In this paper, we propose a multi-level non-binary quasi-cyclic low density parity check (NB-QC-LDPC) coded modulation (CM) scheme to reduce the decoding complexity while maintaining and/or exceeding the super BER performance of the traditional NB-QC-LDPC CM scheme. Firstly, local optimal searching combined with the classical superposition construction is proposed to construct the required NB-QC-LDPC codes with possibly enlarged girth and less number of the shortest cycles. Secondly, by analyzing the changing trend of the BER performance and decoding complexity of the NB-QC-LDPC code defined over 𝐺𝐹(𝑄) incident to 𝑄. We find that the decoding complexity increases proportionally with the increase of 𝑄, but the best BER performance usually corresponds to a smaller 𝑄. Finally, by replacing the high-order NB-QC-LDPC code based CM scheme to the multi-level low-order NB-QC-LDPC code based CM scheme, the decoding complexity can be effectively reduced. Simulation results show that the designed two-level 𝐺𝐹(4)/𝐺𝐹(8) QC-LDPC code based 16QAM/64QAM CM system can perform almost the same or even better BER performance with/than the corresponding traditional 𝐺𝐹(16) / 𝐺𝐹(64) QC-LDPC code based 16QAM/64QAM CM system.
In this paper, we propose a two-stage bit mapping based irregular QC-LDPC coded BICM scheme to further improve the BER performance of BICM system. Firstly, with the aid of EXIT chart, the irregular code ensemble with optimal convergence threshold can be found, then PEG algorithm is used to construct the required irregular QC-LDPC code with possibly enlarged girth from the ensemble. Secondly, a two-stage bit mapping design method is introduced to find the optimal bit mapping distribution and the near optimal bit mapping table, which can further improve the convergence threshold of the BICM system. Simulation results show that, when applying the proposed scheme to BTB coherent optical PM-64QAM system, additional 0.13dB net coding gain can be achieved compared with the traditional BICM scheme at the BER of 10-5.