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http://dx.doi.org/10.17661/jkiiect.2018.11.5.572

A Lower Bound for Performance of Group Testing Problems  

Seong, Jin-Taek (Department of Convergence Software, Mokpo National University)
Publication Information
The Journal of Korea Institute of Information, Electronics, and Communication Technology / v.11, no.5, 2018 , pp. 572-578 More about this Journal
Abstract
This paper considers Group Testing as one of combinatorial problems. The group testing first began to inspect soldier's syphilis infection during World War II and have long established an academic basis. Recently, there has been much interest in related areas because of the rediscovery of the value of the group testing. The group testing is the same as finding a few defect samples out of a large number of samples, which is similar to the inverse problem of Compressed Sensing. In this paper, we introduce the definition of the group testing, and specify the classes of the group testing and the bounds on performance of the group testing. In addition, we show a lower bound for the number of tests required to find defective samples using the theoretical theorem which is mainly used for relationship between conditional entropy and the probability of error in the information theory. We see how our result can be different from other related results.
Keywords
Compressed Sensing; Fano's Inequality; Group Testing; Lower Bound; Probability of Error;
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