Strong Converse for Hypothesis Testing Against Independence over a Two-Hop Network

Cao, Dongpu; Zhou, Lin; Tan, Vincent Y. F.

doi:10.1109/isit.2019.8849768

Cited by 13 publications

(33 citation statements)

References 22 publications

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“…This result is even more remarkable in that the optimum Stein-exponent is not known for the general hypothesis testing problem with a single noise-less link. Tian and Chen [5] and Cao, Zhou, and Tan [15] proved strong converse results for testing against independence in a single-sensor single-decision center setup under noiseless successive refinement communication and in a two-sensor single decision center setup with noiseless multi-hop communication. Two of the main tools for deriving strong converse results are the change of measure approach under the η-image characterization [1] and the blowing-up lemma [21], [22] or the hypercontractivity lemma [23].…”

Section: Introductionmentioning

confidence: 94%

Distributed Hypothesis Testing With Variable-Length Coding

Salehkalaibar

Wigger

2020

IEEE J. Sel. Areas Inf. Theory

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The problem of distributed testing against independence with variable-length coding is considered when the average and not the maximum communication load is constrained as in previous works. The paper characterizes the optimum type-II error exponent of a single-sensor single-decision center system given a maximum type-I error probability when communication is either over a noise-free rate-R link or over a noisy discrete memoryless channel (DMC) with stop-feedback. Specifically, let denote the maximum allowed type-I error probability. Then the optimum exponent of the system with a rate-R link under a constraint on the average communication load coincides with the optimum exponent of such a system with a rate R/(1 −) link under a maximum communication load constraint. A strong converse thus does not hold under an average communication load constraint. A similar observation also holds for testing against independence over DMCs. With variable-length coding and stop-feedback and under an average communication load constraint, the optimum type-II error exponent over a DMC of capacity C equals the optimum exponent under fixed-length coding and a maximum communication load constraint when communication is over a DMC of capacity C(1 −) −1 .

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Section: Introductionmentioning

confidence: 94%

Distributed Hypothesis Testing With Variable-Length Coding

Salehkalaibar

Wigger

2020

IEEE J. Sel. Areas Inf. Theory

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“…The focus of this paper is on weak converses where the type-I errors are also required to vanish asymptotically as n → ∞. The existence of a strong converse for one of these special cases, i.e., a proof that the same exponents are optimal also when type-I error probability > 0 is tolerated, was recently proved in [26].For the second case where X n → Z n → Y n , we present optimality results (in the weak converse sense) for two special cases. In the first special case, P Y Z is same under both hypothesis, so Y n by itself is of no interest to the receiver.…”

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confidence: 99%

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confidence: 99%

Hypothesis Testing Over the Two-Hop Relay Network

Salehkalaibar

Wigger

Wang

2019

IEEE Trans. Inform. Theory

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Coding and testing schemes and the corresponding achievable type-II error exponents are presented for binary hypothesis testing over two-hop relay networks. The schemes are based on cascade source coding techniques and unanimous decisionforwarding, the latter meaning that a terminal decides on the null hypothesis only if all previous terminals have decided on the null hypothesis. If the observations at the transmitter, the relay, and the receiver form a Markov chain in this order, then, without loss in performance, the proposed cascade source code can be replaced by two independent point-to-point source codes, one for each hop. The decoupled scheme (combined with decision-forwarding) is shown to attain the optimal type-II error exponents for various instances of "testing against conditional independence." The same decoupling is shown to be optimal also for some instances of "testing against independence," when the observations at the transmitter, the receiver, and the relay form a Markov chain in this order, and when the relay-to-receiver link is of sufficiently high rate. For completeness, the paper also presents an analysis of the Shimokawa-Han-Amari binning scheme for the point-to-point hypothesis testing setup.S. Salehkalaibar is with the In the second part of the manuscript, we focus on two cases: the first is where X n → Y n → Z n forms a Markov chain under both hypotheses, and the second is where X n → Z n → Y n forms a Markov chain under both hypotheses. The first case models an extreme situation where the relay lies in between the transmitter and the receiver, and thus the signals at the sensor and the receiver are conditionally independent given the signal at the relay. In such a situation, the two-hop network models, for example, short-range wireless communication where the sensor's signal only reaches the relay but not the more distant receiver. The second case models a situation where the receiver lies in between the sensor and the relay, and thus the signals at the transmitter and the relay are conditionally independent given the signal at the receiver. In such a situation, the two-hop network models, for example, communication in a cellular system where the relay is a powerful base station and all communication goes through this base station.We show that, in the first case where X n → Y n → Z n , our schemes simplify considerably in the sense that the source coding scheme for the two-hop relay network decouples into two independent point-to-point source coding schemes. In other words, it suffices to send quantization information about X n from the transmitter to the relay and, independently thereof, to send quantization information about Y n from the relay to the receiver (while also employing unanimous decision-forwarding) This contrasts the general scheme where the relay combines the quantization information about X n with its own observation Y n to create some kind of jointly processed quantization information to send to the receiver. The receiver error exponent achieved by the simplified scheme...

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“…However, it is possible that other approaches different from ours can be used to obtain a strong converse theorem for the current problem. For example, it is interesting to explore whether two recently proposed strong converse techniques in [36,37] can be used for this purpose considering the fact that the methods in [36,37] have been successfully applied to problems including the Wyner-Ziv problem [29], the Wyner-Ahlswede-Körner (WAK) problem [26,27] and hypothesis testing problems with communication constraints [38][39][40].…”

Section: Main Contribution and Challengesmentioning

confidence: 99%

Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information

Zhou

Hero

2019

Entropy

Self Cite

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We consider the k-user successive refinement problem with causal decoder side information and derive an exponential strong converse theorem. The rate-distortion region for the problem can be derived as a straightforward extension of the two-user case by Maor and Merhav (2008). We show that for any rate-distortion tuple outside the rate-distortion region of the k-user successive refinement problem with causal decoder side information, the joint excess-distortion probability approaches one exponentially fast. Our proof follows by judiciously adapting the recently proposed strong converse technique by Oohama using the information spectrum method, the variational form of the rate-distortion region and Hölder’s inequality. The lossy source coding problem with causal decoder side information considered by El Gamal and Weissman is a special case ( k = 1 ) of the current problem. Therefore, the exponential strong converse theorem for the El Gamal and Weissman problem follows as a corollary of our result.

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Strong Converse for Hypothesis Testing Against Independence over a Two-Hop Network

Cited by 13 publications

References 22 publications

Distributed Hypothesis Testing With Variable-Length Coding

Distributed Hypothesis Testing With Variable-Length Coding

Hypothesis Testing Over the Two-Hop Relay Network

Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information

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