A novel construction method of QC-LDPC codes based on the subgroup of the finite field multiplicative group for optical transmission systems

According to the requirements of the increasing development for optical transmission systems,a novel construction method of quasi-cyclic low-density parity-check（QC-LDPC） codes based on the subgroup of the finite field multiplicative group is proposed.Furthermore,this construction method can effectively avoid the girth-4 phenomena and has the advantages such as simpler construction,easier implementation,lower encoding/decoding complexity,better girth properties and more flexible adjustment for the code length and code rate.The simulation results show that the error correction performance of the QC-LDPC（3 780,3 540） code with the code rate of 93.7% constructed by this proposed method is excellent,its net coding gain is respectively 0.3dB,0.55dB,1.4dB and 1.98dB higher than those of the QC-LDPC（5 334,4 962） code constructed by the method based on the inverse element characteristics in the finite field multiplicative group,the SCG-LDPC（3 969,3 720） code constructed by the systematically constructed Gallager（SCG） random construction method,the LDPC（32 640,30 592） code in ITU-T G.975.1 and the classic RS（255,239） code which is widely used in optical transmission systems in ITU-T G.975 at the bit error rate（BER） of 10-7.Therefore,the constructed QC-LDPC（3 780,3 540） code is more suitable for optical transmission systems.