# Distributed Source Coding for Correlated Memoryless Gaussian Sources

## TL;DR

This paper derives explicit bounds for the rate distortion region in distributed Gaussian source coding, aiding understanding of the limits of encoding correlated Gaussian sources with specified estimation accuracy.

## Contribution

It provides the first explicit outer and inner bounds for the rate distortion region in distributed Gaussian source coding with correlated sources.

## Key findings

- Explicit outer and inner bounds for the rate distortion region.
- The bounds facilitate analysis of source coding limits.
- Applicable to systems with Gaussian correlated sources.

## Abstract

We consider a distributed source coding problem of $L$ correlated Gaussian observations $Y_i, i=1,2,...,L$. We assume that the random vector $Y^{L}={}^{\rm t} (Y_1,Y_2,$ $...,Y_L)$ is an observation of the Gaussian random vector $X^K={}^{\rm t}(X_1,X_2,...,X_K)$, having the form $Y^L=AX^K+N^L ,$ where $A$ is a $L\times K$ matrix and $N^L={}^{\rm t}(N_1,N_2,...,N_L)$ is a vector of $L$ independent Gaussian random variables also independent of $X^K$. The estimation error on $X^K$ is measured by the distortion covariance matrix. The rate distortion region is defined by a set of all rate vectors for which the estimation error is upper bounded by an arbitrary prescribed covariance matrix in the meaning of positive semi definite. In this paper we derive explicit outer and inner bounds of the rate distortion region. This result provides a useful tool to study the direct and indirect source coding problems on this Gaussian distributed source coding system, which remain open in general.