Aldridge, M orcid.org/0000-0002-9347-1586 (2017) The Capacity of Bernoulli Nonadaptive Group Testing. IEEE Transactions on Information Theory, 63 (11). pp. 7142-7148. ISSN 0018-9448
Abstract
We consider nonadaptive group testing with Bernoulli tests, where each item is placed in each test independently with some fixed probability. We give a tight threshold on the maximum number of tests required to find the defective set under optimal Bernoulli testing. Achievability is given by a result of Scarlett and Cevher; here we give a converse bound showing that this result is best possible. Our new converse requires three parts: a typicality bound generalising the trivial counting bound, a converse on the COMP algorithm of Chan et al., and a bound on the SSS algorithm similar to that given by Aldridge, Baldassini, and Johnson. Our result has a number of important corollaries, in particular that, in denser cases, Bernoulli nonadaptive group testing is strictly worse than the best adaptive strategies.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Nov 2018 12:15 |
Last Modified: | 31 Jan 2019 15:44 |
Status: | Published |
Publisher: | IEEE |
Identification Number: | 10.1109/TIT.2017.2748564 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:138928 |