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Rational Maps and Maximum Likelihood Decodings

Hold Date 2011-05-25 09:00~2011-05-25 10:00

Place Seminar Room 6, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Yasuaki Hiraoka, Kyushu University

Abstract: In this talk, we study maximum likelihood(ML) decoding in error-correcting codes as rational maps and propose a new approximate ML decoding rule by using a Taylor expansion. The point for the Taylor expansion is properly chosen by considering some dynamical system properties. We have two results about this approximate ML decoding.The first result proves that the order of the first nonlinear terms in the Taylor expansion is determined by the minimum distance of its dual code. As the second result, we give numerical results on bit error probabilities for the approximate ML decoding. These numerical results show better performance than that of BCH codes, and indicate that this proposed method approximates the original ML decoding very well.