基于电压图方法的LDPC码构造与设计研究  

Research on the Construction and Design of LDPC Codes Based on the Voltage Graph Method

作　　者：王成东 马纪成 游龙 邹余 Wang Chengdong;Ma Jicheng;You Long;Zou Yu(Chongqing Jiaotong University,Chongqing 400074,China;Chongqing University of Arts and Sciences,Chongqing 402160,China)

机构地区：[1]重庆交通大学,重庆400074 [2]重庆文理学院,重庆402160

出　　处：《廊坊师范学院学报（自然科学版）》2024年第1期5-11,共7页Journal of Langfang Normal University(Natural Science Edition)

基　　金：重庆市教委科学技术研究重点项目(KJZD-K202101304);重庆市自然科学基金面上项目(cstc2021jcyj-msxmX0831)。

摘　　要：近年来,LDPC码的研究重点是其构造方法和译码算法。已知在LDPC码的构造与译码过程中,对应的Tanner图中短环的存在严重影响译码性能,现有的QC-LDPC码方法虽然在一定程度上规避了长度为6,8的短环,但对大围长的Tanner图的构造理论与算法仍需要进一步研究。为此,引入拓扑图论中电压图的相关理论与算法。首先,对电压图的相关理论与算法进行优化,从算法上缩小了电压图中赋值电压的选取范围;其次,对电压基图的选取作出优化,选取非完全二部图作为基图;最后,通过选取不同的电压群进行提升图的构造与结果分析。已知(J,L)-QC-LDPC码的围长小于等于12,电压图方法所得的LDPC码围长范围被推广到了小于等于16,同时给出了围长为10、12、14、16的提升图实例。因此,利用电压图方法构造的LDPC码能够有效提升围长范围,其中电压基图的选取尤为关键。In recent years,the research of LDPC codes focuses on the construction methods and decoding algorithms of LDPC codes.It is known that the existence of short cycles in the corresponding Tanner graph seriously affects the decoding performance during the construction and decoding process of LDPC codes.Although the existing QC-LDPC code method avoids short cycles with lengths of 6 and 8 to some extent,further research is still needed on the theory and algorithm of constructing Tanner graphs with large girth.Therefore,the relevant theories and algorithms of voltage graphs in topological graph theory are introduced.Firstly,the relevant theories and algorithms of voltage graphs are optimized,and the selection range of assigned voltages in voltage graphs is narrowed from the algorithm.Secondly,the selection of voltage base graphs is optimized,and non-complete bipartite graphs are selected as base graphs.Finally,the construction and result analysis of lifting graphs are carried out by selecting different voltage groups.Compared with the known(J,L)-QC-LDPC codes with girth less than or equal to 12,the girth range of LDPC codes obtained by the voltage graph method is extended to less than or equal to 16,and lifting graph examples with girth of 10,12,14,and 16 are given.Therefore,the LDPC codes constructed using the voltage graph method can effectively improve the girth range,and the selection of voltage base graphs is particularly crucial.

关 键 词：QC-LDPC码 LDPC码 电压图 围长 

分 类 号：TN911.22[电子电信—通信与信息系统]