Broadcasting Correlated Vector Gaussians

TL;DR

This paper investigates the optimal transmission strategies for sending correlated Gaussian sources over a Gaussian broadcast channel, deriving bounds on power-distortion tradeoffs and proposing hybrid schemes for certain cases.

Contribution

It introduces a new bounding technique involving remote sources and characterizes the power-distortion tradeoff, including achievable schemes for scalar source reconstruction.

Findings

Derived a lower bound on power-distortion tradeoff

Introduced a new bounding technique with remote sources

Proposed hybrid schemes for scalar source reconstruction

Abstract

The problem of sending two correlated vector Gaussian sources over a bandwidth-matched two-user scalar Gaussian broadcast channel is studied in this work, where each receiver wishes to reconstruct its target source under a covariance distortion constraint. We derive a lower bound on the optimal tradeoff between the transmit power and the achievable reconstruction distortion pair. Our derivation is based on a new bounding technique which involves the introduction of appropriate remote sources. Furthermore, it is shown that this lower bound is achievable by a class of hybrid schemes for the special case where the weak receiver wishes to reconstruct a scalar source under the mean squared error distortion constraint.