基于Golomb Ruler的QC-LDPC码构造方法

2 Golomb Ruler

摘要:

针对准循环低密度奇偶校验(quasi-cyclic low-density parity-check, 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,再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(bit error rate, BER)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 of quasi-cyclic low-density parity-check (QC-LDPC) codes based on Golomb Ruler is proposed to solve the problem that the short cycle structure will affect the error-correction performance. This method firstly constructs a set by selecting some elements from Golomb Ruler according to the requirements of the code-length and code-rate. Then combined with the girth-4 and girth-6 properties of the location of the elements in the exponential matrix, another set is obtained by using the search algorithm to search for the elements that satisfy the conditions of no girth-4 and no girth-6. Then the corresponding exponent matrix was constructed. Finally, the parity-check matrix was obtained. The simulation results show that the net coding gain (NCG) of the GR-QC-LDPC code constructed by the proposed method is more than those of the other four QC-LDPC codes with the same code-rate and code-length at the bit error rate (BER) of 10-6, and it has no obvious error floor phenomenon.