On Scalable Source Coding for Multiple Decoders with Side Information

The problem of side-information scalable (SIscalable) source coding and the problem of successive refinement in the Wyner-Ziv (SR-WZ) setting are considered in this paper. Both problems can be understood as special cases of the general problem of scalable lossy source coding for multiple decoders with access to side informations, but the encoder does not. In the former problem, the quality of the side informations deteriorates from the early stage to the later stage, while in the latter problem, the quality of the side informations improves with the stages. The SR-WZ problem was considered by Steinberg and Merhav (TIT, 2004) where it was solved for the special case of two stages. We provide a generalization of their characterization to multiple stages. We also provide achievable rate and outer bounds for the SI-scalable coding problem. Furthermore, the notion of generalized successively refinability with multiple side informations is introduced, which captures whether progressive encoding to satisfy the distortion constraints for different side information is as good as encoding without progressive requirement. For the quadratic Gaussian case, by combining the results of SI-scalable and SR-WZ coding, we provide a complete answer to the general scalable source coding problem.