Non-Asymptotic Capacity Upper Bounds for the Discrete-Time Poisson Channel with Positive Dark Current

We derive improved and easily computable upper bounds on the capacity of the discrete-time Poisson channel under an average-power constraint and an arbitrary constant dark current term. This is accomplished by combining a general convex duality framework with a modified version of the digamma distribution considered in previous work of the authors (Cheraghchi, J. ACM 2019; Cheraghchi, Ribeiro, IEEE Trans. Inf. Theory 2019). For most choices of parameters, our upper bounds improve upon previous results even when an additional peak-power constraint is imposed on the input.