Adaptive group testing as channel coding with feedback

TL;DR

This paper establishes that adaptive group testing, where tests can be designed based on previous outcomes, does not significantly reduce the number of tests needed compared to nonadaptive testing, using information theory techniques.

Contribution

It provides the first information theoretic bounds for adaptive group testing, showing that adaptivity offers limited benefits in reducing the number of tests.

Findings

Adaptive testing does not significantly lower the number of tests needed.

The lower bounds for adaptive and nonadaptive testing are essentially the same.

Techniques from channel coding with feedback are applied to group testing.

Abstract

Group testing is the combinatorial problem of identifying the defective items in a population by grouping items into test pools. Recently, nonadaptive group testing - where all the test pools must be decided on at the start - has been studied from an information theory point of view. Using techniques from channel coding, upper and lower bounds have been given on the number of tests required to accurately recover the defective set, even when the test outcomes can be noisy. In this paper, we give the first information theoretic result on adaptive group testing - where the outcome of previous tests can influence the makeup of future tests. We show that adaptive testing does not help much, as the number of tests required obeys the same lower bound as nonadaptive testing. Our proof uses similar techniques to the proof that feedback does not improve channel capacity.