On Relations Between the Relative Entropy and χ2-Divergence, Generalizations and Applications

Abstract

The relative entropy and the chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these relations, their information-theoretic applications, and some generalizations pertaining to the rich class of f-divergences. Applications that are studied in this paper refer to lossless compression, the method of types and large deviations, strong data–processing inequalities, bounds on contraction coefficients and maximal correlation, and the convergence rate to stationarity of a type of discrete-time Markov chains.