Achieving Capacity on Non-Binary Channels with Generalized Reed-Muller Codes
Information Theory
2023-05-16 v1 math.IT
Abstract
Recently, the authors showed that Reed-Muller (RM) codes achieve capacity on binary memoryless symmetric (BMS) channels with respect to bit error rate. This paper extends that work by showing that RM codes defined on non-binary fields, known as generalized RM codes, achieve capacity on sufficiently symmetric non-binary channels with respect to symbol error rate. The new proof also simplifies the previous approach (for BMS channels) in a variety of ways that may be of independent interest.
Cite
@article{arxiv.2305.07779,
title = {Achieving Capacity on Non-Binary Channels with Generalized Reed-Muller Codes},
author = {Galen Reeves and Henry D. Pfister},
journal= {arXiv preprint arXiv:2305.07779},
year = {2023}
}
Comments
Extended version of ISIT 2023 accepted paper