A Layered CPA Decoder for Reed-Muller Codes

When decoding low-rate and short-length Reed-Muller (RM) codes, the recently proposed projection-aggregation (PA) decoder yields near maximum-likelihood decoding performance. However, the practicability of the PA decoder's implementation is nevertheless negatively impacted by its high computational cost. It has been demonstrated that this decoder is closely connected to the belief propagation (BP) decoder based on the parity-check matrix. Techniques inspired by the layered decoding and the broadcast modification for the BP decoder used by the low-density parity-check codes are proposed in this work. The proposed broadcast modification reduces the computational overhead induced by the proposed layered decoding for the collapsed PA (CPA) decoder. The proposed layered and broadcast-based CPA decoder has negligible degradation in decoding performance, and it produces a 47% reduction in the average complexity at $E_{b}/N_{0}=2.5\text{dP}$, when decoding RM(8, 3) codes.