Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of...Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder.For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.展开更多
为降低LDPC(低密度奇偶校验码)码错误平层,提出一种基于环分类搜索的APPS-LDPC(数列分割移位的LDPC)码构造算法。该算法具有码长、码率和列重的任意可设性,同时该类码的Tanner图围长至少为8。循环移位因子可以通过简单的代数表达式描述...为降低LDPC(低密度奇偶校验码)码错误平层,提出一种基于环分类搜索的APPS-LDPC(数列分割移位的LDPC)码构造算法。该算法具有码长、码率和列重的任意可设性,同时该类码的Tanner图围长至少为8。循环移位因子可以通过简单的代数表达式描述,从而降低内存需求。仿真结果表明,当误码率达到10-5时,APPS-LDPC码(496,248)相对于PEG-LDPC(渐进边增长LDPC)码获得了约1.9 d B的性能提升;随着信噪比的升高,两条译码性能曲线之间的差距将更大。此外,列重为3的APPS-LDPC码(6144,5376)在信噪比4.6 d B以后并未出现明显的错误平层。该构造算法与PS-LDPC码相比,在误码率达到10-8时大约获得0.25 d B增益;与围长为4和6的PEG构造算法相比,在错误平层区域其译码性能极优;同时相较于此两者,其构造复杂度和耗时也展现出一定优势。通过基于Tanner图的诱捕集分析方法,统计APPS-LDPC码(496,248)中由8环组成的部分小型诱捕集并不存在,从而证明了其错误平层降低的原因。展开更多
Two new design approaches for constructing Low-Density Parity-Check(LDPC) codes are proposed.One is used to design regular Quasi-Cyclic LDPC(QC-LDPC) codes with girth at least 8.The other is used to design irregular L...Two new design approaches for constructing Low-Density Parity-Check(LDPC) codes are proposed.One is used to design regular Quasi-Cyclic LDPC(QC-LDPC) codes with girth at least 8.The other is used to design irregular LDPC codes.Both of their parity-check matrices are composed of Circulant Permutation Matrices(CPMs).When iteratively decoded with the Sum-Product Algorithm(SPA),these proposed codes exhibit good performances over the AWGN channel.展开更多
This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant...This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant permutation matrices via arithmetic analysis.The proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and fast.Simulation results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.展开更多
基金supported in part by National Nature Science Foundation of China under Grant No.61471286,No.61271004the Fundamental Research Funds for the Central Universitiesthe open research fund of Key Laboratory of Information Coding and Transmission,Southwest Jiaotong University(No.2010-03)
文摘Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder.For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.
文摘为降低LDPC(低密度奇偶校验码)码错误平层,提出一种基于环分类搜索的APPS-LDPC(数列分割移位的LDPC)码构造算法。该算法具有码长、码率和列重的任意可设性,同时该类码的Tanner图围长至少为8。循环移位因子可以通过简单的代数表达式描述,从而降低内存需求。仿真结果表明,当误码率达到10-5时,APPS-LDPC码(496,248)相对于PEG-LDPC(渐进边增长LDPC)码获得了约1.9 d B的性能提升;随着信噪比的升高,两条译码性能曲线之间的差距将更大。此外,列重为3的APPS-LDPC码(6144,5376)在信噪比4.6 d B以后并未出现明显的错误平层。该构造算法与PS-LDPC码相比,在误码率达到10-8时大约获得0.25 d B增益;与围长为4和6的PEG构造算法相比,在错误平层区域其译码性能极优;同时相较于此两者,其构造复杂度和耗时也展现出一定优势。通过基于Tanner图的诱捕集分析方法,统计APPS-LDPC码(496,248)中由8环组成的部分小型诱捕集并不存在,从而证明了其错误平层降低的原因。
基金Supported by the National Natural Science Foundation of China(Nos.61271199,61172022)
文摘Two new design approaches for constructing Low-Density Parity-Check(LDPC) codes are proposed.One is used to design regular Quasi-Cyclic LDPC(QC-LDPC) codes with girth at least 8.The other is used to design irregular LDPC codes.Both of their parity-check matrices are composed of Circulant Permutation Matrices(CPMs).When iteratively decoded with the Sum-Product Algorithm(SPA),these proposed codes exhibit good performances over the AWGN channel.
基金supported by the National Natural Science Foundation of China under Grants No.61172085,No.61103221,No.61133014,No.11061130539 and No.61021004
文摘This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant permutation matrices via arithmetic analysis.The proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and fast.Simulation results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.
