# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1904.05179