非对称信道下离散密度进化及LDPC码设计  

Discrete density evolution and LDPC codes design with asymmetric channels

作　　者：袁涛 马征[1] 庞琦珂 唐小虎[1] Tao YUAN;Zheng MA;Qike PANG;Xiaohu TANG(School of Information Science and Technology,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学信息科学与技术学院,成都611756

出　　处：《中国科学：信息科学》2023年第4期787-802,共16页Scientia Sinica(Informationis)

基　　金：四川省自然科学基金重点项目(批准号:2022NSFSC0043);国家重点研发计划项目(批准号:2018YFB1801104)资助。

摘　　要：为了设计非对称信道下的低密度奇偶校验(low-density parity-check, LDPC)码并分析其性能,本文提出了可实现的基于偏移最小和译码的非对称离散密度进化方法.首先采用组合数学、差分方法和二项式定理等工具推导了低复杂度的非对称信道离散密度进化的迭代公式;应用该迭代公式,进一步对采用偏移最小和译码的LDPC码编码进行优化设计,得到了在非对称信道下不同量化范围和步长的LDPC码的最佳度分布及其性能;最后获得了在高精度量化下的最佳偏移值.结果表明在非对称信道下,改进的基于偏移最小和译码的非对称密度进化方法复杂度比原方法呈指数级降低;当码率固定,规则码变量节点度越小其性能越好,最佳偏移值越小.对非规则LDPC码,使用差分进化算法找到了最佳度分布与偏移值.码率固定时,最大变量节点度越大,非规则码性能越好.To design low-density parity-check(LDPC)codes with asymmetric channels and analyze their performance,an achievable asymmetric discrete density evolution method is proposed,which is based on offset min-sum decoding.First,the iterative formula of low-complexity asymmetric channel discrete density evolution is derived by means of combinatorics,difference method and the binomial theorem.The iterative formula is applied to further optimize the design of the LDPC codes using the offset min-sum decoding,and the optimal degree distributions and performance of the LDPC codes under different quantization ranges and step sizes are obtained under the asymmetric channel.Finally,the optimal offset values under high-precision quantization are obtained.The results show that under the asymmetric channel,the complexity of the proposed asymmetric density evolution method based on the offset min-sum decoding is reduced by an order of magnitude than that using the original method.For a fixed code rate,the smaller the variable node degree of the regular codes,the better the performance and the smaller the optimal offset value.For irregular LDPC codes,the optimal degree distributions and offset values are determined according to the differential evolution algorithm.For a fixed code rate,the larger the maximum variable node degree,the better the performance of irregular codes.

关 键 词：非对称信道 低密度奇偶校验码 最小和 密度进化 度分布 差分进化 

分 类 号：TN911.22[电子电信—通信与信息系统]