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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.
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. Futurertherm, this construction method can effectively avoid the girth-4 phenomena and has the advantages like 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, 4962) code constructed by the method based on the inverse element characteristics in the finite field multiplicative group, the SCG-LDPC (3 969, 3202) code constructed by the systematically c onstructed 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.