Coset-based quasi-cyclic LDPC codes for optimal overlapped message passing decoding

Due to the regular structures of quasi-cyclic (QC) low-density parity-check (LDPC) codes, the message passing decoding of these codes not only has efficient hardware implementation, but also can be overlapped to improve throughput and hardware utilization efficiency (HUE). In previous work, we proposed a scheduling scheme for the overlapped message passing (OMP) decoding of the SFT codes. In this paper, we first show that our scheduling scheme produces the minimum intra-iteration waiting time for QC LDPC codes. Then we propose a coset-based construction of QC LDPC codes, and study the girth and minimum distance properties of our new codes. Given the same parameters, the ensemble of the SFT codes is a subset of the ensemble of our coset-based QC LDPC codes. Our coset-based QC LDPC codes allow the OMP decoding to achieve greater throughput gain and higher HUE while maintaining the same theoretical performances as the SFT codes.