Sending a Bivariate Gaussian Source Over a Gaussian MAC with Unidirectional Conferencing Encoders

TL;DR

This paper analyzes the transmission of a bivariate Gaussian source over a Gaussian multiple-access channel with unidirectional conferencing, providing conditions for achieving certain distortion levels and exploring the optimality of different schemes at high SNR.

Contribution

It extends existing vector-quantizer schemes to include unidirectional conferencing and characterizes the conditions for optimal source-channel coding with conferencing.

Findings

Necessary and sufficient conditions for distortion achievability

High-SNR asymptotics for unlimited conference capacity

Separation scheme optimality at high SNR with unlimited conference capacity

Abstract

We consider the transmission of a memoryless bivariate Gaussian source over a two-user additive Gaussian multiple-access channel with unidirectional conferencing encoders. Here, prior to each transmission block, Encoder 1, which observes the first source component, is allowed to communicate with Encoder 2, which observes the second source component, via a unidirectional noise-free bit-pipe of given capacity. The main results of this work are sufficient conditions and a necessary condition for the achievability of a distortion pair expressed as a function of the channel SNR and of the source correlation. The main sufficient condition is obtained by an extension of the vector-quantizer scheme suggested by Lapidoth-Tinguely, for the case without conferencing, to the case with unidirectional conference. In the high-SNR regime, and when the capacity of the conference channel is unlimited, these necessary and sufficient conditions are shown to agree. We evaluate the precise high-SNR asymptotics for a subset of distortion pairs when the capacity of the conference channel is unlimited in which case we show that a separation based scheme attains these optimal distortion pairs. However, with symmetric average-power constraints and fixed conferencing capacity, at high-SNR the latter separation based scheme is shown to be suboptimal.