離散時間中卜瓦松通道容量分析

Abstract

本論文中將研究離散時間中卜瓦松通道之通道容量。此通道模型可描述一個包含直接感測接收端的光通道，其接收端可視為一個計算光子的計數器，而到達接收端之光子數量由傳送端信號以及環境中游離的光子決定。基於能量消耗和安全的考量，我們將同時對傳送信號的平均能量和瞬時能量作限制。

我們嘗試找出此通道容量的上下界。藉著某些近日研究卜瓦松分布的新成果以及應用通道容量的二元性，可以推導出包含部份數值估計的數學式，其中數值估計的複雜度十分的低。我們上下界所夾的區域並不大，換句話說，我們成功的縮小了估計通道容量時可能的區間。

The capacity of the discrete time Poisson channel is studied. This channel law describes optical communication with a direct-detection receiver, where the output models the receiving photons due to the transmitted laser signal and due to surrounding light. For battery issues and safety reasons the inputs are simultaneously constrained on both their average and peak power.

We try to find an upper and a lower bound on the capacity. Applying some recent results on the Poisson distribution and a dual expression of channel capacity, the bounds are partially analytic and partially numerical, where the computation complexity is very low. The gap between our bounds is not large, i.e. we ave succeeded in narrowing the range of the capacity.