Rate-distortion region of a gray-wyner problem 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. In this model an encoder observes a pair of memoryless sources (S
ⁿ
₁
, S
ⁿ
₂
) and communicates with two receivers over a common error-free rate-limited link of capacity R
₀
, as well as two individual error-free rate-limited links of capacities R
₁
and R
₂
. 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 distortion level D
₁
. Also, Receiver 1 and Receiver 2 observe each a memoryless side information sequence, Y
ⁿ
₁
and Y
ⁿ
₂
, assumed to be arbitrarily correlated among them, and with the source pair (S
ⁿ
₁
, S
ⁿ
₂
).