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

The relative entropy and 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.
Comment: Published in the Entropy journal, May 18, 2020. Journal version (open access) is available at https://www.mdpi.com/1099-4300/22/5/563