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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 alsodoi:10.1109/7.53441 fatcat:2zek4zovxbeebamlahl64x6jme