一种基于伪循环MDS码的准循环LDPC码构造方法

A Quasi-cyclic LDPC Codes Construction Scheme Based on Pseudo-cyclic MDS Codes

该文提出了一种利用两个信息符号的伪循环最大距离可分(MDS)码,构造围长为6的准循环低密度奇偶校验(LDPC)码的方法。在GF(q)中,它通过直接计算长为q+1的伪循环MDS码生成多项式,构造准循环LDPC码的校验矩阵。其主要利用了含两个信息符号的伪循环MDS码字特殊的循环性,及任意两个码字间距离不小于q的特点,使所构造的准循环LDPC码保证无4环。仿真结果表明,基于伪循环MDS码的准循环LDPC码在高斯信道下,能获得较好的误码性能。

This paper proposes a construction scheme of girth-6 quasi-cyclic Low-Density Check-Parity（LDPC） codes based on pseudo-cyclic Maximum Distance Separable（MDS） codes with two information symbols.The parity-check matrix of an quasi-cyclic LDPC code in GF（q） can be constructed by calculating the generator polynomials of pseudo-cyclic MDS code with length q＋1 directly.It utilizes mainly the special characteristic of the circularity of pseudo-cyclic MDS codes with two information symbols.Also the distance between arbitrary two codes is not less than q.Therefore,it guarantees no cycles-4 in the construction of the quasi-cyclic LDPC codes.Simulation results show that the quasi-cyclic LDPC codes based on pseudo-cyclic MDS codes perform well in an AGWN channel.