Sending a Bi-Variate Gaussian over a Gaussian MAC

TL;DR

This paper investigates the optimal power-distortion trade-off for transmitting correlated Gaussian sources over a Gaussian multiple-access channel, providing conditions for achievable distortions and identifying when uncoded transmission is optimal.

Contribution

It offers necessary and sufficient conditions for distortion pairs in Gaussian MAC source transmission, including the optimality of uncoded schemes at low SNR and high-SNR asymptotics.

Findings

Uncoded transmission is optimal below a certain SNR threshold.

Derived necessary and sufficient conditions for achievable distortions.

Characterized high-SNR asymptotic behavior of optimal schemes.

Abstract

We study the power versus distortion trade-off for the distributed transmission of a memoryless bi-variate Gaussian source over a two-to-one average-power limited Gaussian multiple-access channel. In this problem, each of two separate transmitters observes a different component of a memoryless bi-variate Gaussian source. The two transmitters then describe their source component to a common receiver via an average-power constrained Gaussian multiple-access channel. From the output of the multiple-access channel, the receiver wishes to reconstruct each source component with the least possible expected squared-error distortion. Our interest is in characterizing the distortion pairs that are simultaneously achievable on the two source components. We present sufficient conditions and necessary conditions for the achievability of a distortion pair. These conditions are expressed as a function of the channel signal-to-noise ratio (SNR) and of the source correlation. In several cases the necessary conditions and sufficient conditions are shown to agree. In particular, we show that if the channel SNR is below a certain threshold, then an uncoded transmission scheme is optimal. We also derive the precise high-SNR asymptotics of an optimal scheme.