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IEEE International Conference on Information and Automation 2015

作者： Zhang Fu-xing Xu Sheng-wang Beijing Inst Tracking & Telecommun Technol Beijing 100094 Peoples R China

ISBN: (纸本)9781467391047

Rain fade can lead to the deterioration of Ka-band Satellite communication performance, one of the efficient ways against rain fade is using channel coding with better performance. non-binary ldpc codes, as an advanced error correcting code, having strong ability to correct errors, can be used to against rain fade. The paper presents an analysis on influence of rainfalls in Ka-band Satellite communication and establishes the channel model of rain fade. Simulation on system performance based on non-binary codes and rain fade is also conducted, which is brought into comparison to binary ldpc codes and uncoded situations. Result shows, ldpc codes can obtain over 20dB gains over uncoded situation, and non-binary ldpc codes have 1dB performance advantage over binary ldpc codes.

关键词： Ka-band Satellite communication rain fade non-binary ldpc codes coding gains

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Design and Performance of Rate-Compatible non-binary ldpc Convolutional codes

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2011年第11期E94A卷 2135-2143页

作者： Uchikawa, Hironori Kasai, Kenta Sakaniwa, Kohichi Tokyo Inst Technol Dept Commun & Integrated Syst Tokyo 1528550 Japan

In this paper, we present a construction method of nonbinary low-density parity-check (ldpc) convolutional codes. Our construction method is an extension of Felstrom and Zigangirov construction [1] for non-binary ldpc convolutional codes. The rate-compatibility of the non-binary convolutional code is also discussed. The proposed rate-compatible code is designed from one single mother (2,4)-regular nonbinary ldpc convolutional code of rate 1/2. Higher-rate codes are produced by puncturing the mother code and lower-rate codes are produced by multiplicatively repeating the mother code. Simulation results show that non-binary ldpc convolutional codes of rate 1/2 outperform state-of-the-art binary ldpc convolutional codes with comparable constraint bit length. Also the derived low-rate and high-rate non-binary ldpc convolutional codes exhibit good decoding performance without loss of large gap to the Shannon limits.

关键词： non-binary ldpc codes ldpc convolutional codes rate-compatibility

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Low Error-Floor Majority-Logic Decoding Based Algorithm for non-binary ldpc codes

Low Error-Floor Majority-Logic Decoding Based Algorithm for ...

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IEEE International Conference on Communications

作者： Liyuan Song Mu Zhang Qin Huang Zulin Wang School of Electronic and Information Engineering Beihang University

ISBN: (纸本)9781467364300

The traditional majority-logic decoding (MLgD) based algorithms suffer error-floors for decoding non-binary ldpc codes with small column weights. This paper presents a bit-reliability based MLgD (BRB-MLgD) algorithm with low error-floors for non-binary ldpc codes. The proposed algorithm is carried out based on the binary representations of non-binary symbols. The reliability update along each edge of the Tanner graph of a non-binary ldpc code is in terms of bits rather than symbols. Thus, its computational complexity and memory consumption are less than those of the existing MLgD based algorithms. Simulation results indicate that the proposed algorithm can significantly reduce error-floors with small performance degradation in the waterfall region.

关键词： non-binary ldpc codes Majority-logic decoding Bit-reliability Error-floor

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HIGH SPEED DECODING OF non-binary IRREGULAR ldpc codes USING GPUS

HIGH SPEED DECODING OF NON-BINARY IRREGULAR LDPC CODES USING...

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IEEE Workshop on Signal Processing Systems (SiPS)

作者： Beermann, Moritz Monzo, Enrique Schmalen, Laurent Vary, Peter Rhein Westfal TH Aachen Inst Commun Syst & Data Proc I D Aachen Germany

ISBN: (纸本)9781467362382

Low-Density Parity-Check (ldpc) codes are very powerful channel coding schemes with a broad range of applications. The existence of low complexity (i.e., linear time) iterative message passing decoders with close to optimum error correction performance is one of the main strengths of ldpc codes. It has been shown that the performance of these decoders can be further enhanced if the ldpc codes are extended to higher order Galois fields, yielding so called non-binary ldpc codes. However, this performance gain comes at the cost of rapidly increasing decoding complexity. To deal with this increased complexity, we present an efficient implementation of a signed-log domain FFT decoder for non-binary irregular ldpc codes that exploits the inherent massive parallelization capabilities of message passing decoders. We employ Nvidia's Compute Unified Device Architecture (CUDA) to incorporate the available processing power of state-of-the-art Graphics Processing Units (GPUs).

