Soft-decision decoding of Reed-Muller codes based on simple multi-step SISO module

The paper proposes a new multi-step soft-decision decoding for the generic Reed-Muller (RM) code family, which is based on a simple multi-step soft-input soft-output (SISO) module and the inherent merits of the RM codes. In an AWGN channel, the simulation results show that, for RM codes of different code rates and lengths, the introduced approach can offer pronounced performance gains over other soft-decision sub-optimal approaches and a conventional hard majority logic decoder. The results also indicate that the new algorithm can achieve a performance very close to that provided by a maximum likelihood decoder under the same conditions.