This paper addresses the degraded discrete-time Poisson wiretap channel (DT--PWC) in an optical wireless communication system based on intensity modulation and direct detection. Subject to nonnegativity, peak- and average-intensity as well as bandwidth constraints, we study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be unique and discrete with a finite number of mass points; one of them located at the origin. Furthermore, we establish that every point on the boundary of the rate-equivocation region of this wiretap channel is also obtained by a unique and discrete input distribution with finitely many mass points. In general, the number of mass points of the optimal distributions is greater than two. This is in contrast with the degraded continuous-time PWC when the signaling bandwidth is not restricted and where the secrecy capacity and the entire boundary of the rate-equivocation region are achieved by binary distributions. Furthermore, we extend our analysis to the case where only an average-intensity constraint is active. For this case, we find that the secrecy capacity and the entire boundary of the rate-equivocation region are attained by discrete distributions with countably \textit{infinite} number of mass points, but with finitely many mass points in any bounded interval.

翻译：本文论述光学无线通信系统中基于强度调制和直接检测的光学无线通信系统中的离散时间Poisson窃听器频道(DT-PWC)的退化。根据非增强性、峰值和平均强度以及带宽限制等条件,我们研究该窃听频道的保密性能-实现输入分布,证明它独特和离散,质量点数量有限;其中之一位于发源地;此外,我们确定,该窃听频道速率-敏感区边界的每个点也是通过一个独特的和离散的投入分布获得的,有一定质量点;一般而言,最佳分布的质量点数量大于两个。这与信号带宽不受限制,而且通过双轨分布达到保密能力和率-平等区整个边界点的保密性分数不同;此外,我们将我们的分析范围扩大到仅存在平均密度制约的情况。对于这种情况,我们发现,最佳分布的质量点的数量大于两个质量点的连续持续时间点数,每个分点的离异度/边界点的分数。