论文标题
振幅约束矢量高斯窃听通道：秘密容量促进的输入分布的性能
Amplitude Constrained Vector Gaussian Wiretap Channel: Properties of the Secrecy-Capacity-Achieving Input Distribution
论文作者
论文摘要
本文研究了在峰值限制下，$ n $二维高斯窃听通道的保密容量。这项工作确定了最大的峰值约束$ \ bar {\ mathsf {r}} _ n $，以使输入分布在单个球体上均匀分布是最佳的；该制度称为低振幅制度。 $ \ bar {\ mathsf {r}} _ n $的渐近造成$ n $ to to Infinity的渐近是完全表征了两个接收器的噪声方差的函数。此外，秘密容量的表征还以适合计算的形式进行表征。提供了几个数值示例，例如超出低振幅制度的秘密行能分布的示例。此外，对于标量案例$（n = 1）$，我们表明，秘密容量 - 调整输入分布是离散的，在$ \ frac {\ mathsf {\ mathsf {r}^2} {σ_1^2} $的大多数订单中，$ \ mathsf {\ mathsf {\ mathsf {r}^2} $ nery $σ_1^2 $ iS is of variancian noviancian noviancian noviancian noviancian neviancian noviancian noviancian noviancian noviancian noviancian noviancian。
This paper studies secrecy-capacity of an $n$-dimensional Gaussian wiretap channel under a 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 low 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. Several numerical examples are provided, such as the example of the secrecy-capacity-achieving distribution beyond the low amplitude regime. Furthermore, for the scalar case $(n=1)$ we show that the secrecy-capacity-achieving input distribution is discrete with finitely many points at most of the order of $\frac{\mathsf{R}^2}{σ_1^2}$, where $σ_1^2$ is the variance of the Gaussian noise over the legitimate channel.
