Information-theoretic applications of the logarithmic probability comparison bound

TL;DR

This paper explores an extension of probability estimation techniques using Renyi divergence, demonstrating its effectiveness in deriving bounds for channel coding, rate-distortion, and guessing problems in information theory.

Contribution

It introduces a generalized method employing Renyi divergence for probability bounds, extending traditional techniques and providing new results across multiple information-theoretic applications.

Findings

Develops a general methodology for error exponent bounds in channel coding

Provides new bounds for rate-distortion coding

Applies the approach to guessing problems with improved results

Abstract

A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of interest has probability of order one and estimating the probability in question by means of the Kullback-Leibler divergence. A method has recently been proposed in [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 Renyi divergence is used instead. The purpose of this paper is to demonstrate the usefulness of this approach in various information-theoretic settings. For the problem of channel coding, we provide a general methodology 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.