In this paper we propose efficient decoding techniques to significantly improve the error-correction performance of fast successive-cancellation (FSC) and FSC list (FSCL) decoding algorithms for short low-order Reed-Muller (RM) codes. In particular, we first integrate Fast Hadamard Transform (FHT) into FSC (FHT-FSC) and FSCL (FHT-FSCL) decoding algorithms to optimally decode the first-order RM subcodes. We then utilize the rich permutation group of RM codes by independently running the FHT-FSC and the FHT-FSCL decoders on a list of random bit-index permutations of the codes. The simulation results show that the error-correction performance of the FHT-FSC decoders on a list of $L$ random code permutations outperforms that of the FSCL decoder with list size $L$, while requiring lower memory requirement and computational complexity for various configurations of the RM codes. In addition, when compared with the state-of-the-art recursive projection-aggregation (RPA) decoding, the permuted FHT-FSCL decoder can obtain a similar error probability for the RM codes of lengths $128$, $256$, and $512$ at various code rates, while requiring several orders of magnitude lower computational complexity.

翻译：在本文中,我们提出有效的解码技术,以大大改进快速连续取消(FSC)和FSC列表(FSCCL)的错误校正性能,从而大大改进快速连续取消(FSC)和FSC列表(FSCCL)的快速低级Reed-Muller(RM)代码解码算法的错误校正性;特别是,我们首先将快速哈达马德变换(FHT-FSC)纳入FSC(FHT-FSC)和FSCL解码法(FHT-FCL)的错误校正性功能,以优化地解码第一级(FHT-FSC)和FSC清单(FSCL)的错误校正性性能,同时通过独立地运行FHT-FCLCL(FCL)的复杂度(FHT-CRM)的复杂度和复杂度(FA-RMFC-CFC-CL) 的精确度,同时,在每次投影中,可以计算,在每套RM(RMD-CRBRP)的概率中,在计算中,在计算中,在计算中,在计算中,在计算中,在计算中可以进行。