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为了满足光通信对纠错码高码率和低误码率的要求,基于平衡不完全区组设计(BIBD)、循环矩阵分解和循环置换矩阵,提出了准循环低密度奇偶校验(QC-LDPC)码的一种新颖构造方法。该方法利用Bose的第二类方法来构造低密度校验矩阵,并对其进行循环列分解得到相应的模板矩阵,再利用合适的循环置换矩阵对其进行扩展。采用该方法所构造的QC-LDPC码具有良好的结构,且可根据实际需要来灵活地选择调整码长和码率。仿真分析表明:在误码率为10-6时其码率均为93.7%的情况下,用该方法构造所的新颖QC-LDPC(20208,18948)码比ITU-T G.975中RS(255,239)码的净编码增益(NCG)改善了约2.2 d B,且比ITU-T G.975.1中LDPC(32640,30592)码的NCG改善了约1.6 d B。因此该方法所构造的QC-LDPC码具有更好的纠错性能,更适合高速长距离的光通信系统。
In order to meet the requirements of high bit error rate and low bit error rate for optical communication, based on BIBD, cyclic matrix factorization and cyclic permutation matrix, quasi-cyclic low density parity check (QC- LDPC) code of a novel method of construction. This method uses Bose’s second-class method to construct a low-density parity-check matrix, cyclically decomposes it to obtain the corresponding template matrix, and then expands it with an appropriate cyclic permutation matrix. The QC-LDPC code constructed by this method has a good structure, and can flexibly select the adjustment code length and the code rate according to actual needs. The simulation results show that the new QC-LDPC (20208, 18948) code constructed by this method has a lower bit rate than the ITU-T G.975 RS 255, 239) code improves by about 2.2 dB, and improves about 1.6 dB compared to the NCG of the LDPC (32640, 30592) code in ITU-T G.975.1. Therefore, the QC-LDPC code constructed by the method has better error correction performance and is more suitable for high speed and long distance optical communication systems.