Recursive projection-aggregation decoding of Reed-Muller codes

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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.

Original languageEnglish (US)
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2064-2068
Number of pages5
ISBN (Electronic)9781538692912
DOIs
StatePublished - Jul 2019
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: Jul 7 2019Jul 12 2019

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
CountryFrance
CityParis
Period7/7/197/12/19

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Applied Mathematics
  • Modeling and Simulation

Cite this

Abbe, E. (2019). Recursive projection-aggregation decoding of Reed-Muller codes. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 2064-2068). [8849269] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849269