基于减法构造搜索算法的新颖8环QC-LDPC码构造方法

A Novel Construction Method of QC-LDPC Codes with Girth-8 Based on the Search Algorithm of the Subtraction Construction

摘要:

针对准循环低密度奇偶校验(quasi-cyclic low-density parity-check, QC-LDPC)码中存在的短环结构会严重影响码字纠错性能的问题，基于减法构造搜索算法而提出一种新颖的8环QC-LDPC码构造方法，该方法利用减法构造(Subtraction Construction, SC)的搜索算法来构造围长至少为8的QC-LDPC码。该构造方法先用Golomb Ruler序列固定第一行，后两行利用基于减法构造的搜索算法得到，可以构成一个满足无4，6环条件的指数矩阵(exponent matrix, EM)，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，同本文对比的同码率码长的其他QC-LDPC码码型相比较，所构造的SC-QC-LDPC码在码长为1200和3600时,其净编码增益分别最小能改善0.23dB和0.12dB，因此其纠错性能较好。此外，该构造方法不仅提供了灵活的码长码率选择，还具备较低的计算复杂度。

Abstract:

Aiming at the problem that the short-cycle structures in quasi-cyclic low-density parity-check (QC-LDPC) codes can significantly degrade the error correction performance, a novel construction method of QC-LDPC Codes with Girth-8 based on the search algorithm of the subtraction construction is proposed. This method employs the search algorithm of the subtraction construction (SC) to design QC-LDPC codes with the girth at least 8. In the construction method, the first row is firstly fixed by the Golomb Ruler sequence, while the subsequent two rows are derived by using the search algorithm of the SC. This results in the formation of an exponent matrix (EM) that satisfies the condition without girth-4 and girth-6, thus the parity-check matrix is finally obtained. The simulation results show that, compared to other QC-LDPC codes of the same code rate and length, the constructed SC-QC-LDPC code can improve the minimum net coding gain of 0.23dB and 0.12dB for code lengths of 1200 and 3600 respectively at the bit error rate (BER) of 10-6. Therefore, the proposed construction method can better improve the error correction performance. Furthermore, this construction method has not only the flexible choices of the code-length and the code-rate but also the low computational complexity.