Maximum likelihood (ML) decoding is one of important methods of error-correcting codes in information theory and coding theory. Hayashi and Hiraoka represented the ML decoding rule by means of a rational map, showed that the rational map has a simple Taylor expansion and proposed an approximate ML decoding by using the property in the following paper:
K. Hayashi and Y. Hiraoka, Rational maps and maximum likelihood decodings, Jpn. J. Ind. Appl. Math. 29 (2012), 37–62
In this talk I explain their results and state my plans of future work in my graduate thesis.