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A Stopping Criterion for Symbol Flipping Decoding of non-binary ldpc codes

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2021年第11期E104A卷 1644-1648页

作者： Zhao, Zhanzhan Jiao, Xiaopeng Mu, Jianjun Li, Qingqing Xidian Univ Sch Comp Sci & Technol Xian 710071 Peoples R China

YA properly designed stopping criterion for iterative decoding algorithms can save a number of iterations and lead to a considerable reduction of system latency. The symbol flipping decoding algorithms based on prediction (SFDP) have been proposed recently for efficient decoding of non-binary low-density parity-check (ldpc) codes. To detect the decoding frames with slow convergence or even non-convergence, we track the number of oscillations on the value of objective function during the iterations. Based on this tracking number, we design a simple stopping criterion for the SFDP algorithms. Simulation results show that the proposed stopping criterion can significantly reduce the number of iterations at low signal-to-noise ratio regions with slight error performance degradation.

关键词： non-binary ldpc codes symbol flipping decoding stopping criterion

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Large Girth non-binary ldpc codes Based on Finite Fields and Euclidean Geometries

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IEEE SIGNAL PROCESSING LETTERS 2009年第6期16卷 521-524页

作者： Jiang, Xueqin Lee, Moon Ho Chonbuk Natl Univ Inst Informat & Commun Chonju 561756 South Korea

This letter presents an approach to the construction of non-binary low-density parity-check (ldpc) codes based on alpha-multiplied circulant permutation matrices and hyperplanes of two different dimensions in Euclidean geometries. codes constructed by this method have large girth and high binary column weight when the order of Galois field is high. Simulation results show that these codes perform very well with fast Fourier transform (FFT) based sum-product algorithm (SPA).

关键词： Euclidean geometry non-binary ldpc codes alpha-multiplied circulant permutation matrices mu-flats

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Check Node Reliability-Based Scheduling for BP Decoding of non-binary ldpc codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第3期61卷 877-885页

作者： Han, Guojun Guan, Yong Liang Huang, Xinmei Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Guangdong Univ Technol Sch Informat Engn Guangzhou 510006 Guangdong Peoples R China

Scheduling strategy is considered an important aspect of belief-propagation (BP) decoding of low-density parity-check (ldpc) codes because it affects the decoder's convergence rate, decoding complexity and error-correction performance. In this paper, we propose two new scheduling strategies for the BP decoding of non-binary ldpc (NB-ldpc) codes. Both the strategies are devised based on the concept of check node reliability and employ a heuristically defined threshold which can adapt to the communication channel variations. As the scheduling strategies only update a subset of the check nodes in each iteration, they result in reduced iteration cost. Furthermore, since the BP performs suboptimally for finite-length ldpc codes, especially for short-length ldpc codes, by enhancing the message propagation over the Tanner Graphs of short-length NB-ldpc codes, the new scheduling strategies can even improve the error-correction performances of BP decoding. Simulation results demonstrate that the new scheduling strategies provide good performance/complexity tradeoffs.

关键词： Belief-propagation (BP) iterative decoding low-density parity-check (ldpc) codes non-binary ldpc codes scheduling strategy

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Set Message-Passing Decoding Algorithms for Regular non-binary ldpc codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2017年第12期65卷 5110-5122页

作者： Huang, Qin Song, Liyuan Wang, Zulin Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China Collaborat Innovat Ctr Geospatial Technol Wuhan 430079 Hubei Peoples R China

In the check node (CN) update of non-binary message-passing algorithms, each element of reliability vectors takes the same computational complexity. However, our analysis indicates that various elements in the same vector have various correct probabilities, thus have different contributions to error performance. In order to match computational complexity with correct probability, all elements in a vector are partitioned into different sets. For the extended min-sum (EMS) decoding, various strategies are applied for sets according to their correct probability. For the trellis-based EMS decoding, it is interesting that set partition only involves fixed paths, thus it does not need to search over the whole trellis of a CN. Complexity analysis and simulation results show that the proposed algorithms efficiently decode non-binary low-density parity-check codes, including ultra-sparse ones.

关键词： non-binary ldpc codes check node update set partition fixed paths

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Low-Complexity Decoding for non-binary ldpc codes in High Order Fields

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IEEE TRANSACTIONS ON COMMUNICATIONS 2010年第5期58卷 1365-1375页

作者： Voicila, Adrian Declercq, David Verdier, Francois Fossorier, Marc Urard, Pascal Univ Cergy Pontoise CNRS ETIS ENSEA F-95000 Cergy Pontoise France STMicroelectronics Crolles France

In this paper, we propose a new implementation of the Extended Min-Sum (EMS) decoder for non-binary ldpc codes. A particularity of the new algorithm is that it takes into accounts the memory problem of the non-binary ldpc decoders, together with a significant complexity reduction per decoding iteration. The key feature of our decoder is to truncate the vector messages of the decoder to a limited number n(m). of values in order to reduce the memory requirements. Using the truncated messages, we propose an efficient implementation of the EMS decoder which reduces the order of complexity to O(n(m) log(2) n(m)). This complexity starts to be reasonable enough to compete with binary decoders. The performance of the low complexity algorithm with proper compensation is quite good with respect to the important complexity reduction, which is shown both with a simulated density evolution approach and actual simulations.

