Threshold Disjunctive Codes
A.G. D'yachkov, I.V. Vorobyev, N.A. Polyanskii, V.Yu. Shchukin

TL;DR
This paper introduces threshold disjunctive codes for efficient non-adaptive group testing to determine the number of defective elements in a circuit using minimal tests and simple threshold-based decision.
Contribution
It defines a new class of disjunctive codes called threshold disjunctive codes and explores their constructions and bounds on their rate.
Findings
Proposes threshold disjunctive codes for group testing.
Provides constructions of suboptimal threshold disjunctive codes.
Derives random coding bounds on the rate of these codes.
Abstract
Let , be integers and a complex electronic circuit of size is said to be an -active, , and can work as a system block if not more than elements of the circuit are defective. Otherwise, the circuit is said to be an -defective and should be substituted for the similar -active circuit. Suppose that there exists a possibility to check the -activity of the circuit using non-adaptive group tests identified by a conventional disjunctive -code of size~ and length~. As usually, we say that any group test yields the positive response if the group contains at least one defective element. In this case, there is no any interest to look for the defective elements. We need to decide on the number of the defective elements in the circuit without knowing the code~. In addition, the decision has the minimal possible complexity…
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Taxonomy
TopicsAdvanced biosensing and bioanalysis techniques · SARS-CoV-2 detection and testing · Biosensors and Analytical Detection
