A novel construction algorithm of the LDPC code for high-speed long-haul optical transmission systems

According to the transmission characteristics of high-speed long-haul optical transmission system, the main construction method of Low-Density Parity-Check (LDPC) code for optical transmission system is presented and a novel construction algorithm of LDPC code is proposed, the theoretical analysis shows that the parity check matrix of the LDPC code constructed by the proposed construction algorithm has no four-girth phenomenon, this is also theoretically proved out. Both the novel LDPC(3969,3720) code with 6.69% redundancy and the novel LDPC(8281,7920) code with 4.56% redundancy for optical transmission systems are constructed by using the presented construction method and proposed construction algorithm. The simulation results show that the net coding gain (NCG) of the two novel LDPC codes at the eighteenth iteration for the BER of 10⿿12 are respectively 1.63 dB and 1.49 dB more than that of the RS(255,239) code in ITU-T G.975. Moreover, the decoding of the LDPC code in the hardware can parallel be implemented, so the decoding speed of the two novel LDPC codes are very rapid, the complexities of implementing the two novel LDPC codes, compared with the concatenated codes in ITU-T G.975.1, are relatively lower, furthermore, the hardware overhead and storage space can relatively be saved and the computation complexity can be reduced in implementing the hardware in the future. As a result, the two novel LDPC codes can better be suitable for high-speed long-haul optical transmission systems.