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# Recursive projection-aggregation decoding of Reed-Muller codes

## Author(s): Ye, M; Abbe, Emmanuel

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr1bz83
 Abstract: 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 based on list-decoding algorithms and code concatenation.We run our main algorithm for AWGN channels and Binary Symmetric Channels at the short code length (≤ 1024) and low code rate (≤ 0.5) regime. Simulation results show that the new algorithm not only outperforms the previous decoding algorithms for RM codes, it also outperforms the optimal decoder for polar codes (SCL+CRC) with the same parameters by a wide margin. 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. Publication Date: 2019 Citation: Ye, M, Abbe, E. (2019). Recursive projection-aggregation decoding of Reed-Muller codes. 2019-July (2064 - 2068. doi:10.1109/ISIT.2019.8849269 DOI: doi:10.1109/ISIT.2019.8849269 Pages: 2064 - 2068 Type of Material: Conference Article Journal/Proceeding Title: IEEE International Symposium on Information Theory - Proceedings Version: Author's manuscript

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