一种基于循环移位矩阵的LDPC码构造方法

具有准循环结构的低密度奇偶校验码(QC-LDPC Codes)是目前被广泛采用的一类LDPC码。本文提出了一种结合PEG算法构造基于循环移位矩阵的QC-LDPC码的方法。该方法首先将QC-LDPC码传统的基于比特的二分图简化为基于Block的二分图，然后在该图中采用PEG算法遵循的环路最大原则确定每一个循环移位矩阵的位置，最后根据QC-LDPC码的环路特性为每一个循环移位矩阵挑选循环移位偏移量。利用该算法，本文构造了长度从1008bit到8064bit，码率从1/2到7/8各种参数的LDPC码。仿真结果表明，本文构造的LDPC码性能优于目前采用有限几何、两个信息符号的RS码、组合数学等常用的代数方法构造的QC-LDPC码。

Construction of LDPC Codes Based on Circulant Permutation Matrices

Quasi Cyclic LDPC (QC-LDPC) codes are of particular interest in various areas. In this paper, a method to construct a class of QC-LDPC codes based on circulant permutation matrices is showed. The method chooses the position of each non-zero sub-matrix in the bipartite graph based on blocks. Then the circulant permutation value of each sub-matrix is decided. With the proposed algorithm, a few LDPC codes were constructed with the code length from 1008 bit to 8064 bit and with code rate from 1/2 to 7/8. Simulation results show that the proposed LDPC codes are superior to QC-LDPC codes with other construction algorithms.