Equivocations and exponents under various Rényi information measures

In this paper, we evaluate the asymptotics of equivocations and their exponents. Specifically, we consider the effect of applying a hash function on a source and we quantify the level of non-uniformity and dependence of the compressed source from another correlated source. Unlike previous works that use the Shannon information measures to quantify randomness or information, in this paper, we consider a more general class of information measures, i.e., the Rényi information measures and their Gallager forms. We prove tight asymptotic results for the equivocation and its exponential decay rates by establishing new non-asymptotic bounds on the equivocation and evaluating these bounds asymptotically.