光通信中一种准循环非二进制LDPC码的新颖构造方法

A novel construction method of quasi-cyclic non-binary LDPC codes in optical communication

在对目前普遍采用的非二进制低密度奇偶校验(NB-LDPC)码校验矩阵的准循环构造方法进行深入研究的基础上,提出了一种基于有限域的NB-LDPC码的立体构造方法,在构建基于有限域的基础矩阵后,运用立体扩展的方式构成循环子矩阵,最终构造出具备准循环特性的非二进制校验矩阵。通过对采用立体构造法构造的NB-LDPC码的性能仿真发现,与基于GF(29)的RS(511,305)相比,本文构造的NB-LDPC码在误比特率(BER)为10-7时可以增加3.3dB的净编码增益(NCG);在BER为10-6时,本文构造的LDPC码与采用传统准循环方式构造的二进制LDPC码、随机构造的二进制LDPC码、基于有限域构造的32进制准循环LDPC码和基于欧式几何构造的64进制的循环LDPC码比较,分别多获得了0.56、0.56、0.03和0.83dB的NCG。通过对本文构造的NB-LDPC码性能仿真发现,这类具有高度结构化的NB-LDPC码不仅具备准循环特性,有利于硬件实现,同时在中短码长情况时展现出较好的纠错性能。

This paper presents a construction met hod of quasi-cyclic non-binary low density parity-check （NB-LDPC） code based on the finite field three-dimensional construction.After construction of base matrix based on the finite field,a cyclic matrix is constructed with the method of three-dimensional exte nsion.Finally,non-binary parity check matrix with quasi-cyclic feature is constructed.Compared wit h the GF（29）-based RS（511,5） and NB-LDPC code constructed by the three-dimensional construction can increase 3.3dB net code gain （NCG） at the bit error rate （BER） of 10^-7.Compare d with the binary Q C-LDPC codes constructed by the traditional way, the binary LDPC codes randomly constructed,the 32-ary QC-LDPC codes construct ed based on finite fields and the 64-ary cyclic LDPC codes constructed based on Euclidean geometry ,the NB-LDPC code constructed by the three-dimensional construction can increase 0.56dB,0.56dB, 0.03dB and 0.83dB NCG respectively at the BER of 10^-7.Through performan ce simulation of the NB-LDPC code constructed based on this three-dimensional construction,it shows that such an NB-LDPC code not only has quasi-cyclic feat ure,conducive to hardware implementation,but also shows better error corre ction performance in the short code length.