We investigate the achievable rate and capacity of a non-perfect photon-counting receiver assuming that the shot and thermal noise is negligible, and that the sampling interval is not shorter than the dead time. For long and fixed symbol duration, the achievable rate under on-off keying modulation is investigated based on Kullback-Leibler divergence and Chernoff divergence. We prove the tightness of the derived bounds for large peak power with zero background radiation at an exponential convergence rates, and for low peak power at an order-two convergence rates. Moreover, we propose an approximation on the achievable rate, which is more accurate compared with the derived bounds in the medium signal to noise ratio (SNR) regime. We also verify the accuracy of the proposed model on the achievable rate analysis via the comparison with the model with non-negligible shot and thermal noise. As for the capacity analysis, we assume that the symbol duration can be arbitrarily short, and demonstrate that the capacity approaches that of the continuous-time Poisson channel as both the sampling interval and the symbol duration approach zero, and the sampling interval equals the symbol duration. For large peak power, the capacity with a non-perfect receiver converges, while that of continuous Poisson capacity channel linearly increases.

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关于基于样本的实用光子计数接收器的可实现速率和容量


我们研究了非完美光子计数接收器可实现的速率和容量，假设散粒噪声和热噪声可以忽略不计，并且采样间隔不短于死区时间。对于长且固定的符号持续时间，基于 Kullback-Leibler 散度和 Chernoff 散度研究了开关键控调制下可实现的速率。我们证明了在指数收敛速率下零背景辐射的大峰值功率和在二阶收敛速率下的低峰值功率的导出边界的严格性。此外，我们提出了可实现速率的近似值，与中等信噪比（SNR）范围内的导出边界相比，该近似值更加准确。我们还通过与具有不可忽略的炮弹和热噪声的模型进行比较，验证了所提出的模型在可实现速率分析方面的准确性。对于容量分析，我们假设符号持续时间可以任意短，并证明当采样间隔和符号持续时间都接近于零时，容量接近连续时间泊松信道的容量，并且采样间隔等于符号期间。对于大峰值功率，非完美接收器的容量收敛，而连续泊松容量信道的容量线性增加。