基于代数搜索法去环的结构化的LDPC码

Structured LDPC Code Based on Eliminating Circle Using Arithmetic Searching Method

文章将阐述一种结构化的LDPC码系列,包括规则码、非规则码、非规则RA码三种。这种结构把H矩阵分为3×k个块,而每个块都是由单位矩阵循环移位形成的。非规则就是在规则码结构上添加3×m个块,使得H矩阵前面部分列重从3变为6或者9,非规则RA码在非规则基础上将H阵最后部分(3×3块)换成2列下三角结构。生成这类H矩阵的方法就是以下要提到的代数搜索法。搜索法规则就是尽量将低次环去掉,保持H阵的高girth值。这个系列的LDPC码的好处就是译码器结构很好实现,RA码使编码也变得很简单;而完全去除4,6环,最小化8环的H阵结构又保证了LDPC码的性能。

This paper will present a series of structural LDPC code,including regular code,irregular code and irregular-repeat-accumulation code.The referred structure divide the H matrix into 3＊k blocks,the identity matrix shift all its ‘1 ＇s （quasi-cyclic） to construct each blocks.Irregular code is based on regular one,adding 3＊m blocks,then the column weight from 3 goes to 6 or 9 at the front of H matrix.Irregular-repeat-accumulation code is based on irregular one,replaces the bottom of H matrix（3^＊3blocks） with a 2 line down triangular matrices.Generating the three types of H matrix will use the corresponding searching-method mentioned blow.The main rule of the searching-method is to eliminate lower circles in H matrix,keep the average girth of the H matrix high.The advantage of this series of structural LDPC code is that the decoder hardware structure can be comparatively easy implemented.Encode of repeataccumulation code become easy,too.In fact,because of the elimination of 4^th,6^th circle,minimization 8^th circle in H matrix, the performance of this series LDPC code quite good as well.