提出了一种低复杂度的具有等差数列(AP)特性的准循环低密度奇偶校验(QC-LDPC)码构造方法, 该方法结构简单, 节省了存储空间, 可根据实际需要灵活地改变码长和码率。利用该方法构造出的AP-QC-LDPC(4599,4307)码的校验矩阵的每行元素为等差数列, 且公差单调递增, 所以该校验矩阵不含有4环。仿真结果表明: 在误码率(BER)为10-6时, 该AP-QC-LDPC(4599,4307)码比ITU-T G.975中的RS(255,239)码和ITU-T G.975.1中LDPC(32640,30592)码的净编码增益(NCG)分别改善了约2.19和1.48dB, 比基于有限域乘群的eIRA-QC-LDPC(4599,4307)码和QC-LDPC(3780,3540)码的净编码增益分别提高了约0.16和0.2dB。该方法构造的AP-QC-LDPC(4599,4307)码具有更好的纠错性能, 能更好地适应光通信系统的需求。

A low complexity construction method of quasi-cyclic low-density parity check(QC-LDPC) code with the characteristic of arithmetic progression(AP) was proposed. The construction method has simple structure, thus it can save storage space, and regulate the code-length and code-rate flexibly according to the actual demand. A novel AP-QC-LDPC(4599,4307) code is constructed by applying the proposed method, each row elements of the parity check matrix constitutes arithmetic progressions with the monotonically increasing tolerances, so the check matrix does not contain girth-4. The simulation analysis shows that at the bit error rate(BER) of 10-6, the net coding gain(NCG) of the constructed AP-QC-LDPC(4599,4307) code is 2.19dB higher than that of RS(255,239) code in ITU-T G.975, and 1.48dB higher than that of LDPC(32640,30592) code in ITU-T G.975.1. In addition, the NCGs of AP-QC-LDPC(4599,4307) code are respectively 0.16dB and 0.2dB higher than that of both eIRA-QC-LDPC(4599,4307) code and QC-LDPC(3780,3540) code based on finite field multiplicative group. The constructed AP-QC-LDPC(4599,4307) code with better error-correction performance is more suitable for the requirements of optical communication systems.