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 e. We consider the wideband, high-photon-efficiency extreme where e approaches zero, and where the channel's “dark current” approaches zero proportionally with e. Improving over a previously obtained first-order capacity approximation, we derive a refined approximation which also includes the second-order term. We also show that pulse-position modulation is optimal on this channel up to the second-order term in capacity.
['Ligong Wang', 'Gregory W. Wornell']
Refined analysis of the Poisson channel in the high-photon-efficiency regime