THE INTERNATIONAL TECHNION COMMUNICATION DAY IN HONOR OF ISRAEL BAR-DAVID 1 Poisson Communication Theory

This paper gives a literature review of detection theory and information theory in the Poisson regime, where the channel model is a Poisson point process whose instantaneous rate is controlled by the input. I. Communication under the Poisson Regime In the semi-classical model of photodetection, the output of the photodetector (e.g. a p-i-n diode) is the superposition of two independent Poisson point processes: one with constant rate λ0 (“dark current noise”) and another whose instantaneous rate λ(t) is proportional to the instantaneous squared magnitude of the impinging optical field integrated over the receiving aperture. This simple model is representative of the direct-detection photon-limited optical communication channel. In 1969, Israel Bar-David discovered the “Poisson matched filter” in his paper [1] entitled Communication under the Poisson Regime. The Poisson matched filter (matched to rate λ1(·)) processes a point process realization t1, . . . , tn by