  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, we introduce the notion of generalized successive refinability
with multiple degraded side informations. 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,
(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.
