Rate-distortion regions of instances of cascade source coding with side information

In this work, we study a three-terminal cascade source coding problem with side information Yi known to the source encoder and the first user, and side information Y2 known only to the second user. Each user wants to reconstruct some desired function of the source, lossily, to within some fidelity level. We establish single-letter characterization of the rate-distortion region of this model in some important special cases, including when the reconstruction is lossless at the first user. We then establish a connection among the studied model and the so-called side information-scalable source coding problem (i.e., Heegard-Berger problem with side information and successive refinement) to infer single-letter characterization of the rate-distortion region of some instances of the latter problem. In contrast with most previous related works, the results of this paper hold irrespective of the ordering among the source and side information sequences, which are then arbitrarily correlated.