  Reed-Muller (RM) codes are known for their good maximum likelihood (ML)
performance in the short block-length regime. Despite being one of the oldest
classes of channel codes, finding a low complexity soft-input decoding scheme
is still an open problem. In this work, we present a versatile decoding
architecture for RM codes based on their rich automorphism group. The decoding
algorithm can be seen as a generalization of multiple-bases belief propagation
(MBBP) and may use any polar or RM decoder as constituent decoders. We provide
extensive error-rate performance simulations for successive cancellation (SC)-,
SC-list (SCL)- and belief propagation (BP)-based constituent decoders. We
furthermore compare our results to existing decoding schemes and report a
near-ML performance for the RM(3,7)-code (e.g., 0.04 dB away from the ML bound
at BLER of $10^{-3}$) at a competitive computational cost. Moreover, we provide
some insights into the automorphism subgroups of RM codes and SC decoding and,
thereby, prove the theoretical limitations of this method with respect to polar
codes.
