The Capacity of Photonic Erasure Channels with Detector Dead Times

We consider a photonic communication system wherein the photon detector suffers a random ‘dead time’ following each successful photon detection. If subsequent photon arrivals occur during the dead time, the information contained in the photons is assumed to be erased. We refer to such channels as photonic erasure channels and derive fundamental limits on the rate at which classical information can be transmitted on such channels. We assume photon arrivals according to a Poisson process, and consider two classes of detectors - paralyzable and nonparalyzable. We derive explicit expressions for the capacity of photonic erasure channels, for any general distribution of the dead times of the detector. For a photonic erasure channel with a nonparalyzable detector, we show that the capacity depends only on the expected dead time. On the other hand, with a paralyzable detector, the channel capacity depends on the dead time distribution through its Laplace transform.