Decoding Reed-Muller Codes Using Minimum- Weight Parity Checks
Paper in proceedings, 2018

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.

Author

Elia Santi

University of Parma

Christian Häger

Duke University

Chalmers, Electrical Engineering, Communication and Antenna Systems, Communication Systems

Henry D. Pfister

Duke University

IEEE International Symposium on Information Theory - Proceedings

21578095 (ISSN)

Vol. 2018-June 1296-1300 8437637

2018 IEEE International Symposium on Information Theory, ISIT 2018
Vail, USA,

Coding for terabit-per-second fiber-optical communications (TERA)

European Commission (Horizon 2020), 2017-01-01 -- 2019-12-31.

Subject Categories

Telecommunications

Control Engineering

Signal Processing

DOI

10.1109/ISIT.2018.8437637

More information

Latest update

1/20/2019