## Converse Bounds for Noisy Group Testing with Arbitrary Measurement Matrices

We consider the group testing problem, in which one seeks to identify a subset of defective items within a larger set of items based on a number of noisy tests. While matching achievability and converse bounds are known in several cases of interest for i.i.d.~measurement matrices, less is known regarding converse bounds for arbitrary measurement matrices. We address this by presenting two converse bounds for arbitrary matrices and general noise models. First, we provide a strong converse bound ($\mathbb{P}[\mathrm{error}] \to 1$) that matches existing achievability bounds in several cases of interest. Second, we provide a weak converse bound ($\mathbb{P}[\mathrm{error}] \not\to 0$) that matches existing achievability bounds in greater generality.

Published in:
2016 Ieee International Symposium On Information Theory, 2868-2872
Presented at:
International Symposium on Information Theory (ISIT), Barcelona, July 10-15, 2016
Year:
2016
Publisher:
New York, Ieee
ISBN:
978-1-5090-1806-2
Keywords:
Laboratories: