Source Coding with Mismatched Distortion Measures

TL;DR

This paper analyzes the robustness of lossy source coding when the actual distortion measure differs from the one used in code design, providing a single-letter characterization of mismatch distortion.

Contribution

It introduces a single-letter characterization of mismatch distortion, offering insights into robustness and approximation strategies in source coding.

Findings

Provides a single-letter formula for mismatch distortion

Shows how to evaluate distortion guarantees under measure mismatch

Offers guidelines for choosing tractable distortion approximations

Abstract

We consider the problem of lossy source coding with a mismatched distortion measure. That is, we investigate what distortion guarantees can be made with respect to distortion measure $\tilde{\rho}$, for a source code designed such that it achieves distortion less than $D$ with respect to distortion measure $\rho$. We find a single-letter characterization of this mismatch distortion and study properties of this quantity. These results give insight into the robustness of lossy source coding with respect to modeling errors in the distortion measure. They also provide guidelines on how to choose a good tractable approximation of an intractable distortion measure.