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 Multi-Accessing (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 less to a large extent. *A. Lapidoth is with department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139-4307. S. Shamai is with the department of Electrical Engineering, TechnionIsrael Institute of Technology, Haifa 32000, Israel. The work of A. Lapidoth was supported in part by the U.S. Army under grant DAAH04-95-1-0103. The work of of S. Shamai was supported in part by the consortium of wide-band communications administered by the Israeli Ministry of Commerce and Industry. This paper was presented in part at the IEEE Information Theory Workshop, June 9-13, 1996, Haifa, Israel.