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

Abstract

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 n 1 , S n 2 ) 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 n 2 losslessly; and Receiver 1 also reproduces the source component S n 1 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 n 1 and Y n 2 . Important in this setup, the side information sequences are arbitrarily correlated among them, and with the source pair (S n 1 , S n 2 ); 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.

A Game Theoretical Analysis on the Gray-Wyner System and Generalised Common Information

“…One can now define a stochastic Stackelberg game 15 in which the Leader 𝒰 0 is a Major-Player who has a dominant effect on other minor players 𝒰 𝓀 , 𝑘 ≠ 0 − call the Followers. In this game, the Leader is non-stationary, so, one can apply a bi-level probabilistic optimisation method 16 .…”

“…4) Generalised common information: In relation to the generalised common information in the generalised Gray-Wyner schemes, some works have also been perfectly presented in the literature such as [12], [13], [14], [15], [16], [17], [18], [19], [20]. However, the distortion bounds derived in the aforementioned work for source broadcast issues with the generalised common information were of a purely information-theoretic nature.…”

“…In [15], the total correlation of Gaussian vector sources for the aforementioned systems was analysed as well. In [16], [17], the issue of rate-distortion region of Gray-Wyner frameworks with helpers was theoretically evaluated. In [18], for a tuple of correlated multivariate Gaussian RVs, a novel lossy network compression method was newly proposed.…”

A Realization Approach to Lossy Network Compression of a Tuple of Correlated Multivariate Gaussian RVs

“…Gács and Körner [ 5 ] introduced another definition of common randomness between a tuple of jointly independent and identically distributed random variables. Benammar and Zaidi [ 6 , 7 ] characterized the Gray–Wyner rate region, when there is side information at the decoders, under various scenarios that include both receivers and reproduce the source symbols without distortion. Insightful application examples for binary sources are considered in [ 7 ] ( Section 4.2 ).…”

Special Issue on Rate Distortion Theory and Information Theory

“…As was stated in the invitation to the Special Issue, “It is the goal of this Special Issue to reemphasize the critical accomplishments of rate distortion theory and to highlight new directions in rate distortion theoretic and information theoretic research.” Toward this end, we have collected 10 papers that examine source models that are relevant to real-world sources [ 4 , 5 , 6 , 7 ], consider new distortion measures [ 8 ], extend prior work in multiterminal source coding [ 9 , 10 ], examine source model identification and coding [ 11 ], study rate-distortion optimization for 3D video coding [ 12 ] and present a review of the field of information theory and cognition [ 13 ]. These papers not only make significant contributions to the rate distortion theory literature, but also highlight new research directions and indicate that there is much more to be done to harness the full promise of rate distortion theory as defined by Shannon.…”