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Maximum likelihood decoding of Reed Solomon codes

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1 Author(s)
Sudan, M. ; IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA

We present a randomized algorithm which takes as input n distinct points {(xi,yi)}i=1n from F×F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable a of degree at most d which agree with the given set of points in at least t places (i.e., yi=f(xi) for at least t values of i), provided t=Ω(√(nd)). The running time is bounded by a polynomial in n. This immediately provides a maximum likelihood decoding algorithm for Reed Solomon Codes, which works in a setting with a larger number of errors than any previously known algorithm. To the best of our knowledge, this is the first efficient (i.e., polynomial time bounded) algorithm which provides some maximum likelihood decoding for any efficient (i.e., constant or even polynomial rate) code

Published in:

Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on

Date of Conference:

14-16 Oct 1996