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Strong Converse Bounds in Quantum Network Information Theory

IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第4期67卷 2269-2292页

作者： Cheng, Hao-Chung Datta, Nilanjana Rouze, Cambyse Natl Taiwan Univ Dept Elect Engn Grad Inst Commun Engn Taipei 10617 Taiwan Natl Taiwan Univ Dept Math Taipei 10617 Taiwan Natl Taiwan Univ Inst Appl Math Sci Taipei 10617 Taiwan Univ Cambridge Dept Appl Math & Theoret Phys Cambridge CB2 1TN England Tech Univ Munich Dept Math D-80333 Mtinchen Germany

In this paper, we develop the first method for finding strong converse bounds in quantum network information theory. The general scheme relies on a recently obtained result in the field of non-commutative functional inequalities, namely the tensorization property of quantum reverse hypercontractivity for the quantum depolarizing semigroup. We develop a novel technique to employ this result to find both finite blocklength and exponential strong converse bounds for the tasks of quantum source coding with compressed classical side information, and distributed quantum hypothesis testing with communication constraints for a classical-quantum state. In the classical setting, these two problems can be reformulated in a unified framework in terms of the so-called image-size characterization problem, which we extend to the classical-quantum setting. We also use this technique to establish analogous strong converse bounds in broadcast communication scenarios. In particular, we consider the transmission of classical information through a degraded broadcast channel, whose outputs are two quantum systems, with the state of one being a degraded version of the other. In establishing this last result, we prove a second-order Fano-type inequality, which is of independent interest. Our method to study strong converses has potential applications in other important tasks of quantum network information theory.

关键词： Task analysis testing Information theory Source coding Entropy Quantum networks Error probability Strong converse quantum network information theory quantum reverse hypercontractivity degraded broadcast channel (DBC) distributed hypothesis testing

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testing Against Independence with an Eavesdropper

Testing Against Independence with an Eavesdropper

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IEEE Information Theory Workshop (ITW)

作者： Faour, Sara Hamad, Mustapha Sarkiss, Mireille Wigger, Michele IP Paris Telecom Paris LTCI Palaiseau France Paris Res Ctr Huawei Math & Algorithm Sci Lab Paris France IP Paris Telecom SudParis SAMOVAR Palaiseau France

ISBN: (纸本)9798350301496

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 falsealarm (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.

关键词： distributed hypothesis testing error exponents security constraints side information

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REACHING BAYESIAN CONSENSUS IN COGNITIVE SYSTEMS BY DECISION EXCHANGES

REACHING BAYESIAN CONSENSUS IN COGNITIVE SYSTEMS BY DECISION...

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21st European Signal Processing Conference (EUSIPCO)

作者： Wang, Yunlong Djuric, Petar M. SUNY Stony Brook Dept Elect & Comp Engn Stony Brook NY 11794 USA

ISBN: (纸本)9781479936878

We consider the problem of distributed Bayesian hypothesis testing on a set of time invariant hypotheses in a cognitive system of cooperative agents. Each agent in the system obtains one set of private observations and then at every time slot two randomly selected agents repeatedly exchange their decisions and update their beliefs. We propose a method that allows the agents to reach an optimal local consensus by just exchanging decisions. It can be shown that with this strategy, all agents in the system can achieve a consensus in decision, which is also the global optimal decision held by a fictitious fusion center. We provide performance and convergence analysis of the proposed method as well as simulation results that demonstrate its asymptotical properties.

关键词： Cognitive system Bayesian consensus distributed hypothesis testing cooperative agents

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Complexity of Bayesian Belief Exchange over a Network 56

Complexity of Bayesian Belief Exchange over a Network

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56th Annual IEEE Conference on Decision and Control (CDC)

作者： Rahimian, M. Amin Jadbabaie, Ali Mossel, Elchanan MIT IDSS 77 Massachusetts Ave Cambridge MA 02139 USA

