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

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 (Sn1,Sn2) and communicat...

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Published inEntropy (Basel, Switzerland) Vol. 20; no. 1; pp. 2 - 2.23
Main Authors Benammar, Meryem, Zaidi, Abdellatif
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2018
MDPI
SeriesTransfer Entropy as a Tool for Hydrodynamic Model Validation
Subjects
Communication channels
Computer Science
Decoders
Distortion
Gray–Wyner
Heegard–Berger
Information Theory
rate-distortion
Receivers
side-information
successive refinement
Heegard-Berger
successive refinement
side-information
Rate-distortion
Gray-Wyner
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Summary: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 (Sn1,Sn2) and communicates with two receivers over an error-free rate-limited link of capacity R0 , as well as error-free rate-limited individual links of capacities R1 to the first receiver and R2 to the second receiver. Both receivers reproduce the source component Sn2 losslessly; and Receiver 1 also reproduces the source component Sn1 lossily, to within some prescribed fidelity level D1 . In addition, Receiver 1 and Receiver 2 are equipped, respectively, with memoryless side information sequences Yn1 and Yn2 . Important in this setup, the side information sequences are arbitrarily correlated among them, and with the source pair (Sn1,Sn2) ; 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.
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Current address: Institut d’Électronique et d’Informatique Gaspard-Monge, Université Paris-Est, 77454 Champs-sur-Marne, France.
ISSN:1099-4300
1099-4300
DOI:10.3390/e20010002