Side-information Scalable Source Coding

TL;DR

This paper investigates side-information scalable source coding, providing bounds, conditions for perfect scalability, and characterizations for Gaussian and binary sources with various side information qualities.

Contribution

It introduces inner and outer bounds for SI-scalable coding, defines perfect scalability, and characterizes optimal coding for Gaussian and binary sources with side information.

Findings

Bounds are tight for lossless or deterministic distortion cases.

Constant gap between bounds under square error distortion.

Complete characterization for Gaussian sources with multiple side informations.

Abstract

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.