基于PEG算法的准循环LDPC码构造研究

摘要

为了兼顾LDPC码较高的纠错性能和较简单的硬件实现,提出了一种基于PEG算法的准循环LDPC码校验矩阵的构造方法,该方法首先利用PEG算法构造基矩阵,然后利用提出的移位参数公式来构造循环移位矩阵,再用循环移位矩阵和全零矩阵对基矩阵进行优化扩展,形成的校验矩阵最短环长至少为8环.该方法具有与PEG算法非常接近的纠错性能,尤其是当信噪比高于1.2 dB时要优于PEG直接构造法,而硬件实现比PEG算法简单,且参数选择灵活方便.%In order to take into account the requirements of high error correction performance and simple hardware implementation of LDPC codes, this paper presents a new algorithm for constructing check matrix of LDPC codes based on PEG algorithm. After constructing a basic matrix with PEG algorithm,we can get cyclic shift matrix under the proposed formula of shift parameter, and then, using the cyclic shift matrix and all-zero matrix to extend the basic matrix optimally,we can get the quasi-cyclic LDPC matrix in which the girth is 8 at least. The algorithm's error correction performance is very close to that of PEG algorithm, and is particularly better than that of PEG algorithm when S/N is higher than 1.2 dB. It's hardware implementation is more simple than that of PEG algorithm, and the algorithm is flexibly to set the parameters of the LDPC codes.