Rate distortion regions of Heegard-Berger problems with successive refinement and scalable coding

In this work, we study two instances of the Heegard-Berger problem. In both settings, an encoder observes a pair of memoryless, arbitrarily correlated, sources (S₁ⁿ, S₂ⁿ) and communicates with two receivers over an error-free rate-limited link of capacity R. Both receivers reproduce the source component S₂ⁿ losslessly; and Receiver 1 also reproduces the source component S₁ⁿ lossily, to within some prescribed fidelity level D₁. Also, Receiver 1 and Receiver 2 are equipped respectively with memoryless side information sequences Y₁ⁿ and Y₂ⁿ. The side information sequences are arbitrarily correlated among them, and with the source pair (S₁ⁿ, S₂ⁿ). In addition, in the first setting, which is of successive refinement type, the encoder is also connected to Receiver 1 through an additional error-free rate-limited link of capacity R₁. In the second setting, which is of reconstruction-scalable coding type, the individual link, of capacity R₂, is provided to Receiver 2. We establish single-letter characterizations of the rate-distortion regions of both models in the discrete memoryless case.