A new coding scheme of QC-LDPC codes for optical transmission systems

Based on Galois Field (GF(q)) multiplicative group, a new coding scheme for Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes is proposed, and the new coding scheme has some advantages such as the simpler construction, the easier implementation encoding, the lower complexity of the encoding and decoding, the more flexible adjustment of the code length as well as the code rate and so forth. Under the condition of considering the characteristics of optical transmission systems, an irregular QC-LDPC (3843,3603) code to be suitable for optical transmission systems is constructed by applying the proposed new coding scheme. The simulation result shows that the net coding gain (NCG) of the irregular QC-LDPC (3843,3603) code is respectively improved 2.14 dB, 1.19 dB, 0.24 dB and 0.14 dB more than those of the classic RS (255,239) code in ITU-T G.975, the LDPC (32640,30592) code in ITU-T G.975.1, the regular SCG-LDPC (3969,3720) code constructed by the Systematically Constructed Gallager (SCG) coding scheme and the regular QC-LDPC (4221,3956) code at the bit error rate (BER) of 10-8. Furthermore, all the five codes have the same code rate of 93.7%. Therefore, the irregular QC-LDPC (3843,3603) code constructed by the proposed new coding scheme has the more excellent error-correction performance and can be better suitable for optical transmission systems.