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

2025/08/22 by Stylianou, Evagoras, Charalambous, Charalambos D., Charalambous, Themistoklis
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2508.16301

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.

Citations

• Computability of Optimizers
• Semantic Compression with Side Information: A Rate-Distortion Perspective
• An Indirect Rate-Distortion Characterization for Semantic Sources: General Model and the Case of Gaussian Observation
• A Rate-Distortion Framework for Characterizing Semantic Information
• Joint Nonanticipative Rate Distortion Function for a Tuple of Random\n Processes with Individual Fidelity Criteria
• Joint Rate Distortion Function of a Tuple of Correlated Multivariate\n Gaussian Sources with Individual Fidelity Criteria
• The Lossy Common Information of Correlated Sources

Related

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• Joint Nonanticipative Rate Distortion Function for a Tuple of Random\n Processes with Individual Fidelity Criteria
• Characterization of the Gray-Wyner Rate Region for Multivariate Gaussian Sources: Optimality of Gaussian Auxiliary RV