On the Scalar-Help-Vector Source Coding Problem

TL;DR

This paper investigates a Gaussian source coding problem involving multiple noisy linear observations and a primary vector source, deriving bounds for the achievable rate regions under certain independence conditions.

Contribution

It introduces an outer region for the scalar-help-vector Gaussian source coding problem and an inner region for a special case with scalar sources.

Findings

Derived an outer region for the case with conditionally independent sources.

Established an inner region for the case where the vector source is equivalent to multiple scalar sources.

Abstract

In this paper, we consider a scalar-help-vector source coding problem for $L+1$ correlated Gaussian memoryless sources. We deal with the case where $L$ encoders observe noisy linear combinations of $K$ correlated Gaussian scalar sources which work as partial side information at the decoder, while the remaining one encoder observes a vector Gaussian source which works as the primary source we need to reconstruct. We determine an outer region for the case where the $L$ sources are conditionally independent of the vector source. We also show an inner region for a special case when the vector source can be regard as $K$ scalar sources.