The capacity of non-identical adaptive group testing

TL;DR

This paper analyzes a group testing algorithm tailored for items with non-uniform defect probabilities, demonstrating near-optimal performance and providing bounds on testing efficiency, with applications in spectrum allocation for cognitive radios.

Contribution

It introduces and analyzes a novel adaptive group testing algorithm for non-identical defect probabilities, establishing conditions for near-optimal information-theoretic capacity.

Findings

Algorithm achieves near-optimal capacity under certain conditions

Concentration results bound additional testing requirements

Applicable to spectrum allocation with prior information

Abstract

We consider the group testing problem, in the case where the items are defective independently but with non-constant probability. We introduce and analyse an algorithm to solve this problem by grouping items together appropriately. We give conditions under which the algorithm performs essentially optimally in the sense of information-theoretic capacity. We use concentration of measure results to bound the probability that this algorithm requires many more tests than the expected number. This has applications to the allocation of spectrum to cognitive radios, in the case where a database gives prior information that a particular band will be occupied.