ISBN: (纸本)9781509028733

Many important real-world decision making problems involve group interactions among individuals with purely informational externalities, such situations arise for example in jury deliberations, expert committees, medical diagnosis, etc. In this paper, we will use the framework of iterated eliminations to model the decision problem as well as the thinking process of a Bayesian agent in a group decision/discussion scenario. We model the purely informational interactions of rational agents in a group, where they receive private information and act based upon that information while also observing other people's beliefs. As the Bayesian agent attempts to infer the true state of the world from her sequence of observations which include her neighbors' beliefs as well as her own private signal, she recursively refines her belief about the signals that other players could have observed and beliefs that they would have hold given the assumption that other players are also rational. We further analyze the computational complexity of the Bayesian belief formation in groups and show that it is NP-hard. We also investigate the factors underlying this computational complexity and show how belief calculations simplify in special network structures or cases with strong inherent symmetries. We finally give insights about the statistical efficiency (optimality) of the beliefs and its relations to computational efficiency.

关键词： Rational Choice theory Computational social choice distributed hypothesis testing Bayesian inference Computational complexity Bayesian computations

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Cooperative Multi-Sensor Detection under Variable-Length Coding

Cooperative Multi-Sensor Detection under Variable-Length Cod...

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IEEE Information Theory Workshop (ITW)

作者： Hamad, Mustapha Wigger, Michele Sarkiss, Mireille Telecom Paris IP Paris LTCI F-91120 Palaiseau France Telecom SudParis IP Paris SAMOVAR F-91011 Evry France

ISBN: (纸本)9781728159621

We investigate the testing-against-independence problem over a cooperative MAC with two sensors and a single detector under an average rate constraint on the sensors-detector links. For this setup, we design a variable-length coding scheme that maximizes the achievable type-II error exponent when the type-I error probability is limited to epsilon. Similarly to the single-link result, we show here that the optimal error exponent depends on epsilon and that variable-length coding allows to increase the rates over the optimal fixed-length coding scheme by the factor (1 - epsilon)(-1).

关键词： distributed hypothesis testing Cooperative MAC Variable-Length Coding Error Exponent

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Communication-Efficient Distribution-Free Inference Over Networks 57

Communication-Efficient Distribution-Free Inference Over Net...

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57th Asilomar Conference on Signals, Systems and Computers

作者： Pournaderi, Mehrdad Xiang, Yu Univ Utah Dept Elect & Comp Engn 50 Cent Campus Dr 2110 Salt Lake City UT 84112 USA

ISBN: (纸本)9798350325744

Consider a star network where each local node possesses a set of test statistics that exhibit a symmetric distribution around zero when their corresponding null hypothesis is true. This paper investigates statistical inference problems in networks concerning the aggregation of this general type of statistics and global error rate control under communication constraints in various scenarios. The study proposes communication-efficient algorithms that are built on established non-parametric methods, such as the Wilcoxon and sign tests, as well as modern inference methods such as the Benjamini-Hochberg (BH) and Barber-Candes (BC) procedures, coupled with sampling and quantization operations. The proposed methods are evaluated through extensive simulation studies.

关键词： distributed hypothesis testing FDR control distribution-free methods communication efficiency

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HIDDEN MARKOV MODELING OVER GRAPHS

HIDDEN MARKOV MODELING OVER GRAPHS

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IEEE Data Science and Learning Workshop (DSLW)

作者： Kayaalp, Mert Bordignon, Virginia Vlaski, Stefan Sayed, Ali H. Ecole Polytech Fed Lausanne EPFL Lausanne Switzerland Imperial Coll London London England

ISBN: (纸本)9781665454261

This work proposes a multi-agent filtering algorithm over graphs for finite-state hidden Markov models (HMMs), which can be used for sequential state estimation or for tracking opinion formation over dynamic social networks. We show that the difference from the optimal centralized Bayesian solution is asymptotically bounded for geometrically ergodic transition models. Experiments illustrate the theoretical findings and in particular, demonstrate the superior performance of the proposed algorithm compared to a state-of-the-art social learning algorithm.

关键词： Hidden Markov models distributed hypothesis testing social learning sequential state estimation

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distributed Estimation and Learning over Heterogeneous Networks

Distributed Estimation and Learning over Heterogeneous Netwo...

