Sending a Bi-Variate Gaussian Source over a Gaussian MAC

TL;DR

This paper investigates transmitting a correlated bi-variate Gaussian source over a Gaussian multiple-access channel, identifying when uncoded communication is optimal and providing bounds on achievable distortions at different SNR levels.

Contribution

It characterizes the optimality of uncoded transmission in the symmetric case and derives bounds on distortions for high SNRs, advancing understanding of joint source-channel coding.

Findings

Uncoded communication is optimal below a certain SNR threshold.

Outer and inner bounds on distortions are provided for SNRs above the threshold.

The threshold depends on the source correlation.

Abstract

We consider a problem where a memoryless bi-variate Gaussian source is to be transmitted over an additive white Gaussian multiple-access channel with two transmitting terminals and one receiving terminal. The first transmitter only sees the first source component and the second transmitter only sees the second source component. We are interested in the pair of mean squared-error distortions at which the receiving terminal can reproduce each of the source components. It is demonstrated that in the symmetric case, below a certain signal-to-noise ratio (SNR) threshold, which is determined by the source correlation, uncoded communication is optimal. For SNRs above this threshold we present outer and inner bounds on the achievable distortions.