关键词： non-binary ldpc codes iterative decoding GPU implementation

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non-binary QC-ldpc codes for non-Gaussian optical channels

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OPTICAL AND QUANTUM ELECTRONICS 2021年第11期53卷 626-626页

作者： Sethu, P. Sajith Gopchandran, K. G. Solomon, Sam Sree Chitra Thirunal Coll Engn Dept Elect & Commun Engn Thiruvananthapuram 695018 Kerala India Univ Kerala Dept Optoelect Thiruvananthapuram 695581 Kerala India

Low density parity check (ldpc) code is an attractive solution to improve data reliability while ensuring high speed data transmission in long haul optical communication systems. However, capacity approaching coding gains can be achieved only by employing extremely long binary ldpc codes. non-binary ldpc codes provide same coding gain of binary ldpc codes with smaller codelength. But the decoding performance of these codes depends on the accurate realization of channel characteristics. All the existing works assume additive white Gaussian noise (AWGN) channel model for simplicity, which is not realistic. So mathematical analysis of photodetected signal is carried out and proved that the optical channel noise can be more efficiently modelled using chi-square distrubtion. Hence a non-binary quasi cyclic (NB QC) ldpc code based optical system with chi-square channel model is proposed for attaining large coding gains with smaller codeword lengths. non-binary ldpc codes provide better error performance compared to their binary version while its quasi-cyclic property helps to reduce the encoding complexity. In order to reduce the decoding complexity, FFT based q-ary sum product algorithm is employed for ldpc decoding. The error performance analysis shows that the NB QC-ldpc codes with chi-square channel model gives more than 1dB coding gain than the AWGN channel model. The performance of the proposed system is also evaluated in terms of modulation schemes, data rates, dispersion effects and link distance. The results show that the NB QC-ldpc codes give better performace compared to their binary version for the proposed channel model.

关键词： non-binary ldpc codes Chi-square channel Forward error correction Optical communication

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non-binary Quasi-Cyclic Quantum ldpc codes

Non-Binary Quasi-Cyclic Quantum LDPC Codes

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IEEE International Symposium on Information Theory (ISIT)

作者： Kasai, Kenta Hagiwara, Manabu Imai, Hideki Sakaniwa, Kohichi Tokyo Inst Technol Dept Commun & Integrated Syst Tokyo 1528550 Japan Natl Inst Adv Ind Sci & Technol Res Ctr Informat Secur Tokyo 101 Japan Chuo Univ Dept Elect Elect & Commun Engn Fac Sci & Engn Tokyo 112 Japan

ISBN: (纸本)9781457705953

In this paper, we propose a construction method for two-level quantum error-correcting codes via non-binary ldpc codes over an extended field of order 2(p), p an integer p > 1. The proposed quantum error-correcting codes are based on binary quasi-cyclic ldpc codes which have almost achieved a "Bounded Distance Decoding (BDD)" limit but have not surpassed the limit yet. Quantum codes constructed from the proposed method surpass the BDD limit. Furthermore the codes outperform the efficiently-decodable state-of-the-art quantum codes.

关键词： ldpc code non-binary ldpc codes belief propagation Galois field iterative decoding CSS codes quantum error-correcting codes

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P-Adic ldpc codes at Precision k

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WIRELESS PERSONAL COMMUNICATIONS 2024年第2期139卷 1269-1283页

作者： Waweru, Daniel Kariuki Yang, Fengfan Zhao, Chunli Paul, Lawrence Muthama Nanjing Univ Aeronaut & Astronaut Dept Commun & Informat Engn Nanjing 210016 Jiangsu Provinc Peoples R China Egerton Univ Dept Math Njoro 20115 Egerton Kenya

In this paper, we propose the construction of p-adic ldpc codes and develop a multi-stage decoding algorithm for these codes. The novel type of non-binary error-correcting codes operates over the p-adic integers. We evaluate the error performance of these codes through simulations and compare them with existing nonbinary ldpc and Reed-Solomon codes of the same rates. Our results show that p-adic ldpc codes achieve better error performance than the existing codes. Moreover, we demonstrate the potential use of p-adic ldpc codes in byte error correction by treating each byte as an element in the p-adic integers at a chosen precision level. The p-adic ldpc codes can be designed and optimized for specific applications that require byte error correction, with the flexibility to vary the byte under different precision levels.

