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

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Conference article in proceedings
Date
2021-09-01
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Language
en
Pages
6
2167-2172
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Proceedings of IEEE International Symposium on Information Theory, ISIT 2021, IEEE International Symposium on Information Theory - Proceedings, Volume 2021-July
Abstract
In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural properties of the realizations of the reproduction Random Variables (RVs), which induce the corresponding optimal test channel distributions of the joint RDF. Second, we consider a tuple of correlated multivariate jointly Gaussian RVs, X_{1}:\Omega\rightarrow \mathbb{R}^{p_{1, X_{2}:\Omega\rightarrow \mathbb{R}^{p_{2 with two square-error fidelity criteria, and we derive additional structural properties of the optimal realizations, and use these to characterize the RDF as a convex optimization problem with respect to the parameters of the realizations. We show that the computation of the joint RDF can be performed by semidefinite programming. Further, we derive closed-form expressions of the joint RDF, such that Gray's [1] lower bounds hold with equality, and verify their consistency with the semidefinite programming computations.
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Funding Information: VII. ACKNOWLEDGMENTS This work was supported in parts by the European Regional Development Fund and the Republic of Cyprus through the Research Promotion Foundation Projects EXCELLENCE/1216/0365 and EXCELLENCE/1216/0296. Publisher Copyright: © 2021 IEEE.
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Stylianou , E , Charalambous , C D & Charalambous , T 2021 , Joint Rate Distortion Function of a Tuple of Correlated Multivariate Gaussian Sources with Individual Fidelity Criteria . in Proceedings of IEEE International Symposium on Information Theory, ISIT 2021 . IEEE , pp. 2167-2172 , IEEE International Symposium on Information Theory , Melbourne , Australia , 12/07/2021 . https://doi.org/10.1109/ISIT45174.2021.9518279