Communicating the Difference of Correlated Gaussian Sources Over a MAC

This paper considers the problem of transmitting the difference of two positively correlated 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 for correlation coefficients above a threshold. An alternative lattice coding scheme is also presented that can potentially improve on the performance of uncoded transmission.