On the optimal power-distortion tradeoff in asymmetric gaussian sensor network

We present necessary and sufficient conditions, similar to the recent results of Gastpar (2007), for the achievability of all power-distortion tuples (P,D) = (P₁, P₂, middot middot middot , P_L,D) in an asymmetric Gaussian sensor network where L distributed sensors transmit noisy observations of a Gaussian source through a Gaussian multiple access channel to a fusion center. We show numerically that in general the gap between the provided upper bound and the lower bound of the distortion D is small. We also provide an optimal power allocation that minimizes the total power consumption, Pmacr = Sigma_i=1 ^L Pi, for uncoded transmission scheme while satisfying a given distortion constraint D. Numerical evaluations show that by applying the optimal power allocation uncoded transmission can perform nearly optimal in an asymmetric sensor network subject to a sum-power constraint. In the symmetric case both bounds agree and provide the optimal power-distortion tradeoff (P,D); this agrees with result of (M. Gastpar, 2007). Thus, in the sense of achieving the optimal (P,D) tradeoff, uncoded transmission is optimal in the symmetric case and can be nearly-optimal in the asymmetric case.