利用完备差集构造QC-LDPC码

针对准循环低密度奇偶校验( QC-LDPC)码中循环置换矩阵的移位次数的确定问题,提出了一种利用组合设计中完备差集( PDF)构造QC-LDPC码的新颖方法。当循环置换矩阵的维度大于一定值时,该方法所构造的规则QC-LDPC码围长至少为6,具有灵活选择码长和码率的优点,且所需的存储空间更少,降低了硬件实现的复杂度。仿真结果表明：在误码率为10-5时,所构造的码率为3/4的PDF-QC-LDPC(3136,2352)与基于最大公约数(GCD)构造的GCD-QC-LDPC(3136,2352)码和基于循环差集(CDF)构造的CDF-QC-LDPC(3136,2352)码相比,其净编码增益(NCG)分别有0.41 dB和0.32 dB的提升；且在码率为4/5时,所构造的PDF-QC-LDPC (4880,3584)码比GCD-QC-LDPC(4880,3584)码和CDF-QC-LDPC(4880,3584)码的NCG分别改善了0.21 dB和0.13 dB。

Constructing QC-LDPC codes by using perfect difference families

For the problem of determining shift times of the circulant permutation matirx( CPM) in quasi-cy-clic low-density parity-check(QC-LDPC) codes,a novel construction method based on the perfect differ-ence family( PDF) among combinatorial mathematics is proposed. When the dimension of the CPM exceeds a certain particular value,the girth of the Tanner graph of QC-LDPC codes constructed by this method is at least six,and the proposed algorithm has high flexibility with respect to the design of code-length and code-rate. In addition,it has less requirement about storage space,so the complexity of the hardware implementa-tion is reduced. The simulation results show that the net coding gain(NCG) of the PDF-QC-LDPC(3136, 2352) code with the code-rate of 3/4 is respectively improved 1. 15 dB and 0. 58 dB than those of the GCD-QC-LDPC(3136,2352) code based on the greatest common divisor(GCD) and the CDF-QC-LDPC(3136, 2352) code based on the cyclic difference family(CDF) at the bit error rate(BER) of 10-5. In addition,the NCG of the proposed PDF-QC-LDPC(4880,3584) code is improved 0. 21 dB and 0. 13 dB than those of the GCD-QC-LDPC(4880,3584) code and the CDF-QC-LDPC(4880,3584) code with the same conditions correspondingly with the code-rate of 4/5 and the BER of 10-5 .