On the Design of Capacity-Achieving Distributions for Discrete-Time Poisson Channel with Low-Precision ADCs

This paper investigates the design of the capacity-achieving input distribution for the discrete-time Poisson channel (DTPC) under dark current effects with low-precision analog-to-digital converters (ADCs). This study introduces an efficient optimization algorithm that integrates the Newton-Raphson and Blahut-Arimoto (BA) methods to determine the capacity-achieving input distribution and the corresponding amplitudes of input mass points for the DTPC, subject to both peak and average power constraints. Additionally, the Karush-Kuhn-Tucker (KKT) conditions are established to provide necessary and sufficient conditions for the optimality of the obtained capacity-achieving distribution. Simulation results illustrate that the proposed algorithm attains $72%$ and $83%$ of the theoretical capacity at 5 dB for 1-bit and 2-bit quantized DTPC, respectively. Furthermore, for a finite-precision quantized DTPC (i.e., log ₂K bits), the capacity can be achieved by a non-uniform discrete input distribution with support for K mass points, under the given power constraints.