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Entropy 2018, 20(1), 2; https://doi.org/10.3390/e20010002

Rate-Distortion Region of a Gray–Wyner Model with Side Information

1
Department of Electronics Optronics and Signal Processing (DEOS), Institut Superieur de l’Aéronautique et de l’Espace Supaéro (ISAE Supaéro), 31400 Toulouse, France
2
Mathematics and Algorithmic Sciences Lab, Huawei Technologies France, 92100 Boulogne-Billancourt, France
Current address: Institut d’Électronique et d’Informatique Gaspard-Monge, Université Paris-Est, 77454 Champs-sur-Marne, France.
*
Author to whom correspondence should be addressed.
Received: 29 November 2017 / Revised: 13 December 2017 / Accepted: 15 December 2017 / Published: 22 December 2017
(This article belongs to the Special Issue Rate-Distortion Theory and Information Theory)
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Abstract

In this work, we establish a full single-letter characterization of the rate-distortion region of an instance of the Gray–Wyner model with side information at the decoders. Specifically, in this model, an encoder observes a pair of memoryless, arbitrarily correlated, sources ( S 1 n , S 2 n ) and communicates with two receivers over an error-free rate-limited link of capacity R 0 , as well as error-free rate-limited individual links of capacities R 1 to the first receiver and R 2 to the second receiver. Both receivers reproduce the source component S 2 n losslessly; and Receiver 1 also reproduces the source component S 1 n lossily, to within some prescribed fidelity level D 1 . In addition, Receiver 1 and Receiver 2 are equipped, respectively, with memoryless side information sequences Y 1 n and Y 2 n . Important in this setup, the side information sequences are arbitrarily correlated among them, and with the source pair ( S 1 n , S 2 n ) ; and are not assumed to exhibit any particular ordering. Furthermore, by specializing the main result to two Heegard–Berger models with successive refinement and scalable coding, we shed light on the roles of the common and private descriptions that the encoder should produce and the role of each of the common and private links. We develop intuitions by analyzing the developed single-letter rate-distortion regions of these models, and discuss some insightful binary examples. View Full-Text
Keywords: rate-distortion; Gray–Wyner; side-information; Heegard–Berger; successive refinement rate-distortion; Gray–Wyner; side-information; Heegard–Berger; successive refinement
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Benammar, M.; Zaidi, A. Rate-Distortion Region of a Gray–Wyner Model with Side Information. Entropy 2018, 20, 2.

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