Cutoff Rate for PPM Noisy Photon Counting Channel with Soft Decision

A new method for bounding the cutoff rate
R
is presented. As an application, the case of ideal laser input signal with thermal noise on the photon counting PPM channel with soft decision decoding is given. The main result is that the cutoff rate efficiency (defined as
lim_{s\rightarrow + \infty} R/s
, where
s
is the average signal photon number) is given by (
1- \gamma)/(1 + \gamma)
(where
\gamma = n_{0}/(1 + n_{0}), n_{0}
being the average thermal noise photons). This value is much smaller than the capacity efficiency,
log (1/gamma)
, given by Pierce et al. in [1].