针对准循环低密度奇偶校验(LDPC)码在高信噪比区域可能存在错误平层的问题, 提出了一种基于等差数列(AP)和消除基本陷阱集(ETS)的低错误平层QC-LDPC码构造方法。该方法利用改进的ETS消除算法构造基矩阵, 以减少基本矩阵中的小基本陷阱集。然后利用特殊性质的等差数列(AP)确定循环移位系数, 扩展得到最终的校验矩阵。该构造方法的计算复杂度低且码字的码长、码率可灵活设计。并且仿真结果表明, 所构造码率为0.5的PEG-Trap set-AP(PTAP)-QC-LDPC(1200,600)码, 在误码率为10-6时, 与IEEE 802.16标准中QC-LDPC(1200,600)码、利用PEG算法与AP的PEG-AP-QC-LDPC(1200,600)码、通过控制环(CC)的CC-QC-LDPC(1200,600)码和基于等差数列的AP-QC-LDPC(1200,600)码相比较, 其净编码增益分别提升了0.08, 0.31, 0.57和0.64dB, 有效地改善了高信噪比区域的纠错性能, 且未出现明显的错误平层。

Aiming at the problem that there may be an error floor of quasi-cyclic low-density parity-check (QC-LDPC) codes in the higher signal-to-noise ratio (SNR) region, a novel construction method of QC-LDPC codes based on the arithmetic sequence (AP) and eliminating elementary trap sets (ETS) is proposed. The method uses the improved ETS elimination algorithm to construct the base matrix and reduce the small ETS, and then applies the AP with the specific character to confirm the cyclic shift coefficient, thus the base matrix is extended to obtain the final check matrix, furthermore, the proposed construction method has the low computing complexity and can flexibly design the code-length and the code-rate. The simulation results show that at the bit error rate of 10-6, the net coding gain of the progressive edge growth(PEG)-trap set-AP(PTAP)-QC-LDPC(1200,600) code with a code-rate of 0.5, compared with those of the QC-LDPC (1200,600) code in IEEE 802.16 standard, the PEG-AP-QC-LDPC(1200,600) code based on PEG algorithm and AP, the CC-QC-LDPC(1200,600)code based on controlling cycles (CC) and the AP-QC-LDPC(1200,600) code based on AP, is improved up to 0.08, 0.31, 0.57 and 0.64dB respectively, the constructed PTAP-QC-LDPC(1200,600) code can effectively improve the error correction performance in the higher SNR region without the obvious error floor.