IEICE TRANSACTIONS on Information
Density of Pooling Matrices vs. Sparsity of Signals for Group Testing Problems
Summary :
In this paper, we consider a group testing (GT) problem. We derive a lower bound on the probability of error for successful decoding of defected binary signals. To this end, we exploit Fano's inequality theorem in the information theory. We show that the probability of error is bounded as an entropy function, a density of a pooling matrix and a sparsity of a binary signal. We evaluate that for decoding of highly sparse signals, the pooling matrix is required to be dense. Conversely, if dense signals are needed to decode, the sparse pooling matrix should be designed to achieve the small probability of error.
- Publication
- IEICE TRANSACTIONS on Information Vol.E102-D No.5 pp.1081-1084
- Publication Date
- 2019/05/01
- Publicized
- 2019/02/04
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.2018EDL8200
- Type of Manuscript
- LETTER
- Category
- Fundamentals of Information Systems
Authors
Jin-Taek SEONG
Mokpo National University
Keyword
Latest Issue
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Jin-Taek SEONG, "Density of Pooling Matrices vs. Sparsity of Signals for Group Testing Problems" in IEICE TRANSACTIONS on Information,
vol. E102-D, no. 5, pp. 1081-1084, May 2019, doi: 10.1587/transinf.2018EDL8200.
Abstract: In this paper, we consider a group testing (GT) problem. We derive a lower bound on the probability of error for successful decoding of defected binary signals. To this end, we exploit Fano's inequality theorem in the information theory. We show that the probability of error is bounded as an entropy function, a density of a pooling matrix and a sparsity of a binary signal. We evaluate that for decoding of highly sparse signals, the pooling matrix is required to be dense. Conversely, if dense signals are needed to decode, the sparse pooling matrix should be designed to achieve the small probability of error.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2018EDL8200/_p
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@ARTICLE{e102-d_5_1081,
author={Jin-Taek SEONG, },
journal={IEICE TRANSACTIONS on Information},
title={Density of Pooling Matrices vs. Sparsity of Signals for Group Testing Problems},
year={2019},
volume={E102-D},
number={5},
pages={1081-1084},
abstract={In this paper, we consider a group testing (GT) problem. We derive a lower bound on the probability of error for successful decoding of defected binary signals. To this end, we exploit Fano's inequality theorem in the information theory. We show that the probability of error is bounded as an entropy function, a density of a pooling matrix and a sparsity of a binary signal. We evaluate that for decoding of highly sparse signals, the pooling matrix is required to be dense. Conversely, if dense signals are needed to decode, the sparse pooling matrix should be designed to achieve the small probability of error.},
keywords={},
doi={10.1587/transinf.2018EDL8200},
ISSN={1745-1361},
month={May},}
Copy
TY - JOUR
TI - Density of Pooling Matrices vs. Sparsity of Signals for Group Testing Problems
T2 - IEICE TRANSACTIONS on Information
SP - 1081
EP - 1084
AU - Jin-Taek SEONG
PY - 2019
DO - 10.1587/transinf.2018EDL8200
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E102-D
IS - 5
JA - IEICE TRANSACTIONS on Information
Y1 - May 2019
AB - In this paper, we consider a group testing (GT) problem. We derive a lower bound on the probability of error for successful decoding of defected binary signals. To this end, we exploit Fano's inequality theorem in the information theory. We show that the probability of error is bounded as an entropy function, a density of a pooling matrix and a sparsity of a binary signal. We evaluate that for decoding of highly sparse signals, the pooling matrix is required to be dense. Conversely, if dense signals are needed to decode, the sparse pooling matrix should be designed to achieve the small probability of error.
ER -
English
