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IEEE International Symposium on Information Theory (ISIT)

Secure lossy transmission of vector Gaussian sources

Ersen Ekrem, Şennur Ulukuş

Published Jul 1, 2011• 2 citations
Publisher

Abstract

We study the secure lossy transmission of a Gaussian vector source to a legitimate user in the presence of an eaves-dropper, where both the legitimate user and the eavesdropper have Gaussian vector side information. The transmitter describes the source to the legitimate user in a way that the legitimate user can reconstruct the source within a certain distortion while the eavesdropper is kept ignorant of the source as much as possible. 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.

DOI
10.1109/isit.2011.6034194

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We study the secure lossy transmission of a Gaussian vector source to a legitimate user in the presence of an eaves-dropper, where both the legitimate user and the eavesdropper have Gaussian vector side information. The transmitter describes the source to the legitimate user in a way that the legitimate user can reconstruct the source within a certain distortion while the eavesdropper is kept ignorant of the source as much as possible. 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.
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.
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 non-trivial 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.
The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate—average uncertainty—at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger–Tung and the secure source coding setups. Inner and outer bounds on the so-called rate-distortion-equivocation region are derived. The inner region turns to be tight for two cases: 1) uncoded side information at Bob and 2) lossless reconstruction of both sources at Bob—secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (respectively) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a nonzero distortion at Bob can be fully exploited to guarantee secrecy.
This paper investigates the problem of source-channel coding for secure transmission of a Gaussian source over a Gaussian wiretap channel in presence of arbitrarily correlated side informations at both receivers. By means of an appropriate coding scheme (either hybrid digital/analog or pure digital), the optimal rate-distortion-equivocation region is characterized for most of the scenarios. These results provide the best achievable tradeoff between the requirement on the distortion level at the legitimate receiver and the equivocation rate at the eavesdropper.
The problem of secure lossy source-channel wiretapping with arbitrarily correlated side informations at both receivers is investigated. This scenario consists of an encoder (referred to as Alice) that wishes to compress a source and send it through a noisy channel to a legitimate receiver (referred to as Bob). In this context, Alice must simultaneously satisfy the desired requirements on the distortion level at Bob, and the equivocation rate at the eavesdropper (referred to as Eve). This setting can be seen as a generalization of the conventional problems of secure source coding with side information at the decoders, and the wiretap channel. Inner and outer bounds on the rate-distortion-equivocation region for the case of arbitrary channels and side informations are derived. In some special cases of interest, it is shown that separation holds. By means of an appropriate coding, the presence of any statistical difference among the side informations, the channel noises, and the distortion at Bob can be fully exploited in terms of secrecy.
A lossy source coding problem with secrecy constraints is considered where a remote information source should be transmitted to a single destination via multiple agents in the presence of an eavesdropper. The agents observe noisy versions of the source and independently encode and transmit their observations to the destination via noiseless rate-limited links. Unbeknownst to the agents, an eavesdropper intercepts one of the links from the agents to the destination to learn as much as possible about the source. The destination should estimate the remote source subject to a mean distortion threshold. This problem can be viewed as the CEO problem with addition of secrecy constraints. We establish inner and outer bounds on the rate-distortion-equivocation region. In addition, we provide the optimal rate-distortion-equivocation region for the quadratic Gaussian case when the eavesdropper has no side information.