关键词： non-binary ldpc codes Hensel's lemma p-th power transform Multistage Iterative Decoder

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Design of Regular (2, d_c)-ldpc codes over GF(q) Using Their binary Images

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IEEE TRANSACTIONS ON COMMUNICATIONS 2008年第10期56卷 1626-1635页

作者： Poulliat, Charly Fossorier, Marc Declercq, David ENSEA UCP CNRS ETIS F-95014 Cergy Pontoise France Univ Hawaii Manoa Dept Elect Engn Honolulu HI 96822 USA

In this paper, a method to design regular (2, d(c))-ldpc codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping sets associated with the underlying Tanner graph are studied and linked to the global binary minimum distance of the code. Finally, simulations are presented to illustrate the excellent performance of the designed codes.

关键词： Channel coding error correction coding non-binary ldpc codes iterative decoding binary image

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Stochastic Decoding of ldpc codes over GF(q)

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第3期61卷 939-950页

作者： Sarkis, Gabi Hemati, Saied Mannor, Shie Gross, Warren J. McGill Univ Dept Elect & Comp Engn Montreal PQ H3A 2A7 Canada Linkoping Univ Dept Elect Engn Elect Syst Div S-58183 Linkoping Sweden Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

Despite the outstanding performance of non-binary low-density parity-check (ldpc) codes over many communication channels, they are not in widespread use yet. This is due to the high implementation complexity of their decoding algorithms, even those that compromise performance for the sake of simplicity. In this paper, we present three algorithms based on stochastic computation to reduce the decoding complexity. The first is a purely stochastic algorithm with error-correcting performance matching that of the sum-product algorithm (SPA) for ldpc codes over Galois fields with low order and a small variable node degree. We also present a modified version which reduces the number of decoding iterations required while remaining purely stochastic and having a low per-iteration complexity. The second algorithm, relaxed half-stochastic (RHS) decoding, combines elements of the SPA and the stochastic decoder and uses successive relaxation to match the error-correcting performance of the SPA. Furthermore, it uses fewer iterations than the purely stochastic algorithm and does not have limitations on the field order and variable node degree of the codes it can decode. The third algorithm, NoX, is a fully stochastic specialization of RHS for codes with a variable node degree 2 that offers similar performance, but at a significantly lower computational complexity. We study the performance and complexity of the algorithms;noting that all have lower per-iteration complexity than SPA and that RHS can have comparable average per-codeword computational complexity, and NoX a lower one.

关键词： non-binary ldpc codes ldpc codes over GF(q) stochastic decoding relaxed half-stochastic decoding

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On Bit-Level Decoding of nonbinary ldpc codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2018年第9期66卷 3736-3748页

作者： Zhang, Mu Cai, Kui Huang, Qin Yuan, Shuai Singapore Univ Technol & Design Sci & Math Cluster Singapore 117608 Singapore Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China China Acad Space Technol Qian Xuesen Lab Space Technol Beijing 100094 Peoples R China

This paper addresses binary message-passing (MP) decoding for nonbinary low-density parity-check (NB-ldpc) codes based on the binary image of Galois field symbols. The parity-check matrix of NB-ldpc codes in binary form is used to perform MP. The corresponding nonbinary check node (CN) update and variable node (VN) update can thus be decomposed to a set of binary sub-CN updates and sub-VN updates with much lower computational complexity. In particular, we start from adapting the binary parity-check matrix with Gaussian elimination. Then, we add redundant rows to the parity-check matrix instead of adaptation to further improve the performance. A min-max operation based on the expanded matrix is proposed for the CN update. It not only decreases the computational complexity incurred by Gaussian elimination but also improves the error performance. Simulation results show that the hitlevel decoding with min-max operation can achieve similar error performance as the extended min-sum algorithm, but the computational complexity can be lower than the min-sum algorithm for binary ldpc codes.

关键词： non-binary ldpc codes binary image massage passing bit-level adaptation min-max

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