Broadcasting Correlated Gaussians

TL;DR

This paper analyzes the optimal transmission strategies for a correlated Gaussian source over a Gaussian broadcast channel, identifying conditions under which uncoded linear transmission achieves the best power-distortion trade-off.

Contribution

It establishes the optimality of uncoded linear schemes for transmitting correlated Gaussian sources over broadcast channels below a certain SNR threshold.

Findings

Uncoded linear transmission is optimal below a specific SNR threshold.

The threshold depends on source correlation and weaker noise distortion.

The scheme achieves the best power-distortion trade-off under these conditions.

Abstract

We consider the transmission of a memoryless bivariate Gaussian source over an average-power-constrained one-to-two Gaussian broadcast channel. The transmitter observes the source and describes it to the two receivers by means of an average-power-constrained signal. Each receiver observes the transmitted signal corrupted by a different additive white Gaussian noise and wishes to estimate the source component intended for it. That is, Receiver~1 wishes to estimate the first source component and Receiver~2 wishes to estimate the second source component. Our interest is in the pairs of expected squared-error distortions that are simultaneously achievable at the two receivers. We prove that an uncoded transmission scheme that sends a linear combination of the source components achieves the optimal power-versus-distortion trade-off whenever the signal-to-noise ratio is below a certain threshold. The threshold is a function of the source correlation and the distortion at the receiver with the weaker noise.