Decoding Reed-Muller Codes Using Minimum- Weight Parity Checks

Published

Journal Article

© 2018 IEEE. Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve near-ML performance in practice. The main idea is to apply iterative decoding to a highly-redundant parity-check (PC) matrix that contains only the minimum-weight dual codewords as rows. As examples, we consider the peeling decoder for the binary erasure channel, linear-programming and belief propagation (BP) decoding for the binary-input additive white Gaussian noise channel, and bit-flipping and BP decoding for the binary symmetric channel. For short block lengths, it is shown that near-ML performance can indeed be achieved in many cases. We also propose a method to tailor the PC matrix to the received observation by selecting only a small fraction of useful minimum-weight PCs before decoding begins. This allows one to both improve performance and significantly reduce complexity compared to using the full set of minimum-weight PCs.

Full Text

Duke Authors

Cited Authors

  • Santi, E; Hager, C; Pfister, HD

Published Date

  • August 15, 2018

Published In

Volume / Issue

  • 2018-June /

Start / End Page

  • 1296 - 1300

International Standard Serial Number (ISSN)

  • 2157-8095

Digital Object Identifier (DOI)

  • 10.1109/ISIT.2018.8437637

Citation Source

  • Scopus