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.