基于Golomb Ruler的QC-LDPC码构造方法

Construction Method of QC-LDPC Codes Based on Golomb Ruler

摘要:

针对准循环低密度奇偶校验(QC-LDPC)码中短环结构会影响其纠错性能的问题,基于Golomb Ruler提出了一种新颖的围长为8的QC-LDPC码构造方法。该方法先根据码长码率的需求,从Golomb Ruler中选择部分元素构造一个集合,结合指数矩阵中元素所在位置的四六环特性,通过搜索算法,依次找出符合无四六环条件的元素得到另一个集合,然后构造相应的指数矩阵,最后得到其奇偶校验矩阵。仿真结果表明:在误码率为10-6时,所构造的GR-QC-LDPC码与同码率码长的其他4种QC-LDPC码的码型相比,其净编码增益均有一定的提高,且无明显错误平层现象。

Abstract:

A novel construction method with grith-8 quasi-cyclic low-density parity-check (QC-LDPC) codes based on the Golomb ruler is proposed to solve the issue of short-cycle structures affecting error-correction performance. First, a set is constructed by selecting some elements from the Golomb ruler based on the code-length and code-rate requirements. Subsequently, by combining the girth-4 and girth-6 properties of the elemental locations in the exponential matrix, another set is obtained using the search algorithm to search for elements that satisfy the conditions of no girth-4 and no girth-6. Subsequently, the corresponding exponential matrix is constructed. Finally, a parity-check matrix is obtained. Simulation results show that the net coding gain of the GR-QC-LDPC code constructed using the proposed method is greater than those yielded by four other QC-LDPC codes with the same code-rate and code-length at a bit error rate of 10-6; moreover, its error floor is insignificant.