The aim of this paper is to show an upper bound for finding defective samples in a group testing framework. To this end, we exploit minimization of Hamming weights in coding theory and define probability of error for our decoding scheme. We derive a new upper bound on the probability of error. We show that both upper and lower bounds coincide with each other at an optimal density ratio of a group matrix. We conclude that as defective rate increases, a group matrix should be sparser to find defective samples with only a small number of tests.
Jin-Taek SEONG
Mokpo National University
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Jin-Taek SEONG, "A New Upper Bound for Finding Defective Samples in Group Testing" in IEICE TRANSACTIONS on Information,
vol. E103-D, no. 5, pp. 1164-1167, May 2020, doi: 10.1587/transinf.2019EDL8187.
Abstract: The aim of this paper is to show an upper bound for finding defective samples in a group testing framework. To this end, we exploit minimization of Hamming weights in coding theory and define probability of error for our decoding scheme. We derive a new upper bound on the probability of error. We show that both upper and lower bounds coincide with each other at an optimal density ratio of a group matrix. We conclude that as defective rate increases, a group matrix should be sparser to find defective samples with only a small number of tests.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2019EDL8187/_p
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@ARTICLE{e103-d_5_1164,
author={Jin-Taek SEONG, },
journal={IEICE TRANSACTIONS on Information},
title={A New Upper Bound for Finding Defective Samples in Group Testing},
year={2020},
volume={E103-D},
number={5},
pages={1164-1167},
abstract={The aim of this paper is to show an upper bound for finding defective samples in a group testing framework. To this end, we exploit minimization of Hamming weights in coding theory and define probability of error for our decoding scheme. We derive a new upper bound on the probability of error. We show that both upper and lower bounds coincide with each other at an optimal density ratio of a group matrix. We conclude that as defective rate increases, a group matrix should be sparser to find defective samples with only a small number of tests.},
keywords={},
doi={10.1587/transinf.2019EDL8187},
ISSN={1745-1361},
month={May},}
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TY - JOUR
TI - A New Upper Bound for Finding Defective Samples in Group Testing
T2 - IEICE TRANSACTIONS on Information
SP - 1164
EP - 1167
AU - Jin-Taek SEONG
PY - 2020
DO - 10.1587/transinf.2019EDL8187
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E103-D
IS - 5
JA - IEICE TRANSACTIONS on Information
Y1 - May 2020
AB - The aim of this paper is to show an upper bound for finding defective samples in a group testing framework. To this end, we exploit minimization of Hamming weights in coding theory and define probability of error for our decoding scheme. We derive a new upper bound on the probability of error. We show that both upper and lower bounds coincide with each other at an optimal density ratio of a group matrix. We conclude that as defective rate increases, a group matrix should be sparser to find defective samples with only a small number of tests.
ER -