The Poisson Multiple-Access Channel

The Poisson multiple-access channel (MAC) models many-to-one optical communication through an optical fiber or in free space. For this model we compute the capacity region for the two-user case as a function of the allowed peak power. Focusing on the maximum throughput we generalize our results to the case where the users are subjected to an additional average-power constraint and to the many-users case. We show that contrary to the Gaussian MAC, in the Poisson MAC the maximum throughput is bounded in the number of users. We quantify the loss that is incurred when time-division multiple access (TDMA) is employed and show that while in the two-user case and in the absence of dark current the penalty is rather mild, the penalty can be quite severe in the many-users case in the presence of large dark current. We introduce a generalized TDMA technique that mitigates this loss to a large extent.