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In this paper we analyze the joint rate distortion function (RDF), for atuple of correlated sources taking values in abstract alphabet spaces (i.e.,continuous) subject to two individual distortion criteria. First, we derivestructural properties of the realizations of the reproduction Random Variables(RVs), which induce the corresponding optimal test channel distributions of thejoint RDF. Second, we consider a tuple of correlated multivariate jointlyGaussian RVs, $X_1 : \Omega \rightarrow {\mathbb R}^{p_1}, X_2 : \Omega\rightarrow {\mathbb R}^{p_2}$ with two square-error fidelity criteria, and wederive additional structural properties of the optimal realizations, and usethese to characterize the RDF as a convex optimization problem with respect tothe parameters of the realizations. We show that the computation of the jointRDF can be performed by semidefinite programming. Further, we deriveclosed-form expressions of the joint RDF, such that Gray's [1] lower boundshold with equality, and verify their consistency with the semidefiniteprogramming computations.

Joint Rate Distortion Function of a Tuple of Correlated Multivariate Gaussian Sources with Individual Fidelity Criteria