基于PEG算法的准循环LDPC码构造研究

Research on Construction of Quasi-Cyclic LDPC Codes Based on PEG Algorithm

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 SIN 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.