Low complexity multi-level NB-QC-LDPC coded modulation scheme for optical communication systems

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.