Efficient hard-decision and soft-decision decoding algorithms for polar codes

While polar codes are capacity-achieving and adopted in the 5G standard, most practical decoders rely on soft decisions. Few works have considered efficient hard-decision decoding. In this work, we propose a majority-logic-based hard-decision decoder for polar codes by exploiting their nested subcode relations with Reed–Muller (RM) codes. The proposed decoder can achieve the error correction capability up to the theoretical bound determined by the minimum distance of the code. Moreover, we utilize the positions of non-information bits to design a complexity reduction mechanism and introduce a verification criterion to identify successful decoding outcomes. We further extend the hard-decision decoding to a soft-decision approximate maximum likelihood (ML) decoder based on the approach proposed by Kaneko et al. To improve the decoding efficiency, a termination strategy is employed, which stops the decoding process once a predefined number of candidate codewords is found. Simulation results demonstrate that the proposed decoder achieves near-ML performance while reducing computational complexity compared to existing soft-decision algorithms for polar codes.