Uncertainty in Identification Systems

2019 IEEE International Symposium on Information Theory (ISIT)

2019

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In this paper we revisit the connections of the distributed hypothesis testing against independence (HT) problem with the Wyner-Ahlswede-Körner (WAK) problem and the identification systems (ID). We show that the strong converse for the WAK problem is equivalent to the strong converse for the HT problem via constructive and nonconstructive transformations of codes. As another consequence of the transformation we provide a new exponentially strong converse equivalence statement. Applying the same idea, we prove a new result that the-identification capacity of the ID problem is equal to the maximum-exponent of type II of error in the HT problem when both side compression is allowed.

Section: Introductionmentioning

confidence: 59%

“…A connection between the achievable regions of these two problems has been drawn recently in [19] via the entropy characterization. We first establish the following useful lemma, which is a generalization of [15,Lemma 3]. Lemma 1.…”

Section: Equivalence Between Ht and Identificationmentioning

confidence: 99%

Operational Equivalence of Distributed Hypothesis Testing and Identification Systems

2019 IEEE International Symposium on Information Theory (ISIT)

2019

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“…Strong converse proofs for the identical compression mapping setting in [3] have been given in [35] and [36]. Theorem 10 shows that allowing user-dependent compression mappings does not change the optimal performance of the system in the strong converse sense.…”

Section: Equivalence Between Single-user Ht and Identification Systemsmentioning

confidence: 99%

Hypothesis Testing and Identification Systems

IEEE Trans. Inform. Theory

2021

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We study hypothesis testing problems with fixed compression mappings and with user-dependent compression mappings to decide whether or not an observation sequence is related to one of the users in a database, which contains compressed versions of previously enrolled users' data. We first provide the optimal characterization of the exponent of the probability of the second type of error for the fixed compression mappings scenario when the number of users in the database grows exponentially. We then establish operational equivalence relations between the Wyner-Ahlswede-Körner network, the single-user hypothesis testing problem, the multi-user hypothesis testing problem with userdependent compression mappings and the identification systems with user-dependent compression mappings. These equivalence relations imply the strong converse and exponentially strong converse for the multi-user hypothesis testing and the identification systems both with user-dependent compression mappings. Finally they also show how an identification scheme can be turned into a multi-user hypothesis testing scheme with an explicit transfer of rate and error probability conditions and vice versa.

“…The (conditional) probability of estimation error E es goes to zero by Lemma 1 and 2. Additionally, it can be shown, see [11] for full proof, that if…”

Section: B Proof Of Theoremmentioning

confidence: 99%

“…In [11] we provide an inner bound and an outer bound for the region of the setting with arbitrarily varying observation channel. In the case when compression rate is large enough, both regions coincides.…”

Section: B a Connection To Wyner-ahlswede-körner Networkmentioning

confidence: 99%

Uncertainty in Identification Systems

IEEE Trans. Inform. Theory

et al. 2021

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We study the high-dimensional identification systems under the presence of statistical uncertainties. The task is to design mappings for enrollment and identification purposes. The identification mapping compresses users' information then stores the index in the corresponding position in a database. The identification mapping combines the information in the database and the observation which originates randomly from an enrolled user to produce an estimate of the underlying user index. We study two scenarios. Users' data are generated from the same unknown distribution while the observation channel is also subjected to uncertainty. Each user's data are generated iid from the distribution corresponding to its own state, while the observation channel is known. We provide an achievable compression-identification trade-off for the first and second settings considering both discrete and continuous cases. In the discrete scenario, the described regions are also the correspondingly complete characterizations.