关键词： Iterative decoding non-binary ldpc codes low complexity algorithm

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Momentum-Based Symbol Flipping Decoding Algorithms for non-binary ldpc codes

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2023年第7期72卷 9579-9584页

作者： Zhao, Zhanzhan Jiao, Xiaopeng Mu, Jianjun Han, Hui He, Yu-Cheng Xidian Univ Sch Comp Sci & Technol Xian 710071 Peoples R China Huaqiao Univ Xiamen Key Lab Mobile Multimedia Commun Xiamen 361021 Peoples R China Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Peoples R China

This paper investigates the application of gradient descent with momentum in symbol flipping decoding algorithms based on prediction (SFDP) for non-binary low-density parity-check (NB-ldpc) codes. The momentum added in the objective function of SFDP algorithms can provide inertia to the decoding process by considering the flipping states in the past iterations. Simulation results show that the proposed momentum-based SFDP algorithms perform significantly better than the original SFDP algorithms with low extra complexity. Furthermore, to lower the error floor of momentum-based SFDP algorithms, we also introduce artificial noises into the objective functions of momentum-based SFDP algorithms to help the iterative decoding escape from local optimum.

关键词： Gaussian noise non-binary ldpc codes momentum symbol flipping decoding

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Fast-Converging Flipping Rules for Symbol Flipping Decoding of non-binary ldpc codes

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2019年第7期E102A卷 930-933页

作者： Zhao, Zhanzhan Jiao, Xiaopeng Mu, Jianjun He, Yu-Cheng Guo, Junjun Xidian Univ Sch Comp Sci & Technol Xian 710071 Shaanxi Peoples R China Huaqiao Univ Xiamen Key Lab Mobile Multimedia Commun Xiamen 361021 Fujian Peoples R China Xian Technol Univ Sch Comp Sci & Engn Xian 710021 Shaanxi Peoples R China

The symbol flipping decoding algorithms based on prediction (SFDP) for non-binary ldpc codes perform well in terms of error performances but converge slowly when compared to other symbol flipping decoding algorithms. In order to improve the convergence rate, we design new flipping rules with two phases for the SFDP algorithms. In the first phase, two or more symbols are flipped at each iteration to allow a quick increase of the objective function. While in the second phase, only one symbol is flipped to avoid the oscillation of the decoder when the objective function is close to its maximum. Simulation results show that the SFDP algorithms with the proposed flipping rules can reduce the average number of iterations significantly, whereas having similar performances when compared to the original SFDP algorithms.

关键词： non-binary ldpc codes symbol flipping decoding flipping rules

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A Hybrid Decoding Scheme for Short non-binary ldpc codes

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IEEE COMMUNICATIONS LETTERS 2014年第12期18卷 2093-2096页

作者： Baldi, Marco Chiaraluce, Franco Maturo, Nicola Liva, Gianluigi Paolini, Enrico Univ Politecn Marche Dipartimento Ingn Informaz I-60131 Ancona Italy German Aerosp Ctr DLR Inst Commun & Nav D-82234 Wessling Germany Univ Bologna Dept Elect Elect & Informat Engn G Marconi I-47521 Bologna Italy

In this paper, an iterative soft-decision hybrid decoding algorithm for non-binary low-density parity-check (ldpc) codes with short codeword lengths is proposed. The rationale of the approach is to combine the classical belief propagation (BP) iterative ldpc decoding algorithm with the most reliable basis (MRB) decoding algorithm. This allows to achieve significant performance improvements, with a complexity that, for medium/low error rates, is only slightly higher than that of the BP algorithm alone. The performance improvement with respect to pure BP decoding is up to 0.7 dB at codeword error rate (CER) approximate to 10(-5). Notably, for a fixed MRB order, hybrid decoding achieves a gain up to 0.5 dB at CER approximate to 10(-5) with respect to BP decoding and MRB decoding used alone.

关键词： Decoding complexity iterative decoding MRB decoding non-binary ldpc codes

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Blind Recognition of non-binary ldpc codes Based on Ant Colony Optimization

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China Communications 2024年第10期21卷 59-69页

作者： Guan Mengsheng Gao Wanting Chen Qi Zhu Min Bai Baoming State Key Laboratory of Integrated Services Networks Xidian UniversityXi'an 710071China

This paper introduces a novel blind recognition of non-binary low-density parity-check(ldpc)codes without a candidate set,using ant colony optimization(ACO)algorithm over additive white Gaussian noise(AWGN)***,the scheme that effectively combines the ACO algorithm and the non-binary elements over finite fields is ***,an improved,simplified elitist ACO algorithm based on soft decision reliability is introduced to recognize the parity-check matrix over noisy *** results show that the recognition rate continuously increases with an increased signalto-noise ratio(SNR)over the AWGN channel.

关键词： ACO blind recognition non-binary ldpc codes open-set

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Puncturing Schemes for Rate-Compatible non-binary ldpc codes

Puncturing Schemes for Rate-Compatible Non-binary LDPC Codes

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IEEE International Conference on Electronics, Communications and Control (ICECC)

作者： Zhang, Bing Su, He-Guang Xia, Shu-Tao Tsinghua Univ Grad Sch Shenzhen Shenzhen 518055 Peoples R China

ISBN: (纸本)9781457703218

Finding good puncturing patterns for rate-compatible non-binary ldpc codes are considered over additive white Gaussian noise (AWGN) channels in this paper. We first study several popular puncturing schemes for binary ldpc codes and generalize them to non-binary ldpc codes, where the effects of short cycles in Tanner graph are rarely investigated. By carefully studying the impacts of short cycles when puncturing, we put forward a novel puncturing scheme for rate-compatible non-binary ldpc codes. Simulation results show that the proposed puncturing scheme is superior to the above known ones for rate-compatible non-binary ldpc codes over AWGN channels at certain cases.

关键词： rate-compatible non-binary ldpc codes Tanner graph puncturing

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