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New capacity upper bounds are presented for the discrete-time Poisson channelwith no dark current and an average-power constraint. These bounds are a simpleconsequence of techniques developed for the seemingly unrelated problem ofupper bounding the capacity of binary deletion and repetition channels.Previously, the best known capacity upper bound in the regime where theaverage-power constraint does not approach zero was due to Martinez (JOSA B,2007), which is re-derived as a special case of the framework developed in thispaper. Furthermore, this framework is carefully instantiated in order to obtaina closed-form bound that noticeably improves the result of Martinez everywhere.Finally, capacity-achieving distributions for the discrete-time Poisson channelare studied under an average-power constraint and/or a peak-power constraintand arbitrary dark current. In particular, it is shown that the support of thecapacity-achieving distribution under an average-power constraint only must becountably infinite. This settles a conjecture of Shamai (IEE Proceedings I,1990) in the affirmative. Previously, it was only known that the support mustbe unbounded.

Structural Results and Improved Upper Bounds on the Capacity of the Discrete-Time Poisson Channel