The poisson channel at lowinput powers

The asymptotic capacity at low input powers of an average- power limited or an average- and peak-power limited discrete- time Poisson channel is considered. For a Poisson channel whose dark current is zero or decays to zero linearly with its average input power ¿, capacity scales like ¿ log 1/¿ for small ¿. For a Poisson channel whose dark current is a nonzero constant, capacity scales, to within a constant, like ¿ log log 1/¿ for small ¿.