基于完备循环差集的大围长Type-Ⅱ QC-LDPC码的构造

针对当前type-Ⅱ准循环低密度奇偶校验(quasi-cyclic low-density parity-check, QC-LDPC)码的校验矩阵中存在权重为2的循环矩阵(weight-2 circulant matrices, W2CM)导致Tanner图更容易产生短环,从而影响迭代译码收敛性的问题,基于完备循环差集(cyclic difference sets, CDS)提出了一种围长为8的type-Ⅱ QC-LDPC码的新颖构造方法。该方法构造的校验矩阵由权重为0的零矩阵、权重为1的循环置换矩阵和W2CM组成,保留了type-Ⅱ QC-LDPC码的具有更高最小距离上界的优点,改善了码的纠错性能;且Tanner图中无4、6环的出现,译码时具有较快的收敛速度。仿真结果表明:所构造的围长为8的type-Ⅱ QC-LDPC码在加性高斯白噪声信道下采用和积算法迭代译码时具有较好的纠错性能且无错误平层现象。

Construction of type-Ⅱ QC-LDPC codes with a large girth based on perfect cyclic difference sets

To cope with the issue that the existence of weight-2 circulant matrices (W2CM) in parity check matrix of type-Ⅱ quasi-cyclic low-density parity-check (QC-LDPC) codes inevitably makes the Tanner graph be easier to have short cycles, which affects the convergence of iterative decoding, a novel construction method of girth-8 type-Ⅱ QC-LDPC codes based on cyclic difference sets (CDS) is proposed. The parity check matrices constructed by the proposed method consist of weight-0 zero matrices, weight-1 circulant permutation matrices and W2CM, which hold the advantage of the higher upper bound for the minimum distance and makes the error correction performance of the code better. In addition, the Tanner graphs of these codes have no girth-4 and girth-6, and thus they have the characteristics of the excellent decoding convergence. Simulation results show that the type-Ⅱ QC-LDPC codes with the girth-8 can achieve a more excellent error-correction performance and has no error-floor phenomenon over the additive white Gaussian noise channel with the iterative decoding algorithm of the sum-product algorithm.