Decoding Reed-Muller Codes Using Minimum- Weight Parity Checks
Paper i proceeding, 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.


Elia Santi

Universita degli Studi di Parma

Christian Häger

Duke University

Chalmers, Elektroteknik, Kommunikations- och antennsystem, Kommunikationssystem

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)

Europeiska kommissionen (Horisont 2020), 2017-01-01 -- 2019-12-31.







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