Construction of Quasi-cyclic Low-density Parity-check Codes with a Large Girth Based on Arithmetic Progression

To cope with the issue of determining cyclic shift coefficients of the quasi-cyclic sub-matrix in the Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes, a method is presented based on the Arithmetic Progression (AP) to compute the cyclic shift coefficients. By this method, the girth of its Tanner graph is at least eight, and the cyclic shift coefficients can be expressed in simple analytic expressions to reduce required memory usage. The simulation results show that the proposed algorithm has high flexibility with respect to the design of code length and rate. Furthermore, over an Additive White Gauss Noise (AWGN) channel and under the Belief Propagation (BP) decoding algorithm, the simulation result also represents that the SNR of the proposed QC-LDPC codes is better than the Progressive Edge-Growth (PEG) codes close to 0.3 dB at the code length of 1008 and BER performance of 10-5.