Explicit Solutions for Some Simple Decentralized Detection Problems

We consider a decentralized detection problem in which a number of identical sensors transmit a finite-valued function of their observations to a fusion center which makes a final decision on one of M alternative hypotheses. We consider the case where the number of sensors is large and we derive (asymptotically) optimal rules for determining the messages of the sensors, for the case where the observations are generated from a simple and symmetrical set of discrete distributions. We also consider the trade-off between the number of sensor and the communication rate of each sensor when there is a constraint on the total communication rate from the sensors to the fusion center.