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Quantization for distributed binary detection under secrecy constraints

Maggie Mhanna, Pablo Piantanida, Pierre Duhamel

Published May 23, 2016• 3 citations
OpenAlex

Abstract

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.

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Quantization for distributed binary detection under secrecy constraints

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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.

arXiv:1410.8100•IEEE Transactions on Signal Processing•Feb 11, 2016•31 citations
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.
The distributed binary hypothesis testing problem with communication and security constraints is investigated. A legitimate statistician (referred to as Bob) is interested in detecting the joint probability distribution of two remotely located sources. To this end, Bob has access to analog and coded data where the later is observed at another node (referred to as Alice) and communicated over a public noise-less channel of finite rate. An eavesdropper (referred to as Eve) has access to the encoded bits. In this framework, we study the tradeoff between the maximum achievable error exponent at Bob, i.e., the minimum Type II error probability for a fixed Type I probability of error, the rate and the equivocation rate. We first derive an achievable rate-exponent-equivocation region. Then, we investigate the special case of testing against independence for which we provide the optimal rate-exponent-equivocation region. An application example to binary sources is also considered.
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.
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.
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.