Communicating Linear Functions of Correlated Gaussian Sources Over a MAC

This paper considers the problem of transmitting linear functions of two correlated Gaussian sources over a two-user additive Gaussian noise multiple access channel. The goal is to recover this linear function 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 paper, a lattice coding scheme and two lower bounds on the achievable distortion are presented. The lattice scheme achieves within a constant of a distortion lower bound if the signal-to-noise ratio is greater than a threshold. Furthermore, for the difference of correlated Gaussian sources, uncoded transmission is shown to be worse in performance to lattice coding methods for correlation coefficients above a threshold.