We consider the problem of slotted asynchronous coded communication, where ineach time frame (slot), the transmitter is either silent or transmits acodeword from a given (randomly selected) codebook. The task of the decoder isto decide whether transmission has taken place, and if so, to decode themessage. We derive the optimum detection/decoding rule in the sense of the besttrade-off among the probabilities of decoding error, false alarm, andmisdetection. For this detection/decoding rule, we then derive single-lettercharacterizations of the exact exponential rates of these three probabilitiesfor the average code in the ensemble.
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