Implicit and Explicit Formulas of the Joint RDF for a Tuple of Multivariate Gaussian Sources with Individual Square-Error Distortions

TL;DR

This paper derives explicit formulas for the joint rate distortion function of correlated multivariate Gaussian sources with individual square-error distortions, using Hotelling's canonical variables and water-filling solutions.

Contribution

It provides a closed-form characterization of the joint RDF, including explicit formulas for symmetric distortions, advancing the theoretical understanding of Gaussian source coding.

Findings

Closed-form joint RDF for multivariate Gaussian sources derived.

Explicit water-filling solutions for symmetric distortions obtained.

Enhanced understanding of source coding with individual distortions achieved.

Abstract

This paper analyzes the joint Rate Distortion Function (RDF) of correlated multivariate Gaussian sources with individual square-error distortions. Leveraging Hotelling's canonical variable form, presented is a closed-form characterization of the joint RDF, that involves {a system of nonlinear equations. Furthermore, for the special case of symmetric distortions (i.e., equal distortions), the joint RDF is explicitly expressed in terms of} two water-filling variables. The results greatly improve our understanding and advance the development of closed-form solutions of the joint RDF for multivariate Gaussian sources with individual square-error distortions.