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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。
Aiming at the problems of high coding complexity and inflexible code length selection in Quasi-Cyclic Low-Density Parity Check (QC-LDPC) codes, based on Perfect Cyclic Difference Sets , PCDS) proposed a deterministic construction method. The number of shifts in the Base Matrix (BM) can be obtained by simply adding and subtracting the complete cyclic difference set. The combination of the special matrix and the complete cyclic difference saves memory space and reduces the complexity of the hardware implementation , Its girth is at least 6, and the code length rate can be flexibly selected. The simulation results show that the Sum-Product Algorithm (SPA) iterative decoding is implemented in the additive additive white Gaussian noise (AWGN) channel with a bit rate of 0.5 and a bit error rate of 10 -6 ), An irregular PCDS-QCLDPC (2680,1340) code based on a complete cyclic difference set was constructed than a discrete array AD-MASK-QCLDPC (2680,1340) based on PEG-QC-LDPC ) Codes increase the Net Coding Gain (NCG) by 0.13 and 0.32 dB, respectively.