Simple one-shot bounds for various source coding problems using smooth Renyi quantities

TL;DR

This paper establishes simple one-shot bounds for various source coding problems using smooth Renyi quantities, providing non-asymptotic insights that unify and extend classical asymptotic results.

Contribution

It introduces one-shot achievability and converse bounds for multiple source coding scenarios based on smooth max Renyi entropy and divergence, applicable in both i.i.d. and non-i.i.d. settings.

Findings

Bounds recover known asymptotic results

Applicable to distributed source coding and side information scenarios

Effective in non-asymptotic regimes

Abstract

We consider the problem of source compression under three different scenarios in the one-shot (non- asymptotic) regime. To be specific, we prove one-shot achievability and converse bounds on the coding rates for distributed source coding, source coding with coded side information available at the decoder and source coding under maximum distortion criterion. The one-shot bounds obtained are in terms of smooth max Renyi entropy and smooth max Renyi divergence. Our results are powerful enough to yield the results that are known for these problems in the asymptotic regime both in the i.i.d. (independent and identically distributed) and non-i.i.d. settings