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An Improved reliability-based decoding Algorithm for NB-LDPC Codes

IEEE COMMUNICATIONS LETTERS 2021年第4期25卷 1153-1157页

作者： Song, Suwen Tian, Jing Lin, Jun Wang, Zhongfeng Nanjing Univ Sch Elect Sci & Engn Nanjing 210023 Peoples R China

When non-binary low-density parity-check (NB-LDPC) codes with low column weights are adopted, the iterative reliability-based majority-logic decoding (IRB-MLGD) algorithms suffer from severe performance degradation compared to message passing algorithms. In this brief, based on the improved iterative soft reliability-based (IISRB)-MLGD algorithm, we propose a perturbation-injected (P)-IISRB algorithm, where a regular perturbation is introduced to alleviate the periodic point problem that is the main reason for IISRB decoding failure. Compared with the conventional IISRB, the new algorithm significantly improves the decoding performance, lowering the error-floor by at least two orders of magnitude for the example code. Besides, instead of traditionally pre-computing and storing all the q-ary channel reliability measures, a real-time computing method is presented, which reduces the memory cost from O(q) to O(log(2) q).

关键词： reliability Iterative decoding Perturbation methods decoding Real-time systems Memory management Computational complexity Error-correction codes non-binary LDPC codes reliability-based decoding majority-logic decoding perturbation

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Error performance analysis for reliability-based decoding algorithms

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IEEE TRANSACTIONS ON INFORMATION THEORY 2002年第1期48卷 287-293页

作者： Fossorier, MPC Lin, S Univ Hawaii Dept Elect Engn Honolulu HI 96822 USA Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

In this correspondence, the statistical approach proposed by Agrawal and Vardy to evaluate the error performance of the generalized minimum distance (GMD) decoding is extended to other reliability-based decoding algorithms for binary linear block codes, namely Chase-type, combined GMD and Chase-type, and order statistic decodings (OSDs). In all cases, tighter and simpler bounds than those previously proposed have been obtained with this approach.

关键词： block codes decoding order statistics reliability-based decoding soft-decision decoding

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reliability-based Windowed decoding for Spatially Coupled LDPC Codes

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IEEE COMMUNICATIONS LETTERS 2018年第7期22卷 1322-1325页

作者： Kang, Peng Xie, Yixuan Yang, Lei Yuan, Jinhong Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia

In this letter, we propose a reliability-based windowed decoding scheme for spatially coupled (SC) low-density parity-check (LDPC) codes. To mitigate the error propagation along the sliding windowed decoder of the SC LDPC codes, a partial message reservation method is proposed where only the reliable messages generated in the previous decoding window are reserved for the next decoding window. We also propose a partial syndrome check stopping rule for each decoding window, in which only the complete variable nodes are checked. Simulation results show that our proposed scheme significantly improves the error-floor performance compared to the sliding windowed decoder with the conventional weighted bit-flipping algorithm.

关键词： Spatially-coupled (SC) LDPC codes reliability-based decoding windowed decoding

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Comparisons Between reliability-based Iterative Min-Sum and Majority-Logic decoding Algorithms for LDPC Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2011年第7期59卷 1766-1771页

作者： Chen, Haiqiang Zhang, Kai Ma, Xiao Bai, Baoming Sun Yat Sen Univ Dept Elect & Commun Engn Guangzhou 510275 Guangdong Peoples R China Guangxi Univ Sch Comp Elect & Informat Nanning 530004 Peoples R China Xidian Univ State Key Lab ISN Xian Peoples R China

A modified reliability-based iterative majority-logic decoding (MRBI-MLGD) algorithm for two classes of structured LDPC codes is presented based on a recent work by Huang et al. Compared with the original one, the modified algorithm has better performance with slightly increased complexity. Then a reliability-based iterative min-sum decoding (RBI-MSD) algorithm is presented. For the presented RBI-MSD algorithm, reliability-based integer messages are processed and exchanged between variable nodes and check nodes. The main computations include only binary logical operations and integer additions. Different from the conventional min-sum algorithm, the variable nodes pass full messages rather than extrinsic messages to check nodes. This can reduce the memory loads and the computational complexity but with a little (or negligible) performance degradation. Simulation results show that, compared with the (M) RBI-MLGD algorithms, the presented RBI-MSD algorithm achieves better error performance, faster decoding convergence rate and fewer quantization bits with moderate increased computational complexity. Furthermore, the RBI-MSD algorithm is also applicable to decoding random LDPC codes, a distinct difference from the (M) RBI-MLGD algorithms. Finally, we point out that the scaling factors employed in the MRBI-MLGD algorithm and the RBI-MSD algorithm can be optimized using discretized density evolution.

