Mutual Information Bounds for Lossy Common Information

TL;DR

This paper explores mutual information bounds in Gray-Wyner networks, generalizing previous lossless results to the lossy case, and clarifies the relationship between different notions of lossy common information.

Contribution

It introduces bounds on mutual information that distinguish between Wyner's and Gács-Körner's lossy common information, extending classical results to lossy scenarios.

Findings

Mutual information bounds separate different lossy common information concepts

Generalization of Wyner's lossless results to lossy case

Provides theoretical framework for lossy common information analysis

Abstract

We show the mutual information between the targets in a Gray-Wyner Network as a bound that separates Wyner's lossy common information and G\'acs-K\"orner lossy common information. The results are a generalization of the lossless case presented by Wyner (1975).