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Strong converses for group testing in the finite blocklength regime

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Strong converses for group testing in the finite blocklength regime. / Johnson, Oliver.

In: IEEE Transactions on Information Theory, Vol. 63, No. 9, 21.08.2017, p. 5923 - 5933.

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Johnson, O 2017, 'Strong converses for group testing in the finite blocklength regime', IEEE Transactions on Information Theory, vol. 63, no. 9, pp. 5923 - 5933. https://doi.org/10.1109/TIT.2017.2697358

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Johnson, Oliver. / Strong converses for group testing in the finite blocklength regime. In: IEEE Transactions on Information Theory. 2017 ; Vol. 63, No. 9. pp. 5923 - 5933.

Bibtex

@article{596a82bbfe77437eaab16a87324a35c1,
title = "Strong converses for group testing in the finite blocklength regime",
abstract = "We prove new strong converse results in a variety of group testing settings, generalizing a result of Baldassini, Johnson and Aldridge. First, in the non-adaptive case, we mimic the hypothesis testing argument introduced in the finite blocklength channel coding regime by Polyanskiy, Poor and Verdu, and using joint source–channel coding arguments of Kostina and Verdu. In the adaptive case, we combine this approach with a novel model formulation based on causal probability and directed information theory. In both cases, we prove results which are valid for finite sized problems, and imply capacity results in the asymptotic regime. These results are illustrated graphically for a range of models.",
keywords = "Group testing, Converse bounds, Finite block-length, Sparse models",
author = "Oliver Johnson",
year = "2017",
month = "8",
day = "21",
doi = "10.1109/TIT.2017.2697358",
language = "English",
volume = "63",
pages = "5923 -- 5933",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers (IEEE)",
number = "9",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - Strong converses for group testing in the finite blocklength regime

AU - Johnson, Oliver

PY - 2017/8/21

Y1 - 2017/8/21

N2 - We prove new strong converse results in a variety of group testing settings, generalizing a result of Baldassini, Johnson and Aldridge. First, in the non-adaptive case, we mimic the hypothesis testing argument introduced in the finite blocklength channel coding regime by Polyanskiy, Poor and Verdu, and using joint source–channel coding arguments of Kostina and Verdu. In the adaptive case, we combine this approach with a novel model formulation based on causal probability and directed information theory. In both cases, we prove results which are valid for finite sized problems, and imply capacity results in the asymptotic regime. These results are illustrated graphically for a range of models.

AB - We prove new strong converse results in a variety of group testing settings, generalizing a result of Baldassini, Johnson and Aldridge. First, in the non-adaptive case, we mimic the hypothesis testing argument introduced in the finite blocklength channel coding regime by Polyanskiy, Poor and Verdu, and using joint source–channel coding arguments of Kostina and Verdu. In the adaptive case, we combine this approach with a novel model formulation based on causal probability and directed information theory. In both cases, we prove results which are valid for finite sized problems, and imply capacity results in the asymptotic regime. These results are illustrated graphically for a range of models.

KW - Group testing

KW - Converse bounds

KW - Finite block-length

KW - Sparse models

UR - http://arxiv.org/abs/1509.06188

U2 - 10.1109/TIT.2017.2697358

DO - 10.1109/TIT.2017.2697358

M3 - Article

VL - 63

SP - 5923

EP - 5933

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 9

ER -