Distributed hypothesis testing over noisy channels

Sreekumar, Sreejith; Gündüz, Deniz

doi:10.1109/isit.2017.8006675

Cited by 22 publications

(25 citation statements)

References 13 publications

(26 reference statements)

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“…The detector performs a binary hypothesis test on the joint distribution of the data (U k , V k ) to decide between them, based on This work is supported in part by the European Research Council (ERC) through Starting Grant BEACON (agreement #677854). A part of this work was presented at the International Symposium on Information theory (ISIT), Aachen, 2017 [15]. the channel outputs Y n as well as its own observations V k .…”

Section: Introductionmentioning

confidence: 99%

Distributed Hypothesis Testing Over Discrete Memoryless Channels

Sreekumar

Gündüz

2020

IEEE Trans. Inform. Theory

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A distributed binary hypothesis testing (HT) problem involving two parties, one referred to as the observer and the other as the detector is studied. The observer observes a discrete memoryless source (DMS) and communicates its observations to the detector over a discrete memoryless channel (DMC). The detector observes another DMS correlated with that at the observer, and performs a binary HT on the joint distribution of the two DMS's using its own observed data and the information received from the observer. The trade-off between the type I error probability and the type II error-exponent of the HT is explored. Single-letter lower bounds on the optimal type II error-exponent are obtained by using two different coding schemes, a separate HT and channel coding scheme and a joint HT and channel coding scheme based on hybrid coding for the matched bandwidth case. Exact single-letter characterization of the same is established for the special case of testing against conditional independence, and it is shown to be achieved by the separate HT and channel coding scheme. An example is provided where the joint scheme achieves a strictly better performance than the separation based scheme. arXiv:1802.07665v8 [cs.IT] 3 Dec 2019showed that for the case of a single-observer, the quantize-bin-test scheme achieves the optimal error-exponent for testing against conditional independence (TACI), in which, V = (E, Z) and Q U EZ = P U Z P E|Z . Extensions of the distributed HT problem has also been considered in several other interesting scenarios involving multiple detectors [9], multiple observers [10], interactive HT [11], [12], collaborative HT [13], HT with lossy source reconstruction [14], HT over a multi-hop relay network [16], etc., in which, the authors obtain a single-letter characterization of the optimal error-exponent in some special cases.While the works mentioned above have studied the unsymmetric case of focusing on the error-exponent for a constraint on the type I error probability, other works have analyzed the trade-off between the type I and type II error probabilities in the exponential sense. In this direction, the optimal trade-off between the type I and type II error-exponents in the centralized scenario is obtained in [17]. The distributed version of this problem is first studied in [18], where inner bounds on the above trade-off are established. This problem has also been explored from an information-geometric perspective for the zero-rate compression scenario in [19] and [20], which provide further insights into the geometric properties of the optimal trade-off between the two exponents. A Neyman-Pearson like test in the zero-rate compression scenario is proposed in [21], which, in addition to achieving the optimal trade-off between the two exponents, also achieves the optimal second order asymptotic performance among all symmetric (type-based) encoding schemes. However, the optimal trade-off between the type I and type II error-exponents for the general distributed HT problem remains open. Recently, an in...

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Section: Introductionmentioning

confidence: 99%

Distributed Hypothesis Testing Over Discrete Memoryless Channels

Sreekumar

Gündüz

2020

IEEE Trans. Inform. Theory

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“…The second term in (C.41) corresponds to A ′ rc defined in (53). The third term corresponds to A ′′ rc defined in (54), when using ρ s = ρ − ρ c , and noting that when…”

Section: Appendix C Proof Of Theorems 8 Andmentioning

confidence: 99%

On the Reliability Function of Distributed Hypothesis Testing Under Optimal Detection

