Information-theoretic applications of the logarithmic probability comparison bound

A well-known technique in assessing probabilities of rare events (used, e.g., in the sphere-packing bound), is that of finding a reference measure under which the event of interest has probability of order one and estimating the probability in question using the Kullback-Leibler divergence (KLD). A recent method has been proposed [2], that can be viewed as an extension of this idea in which the probability under the reference measure may itself be decaying exponentially, and the Rényi divergence (RD) is used instead. We demonstrate the usefulness of this approach in various information-theoretic settings. For channel coding, we provide a method for obtaining matched, mismatched and robust error exponent bounds, as well as new results in a variety of particular channel models. Other applications we address include rate-distortion coding and the problem of guessing.