This paper studies secrecy-capacity of an $n$-dimensional Gaussian wiretap channel under the peak-power constraint. This work determines the largest peak-power constraint $\bar{\mathsf{R}}_n$ such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the small-amplitude regime. The asymptotic of $\bar{\mathsf{R}}_n$ as $n$ goes to infinity is completely characterized as a function of noise variance at both receivers. Moreover, the secrecy-capacity is also characterized in a form amenable for computation. Furthermore, several numerical examples are provided, such as the example of the secrecy-capacity achieving distribution outside of the small amplitude regime.

翻译：本文研究在峰值功率限制下,一美元维面高斯窃听频道的保密能力。 这项工作确定了最大的峰值功率限制 $\ bar\ mathsf{R ⁇ n$, 这样, 在一个单一领域统一分布的输入分布是最佳的; 这个制度被称为小标度制度。 以无价方式将$\ bar\ mathsf{R ⁇ n$作为无价之物完全定性为两个接收器的噪声差异功能。 此外, 保密能力也以可计算的形式定性。 此外, 还提供了几个数字例子, 例如, 在小标度制度之外实现保密能力分配的例子 。