Weinberger

Kochman

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is reduced to the problem of determining the reliability function of channel codes designed for detection (in analogy to a similar result which connects the reliability function of distributed lossless compression and ordinary channel codes). Second, a single-letter random-coding bound based on a hierarchical ensemble, as well as a single-letter expurgated bound, are derived for the reliability of channel-detection codes. Both bounds are derived for a system which employs the optimal detection rule. We conjecture that the resulting random-coding bound is ensemble-tight, and consequently optimal within the class of quantization-and-binning schemes. Index TermsBinning, channel-detection codes, distributed hypothesis testing, error exponents, expurgated bounds, hierarchical ensembles, multiterminal data compression, random coding, side information, statistical inference, superposition codes. 2 results from [4], [5] to fully characterize Stein's exponent in the testing against independence case (i.e., when the null hypothesis states that (X, Y ) ∼ P XY , whereas the alternative hypothesis states that (X, Y ) ∼ P X × P Y ).Further, they have used quantization-based encoding to derive an achievable Stein's exponent for a general pair of memoryless hypotheses [2, Th. 5], but without a converse bound. Consecutive progress on this problem, as well as on the symmetric case (in which the Y -observations must also be compressed) is summarized in [27, Sec. IV], with notable contributions from [26], [28], [49]. The the zero-rate case was also considered, for which [26], [28], [48] and [27, Th. 5.5] derived matching achievable and converse bounds under various kind of assumptions on the distributions induced each of the hypotheses. In the last decade, a renewed interest in the problem arose, aimed both at tackling more elaborate models, as well as at improving the results on the basic model. As for the former, notable examples include the following. Stein's exponents under positive rates were explored in successive refinement models [56], for multiple encoders [43], for interactive models [31], [67], under privacy constraints [38], combined with lossy compression [33], over noisy channels [54], [58], for multiple decision centers [46], as well as over multi-hop networks [47]. Exponents for the zero-rate problem were studied under restricted detector structure [41] and for multiple encoders [68]. The finite blocklength and second-order regimes were addressed in [61].Notwithstanding the foregoing progress, the encoding approach proposed in [49] is still the best known in general for the basic model we study in this paper. It is based on quantization and binning, just as used, e.g., for distributed lossy compression (the Wyner-Ziv problem [22, Ch. 11] [66]). First, the encoding rate is reduced by quanti...

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“…Proof: The first two conditions follow directly from the converse of the TACI problem considered in [6], when the noisy channel between the source U n and the detector is replaced by a noiseless channel of rate R. Eqn. (34) follows by noting that the distortion at the adversary cannot be more than that can be obtained by a symbol-by-symbol reconstruction U i = φ(E i ) using only the side-information E n (ignoring the message from the observer).…”

Section: Analysis Of Probability Of Errormentioning

confidence: 99%

“…Various multi-terminal scenarios have been studied in [4] and [5]. Recently, the optimal T2EE for TACI over a noisy channel is established in [6]. The information theoretic framework for analyzing secrecy is first introduced in the seminal paper of Shannon [7].…”

Section: Introductionmentioning

confidence: 99%

Testing Against Conditional Independence Under Security Constraints

Sreekumar

Gündüz

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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A distributed binary hypothesis testing problem involving three parties, a remote node, called the observer, a legitimate decoder, called the detector, and an adversary, is studied. The remote node observes a discrete memoryless source, and communicates its observations over a rate-limited noiseless public channel to the detector, which tests for the conditional independence of its own observations from that of the remote node, conditioned on some additional side information. The adversary, in addition to observing the public message, has access to its own correlated side-information. Considering the type 2 error exponent for a given type 1 error probability constraint as the performance measure for the hypothesis test at the detector, and equivocation of the source at the adversary as the secrecy measure, a single-letter characterization of the rate-error exponent-equivocation trade-off is established. Additionally, for a general distortion measure, imposing the average distortion at the adversary as the measure of secrecy achieved, an inner bound on the trade-off between the rate, error exponent and average distortion is obtained. This bound is shown to be tight under the less noisy condition on the adversary's side information.

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Distributed hypothesis testing over noisy channels

Cited by 22 publications

References 13 publications

Distributed Hypothesis Testing Over Discrete Memoryless Channels

Distributed Hypothesis Testing Over Discrete Memoryless Channels

On the Reliability Function of Distributed Hypothesis Testing Under Optimal Detection

Testing Against Conditional Independence Under Security Constraints

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