Data fusion with minimal communication

Two sensors obtain data vectors x and y, respectively, and transmit real vectors mri(z) and rm 2 (y), respectively, to a fusion center. We obtain tight lower bounds on the number of messages (the sumI of the dimensions of mil and r1 2) that have to be transmitted for the fusion center to be able to evaluate a given function fxI, y). When the function f is linear, we show that these bounds are effectively computable. Certain decentralized estimation problems can be cast in our framework and are discussed in some detail. In particular, we consider the case where x and y are random variables representing noisy measurements and f(z, y) = E[z I x, y], where z is a random variable to be estimated. Furthermore, we establish that a standard method for combining decentralized estimates of Gaussian random variables has nearly optimal communication requirements.