Side-Information Scalable Source Coding

We consider the problem of side-information scalable (SI-scalable) source coding, where the encoder constructs a two-layer description, such that the receiver with high quality side information will be able to use only the first layer to reconstruct the source in a lossy manner, while the receiver with low quality side information will have to receive both layers in order to decode. We provide inner and outer bounds to the rate-distortion (R-D) region for general discrete memoryless sources. The achievable region is tight when either one of the decoders requires a lossless reconstruction, and when the distortion measures are degraded and deterministic. Furthermore, the gap between the inner and the outer bounds can be bounded by certain constants when the squared error distortion measure is used. The notion of perfect scalability is introduced, for which 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, we provide a complete characterization of the rate-distortion region for the important quadratic Gaussian source with multiple jointly Gaussian side informations, where the side information quality is not necessarily monotonic along the scalable coding order. A partial result is provided for the doubly symmetric binary source under the Hamming distortion measure when the worse side information is a constant, for which one of the outer bounds is strictly tighter than the other.