On scalable source coding with decoder side informations

We consider the problem of scalable source coding with decoder side informations. Two special cases of this problem have been investigated in the literature, namely successive refinement Wyner-Ziv (SR-WZ) coding and side-information scalable (SI-Scalable) coding, whose distinction Res in the degradedness of the side informations. In this work, we first show the achievable region for the SI-scalable problem provided in a previous work is tight when either the first stage or the second stage requires lossless reconstruction. Then the notion of perfectly scalable coding is introduced as both the stages operate on the Wyner-Ziv bound, and a set of necessary and sufficient conditions is given for sources satisfying a mild support condition. Furthermore, generalizing the coding scheme for the SR-WZ and SI-scalable coding, we provide a conclusive solution for the (multi-stage) quadratic Gaussian scalable coding problem with jointly Gaussian side informations in an arbitrary order of quality.