A novel construction scheme of QC-LDPC codes based on the RU algorithm for optical transmission systems

A novel lower-complexity construction scheme of quasi-cyclic low-density parity-check（QC-LDPC） codes for optical transmission systems is proposed based on the structure of the parity-check matrix for the Richardson-Urbanke（RU） algorithm. Furthermore, a novel irregular QC-LDPC（4 288, 4 020） code with high code-rate of 0.937 is constructed by this novel construction scheme. The simulation analyses show that the net coding gain（NCG） of the novel irregular QC-LDPC（4 288,4 020） code is respectively 2.08 d B, 1.25 d B and 0.29 d B more than those of the classic RS（255, 239） code, the LDPC（32 640, 30 592） code and the irregular QC-LDPC（3 843, 3 603） code at the bit error rate（BER） of 10;. The irregular QC-LDPC（4 288, 4 020） code has the lower encoding/decoding complexity compared with the LDPC（32 640, 30 592） code and the irregular QC-LDPC（3 843, 3 603） code. The proposed novel QC-LDPC（4 288, 4 020） code can be more suitable for the increasing development requirements of high-speed optical transmission systems.