Multistage successive refinement for Wyner-Ziv source coding with degraded side informations

We provide a complete characterization of rate region for the multistage successive refinement of Wyner-Ziv source coding problem with degraded side information at the decoder. This problem was left open in a recent work by Steinberg and Merhav (T-IT, 2004), where it was solved for the special case of two stages. Furthermore, we introduce the notion of generalized successive refinability with multiple side informations. This captures whether progressive encoding to satisfy the distortion constraints for different side information as good as encoding without progressive requirement. For degraded side-information, we give necessary and sufficient conditions for generalized successive refinability. Using this, we show that for Gaussian source, the failure of being successively refinable with multiple side informations is only due to the inherent uncertainty on which side information will occur at the decoder, but not the progressive encoding requirement