Communicating the Difference of Correlated Gaussian Sources Over a MAC

TL;DR

This paper introduces lattice coding schemes for transmitting the difference of correlated Gaussian sources over a Gaussian MAC, achieving near-optimal distortion and outperforming uncoded transmission under certain SNR conditions.

Contribution

The paper proposes novel lattice coding strategies for Gaussian MACs that improve upon uncoded transmission and approach the theoretical distortion lower bounds.

Findings

Lattice coding achieves distortion within a constant of the lower bound at high SNR.

Uncoded transmission performs worse than lattice coding schemes.

An alternative lattice scheme can potentially outperform uncoded transmission.

Abstract

This paper considers the problem of transmitting the difference of two jointly Gaussian sources over a two-user additive Gaussian noise multiple access channel (MAC). The goal is to recover this difference within an average mean squared error distortion criterion. Each transmitter has access to only one of the two Gaussian sources and is limited by an average power constraint. In this work, a lattice coding scheme that achieves a distortion within a constant of a distortion lower bound is presented if the signal to noise ratio (SNR) is greater than a threshold. Further, uncoded transmission is shown to be worse in performance to lattice coding methods. An alternative lattice coding scheme is presented that can potentially improve on the performance of uncoded transmission.