Hypothesis test for upper bound on the size of random defective set

Arkadii D'yachkov, Ilya Vorobyev, Nikita Polyanskii, Vladislav Shchukin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)

Abstract

Let 1 ≤ s < t, N ≥ 2 be fixed integers and a complex electronic circuit of size t is said to be an s-active, s ≪ t, and can work as a system block if not more than s elements of the circuit are defective. Otherwise, the circuit is said to be an s-defective and should be replaced by a similar s-active circuit. Suppose that there exists a possibility to run N non-adaptive group tests to check the s-activity of the circuit. As usual, we say that a (disjunctive) group test yields the positive response if the group contains at least one defective element. In this paper, we will interpret the unknown set of defective elements as a random set and discuss upper bounds on the error probability of the hypothesis test for the null hypothesis {H0: the circuit is s-active} versus the alternative hypothesis {H1: the circuit is s-defective}. Along with the conventional decoding algorithm based on the known random set of positive responses and disjunctive s-codes, we consider a T-weight decision rule which is based on the simple comparison of a fixed threshold T, 1 ≤ T < N, with the known random number of positive responses p, 0 ≤ p ≤ N.

Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages978-982
Number of pages5
ISBN (Electronic)9781509040964
DOIs
Publication statusPublished - 9 Aug 2017
Externally publishedYes
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: 25 Jun 201730 Jun 2017

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Conference

Conference2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/TerritoryGermany
CityAachen
Period25/06/1730/06/17

Keywords

  • Disjunctive codes
  • Error exponent
  • Group testing
  • Hypothesis test
  • Maximal error probability
  • Random coding bounds

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