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

Abstract

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 0.3 dB, 0.55 dB, 1.4 dB and 1.98 dB 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.

Keywords

Code Rate / Forward Error Correction / Basic Matrix / Parity Check Matrix / Error Correction Performance

References

[1] BinhL. N., HuynhT. L., PangK. K., SivahumaranT.. Journal of Lightwave Technology, 2008, 26: 1586

[2] YuanJ., YeW., JiangZ., MaoY., WangW.. Optics Communications, 2007, 273: 421

[3] ZhangP., YuS., LiuC., JiangL.. Electronics Letters, 2014, 50: 320

[4] YuanJ., LiuF., YeW., HuangS., WangY.. OPTIK, 2014, 125: 1016

[5] DjordjevicI. B., CvijeticM., XuL., WangT.. Journal of Lightwave Technology, 2007, 25: 3619

[6] ParkH., HongS., NoJ.-S., ShinD.-J.. IEEE Transactions on Communications, 2013, 61: 3108

[7] SungL.k. P., HeungM.o.o.k. K., WuY.-y., JeongchangK.. IEEE Transactions on Broadcasting, 2013, 59: 155

[8] ZHUL.-x., YANGH.-y.. Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition), 2011, 23: 570

[9] SongS.-m., ZhouB., LinS., Abdel-GhaffarK.. IEEE Transactions on Communications, 2009, 57: 84

[10] JuaneL., LiuK.-k., LinS., Abdel-GhaffarK.. IEEE Transactions on Communications, 2014, 62: 2626

[11] YuanJ.-g., XuL., TongQ.-z.. Optoelectronics Letters, 2013, 9: 378

[12] KangJ.-y., HuangQ., ZhangL., ZhouB., LiS.. IEEE Transactions on Communications, 2010, 58: 1383

[13] ITU-T G.975, Forward Error Correction for Submarine Systems, 2000.

[14] ITU-T G.975.1, Forward Error Correction for High Bit-rate DWDM Submarine Systems, 2004.

[15] YuanJ.-g., XieY., WangL., HuangS., WangY.. Optoelectronics Letters, 2013, 9: 0042

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