The Poisson Channel With Varying Dark Current Known to the Transmitter

Abstract

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). In 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. In the "very noisy" limit, the capacity gain provided by noncausal CSI is shown to be same as that provided by causal CSI.