This data is related to the submitted paper "Optimal Power Allocation in Poisson Shot-Noise-Limited M-ary PPM Photon-Counting NOMA Systems" by Yongkang Chen, Xiaolin Zhou, Haitao Zhou, Dailing Shen, Chongbin Xu, Xin Wang, and Lajos Hanzo. We formulate the power allocation optimization problem of nonlinear discrete-time Poisson (DTP) multiple-access channels (MAC), which is easier than reconfiguring the modulation mode or the duty cycle of signaling.