English

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

Information Theory 2025-08-25 v1 math.IT

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.

Keywords

Cite

@article{arxiv.2508.16301,
  title  = {Implicit and Explicit Formulas of the Joint RDF for a Tuple of Multivariate Gaussian Sources with Individual Square-Error Distortions},
  author = {Evagoras Stylianou and Charalambos D. Charalambous and Themistoklis Charalambous},
  journal= {arXiv preprint arXiv:2508.16301},
  year   = {2025}
}