Abstract:

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.