Common Reconstructions in the Successive Refinement Problem with Receiver Side Information

TL;DR

This paper investigates a variant of the successive refinement problem with receiver side information, providing bounds and a single-letter characterization of the rate region where reconstruction functions depend on shared randomness.

Contribution

It introduces a simplified characterization of the rate region for this variant, requiring only one auxiliary variable, and explores the impact of side information and shared randomness.

Findings

The rate region can be fully characterized for several classes of source and side information.

Side information reduces communication rates through binning techniques.

The admissible rate region is discontinuous with respect to the source distribution.

Abstract

We study a variant of the successive refinement problem with receiver side information where the receivers require identical reconstructions. We present general inner and outer bounds for the rate region for this variant and present a single-letter characterization of the admissible rate region for several classes of the joint distribution of the source and the side information. The characterization indicates that the side information can be fully used to reduce the communication rates via binning; however, the reconstruction functions can depend only on the G\'acs-K\"orner common randomness shared by the two receivers. Unlike existing (inner and outer) bounds to the rate region of the general successive refinement problem, the characterization of the admissible rate region derived for several settings of the variant studied requires only one auxiliary random variable. Using the derived characterization, we establish that the admissible rate region is not continuous in the underlying source source distribution even though the problem formulation does not involve zero-error or functional reconstruction constraints.