The Meta-Converse and Perfect Codes

Albert Guillén i Fàbregas (ICREA and Universitat Pompeu Fabra)

Abstract:
The decoding process in the point-to-point communication problem is an instance of Bayesian M-ary hypothesis testing. This talk will illustrate how the error probability of an arbitrary code can be expressed as a function of a non-Bayesian binary hypothesis test, proving the tightness of the so-called meta-converse bound. Furthermore, for symmetric channels, the error probability of the best code is shown to coincide with that of a binary hypothesis test with certain parameters. The points in which they coincide, are precisely the points at which perfect or quasi-perfect codes exist.