Strong Asymptotic Composition Theorems for Mutual Information Measures

Benjamin Wu, Aaron B. Wagner, Ibrahim Issa, G. Edward Suh

Abstract: We characterize the growth of the Sibson and Arimoto mutual informations and $\alpha $ -maximal leakage, of any order that is at least unity, between a random variable and a growing set of noisy, conditionally independent and identically-distributed observations of the random variable. Each of these measures increases exponentially fast to a limit that is order- and measure-dependent, with an exponent that is order- and measure-independent.