A transform approach for analyzing and constructing quasi-cyclic low-density parity-check codes

Qiuju Diao, Qin Huang, Shu Lin, K. Abdel-Ghaffar
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引用次数: 13

Abstract

An approach for studying quasi-cyclic codes based on matrix transformations via Fourier transforms and row and column permutations is presented. These transformations put a parity-check matrix in the form of an array of circulant matrices into a diagonal array of matrices of the same size over an extension field. The approach is used to characterize certain structural properties of low-density parity-check (LDPC) codes such as the girths of their Tanner graphs. Many constructions of quasi-cyclic LDPC codes can be unified under the proposed approach.
一种分析和构造准循环低密度奇偶校验码的变换方法
提出了一种基于傅里叶变换和行列置换的矩阵变换研究拟循环码的方法。这些变换将循环矩阵数组形式的奇偶校验矩阵转化为扩展域上相同大小的矩阵对角数组。该方法用于描述低密度奇偶校验码(LDPC)的某些结构性质,如Tanner图的周长。该方法可以统一拟循环LDPC码的许多结构。
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