关键词： Low-density parity-check (LDPC) codes min-sum decoding reliability-based decoding soft-decision decoding structured LDPC codes

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reliability-based Joint Detection-decoding Algorithm for Nonbinary LDPC-Coded Modulation Systems

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IEEE TRANSACTIONS ON COMMUNICATIONS 2016年第1期64卷 2-14页

作者： Zhu, Min Guo, Quan Bai, Baoming Ma, Xiao Xidian Univ State Key Lab ISN Xian 710071 Peoples R China Sun Yat Sen Univ Dept Elect & Commun Engn Guangzhou 510275 Guangdong Peoples R China

This paper studies an extension and improvement of the joint detection-decoding algorithm for nonbinary LDPC-coded modulation systems. The iterative joint detection-decoding (IJDD) algorithm in [1] combines nonbinary LDPC decoding with signal detection based on the hard-message passing strategy, resulting in significantly reduced decoding complexity. However, it applies only to majority-logic decodable nonbinary LDPC codes with high column weight. For nonbinary LDPC codes with low column weight, a noticeable performance loss will be incurred. To handle this problem, we propose a reliability-based iterative joint detection-decoding (also termed improved IJDD) algorithm, which combines the accumulated reliability of symbols based on the one-step majority-logic decoding (MLGD) algorithm and a Chase-like local list decoding algorithm. Simulation results show that the improved IJDD algorithm outperforms the IJDD algorithm by about 0.3 dB using nonbinary LDPC codes with high column weight, and by about 3 dB using nonbinary LDPC codes with low column weight (d(v) = 4), while maintaining the low complexity of decoding. Compared to the FFT-QSPA, the proposed algorithm has a performance degradation of 0.5 dB in the high column weight regime, and about 1 dB in the low column weight regime.

关键词： Coded modulation joint detection-decoding algorithm majority-logic decoding nonbinary LDPC codes reliability-based decoding

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reliability-based Iterative Proportionality-logic decoding of LDPC Codes with Adaptive Decision

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JOURNAL OF COMMUNICATIONS AND NETWORKS 2015年第3期17卷 213-220页

作者： Sun, Youming Chen, Haiqiang Li, Xiangcheng Luo, Lingshan Qin, Tuanfa S China Univ Technol Sch Elect & Informat Engn Guangzhou 510641 Guangdong Peoples R China Guangxi Univ Sch Phys Sci & Technol Nanning 530004 Peoples R China Guangxi Univ Sch Comp Elect & Informat Nanning 530004 Peoples R China Guangxi Univ Guangxi Coll & Univ Key Lab Multimedia Commun & I Guangxi Key Lab Multimedia Commun & Network Techn Cultivating Base Nanning 530004 Peoples R China

In this paper, we present a reliability-based iterative proportionality-logic decoding algorithm for two classes of structured low-density parity-check (LDPC) codes. The main contributions of this paper include: 1) Syndrome messages instead of extrinsic messages are processed and exchanged between variable nodes and check nodes, which can reduce the decoding complexity;2) a more flexible decision mechanism is developed in which the decision threshold can be self-adjusted during the iterative process. Such decision mechanism is particularly effective for decoding the majority-logic decodable codes;3) only part of the variable nodes satisfying the pre-designed criterion are involved for the presented algorithm, which is in the proportionality-logic sense and can further reduce the computational complexity. Simulation results show that, when combined with factor correction techniques and appropriate proportionality parameter, the presented algorithm performs well and can achieve fast decoding convergence rate while maintaining relative low decoding complexity, especially for small quantized levels (3-4 bits). The presented algorithm provides a candidate for those application scenarios where the memory load and the energy consumption are extremely constrained.

