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arXiv:1410.8100 · IEEE Transactions on Signal Processing

Design of Binary Quantizers for Distributed Detection Under Secrecy Constraints

Venkata Sriram Siddhardh Nadendla, Pramod K. Varshney

Published Feb 11, 2016• 31 citations
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Abstract

In this paper, we investigate the design of distributed detection networks in the presence of an eavesdropper (Eve). We consider the problem of designing binary sensor quantizers that maximize the Kullback-Leibler (KL) divergence at the fusion center (FC), when subject to a tolerable constraint on the KL divergence at Eve. We assume that the channels between the sensors and the FC (likewise the channels between the sensors and the Eve) are modeled as binary symmetric channels (BSCs). In the case of i.i.d. received symbols at both the FC and Eve, we prove that the structure of the optimal binary quantizers is a likelihood ratio test (LRT). We also present an algorithm to find the threshold of the optimal LRT, and illustrate it for the case of Additive white Gaussian noise (AWGN) observation models at the sensors. In the case of non-i.i.d. received symbols at both FC and Eve, we propose a dynamic-programming based algorithm to find efficient quantizers at the sensors. Numerical results are presented to illustrate the performance of the proposed network.

DOI
10.1109/tsp.2016.2529583

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In this paper, we investigate the design of distributed detection networks in the presence of an eavesdropper (Eve). We consider the problem of designing binary sensor quantizers that maximize the Kullback-Leibler (KL) divergence at the fusion center (FC), when subject to a tolerable constraint on the KL divergence at Eve. We assume that the channels between the sensors and the FC (likewise the channels between the sensors and the Eve) are modeled as binary symmetric channels (BSCs). In the case of i.i.d. received symbols at both the FC and Eve, we prove that the structure of the optimal binary quantizers is a likelihood ratio test (LRT). We also present an algorithm to find the threshold of the optimal LRT, and illustrate it for the case of Additive white Gaussian noise (AWGN) observation models at the sensors. In the case of non-i.i.d. received symbols at both FC and Eve, we propose a dynamic-programming based algorithm to find efficient quantizers at the sensors. Numerical results are presented to illustrate the performance of the proposed network.
The design of scalar quantization for distributed binary decision in presence of an eavesdropper (Eve) is investigated. An encoder/quantizer (Alice) observes a memoryless source and communicate via a public noiseless rate-limited channel with the detector (Bob) who has also access to a correlated analog source. Bob can take advantage of both informations to perform a binary decision on the joint probability law of these observations. Eve is further assumed to have access to a different correlated analog source and perfectly observe the information bits sent by Alice. This paper evaluates the various tradeoffs between the probabilities of error (on the decision) depending on the amount of information leakage from Alice to Eve. The Bhattacharyya distance; one of the distances measuring the difference between two probability distributions; is taken as a criterion to optimize the scalar quantizer subject to a tolerable constraint on the information leakage at the level of Eve. Numerical results for memoryless Gaussian sources demonstrate the performance of the proposed quantization method.
The design of scalar quantization for distributed binary decision in presence of an eavesdropper (Eve) is investigated. An encoder/quantizer (Alice) observes a memoryless source and communicate via a public noiseless rate-limited channel with the detector (Bob) who has also access to a correlated analog source. Bob can take advantage of both informations to perform a binary decision on the joint probability law of these observations. Eve is further assumed to have access to a different correlated analog source and perfectly observe the information bits sent by Alice. This paper evaluates the various tradeoffs between the probabilities of error (on the decision) depending on the amount of information leakage from Alice to Eve. The Bhattacharyya distance; one of the distances measuring the difference between two probability distributions; is taken as a criterion to optimize the scalar quantizer subject to a tolerable constraint on the information leakage at the level of Eve. Numerical results for memoryless Gaussian sources demonstrate the performance of the proposed quantization method.
Vector Quantization (VQ) design for distributed binary decision in the presence of an eavesdropper (Eve) is investigated. An encoder/quantizer (Alice) observes i.i.d. samples and communicates them via a public noiseless rate-limited channel to the detector (Bob) who has also access to a correlated analog source. Bob can take advantage of both informations to perform a binary decision on the joint probability law of these observations. Eve is further assumed to have access to another correlated analog source. This paper evaluates relevant trade-offs between the error probability of the two types and the amount of tolerated information leakage, for the particular case of testing against independence. An application to illustrate our results to real-data measured from the electric consumption at houses to perform anomaly detection is also provided.
This paper considers the problem of filter design with secrecy constraints, where two legitimate parties (Alice and Bob) communicate in the presence of an eavesdropper (Eve) over a Gaussian multiple-input-multiple-output (MIMO) wiretap channel. This problem involves designing, subject to a power constraint, the transmit and the receive filters which minimize the mean-squared error (MSE) between the legitimate parties whilst assuring that the eavesdropper MSE remains above a certain threshold. We consider a general MIMO Gaussian wiretap scenario, where the legitimate receiver uses a linear zero-forcing (ZF) filter and the eavesdropper receiver uses either a ZF or an optimal linear Wiener filter. We provide a characterization of the optimal filter designs by demonstrating the convexity of the optimization problems. We also provide generalizations of the filter designs from the scenario where the channel state is known to all the parties to the scenario where there is uncertainty in the channel state. A set of numerical results illustrates the performance of the novel filter designs, including the robustness to channel modeling errors. In particular, we assess the efficacy of the designs in guaranteeing not only a certain MSE level at the eavesdropper, but also in limiting the error probability at the eavesdropper. We also assess the impact of the filter designs on the achievable secrecy rates. The penalty induced by the fact that the eavesdropper may use the optimal nonlinear receive filter rather than the optimal linear one is also explored in the paper.
We study a distributed binary hypothesis testing (HT) problem with communication and security constraints, involving three parties: a remote sensor called Alice, a legitimate decision center called Bob, and an eavesdropper called Eve, all having their own source observations. In this system, Alice conveys a rate-R description of her observations to Bob, and Bob performs a binary hypothesis test on the joint distribution underlying his and Alice’s observations. The goal of Alice and Bob is to maximize the exponential decay of Bob’s miss-detection (type-II error) probability under two constraints: Bob’s false-alarm (type-I error) probability has to stay below a given threshold and Eve’s uncertainty (equivocation) about Alice’s observations should stay above a given security threshold even when Eve learns Alice’s message. For the special case of testing against independence, we characterize the largest possible type-II error exponent under the described type-I error probability and security constraints.
In this paper, the problem of function computation with privacy and secrecy constraints is considered. The considered model consists of three legitimate nodes (i.e., two transmitters, Alice and Bob, and a fusion center that acts as the receiver) that observe correlated sources and are connected by noiseless public channels, and an eavesdropper Eve who has full access to the public channels and also has its own source observations. The fusion center would like to compute a function of the distributed sources within a prefixed distortion level under a certain distortion metric. To facilitate the function computation, Alice and Bob will send messages to the fusion center. Different from the existing setups in function computation, we assume that there is a privacy constraint on the sources at Alice and Bob. In particular, Alice and Bob would like to enable the fusion center to compute the function, but at same time, they do not want the fusion center to learn too much information about the source observations. We introduce a quantity to precisely measure the privacy leakage to the fusion center. In addition to this privacy constraint, we also have a secrecy constraint to Eve and use equivocation of sources to measure this quantity. Under this model, we study the tradeoffs among message rates, private information leakage, equivocation, and distortion. We first consider a scenario that has only one transmitter, i.e., the source at Bob is empty, and fully single-letter characterize the corresponding regions. Then, we consider the more general case and provide both outer and inner bounds on the corresponding regions.