The Poisson Channel With Varying Dark Current Known to the Transmitter

This paper studies the continuous-time Poisson channel whose dark current is random and may change for every τ-second time interval, where the actual values of the dark current are known to the transmitter as channel-state information (CSI). !n the limit where τ tends to zero, the capacity gain provided by both causal and noncausal CSI is shown to vanish linearly with τ, so CSI at the transmitter provides almost no capacity improvement. The paper also considers a related problem of the state-dependent very noisy channel. !n the very noisy limit, the capacity gain provided by noncausal CSI is shown to be the same as that provided by causal CSI.