Reduced-Complexity Projection-Aggregation List Decoder for Reed-Muller Codes

Abstract

Projection-aggregation decoders have been used in conjunction with a list structure to achieve near maximum-likelihood decoding for short-length and low-rate Reed-Muller (RM) codes but suffer from high computational complexity. We reduce the worst-case computational complexity of projection-aggregation (PA) decoders by more than 50% using a scheduling scheme compared to PA decoders without the scheduling scheme, and propose a redesigned syndrome check pattern to avoid repeated syndrome computations in the decoder. A latency model based on the existing hardware architecture is proposed. Input distribution aware (IDA) decoding is adopted as a pre-possessing tool, and the average list size when using IDA decoding is analytically derived under additive white Gaussian noise and uncorrelated normalized Rayleigh fading channels. Using IDA, the average list size is reduced by 30% with less than 0.1 dB loss. The proposed list decoders require a smaller computational complexity than the state-of-the-art iterative decoder, automorphism ensemble decoding with the belief propagation constituent decoder (AED-BP) for decoding RM(7, 3) and RM(8, 3) codes. Based on the developed latency models, the PA list decoder has a smaller latency than the AED-BP and the successive cancellation list decoder to reach near maximum-likelihood decoding performance.