一种低差错平底线性复杂度的QC-LDPC码构造方法

A class of QC-LDPC codes with low error floor and linear encoding complexity

本文给出了一种低差错平底QC-LDPC码构造方法。首先,提出了扩展近似下三角阵eALT(extern ApproximateLower Triangular)的全局矩阵构造法,通过对改进后的全局矩阵M进行矩阵置换,生成LDPC码的校验矩阵H以达到减少小停止集(Stopping Set)数量,降低差错平台(Error floor)的目的;接着,研究了校验矩阵H中短环(Short Cycle)长度与置换矩阵循环移位系数的关系,通过设置短环满足的条件搜索循环移位系数;为了降低搜索移位系数的复杂度,本文提出了一种基于等差数列的移位系数设计方法,采用数学公式计算循环移位系数,无需计算机搜索即可完全消除长度为4的短环。仿真结果表明,本文所提出的构造方法在保证线性编码复杂度的前提下,增大了码字间最小距离,提高了码字性能,同时循环移位系数设计采用结构化的方法,无需计算机搜索即可完全消除4环。

A class of QC-LDPC codes with low error floor and low complexity is proposed in this paper. First, a global matrix M with extern approximate lower triangular（eALT） method is designed, each ＇1＇ in the global matrix M is replaced by a permutation matrix; each ＇0＇ is replaced by a null matrix to reduce the number of small stopping set and error floor. Then, the relationship between the length of short cyclic in the parity matrix H and the cyclic shift coefficient is given. Based on the relationship, proper cyclic shift coefficient of each permutation matrix is selected. In order to lower the complexity of searching cyclic shift coefficient, a arithmetic progression sequence method is put forward, which use a given formula to generate coefficient and does not need search by computer. At last, the linear encoding process is given with the proposed QC-LDPC. Simulation shows that the proposed method can reduce the number of small stopping set, increase the minimum distance of LDPC codes, and achieve very low error floor with linear encoding complexity. What＇s more, the cyclic coefficient was generate by structured method.