关键词： Adaptive decision decoding function low-density parity-check (LDPC) codes proportionality-logic reliability-based decoding

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Performance of reliability-based iterative soft-decision Reed-Solomon decoding on magnetic recording channels

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IEEE TRANSACTIONS ON MAGNETICS 2007年第7期43卷 3320-3323页

作者： Xia, Haitao Cruz, J. R. Link A Media Devices Corp Santa Clara CA 95051 USA Univ Oklahoma Sch Elect & Comp Engn Norman OK 73019 USA

We have investigated an adaptive reliability-based iterative soft-decision Reed-Solomon decoding algorithm using belief propagation and we propose a reduced-complexity version of this algorithm. We discuss implementat... 详细信息

关键词： belief propagation iterative decoding magnetic recording reduced-complexity algorithms Reed-Solomon codes reliability-based decoding soft-decision decoding

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reliability-based Soft-Decision decoding with Iterative Information Set Reduction¹ 1 Supported by NSF Grant CCR-97-32959.

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Electronic Notes in Discrete Mathematics 2001年 6卷 356-363页

作者： Fossorier, Marc Dept. of Electrical Engineering University of Hawaii Honolulu HI 96822 2540 Dole St. Holmes Hall 455 United States

In this paper, the reliability-based decoding approach using the reprocessing of the most reliable information set only is extended into the reprocessing of several information sets. At the end of each information set reprocessing, some information bits are delivered by the decoder. Consequently, information sets with decreasing cardinality are considered at each reprocessing stage. A tight upper bound on the error performance achieved by this method is derived. Compared with previously proposed competitive approaches, this new method not only reduces the number of candidate codewords needed to achieve practically optimum decoding, but also allows to achieve nearly any desired level of error performance. © 2001.

关键词： Block Codes Information Set decoding Ordered Statistics reliability-based decoding Soft Decision decoding

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Bit reliability-based Decoders for Non-Binary LDPC Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2016年第1期64卷 38-48页

作者： Huang, Qin Yuan, Shuai China Acad Space Technol Qian Xuesen Lab Space Technol Beijing 100094 Peoples R China Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China

Message-passing decoders typically perform well for nonbinary low-density parity-check (NB-LDPC) codes with large computational complexity. As another type of simplified decoders, symbol-reliability-based decoders further reduce the computational complexity. However, the previously proposed algorithms suffer severe error performance degradation for NB-LDPC codes with low column weights. In this paper, a weighted bit-reliability based (wBRB) decoder for NB-LDPC codes is developed and implemented with efficient layered partial-parallel structure. It not only balances the tradeoff between complexity and error performance, but also reduces the memory usage significantly. Furthermore, to enhance the performance of the wBRB decoder, a full bit-reliability-based (FBRB) decoder is proposed. The FBRB decoder is derived based on the binary matrix representation of the nonzero entries in the parity-check matrix. Since more bit-reliability values are passed through the edges of the Tanner graph, the FBRB decoder can achieve better error performance and faster convergence rate than the wBRB decoder. Both of the decoders are implemented on a Xilinx Virtex-5 XC5VLX155T FPGA device for a (403,226) code over GF(2(5)). The results shows that they achieve 118.98 and 95.73 Mbps throughput with 15 iterations, respectively.

关键词： Non-binary LDPC codes reliability-based decoding soft bit-reliability hard-reliability memory consumption

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Reduced GMD decoding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第4期49卷 1013-1027页

作者： Weber, JH Abdel-Ghaffar, KAS Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

A framework is presented for generalized minimum distance (GMD) decoding with a limited number of decoding trials and a restricted set of reliability values. In GMD decoding, symbols received from the channel may be erased before being fed into an algebraic error-erasure decoder for error correction, in subsequent or simultaneous trials with different erasing patterns. The decision whether or not to erase a symbol in a certain trial is taken by an erasure-choosing algorithm which takes into account reliability information from the channel. The final GMD decoder output is a codeword which results from a decoding trial and satisfies a certain distance criterion. For various erasing strategies and reliability sets, the guaranteed error-correction radius and the unsuccessful decoding probability of this technique are studied. Both known and new results, with applications to concatenated coding, follow from the unified approach presented in this correspondence.

关键词： concatenated codes generalized distance multitrial decoding reliability-based decoding

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