On Finding a Subset of Non-Defective Item From a Large Population

Sharma, Abhay and Murthy, Chandra R (2018) On Finding a Subset of Non-Defective Item From a Large Population. In: IEEE TRANSACTIONS ON SIGNAL PROCESSING, 66 (21). pp. 5762-5775.

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Abstract

In this paper, we derive mutual information based upper bounds on the number of nonadaptive group tests required to identify a given number of ``non-defective'' items from a large population containing a small number of ``defective'' items. In the asymptotic regime with the population size N -> infinity, to identify L nondefective items out of a population containing K defective items, our results show that CsK/1-o(1) (Phi(alpha(0), beta(0)) o(1)) measurements are sufficient when the tests are reliable. Here, C-s is a constant independent of N, K, and L, and Phi(alpha(0), beta(0)) is a bounded function of alpha(0) (sic) lim(N ->infinity) L/N - K and beta(0) (sic) lim(N ->infinity) K/N - K. In contrast, the necessary number of tests using the conventional approach of first identifying the K defective items and picking the required number of nondefective items from the complement set grows with N as O (K log N). We also derive upper bounds on the number of tests under both dilutionand additive noise models. Our results are obtained under a very general sparse signal model, by virtue of which, they are also applicable to other important sparse signal based applications such as compressive sensing.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON SIGNAL PROCESSING
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	Copy right for this article belong to Copy right for this article belong to
Keywords:	Sparse signal models; nonadaptive group testing; inactive subset recovery
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	22 Oct 2018 15:03
Last Modified:	22 Oct 2018 15:03
URI:	http://eprints.iisc.ac.in/id/eprint/60926

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