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Minimum-Set Min-Sum Decoding Algorithms for non-binary ldpc codes

IEEE TRANSACTIONS ON COMMUNICATIONS 2025年第2期73卷 740-751页

作者： Liu, Zhanxian Zhang, Haijun Huo, Jiahao Wang, Ning Univ Sci & Technol Beijing Sch Comp & Commun Engn Beijing 100083 Peoples R China Zhengzhou Univ Sch Informat Engn Henan Joint Int Res Lab Intelligent Networking & D Zhengzhou 450001 Peoples R China

During the check node (CN) update, the elements of input message vectors are redundant for the output message vectors. Hence, in this paper, we exactly select from the input message vectors the elements, which really have contributions to the error-correction performance and constitute the minimum set for the CN update. With adoption of the forward and backward (FB) scheme, an adaptive minimum-set min-sum algorithm (AMSA) is proposed to reduce the computation complexity of the FB process. In order to concurrently update the output vectors belonging to the same CN, we present a parallel minimum-set min-sum algorithm (PMSA) with lower memory complexity than the AMSA. Compared with the min-sum algorithms, the two proposed minimum-set based algorithms introduce no error performance loss.

关键词： Vectors Reliability Decoding Schedules Symbols Computational complexity Reviews non-binary ldpc codes min sum minimum set adaptive decoding parallel decoding

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non-binary ldpc codes under Rotor Occlusion in Helicopter Communication 5

Non-binary LDPC Codes under Rotor Occlusion in Helicopter Co...

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Fifth International Conference on Instrumentation & Measurement, Computer, Communication, and Control (IMCCC)

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

ISBN: (纸本)9781467377232

Satellite communication is important in helicopter communication, it can effectively improve the communication range and communication capacity. Controlled by the installation conditions, satellite antenna will be influenced by helicopter rotor periodically, signal transmission will suffer periodic continuous fading and occur periodic burst errors. non-binary ldpc code is a kind of advanced channel coding scheme, it has strong ability of error correcting. It can convert continuous bit burst errors into less M-ary symbol errors, so it has a good ability to anti burst error. In this paper, simulation of using non-binary ldpc codes to resist the burst errors in the helicopter satellite communication is placed, the results show that non-binary ldpc codes can correct the burst error well which are caused by helicopter rotors. In addition, this paper also discusses a method of decoding initialization in which zero is set in positions under covered, the results demonstrate that the way to set zero can obtain better decoding performance advantages, the performance improvement is about 0.2dB.

关键词： helicopter satellite communication rotor occlusion non-binary ldpc codes

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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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GPU Accelerated Belief Propagation Decoding of non-binary ldpc codes with Parallel and Sequential Scheduling

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JOURNAL OF SIGNAL PROCESSING SYSTEMS FOR SIGNAL IMAGE AND VIDEO TECHNOLOGY 2015年第1期78卷 21-34页

作者： Beermann, Moritz Monzo, Enrique Schmalen, Laurent Vary, Peter Rhein Westfal TH Aachen Inst Commun Syst & Data Proc Aachen Germany Alcatel Lucent Bell Labs IP Transport Program High Speed Syst Signals & Proc Grp Stuttgart Germany Philips Res Eindhoven Netherlands

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 which 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). Furthermore, we present a CUDA implementation of the signed-log domain FFT decoder using the so-called layered update rule, in which check nodes are updated one after another. This sequential updating of nodes has been shown to converge about twice as fast as the traditional flooding scheme. To achieve a high speedup of the layered CUDA implementation, we employ quasi-cyclic non-binary ldpc codes since they allow to update multiple neighboring check nodes in parallel without any performance loss.

关键词： Graphical processing units (GPUs) Error correction coding Low-density parity-check codes non-binary ldpc codes Iterative decoding

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Dynamic Check Message Majority-Logic Decoding Algorithm for non-binary ldpc codes

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2014年第6期E97A卷 1356-1364页

作者： Lu, Yichao Peng, Xiao Tian, Guifen Goto, Satoshi Waseda Univ Grad Sch IPS Kitakyushu Fukuoka 8080135 Japan NEC Corp Ltd Kawasaki Kanagawa 2128520 Japan CSRD Toshiba Kawasaki Kanagawa 2118666 Japan

Majority-logic algorithms are devised for decoding non-binary ldpc codes in order to reduce computational complexity. However, compared with conventional belief propagation algorithms, majority-logic algorithms suffer from severe bit error performance degradation. This paper presents a low-complexity reliability-based algorithm aiming at improving error correcting ability of majority-logic algorithms. Reliability measures for check nodes are novelly introduced to realize mutual update between variable message and check message, and hence more efficient reliability propagation can be achieved, similar to belief-propagation algorithm. Simulation results on NB-ldpc codes with different characteristics demonstrate that our algorithm can reduce the bit error ratio by more than one order of magnitude and the coding gain enhancement over ISRB-MLGD can reach 0.2-2.0 dB, compared with both the ISRB-MLGD and IISRB-MLGD algorithms. Moreover, simulations on typical ldpc codes show that the computational complexity of the proposed algorithm is closely equivalent to ISRB-MLGD algorithm, and is less than 10% of Min-max algorithm. As a result, the proposed algorithm achieves a more efficient trade-off between decoding computational complexity and error performance.

