Generalized source coding theorems and hypothesis testing: Part I - Information measures

Abstract

Expressions for epsilon-entropy rate, epsilon-mutual information rate and epsilon-divergence rate are introduced. These quantities, which consist of the quantiles of the asymptotic information spectra, generalize the inf/supentropy/information/divergence rates of Han and Verdu. The algebraic properties of these information measures are rigorously analyzed, and examples illustrating their use in the computation of the E-capacity are presented. In Part II of this work, these measures are employed to prove general source coding theorems for block codes, and the general formula of the Neyman-Pearson hypothesis testing type-II error exponent subject to upper bounds on the type-I error probability.