On threshold rules in decentralized detection

We consider a decentralized detection problem in which a number of identical sensors transmit a binary function of their observations to a fusion center which then decides which one of two alternative hypotheses is true. We show that, when the number of sensors grows to infinity, optimality is not lost (in terms of the probability of error) if we constrain the sensors to use the same decision rule in deciding what to transmit. This results in considerable simplification of the problem. We also discuss the case where the messages may take more than two values and the case of M-ary (M > 2) hypotheses. Next we consider two variants of a decentralized sequential detection problem. For one variant we show that each sensor should decide what to transmit based on a likelihood ratio test; for the other, we demonstrate that such a result fails to hold and that more complicated decision rules are required.