The Discrete-Time Poisson Channel at Low Input 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
ε
, capacity scales like
ε
log 1/
ε
for small
ε
. For a Poisson channel whose dark current is a nonzero constant, capacity scales, to within a constant, like
ε
log log 1/ε for small
ε
.