基于完备循环差集的QC-LDPC码的确定性构造

Deterministric Construction of QC-LDPC Codes Based on Perfect Cyclic Difference Sets

针对准循环低密度奇偶校验(Quasi-Cyclic Low-Density Parity Check,QC-LDPC)码中存在编码复杂度高且码率码长选择不灵活等问题,基于完备循环差集(Perfect Cyclic Difference Sets,PCDS)提出了一种确定性的构造方法。基矩阵(Base Matrix,BM)中的移位次数可由完备循环差集经过简单的加减运算获得,特殊结构的基矩阵和完备循环差集结合,节省了存储空间,降低了硬件实现的复杂度,其围长至少为6,且码长码率可灵活选择。仿真结果表明:在加性高斯白噪声(Additive White Gauss Noise,AWGN)信道下采用和积算法(Sum-Product Algorithm,SPA)迭代译码,码率为0.5、误码率为10^(-6)时,构造的基于完备循环差集的非规则PCDS-QCLDPC(2680,1340)码比基于PEG-QC-LDPC(2680,1340)码和掩模的离散数组AD-MASK-QCLDPC(2680,1340)码的净编码增益(Net Coding Gain,NCG)分别提高了0.13和0.32dB。

For quasi-cyclic low-density parity check（QC-LDPC）codes,the coding complexity is high and the selection of code-rate and code-length is not flexible,thus a deterministic structure is proposed based on the perfect cyclic difference sets.The number of shifts of base matrix（BM）can be obtained by a simple addition and subtraction.The combination of base matrix with special structure and the perfect cyclic difference sets saves the storage space and reduces the complexity of hardware implementation.The girth is at least six and the code-length and code-rate can be selected flexibly.Simulation results demonstrate that the net coding gain（NCG）of the irregular PCDS-QC-LDPC（2680,1340）code based on perfect cyclic difference sets is respectively improved by 0.13 and 0.32 dB compared with that of the code based on PEG-QC-LDPC（2680,1340）and AD-MASK-QC-LDPC（2680,1340）with the rate of 0.5 and the bit error rate（BER）of 10^（-6） by using the sum-product algorithm（SPA）iterative decoding in the additive white Gaussian（AWGN）channel.