On Multistage Successive Refinement for Wyner–Ziv Source Coding With Degraded Side Informations

In this correspondence, we provide a complete characterization of the rate-distortion region for the multistage successive refinement of the Wyner–Ziv source coding problem with degraded side informations at the decoder. Necessary and sufficient conditions for a source to be successively refinable along a distortion vector are subsequently derived. A source–channel separation theorem is provided when the descriptions are sent over independent channels for the multistage case. Furthermore, the notion of generalized successive refinability with multiple degraded side informations is introduced. This notion captures whether progressive encoding to satisfy multiple distortion constraints for different side informations is as good as encoding without progressive requirement. Necessary and sufficient conditions for generalized successive refinability are given. It is shown that the following two sources are generalized successively refinable: 1) the Gaussian source with degraded Gaussian side informations and 2) the doubly symmetric binary source when the worse side information is a constant. Thus for both cases, the failure of being successively refinable is only due to the inherent uncertainty on which side information will occur at the decoder, but not the progressive encoding requirement.