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arXiv 2208.03384cs.ITmath.IT
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幅度约束向量高斯窃听信道:保密容量达到输入分布的性质

Amplitude Constrained Vector Gaussian Wiretap Channel: Properties of the Secrecy-Capacity-Achieving Input Distribution

Antonino Favano, Luca Barletta, Alex Dytso

AI总结:

本文研究峰值功率约束下高斯窃听信道的保密容量,确定低幅度区域的最优性条件,并给出保密容量达到分布的离散性质及计算形式。

摘要:

本文研究了在峰值功率约束下,$n$维高斯窃听信道的保密容量。该工作确定了最大的峰值功率约束$\bar{\mathsf{R}}_n$,使得输入分布均匀分布在单个球面上是最优的;这一区域被称为低幅度区域。当$n$趋于无穷大时,$\bar{\mathsf{R}}_n$的渐近行为完全由两个接收机处的噪声方差函数表征。此外,保密容量也以一种便于计算的形式被表征。文中提供了若干数值示例,例如低幅度区域之外的保密容量达到分布的示例。进一步,对于标量情形($n=1$),我们证明了保密容量达到的输入分布是离散的,且其点数最多为$\frac{\mathsf{R}^2}{σ_1^2}$的量级,其中$σ_1^2$是合法信道上的高斯噪声方差。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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