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54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

作者： Rahimian, M. Amin Jadbabaie, Ali MIT Inst Data Syst & Soc 77 Massachusetts Ave Cambridge MA 02139 USA

ISBN: (纸本)9781509045501

We consider several estimation and learning problems that networked agents face when making decisions given their uncertainty about an unknown variable. Our methods are designed to efficiently deal with heterogeneity in both size and quality of the observed data, as well as heterogeneity over time (intermittence). The goal of the studied aggregation schemes is to efficiently combine the observed data that is spread over time and across several network nodes, accounting for all the network heterogeneities. Moreover, we require no form of coordination beyond the local neighborhood of every network agent or sensor node. The three problems that we consider are (i) maximum likelihood estimation of the unknown given initial data sets, (ii) learning the true model parameter from streams of data that the agents receive intermittently over time, and (iii) minimum variance estimation of a complete sufficient statistic from several data points that the networked agents collect over time. In each case, we rely on an aggregation scheme to combine the observations of all agents;moreover, when the agents receive streams of data over time, we modify the update rules to accommodate the most recent observations. In every case, we demonstrate the efficiency of our algorithms by proving convergence to the globally efficient estimators given the observations of all agents. We supplement these results by investigating the rate of convergence and providing finite-time performance guarantees.

关键词： Statistical Learning distributed Learning distributed hypothesis testing distributed Detection distributed Estimation Online Learning

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Two-Hop Network with Multiple Decision Centers under Expected-Rate Constraints

Two-Hop Network with Multiple Decision Centers under Expecte...

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IEEE Global Communications Conference (GLOBECOM)

作者： Hamad, Mustapha Wigger, Michele Sarkiss, Mireille IP Paris Telecom Paris LTCI F-91120 Palaiseau France IP Paris Telecom SudParis SAMOVAR F-91011 Evry France

ISBN: (纸本)9781728181042

The paper studies distributed binary hypothesis testing over a two-hop relay network where both the relay and the receiver decide on the hypothesis. Both communication links are subject to expected rate constraints, which differs from the classical assumption of maximum rate constraints. We exactly characterize the set of type-II error exponent pairs at the relay and the receiver when both type-I error probabilities are constrained by the same value epsilon > 0. No tradeoff is observed between the two exponents, i.e., one can simultaneously attain maximum type-II error exponents both at the relay and at the receiver. For epsilon(1) not equal epsilon(2), we present an achievable exponents region, which we obtain with a scheme that applies different versions of a basic two-hop scheme that is optimal under maximum rate constraints. We use the basic twohop scheme with two choices of parameters and rates, depending on the transmitter's observed sequence. For epsilon(1) = epsilon(2), a single choice is shown to be sufficient. Numerical simulations indicate that extending to three or more parameter choices is never beneficial.

关键词： Multi-hop distributed hypothesis testing error exponents expected rate constraints variable-length coding

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New Results on testing Against Independence with Rate-Limited Constraints 7

New Results on Testing Against Independence with Rate-Limite...

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7th IEEE Global Conference on Signal and Information Processing (IEEE GlobalSIP)

作者： Espinosa, Sebastian Silva, Jorge F. Piantanida, Pablo Univ Chile Dept Elect Engn Santiago Chile Univ Paris Sud CNRS Cent Supelec Lab Signaux & Syst L2S Orsay France Univ Montreal Montreal Inst Learning Algorithms MILA Montreal PQ Canada

ISBN: (纸本)9781728127231

This work studies error exponent limits in hypothesis testing (HT) in a distributed scenario with partial communication constraints. We derive general conditions on the Type I error restriction under which the error exponent of the optimal Type II error has a closed-form characterization for the task of testing against independence. We show that the error exponent is preserved for a family of decreasing Type I error restrictions. Complementing this analysis, new expressions are derived to bound the optimal Type II error probability for a finite number of observations. These bounds shed light about the velocity at which error exponent limits are attained with the number of samples.

关键词： distributed hypothesis testing multi-terminal source coding error exponent information bottleneck

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