基于中国剩余定理和贪婪算法扩展的QC-LDPC码

QC-LDPC Codes Based on Chinese Remainder Theorem and Greedy Algorithm

在缩短阵列码的基础上运用中国剩余定理(CRT)和贪婪算法提出了一种新颖的大围长、码长更加灵活的QC-LDPC构造方法,且所构造的码字的校验矩阵采用楼梯矩阵循环置换而成。与传统CRT构造方法相比,只需已知一个分量码——缩短阵列码,同时新构造QC-LDPC码码长与码率选择比较灵活,围长更大,如果围长一样,则使最短环数量尽可能地少。仿真分析表明:在误码率为10-6时,在相同码率和码长的条件下,利用所提出的构造方法所构造的girth-8(4,k)QC-LDPC码在加性高斯白噪声(AWGN)和瑞利衰落信道中分别与缩短阵列码相比可获得约1.2 d B和2.0 d B的净编码增益,与CRT码相比分别改善了0.3 d B和0.7 d B的净编码增益,且性能与Gallager随机码性能相似但编码复杂度大大降低。

A new method is proposed to construct a large girth and flexible length QC-LDPC codes by Chi-nese Remainder Theorem（CRT） and greedy algorithm. And the check matrix of the proposed codes is com-posed of the cyclical permutation based on staircase matrix. Compared with traditional CRT method,it onlyneed know a component code-shortened array code,meanwhile,the proposed codes have flexible codelengths and rates with larger girth. If its girth is the same as that via traditional CRT method,it can makethe shortest cycle numbers as less as possible. When the BER is 10-6 in AWGN and Rayleigh fading chan-nel,simulation results show that the proposed girth-8（4,k） QC-LDPC codes with the same code lengthand rate has net coding gain（NCG） of about 1. 2 dB and 2dB over shortened array codes respectively,inaddition,the NCG of the proposed codes is 0. 3 dB and 0. 7dB more than that of CRT codes separately,fur-thermore,the proposed codes have similar performance with Gallager random codes but encoding complexityis reduced greatly.