Recursive Projection-Aggregation Decoding of Reed-Muller Codes

Min Ye, Emmanuel Abbe

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


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.

Original languageEnglish (US)
Article number9023389
Pages (from-to)4948-4965
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2020

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • AWGN channels
  • RPA decoding
  • Reed-Muller codes
  • binary symmetric channels
  • polar codes


Dive into the research topics of 'Recursive Projection-Aggregation Decoding of Reed-Muller Codes'. Together they form a unique fingerprint.

Cite this