The impact of dark current on the wideband Poisson channel

We study the discrete-time Poisson channel under the constraint that its average input power (in photons per channel use) must not exceed some constant ε. We consider the wideband, high-photon-efficiency extreme where ε approaches zero, and where the channel´s “dark current” approaches zero proportionally with ε. Extending our previous work, we show that the influence of the dark current on channel capacity is mainly on the third-order term with respect to ε. We also show that pulse-position modulation with “soft-decision decoding” achieves data rates that accurately reflect such influence.