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