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Secure Lossy Transmission of Vector Gaussian Sources

机译：矢量高斯源的安全有损传输

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摘要

We study the secure lossy transmission of a vector Gaussian source to a legitimate user in the presence of an eavesdropper, where both the legitimate user and the eavesdropper have vector Gaussian side information. The aim of the transmitter is to describe the source to the legitimate user in a way that the legitimate user can reconstruct the source within a certain distortion level while the eavesdropper is kept ignorant of the source as much as possible as measured by the equivocation. We obtain an outer bound for the rate, equivocation and distortion region of this secure lossy transmission problem. This outer bound is tight when the transmission rate constraint is removed. In other words, we obtain the maximum equivocation at the eavesdropper when the legitimate user needs to reconstruct the source within a fixed distortion level while there is no constraint on the transmission rate. This characterization of the maximum equivocation involves two auxiliary random variables. We show that a nontrivial selection for both random variables may be necessary in general. The necessity of two auxiliary random variables also implies that, in general, Wyner-Ziv coding is suboptimal in the presence of an eavesdropper. In addition, we show that, even when there is no rate constraint on the legitimate link, uncoded transmission (deterministic or stochastic) is suboptimal; the presence of an eavesdropper necessitates the use of a coded scheme to attain the maximum equivocation.
机译：我们研究了在窃听者存在的情况下矢量高斯源向合法用户的安全有损传输，其中合法用户和窃听者均具有矢量高斯边信息。发射器的目的是以合法用户可以在一定失真水平内重构源的方式向合法用户描述该源，同时窃听者尽可能地不知道该源是否由歧义测量。我们获得了此安全有损传输问题的速率，模棱两可和失真区域的界线。当去除传输速率约束时，该外部界限很严格。换句话说，当合法用户需要在固定的失真级别内重建源而对传输速率没有限制时，我们在窃听者处获得最大的模棱两可。最大模棱两可的表征涉及两个辅助随机变量。我们表明，一般来说，两个随机变量的非平凡选择可能是必要的。两个辅助随机变量的必要性还意味着，通常，在存在窃听者的情况下，Wyner-Ziv编码次优。另外，我们表明，即使在合法链路上没有速率限制，未编码的传输（确定性或随机性）也不是最优的；窃听者的存在需要使用编码方案来获得最大的模棱两可。

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