Achievable Rate Bounds on Poisson Channel with a Sample-Based Practical Photon-Counting Receiver

We investigate the achievable rate for a practical receiver under on-off keying modulation based on Kullback-Leibler (KL) divergence and Chernoff α-divergence. The asymptotic tightness of the derived bounds is analyzed for large symbol duration and large or low peak power. We prove the tightness of the derived bounds for large symbol duration, large peak power with zero background radiation with exponential convergence rate, and for low peak power of order two. Moreover, we propose an approximation on the achievable rate in the low background radiation and medium symbol duration regime, which is more accurate compared with the derived upper and lower bounds in the medium signal to noise ratio (SNR) regime. The proposed bounds and the approximations are evaluated by the numerical results.