Sending Correlated Gaussian Sources over a Gaussian MAC: To Code, or not to Code

We consider 1-helper problem in which one source provides partial side information to the fusion center (FC) to help reconstruction of the main source signal. Both sources communicate information about their observations to the FC through an additive white Gaussian multiple access channel (MAC) without cooperating with each other. Two types of MAC are considered: orthogonal MAC and interfering (non-orthogonal) MAC. We characterize the tradeoff between the transmission cost, i.e., power, and the estimation distortion, D, using Shannon's separation source and channel coding theorem. We demonstrate that the separation-based coding strategy outperforms the uncoded transmission under an orthogonal MAC. However, in the symmetric case under an interfering MAC, below a certain signal- to-noise ratio (SNR) threshold, uncoded transmission outperforms the separation-based scheme. The threshold can be determined in terms of the correlation coefficient between the sources, p, and in fact is an increasing function of p. Finally, the optimal power scheduling to minimize the total power consumption in the network is derived.