Outer Bounds on the CEO Problem with Privacy Constraints

TL;DR

This paper establishes new outer bounds on the rate-distortion-leakage region of the CEO problem with privacy constraints, considering general distortion measures and eavesdropper side information, advancing understanding of privacy in distributed source coding.

Contribution

It introduces a novel outer bound for the CEO problem with privacy constraints, including a new lemma and analysis for specific source and distortion scenarios.

Findings

Outer bounds closely match inner bounds when distortion is large.

Tight bounds are achieved for discrete and Gaussian sources without eavesdropper side information.

The bounds differ minimally when the eavesdropper has side information, highlighting the impact of privacy constraints.

Abstract

We investigate the rate-distortion-leakage region of the Chief Executive Officer (CEO) problem, considering the presence of a passive eavesdropper and privacy constraints. We start by examining the region where a general distortion measure quantifies the distortion. While the inner bound of the region is derived from previous work, this paper newly develops an outer bound. To derive the outer bound, we introduce a new lemma tailored for analyzing privacy constraints. Next, as a specific instance of the general distortion measure, we demonstrate that the tight bound for discrete and Gaussian sources is obtained when the eavesdropper has no side information, and the distortion is quantified by the log-loss distortion measure. We further investigate the rate-distortion-leakage region for a scenario where the eavesdropper has side information, and the distortion is quantified by the log-loss distortion measure and provide an outer bound for this case. The derived outer bound differs from the inner bound by only a minor quantity that appears in the constraints associated with the privacy-leakage rates, and these bounds match when the distortion is large.