基于Stanley序列的QC-LDPC码新颖构造方法

针对准循环低密度奇偶校验(quasi-cyclic low-density parity-check,QC-LDPC)码的短环结构会严重影响码字纠错性能的问题，基于Stanley序列(Stanley sequence,SS)提出一种围长至少为8的QC-LDPC码新颖构造方法。从Stanley序列中选取某些特定元素构成一个呈递增关系的集合，利用穷举算法搜索出满足无环4和环6条件的元素得到另一个递增集合，构造相应的指数矩阵，得到其奇偶校验矩阵。仿真结果表明，在误码率(bit error rate,BER)为10^-6时，所构造的SS-QC-LDPC码与同码率码长的其他QC-LDPC码码型相比，其净编码增益均有一定提升，因而其纠错性能较好，且无错误平层现象。此外，该构造方法的计算复杂度较低。

Novel construction method on QC-LDPC codes based on the Stanley sequence

A novel construction method of the grith-8 regular quasi-cyclic low-density parity-check (QC-LDPC) code based on Stanley sequence (SS) is proposed to solve the problem that short girth structure will seriously affect the error-correction performance of the code-words. The method firstly constructs a shown increment correlation set by selecting some specific elements from Stanley sequence, and another increment set is obtained by using the exhaustive search algorithm to search for the elements that satisfy the conditions of no girth-4 and no girth-6. Then the corresponding exponent matrix is constructed. Finally, the parity-check matrix is obtained. Simulation results show that the net coding gain (NCG) of the SS-QC-LDPC code constructed by the proposed method is more than that of the other QC-LDPC codes with the same code-rate and code-length at the bit error rate (BER) of 10^-6, so the constructed SS-QC-LDPC code has better error-correction performance and has no error floor phenomenon. In addition, the proposed construction method has low computational complexity.