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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

Jin-Taek SEONG

Mokpo National University

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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},}

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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 -