On the Achievable Rate of a Sample-based Practical Photon-counting Receiver
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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 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. For large peak power with fixed background radiation and low background radiation with fixed peak power, the proposed bound gap is a small positive value for low background radiation and large peak power, respectively. Moreover, we propose an approximation on the achievable rate in the low background radiation and large 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.
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