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Reed-Muller Codes for Random Erasures and Errors

2015
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Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15
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This paper studies the parameters for which Reed-Muller codes over GF (2) can correct random erasures and random errors with high probability, and in particular when can they achieve capacity (namely, the information theoretic limit) for these two classical channels. Necessarily, the paper also studies properties of evaluations of multi-variate GF (2) polynomials on random sets of inputs. For erasures, we prove that RM codes achieve capacity both for very high rate and very low rate regimes.

doi:10.1145/2746539.2746575
dblp:conf/stoc/AbbeSW15
fatcat:3pgrck7nwbe2npiems4iywblwm