Combinatorial quantitative group testing with adversarially perturbed measurements
Journal
2020 IEEE Information Theory Workshop, ITW 2020
Date Issued
2021
Author(s)
Li Y.-H
Abstract
In this work, combinatorial quantitative group testing (QGT) with noisy measurements is studied. The goal of QGT is to detect defective items from a data set of size n with counting measurements, each of which counts the number of defects in a selected pool of items. While most literatures consider either probabilistic QGT with random noise or combinatorial QGT with noiseless measurements, our focus is on the combinatorial QGT with noisy measurements that might be adversarially perturbed by additive bounded noises. Since perfect detection is impossible, a partial detection criterion is adopted. With the adversarial noise being bounded by dn = Θ(nδ) and the detection criterion being to ensure no more than kn = Θ(nκ) errors can be made, our goal is to characterize the fundamental limit on the number of measurement, termed pooling complexity, as well as provide explicit construction of measurement plans with optimal pooling complexity and efficient decoding algorithms. We first show that 1 the fundamental limit is 1?2δ lognn to within a constant factor not depending on (n, κ, δ) for the non-adaptive setting when 0 < 2δ ? κ < 1, sharpening the previous result by Chen and Wang [1]. We also provide deterministic constructions of 1 an adaptive method with 1?2δ logn2 n pooling complexity up to a constant factor and O(n) decoding complexity. An extended version of this paper is accessible at: http://homepage.ntu.edu.tw/~ihwang/Eprint/itw20cqgt.pdf ? 2021 IEEE.
Subjects
Defects
Adaptive setting
Constant factors
Decoding algorithm
Decoding complexity
Detection criteria
Explicit constructions
Extended versions
Noisy measurements
Decoding
SDGs
Type
conference paper