基于环的准循环LDPC码的小停止集计算(英)

应用科学学报

基于环的准循环LDPC码的小停止集计算(英)

孔令军, 肖扬

北京交通大学信息科学研究所，北京 100044

收稿日期:2008-03-04 修回日期:2008-06-16 出版日期:2008-12-10 发布日期:2008-12-10
通信作者: 孔令军

Small Stopping Sets Counting Methods for Quasi-cyclic Low Density Parity Check Codes based on the Cycle Theory

KONG Ling-jun, XIAO Yang

Institute of Information Science, Beijing Jiaotong University, Beijing 100044, China

Received:2008-03-04 Revised:2008-06-16 Online:2008-12-10 Published:2008-12-10
Contact: KONG Ling-jun

摘要/Abstract

摘要： Tanner图最小停止集的大小决定LDPC码在迭代译码时的性能. 为此，提出准循环LDPC码无小停止集的充要条件. 根据该文所提定理及推论，不仅可以设计出无小停止集的准循环LDPC码，而且还给出了小停止集数目的计算方法. 在BER为1e-5时，该文设计的准循环LDPC码与随机LDPC码相比具有0.3 dB的增益. 该算法可有效评估LDPC码的性能，也可计算LDPC码的短环数，较之现有算法具有更低的计算复杂度.

关键词: 准循环LDPC码, 循环矩阵, 停止集, 停止距离, 围长, 环

Abstract: It is well known that performance of low-density parity check (LDPC) codes under iterative decoding is determined by the size of the smallest stopping sets in the Tanner graph. To solve this problem, we propose necessary and sufficient conditions of quasi-cyclic LDPC codes without small stopping sets. According to the proposed theorems and corollaries, we can design good QC-LDPC codes without small stopping sets which outperforms random LDPC codes by SNR=0.3 dB at BER of 1e-5 , and count the number of the small stopping sets. The method can be used effectively to evaluate performance of LDPC codes according to their stopping sets distributions. It can find the number of cycles of LDPC codes which is less complex than existing algorithms.

Key words: quasi-cyclic low density parity check (LDPC) codes, cycle
, circulant matrices, stopping sets, stopping distance, girth

中图分类号:

孔令军;肖扬. 基于环的准循环LDPC码的小停止集计算(英)[J]. 应用科学学报.

KONG Ling-jun;XIAO Yang. Small Stopping Sets Counting Methods for Quasi-cyclic Low Density Parity Check Codes based on the Cycle Theory[J]. Journal of Applied Sciences.