On Multistage Successive Refinement for Wyner-Ziv Source Coding with Degraded Side Informations

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.Comment: Submitted to IEEE Trans. Information Theory Apr. 200

Side-information Scalable Source Coding

The problem of side-information scalable (SI-scalable) source coding is considered in this work, where the encoder constructs a progressive description, such that the receiver with high quality side information will be able to truncate the bitstream and reconstruct in the rate distortion sense, while the receiver with low quality side information will have to receive further data in order to decode. We provide inner and outer bounds for general discrete memoryless sources. The achievable region is shown to be tight for the case that either of the decoders requires a lossless reconstruction, as well as the case with degraded deterministic distortion measures. Furthermore we show that the gap between the achievable region and the outer bounds can be bounded by a constant when square error distortion measure is used. The notion of perfectly scalable coding is introduced as both the stages operate on the Wyner-Ziv bound, and necessary and sufficient conditions are given for sources satisfying a mild support condition. Using SI-scalable coding and successive refinement Wyner-Ziv coding as basic building blocks, a complete characterization is provided for the important quadratic Gaussian source with multiple jointly Gaussian side-informations, where the side information quality does not have to be monotonic along the scalable coding order. Partial result is provided for the doubly symmetric binary source with Hamming distortion when the worse side information is a constant, for which one of the outer bound is strictly tighter than the other one.Comment: 35 pages, submitted to IEEE Transaction on Information Theor