Semi-Random and Quasi-Cyclic LDPC Codes Based on Multiple Parity-Check Codes

This paper introduces a class of Semi-Random (SR) Low-Density Parity-Check (LDPC) codes and a class of Quasi-Cyclic (QC) LDPC codes. Both of them are derived from Multiple Serially Concatenated Multiple Parity-Check (M-SC-MPC) codes and interleavers, therefore, have low encoding complexities. These two codes are called M-SR-LDPC codes and M-QC-LDPC codes, respectively, in this paper. The M-SR-LDPC codes are designed with the modified Progressive Edge-Growth (PEG) algorithm and the M-QC-LDPC codes are designed with the existing cycle-condition formula. Consequently, the proposed codes have large girths. Simulation results show that our codes perform very well over the AWGN channel with iterative decoding.