  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 belief propagation (BP)
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) using polar BP as constituent decoders. We provide extensive
error-rate performance simulations and compare our results to existing decoding
schemes. We report a near-ML performance for the RM(3,7)-code (e.g., 0.05 dB
away from the ML bound at BLER of $10^{-4}$) at a competitive computational
cost. To the best of our knowledge, our proposed decoder achieves the best
performance of all iterative RM decoders presented thus far.
