Following the discovery of a fundamental connection between information measures and
estimation measures in Gaussian channels, this paper explores the counterpart of those
results in Poisson channels. In the continuous-time setting, the received signal is a doubly
stochastic Poisson point process whose rate is equal to the input signal plus a dark current.
It is found that, regardless of the statistics of the input, the derivative of the input-output
mutual information with respect to the intensity of the additive dark current can be expressed …

Following the recent discovery of new connections between information and estimation in
Gaussian channels, this paper reports parallel results in the Poisson regime. Both scalar
and continuous-time Poisson channels are considered. It is found that, regardless of the
statistics of the input, the derivative of the input-output mutual information with respect to the
dark current can be expressed in the expected difference between the logarithm of the input
and the logarithm of its conditional mean estimate (noncausal in case of continuous-time) …