On the Conditional Smooth Renyi Entropy and its Applications in Guessing and Source Coding

TL;DR

This paper introduces a new definition of conditional smooth Renyi entropy and demonstrates its usefulness in deriving bounds for guessing problems and source coding with side information, providing new theoretical insights.

Contribution

The paper proposes a different definition of conditional smooth Renyi entropy and applies it to guessing and source coding, deriving bounds and formulas not previously available.

Findings

New definition of conditional smooth Renyi entropy

Bounds on optimal guessing moments established

Single-letterized formula for mixture of i.i.d. sources

Abstract

A novel definition of the conditional smooth Renyi entropy, which is different from that of Renner and Wolf, is introduced. It is shown that our definition of the conditional smooth Renyi entropy is appropriate to give lower and upper bounds on the optimal guessing moment in a guessing problem where the guesser is allowed to stop guessing and declare an error. Further a general formula for the optimal guessing exponent is given. In particular, a single-letterized formula for mixture of i.i.d. sources is obtained. Another application in the problem of source coding with the common side-information available at the encoder and decoder is also demonstrated.