Optimization of NB-QC-LDPC Codes with Column Weight Not Exceeding Three

The non-binary quasi cyclic low-density parity-check (NB-QC-LDPC) code is a strong candidate code in optical communication. However, the presence of elementary absorbing sets in NB-QC-LDPC codes can degrade the frame error rate (FER) performance of the codes in the error floor region. Additionally, better minimum Hamming distance distribution can improve the FER performance of codes in the waterfall region. In this paper, a joint optimization of absorbing sets and minimum Hamming distance distribution is proposed for NB-QC-LDPC codes with a maximum column weight not exceeding 3. Simulation results show that the constructed codes could achieve comparable or better FER compared to the recently proposed NB-QC-LDPC codes with the same codes parameters.