)

作者： Ren, Fang Yang, Xuefei Zheng, Dong Xian Univ Posts & Telecommun Sch Telecommun & Informat Engn Xian Shaanxi Peoples R China Xian Univ Posts & Telecommun Natl Engn Lab Wireless Secur Xian Shaanxi Peoples R China

ISBN: (纸本)9781538683033

CFS digital signature algorithm, which proposed in 2001, is the most important code based digital signature algorithm and can resist the known attack of quantum algorithms. But the efficiency of CFS is very low because of the extremely low signing speed and the large public key size. In this paper, a variation of CFS algorithm is presented. Instead of the Goppa code and the Patterson decoding algorithm, the new algorithm selects the Quasi-Cyclic Low Density Parity Check (QC-LDPC) code and the Belief Propagation (BP) decoding algorithm in the signing process. Compared with CFS algorithm, the new algorithm greatly reduces the storage space of public key and improves the efficiency of signature without compromising the security.

关键词： code based cryptography digital signature QCLDPC code decoding algorithm

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The error locator polynomial for correctable (t+1)-error of RS codes

The error locator polynomial for correctable (<i>t</i>+1)-er...

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International Symposium on Information Theory and Its Applications

作者： Mohri, Masami Morii, Masakatu Gifu Univ Informat & Multimedia Ctr 1-1 Yanagido Gifu 5011193 Japan Kobe Univ Fac Engn Dept Elect & Elect Engn Kobe Hyogo 6578501 Japan

ISBN: (纸本)9781424420681

The t-error-correcting Reed-Solomon (RS) code can detect more than t errors with high probability [1]. Welch-Berlekamp (WB) algorithm is known as a decoding algorithm for RS codes [2] [3], and it can solved the remainder key-equation. We have shown the condition for detecting the (t+μ)-error of RS code by WB algorithm [4]. In this paper, we show a error locator polynomial for correctable (t+1)-error of RS codes.

关键词： error-locator polynomial Reed-Solomon codes decoding algorithm

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On a Construction of Universal Network Code using LDPC Matrices

On a Construction of Universal Network Code using LDPC Matri...

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IEEE International Symposium on Information Theory

作者： Miyake, Shigeki Muramatsu, Jun Nippon Telegraph & Tel Corp Network Innovat Labs 1-1 Hikarinooka Yokosuka Kanagawa Japan

ISBN: (纸本)9781467325790

An LDPC matrix is used as a local encoding kernel at each link to construct a universal code to address network coding problems. It is also shown that at each terminal node the global encoding kernel that constructs a decoder becomes an LDPC matrix. This provides the perspective that decoding complexity can be reduced to a linear order of a block length by using an efficient decoding algorithm such as the sum-product algorithm.

关键词： universal coding Sum-product algorithm decoding algorithm decoders Perspective end node Codes

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