Abstract —In this paper, the construction of the high rate Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes is presented for the wired or wireless optical communications with high frequency spectrum efficiency, especially at rather good channel environments. The good code performance can be achieved by an improved girth search algorithm, where the girth is optimized by the maximization of the average loop length. It mainly searches the optimal circulant shift offsets in each permutation sub-matrix to maximize the average girth of the variable nodes in the Tanner graph. And the property of the maximum average girth can be exploited in the classic Belief Propagation (BP) LDPC decoding to avoid the unnecessary false message self-feedback by the short loops in the iterative decoding as far as possible. Meanwhile, the proposed codes are also optimally designed for good girth and degree profile with conventional Progressive Edge Growth (PEG) and Extrinsic Information Transfer (EXIT) chart techniques. Simulation results show that the proposed girth optimized QC-LDPC codes obtain a little better Bit-Error-Rate (BER) performance, when compared with the current channel codes of similar code parameters used in the optical communications. Therefore, the proposed code design methodology can be effectively adopted in the construction of the high rate QC-LDPC codes, which can be used in the optical communications for good coding gains.
 
Index Terms—QC-LDPC codes, girth optimization, average girth

Cite: Jianrong Bao, Dan He, Bin Jiang, and Xianghong Tang, “High Rate QC-LDPC Codes with Optimization of Maximum Average Girth," Journal of Communications, vol. 11, no. 10, pp. 936-943, 2016. Doi: 10.12720/jcm.11.10.936-943