2.1.2 Detector

At the receiver, light is focussed on the photodetector, which for this paper we restrict to an APD detector. The detector integrates over slot times to produce ${\bf Y} = ({\bf Y}_1, \ldots, {\bf Y}_n)$, where ${\bf Y}_i = (y_{i,1}, \ldots, y_{i,M})$ are the $M$ soft outputs for the $i$th $M$-PPM symbol, $1 \le i \le n$. The number of photons incident on a detector from an incident optical field of known intensity is a Poisson distributed random variable [4]. The number of photons absorbed by the detector is equal to the number of photons incident times the quantum efficiency $\eta$ of the detector. The secondary electrons at the output of the detector have a more complicated probability distribution [3,13,20]. In this paper, for simplicity we assume perfect timing synchronization and no inter-slot interference, which implies that the number of absorbed photons in each slot is independent of the number of photons absorbed in all other slots. Recent work has developed a method to combat inter-slot interference, assuming Gaussian pulse shapes, by using trellis-coded modulation [10,17].