Sending a Bivariate Gaussian Source over a Gaussian MAC with Feedback

TL;DR

This paper investigates transmitting correlated Gaussian sources over a Gaussian multiple-access channel with feedback, showing that feedback is ineffective below a certain SNR threshold and providing necessary conditions for distortion achievement.

Contribution

It characterizes when feedback improves transmission and offers necessary conditions for achieving specific distortions in Gaussian MAC with correlated sources.

Findings

Feedback is useless below a certain SNR threshold in the symmetric case.

Uncoded transmission achieves minimal distortion below this threshold.

Provides necessary conditions for distortion pairs in the general case.

Abstract

We consider the problem of transmitting a bivariate Gaussian source over a two-user additive Gaussian multiple-access channel with feedback. Each of the transmitters observes one of the source components and tries to describe it to the common receiver. We are interested in the minimal mean squared error at which the receiver can reconstruct each of the source components. In the ``symmetric case'' we show that, below a certain signal-to-noise ratio threshold which is determined by the source correlation, feedback is useless and the minimal distortion is achieved by uncoded transmission. For the general case we give necessary conditions for the achievability of a distortion pair.