Quasi-cyclic LDPC codes based on D and Q matrices through progressive edge growth

We propose a general method for constructing regular and irregular quasi-cyclic LDPC codes based on the modified PEG (progressive edge growth) graph. The idea of permutation vector is introduced. Through permutation vectors, the QC-LDPC codes based on arbitrary circulant permutation matrices, which are not limited to identity matrix, Q-matrix or D-matrix, can be generated with flexible parameters such as block length, code rate, degree distribution. Simulation results demonstrate that QC-LDPC codes using the new PEG algorithm show an error correction performance comparable to the random LDPC codes based on the traditional PEG algorithm. In addition, the PEG QC-LDPC codes have more hardware-friendly parity check matrices than the random PEG LDPC codes and can fulfill linear-time encoding. The QC-LDPC codes based on D-matrix and Q-matrix are more suitable to be used in QC-LDPC codes than identity matrix because they outperform that of identity matrix by 0.1-0.2 dB in the new PEG algorithm.