English

Recursive Decoding and Its Performance for Low-Rate Reed-Muller Codes

Information Theory 2017-03-17 v1 math.IT

Abstract

Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length nn and fixed order r.r. An algorithm is designed that has complexity of order nlognn\log n and corrects most error patterns of weight up to n(1/2ε)n(1/2-\varepsilon) given that ε\varepsilon exceeds n1/2r.n^{-1/2^{r}}. This improves the asymptotic bounds known for decoding RM codes with nonexponential complexity.

Keywords

Cite

@article{arxiv.1703.05306,
  title  = {Recursive Decoding and Its Performance for Low-Rate Reed-Muller Codes},
  author = {Ilya Dumer},
  journal= {arXiv preprint arXiv:1703.05306},
  year   = {2017}
}
R2 v1 2026-06-22T18:46:49.453Z