关键词： non-binary ldpc codes majority-logic decoding iterative decoding message-passing algorithms

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Symbol Flipping Decoding Algorithms Based on Prediction for non-binary ldpc codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2017年第5期65卷 1913-1924页

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

This paper constructs an objective function for symbol flipping decoding algorithms, considering not only soft reliability, but also hard reliability. The maximization of this objective function indicates that the flipping metric should involve both the information before and after symbol flipping, while the existing algorithms consider the information before symbol flipping. Theoretical analysis shows that such prediction mechanism, together with hard reliability, can significantly improve the error performance of symbol flipping algorithms. Simulation results show that the proposed algorithms provide effective tradeoff between error performance and complexity for decoding non-binary ldpc codes.

关键词： non-binary ldpc codes symbol flipping iterative decoding prediction mechanism hard reliability

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Some Results on MAP Decoding of non-binary ldpc codes Over the BEC

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第4期57卷 2225-2242页

作者： Rathi, Vishwambhar Andriyanova, Iryna KTH Royal Inst Technol Commun Theory Lab Stockholm Sweden ENSEA Univ Cergy Pontoise CNRS ETIS Lab ETIS Grp F-95015 Cergy France

In this paper, the transmission over the binary erasure channel (BEC) using non-binary ldpc (NBldpc) codes is considered. The concept of peeling decoder and stopping sets is generalized to NBldpc codes. Using these generalizations, a combinatorial characterization of decoding failures of NBldpc codes is given, under assumption that the Belief Propagation (BP) decoder is used. Then, the residual ensemble of codes resulted by the BP decoder is defined and the design rate and the expectation of total number of codewords of the residual ensemble are computed. The decoding failure criterion combined with the density evolution analysis helps us to compute the asymptotic residual degree distribution for NBldpc codes. Our approach to compute the residual degree distribution on the check node side is not efficient as it is based on enumeration of all the possible connections on the check node side which satisfy the decoding failure criterion. So, the computation of the asymptotic check node side residual degree distribution and further part of our analysis is performed for NBldpc codes over GF(2)(m) with m = 2. In order to show that asymptotically almost every code in such ldpc ensemble has a rate equal to the design rate, we generalize the argument of the Maxwell construction to NBldpc codes, defined over FG(2)(2). It is also observed that, like in the binary setting, the Maxwell construction, relating the performance of MAP and BP decoding holds in this setting.

关键词： BEC design rate MAP performance non-binary ldpc codes peeling decoder stopping sets

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Bit-Reliability Based Low-Complexity Decoding Algorithms for non-binary ldpc codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2014年第12期62卷 4230-4240页

作者： Huang, Qin Zhang, Mu Wang, Zulin Wang, Lu Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China

This paper presents bit-reliability based majority-logic decoding (MLgD) algorithms for non-binary ldpc codes. The proposed algorithms pass only one Galois field element and its reliability along each edge of the Tanner graph of a non-binary ldpc code. Since their reliability updates are in terms of bits rather than symbols, they are more efficient than traditional MLgD based decoding algorithms. By weighting the soft reliability of the extrinsic information-sums based on their hard reliability, the proposed algorithms can achieve good error performance for non-binary ldpc codes with various column weights. Moreover, their computational complexity and memory consumption are remarkably reduced compared with existing MLgD based decoding algorithms. As a result, they provide effective tradeoffs between error performance and complexity for decoding of non-binary ldpc codes.

关键词： non-binary ldpc codes majority-logic decoding bit-reliability binary representation hamming distance

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Fountain Coding via Multiplicatively Repeated non-binary ldpc codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2012年第8期60卷 2077-2083页

作者： Kasai, Kenta Declercq, David Sakaniwa, Kohichi Tokyo Inst Technol Grad Sch Sci & Engn Dept Commun & Integrated Syst Tokyo 1528550 Japan ENSEA UCP CNRS UMR8051 ETIS Lab F-95014 Cergy Pontoise France

We study fountain codes transmitted over the binary-input symmetric-output channel. For channels with small capacity, receivers in fountain coding systems needs to collects many channel outputs to recover information bits. Since a collected channel output yields a check node in the decoding Tanner graph, the channel with small capacity leads to large decoding complexity. In this paper, we introduce a novel fountain coding scheme with non-binary ldpc codes. The decoding complexity of the proposed fountain code does not depend on the channel. Numerical experiments show that the proposed codes exhibit better performance than conventional fountain codes, especially for moderate number of information bits.

关键词： Fountain codes rateless codes non-binary ldpc codes

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Two Low-Complexity Reliability-Based Message-Passing Algorithms for Decoding non-binary ldpc codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2010年第11期58卷 3140-3147页

作者： Chen, Chao-Yu Huang, Qin Chao, Chi-chao Lin, Shu Natl Tsing Hua Univ Inst Commun Engn Hsinchu 30013 Taiwan Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

This paper presents two low-complexity reliability-based message-passing algorithms for decoding ldpc codes over non-binary finite fields. These two decoding algorithms require only finite field and integer operations and they provide effective trade-off between error performance and decoding complexity compared to the non-binary sum product algorithm. They are particularly effective for decoding ldpc codes constructed based on finite geometries and finite fields.

关键词： Reliability-based message-passing algorithms non-binary ldpc codes fast Fourier transform q-ary sum-product algorithm

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