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 [Formula: see text] and communicates with two receivers over an error-free rate-limited link of capacity [Formula: see text] , as well as error-free rate-limited individual links of capacities [Formula: see text] to the first receiver and [Formula: see text] to the second receiver. Both receivers reproduce the source component [Formula: see text] losslessly; and Receiver 1 also reproduces the source component [Formula: see text] lossily, to within some prescribed fidelity level [Formula: see text]. In addition, Receiver 1 and Receiver 2 are equipped, respectively, with memoryless side information sequences [Formula: see text] and [Formula: see text]. Important in this setup, the side information sequences are arbitrarily correlated among them, and with the source pair [Formula: see text]; 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.