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On the continuous-time Poisson channel with varying dark current known to the transmitter

This paper considers a continuous-time Poisson channel whose dark current varies with time. The actual values of the dark current are revealed to the transmitter as channel-state information (CSI), either causally or noncausally. It is shown that, in the limit where the coherence time of the dark current tends to zero, the improvement on capacity provided by both causal and noncausal CSI vanishes linearly with the coherence time.