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arXiv 2201.01841cs.ITmath.IT
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网络物理系统与秘密中断概率:再论

Cyber-Physical-Systems and Secrecy Outage Probability: Revisited

Makan Zamanipour

摘要:

本文从技术上探讨了保密率$Λ$和保密中断概率(SOP)的凹版本为$\mathop{{\rm \mathbb{M}ax}}\limits_{Δ} {\rm \; } \mathbb{P}\mathscr{r} \big( Λ\ge λ\big) $的最大化问题。我们这样做是从一个通用的观点,即使我们使用传统的Wyner的窃听通道,我们的系统模型$-$的东西,可以扩展到每一种保密建模和分析。我们考虑它的黎曼流形,并在数学上定义它的体积为$\mathbb{V}\mathscr{ol}\big \lbrace Λ\big \rbrace$。通过得到黎曼流形及其体积的一个新的界,我们随后将它与相对概率闭包中存在的特征值的个数联系起来。借助\textit{Finsler's}引理、广义\textit{Young's}不等式、广义\textit{Brunn-Minkowski}不等式、\textit{Talagrand's}浓度不等式,证明了一些新的引理.此外,我们提出了一种新的马尔可夫决策过程为基础的强化学习算法,以找到最佳的政策有关的特征值分布$-$的东西,扩展到一个可能的半马尔可夫决策过程的情况下,定期攻击。

英文摘要:

This paper technically explores the secrecy rate $Λ$ and a maximisation problem over the concave version of the secrecy outage probability (SOP) as $\mathop{{\rm \mathbb{M}ax}}\limits_{Δ} {\rm \; } \mathbb{P}\mathscr{r} \big( Λ\ge λ\big) $. We do this from a generic viewpoint even though we use a traditional Wyner's wiretap channel for our system model $-$ something that can be extended to every kind of secrecy modeling and analysis. We consider a Riemannian mani-fold for it and we mathematically define a volume for it as $\mathbb{V}\mathscr{ol}\big \lbrace Λ\big \rbrace$. Through achieving a new bound for the Riemannian mani-fold and its volume, we subsequently relate it to the number of eigen-values existing in the relative probabilistic closure. We prove in-between some novel lemmas with the aid of some useful inequalities such as the \textit{Finsler's} lemma, the generalised \textit{Young's} inequality, the generalised \textit{Brunn-Minkowski} inequality, the \textit{Talagrand's} concentration inequality. We additionally propose a novel Markov decision process based reinforcement learning algorithm in order to find the optimal policy in relation to the eigenvalue distributions $-$ something that is extended to a possibilisitically semi-Markov decision process for the case of periodic attacks.

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