一种基于图论的LDPC码构造算法的研究  

An algorithm for construction of low density parity-check codes based on graph theory

作　　者：邓勇强[1] 朱光喜[1] 刘文明[1] 

机构地区：[1]华中科技大学电子与信息工程系,湖北武汉430074

出　　处：《华中科技大学学报（自然科学版）》2006年第3期58-61,共4页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金重大资助项目(60496315);国家高技术研究发展计划资助项目(2003AA12331005)

摘　　要：在对低密度奇偶校验(LDPC)码进行分析的基础上,提出了一种基于图论的构造算法.该算法从对LDPC码的校验矩阵进行图论分析入手,分析了组成校验矩阵中的圈的校验点之间的关系,得出了由这些校验点对应的结构图是彼此同构的欧拉图的定理,利用这个定理以及根据定理得到的性质,可以通过构造一个辅助的校验点结构图的邻接矩阵,渐进地生成LDPC码的校验矩阵,在生成的过程中避免短长度圈的出现.仿真实验表明提出的算法对中短码长的LDPC码构造具有良好的性能.Low density parity-check （LDPC）codes were studied, and a new algorithm was proposed to construct LDPC codes based on graph theory. After the check-matrix of LDPC codes was discussed with the help of graph theory, the relationship among the check nodes which structure cycles in the matrix were analyzed. It was from the above analysis concluded that the graphs structured by these check nodes are isomorphic Euler graph. On the basis of the theorem and the characters of these check nodes, a new algorithm for the construction of the check matrix was recommended. In this algorithm, the check-matrix could be built pragressively through the adjacent matrix of check nodes graph, and short cycles could not appear during the construction of check matrix. In the simulation results, these codes show their good performance.

关 键 词：低密度奇偶校验码 图论 圈 渐进生成 

分 类 号：TN911.2[电子电信—通信与信息系统]