TY - GEN

T1 - Hypothesis test for upper bound on the size of random defective set

AU - D'yachkov, Arkadii

AU - Vorobyev, Ilya

AU - Polyanskii, Nikita

AU - Shchukin, Vladislav

PY - 2017/8/9

Y1 - 2017/8/9

N2 - Let 1 ≤ s < t, N ≥ 2 be fixed integers and a complex electronic circuit of size t is said to be an s-active, s ≪ t, and can work as a system block if not more than s elements of the circuit are defective. Otherwise, the circuit is said to be an s-defective and should be replaced by a similar s-active circuit. Suppose that there exists a possibility to run N non-adaptive group tests to check the s-activity of the circuit. As usual, we say that a (disjunctive) group test yields the positive response if the group contains at least one defective element. In this paper, we will interpret the unknown set of defective elements as a random set and discuss upper bounds on the error probability of the hypothesis test for the null hypothesis {H0: the circuit is s-active} versus the alternative hypothesis {H1: the circuit is s-defective}. Along with the conventional decoding algorithm based on the known random set of positive responses and disjunctive s-codes, we consider a T-weight decision rule which is based on the simple comparison of a fixed threshold T, 1 ≤ T < N, with the known random number of positive responses p, 0 ≤ p ≤ N.

AB - Let 1 ≤ s < t, N ≥ 2 be fixed integers and a complex electronic circuit of size t is said to be an s-active, s ≪ t, and can work as a system block if not more than s elements of the circuit are defective. Otherwise, the circuit is said to be an s-defective and should be replaced by a similar s-active circuit. Suppose that there exists a possibility to run N non-adaptive group tests to check the s-activity of the circuit. As usual, we say that a (disjunctive) group test yields the positive response if the group contains at least one defective element. In this paper, we will interpret the unknown set of defective elements as a random set and discuss upper bounds on the error probability of the hypothesis test for the null hypothesis {H0: the circuit is s-active} versus the alternative hypothesis {H1: the circuit is s-defective}. Along with the conventional decoding algorithm based on the known random set of positive responses and disjunctive s-codes, we consider a T-weight decision rule which is based on the simple comparison of a fixed threshold T, 1 ≤ T < N, with the known random number of positive responses p, 0 ≤ p ≤ N.

KW - Disjunctive codes

KW - Error exponent

KW - Group testing

KW - Hypothesis test

KW - Maximal error probability

KW - Random coding bounds

UR - http://www.scopus.com/inward/record.url?scp=85034018404&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8006674

DO - 10.1109/ISIT.2017.8006674

M3 - Conference contribution

AN - SCOPUS:85034018404

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 978

EP - 982

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

Y2 - 25 June 2017 through 30 June 2017

ER -