Joint Power-Distortion Optimization in a One-Helper Problem

We consider the joint power-distortion optimization in one-help-one problem, also called the 1-helper problem where one source provides partial side information to the fusion center (FC) to help reconstruction of the other correlated source. Both correlated sources communicate information about their observations to the FC through an orthogonal multiple access channel (MAC) without cooperating with each other. We investigate the joint optimization of source coding and power allocation from an information theory perspective, where the power allocation is verified using Shannon capacity formula and the source coding problem is analyzed using rate-distortion theory. We show that the joint optimization in the Gaussian 1-helper problem can be solved analytically. We provide closed-form expressions for the optimal distortion and the optimal power allocation in terms of the cost weights.