Journal
IEEE TRANSACTIONS ON COMMUNICATIONS
Volume 69, Issue 10, Pages 6424-6438Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCOMM.2021.3098798
Keywords
Maximum likelihood decoding; Polar codes; Iterative decoding; Belief propagation; Encoding; Complexity theory; Generators; Reed-Muller Codes; polar codes; code automorphisms; successive cancellation decoding; belief propagation decoding; list decoding; ensemble decoding
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RM codes are known for their good maximum likelihood performance in the short block-length regime, but finding a low complexity soft-input decoding scheme remains an open problem. We have presented a versatile decoding architecture for RM codes based on their rich automorphism group, which can be seen as a generalization of multiple-bases belief propagation.
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.
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