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We address an application of multiuser information theory to the study of the uplink of a communication system with randomly activated users. We first assume that all the messages are jointly decoded by a multicell processor. Then, we relax this hypothesis and study the network under the assumption that the decoding of the message of a given user is only based on the messages received within a given distance of this user. Our results show that for a general class of models, under adequate hypothesis, local decoding performs almost as well as global decoding and that the difference converges to 0 exponentially fast as the size of the decoding window goes to infinity.