Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 66, Issue 8, Pages 4948-4965Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2020.2977917
Keywords
Decoding; Iterative decoding; AWGN channels; Simulation; Error correction codes; Memoryless systems; Frequency modulation; Reed-Muller codes; polar codes; RPA decoding; AWGN channels; binary symmetric channels
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We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are lower-order RM codes), and aggregating the reconstructions (e.g., using majority votes). We further provide extensions of the algorithms using list-decoding. We run our algorithm for AWGN channels and Binary Symmetric Channels at the short code length (<= 1024) regime for a wide range of code rates. Simulation results show that in both low code rate and high code rate regimes, the new algorithm outperforms the widely used decoder for polar codes (SCL+CRC) with the same parameters. The performance of the new algorithm for RM codes in those regimes is in fact close to that of the maximal likelihood decoder. Finally, the new decoder naturally allows for parallel implementations.
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