English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper considers the problem of Quantitative Group Testing (QGT) wherethere are some defective items among a large population of $N$ items. Weconsider the scenario in which each item is defective with probability $K/N$,independently from the other items. In the QGT problem, the goal is to identifyall or a sufficiently large fraction of the defective items by testing groupsof items, with the minimum possible number of tests. In particular, the outcomeof each test is a non-negative integer which indicates the number of defectiveitems in the tested group. In this work, we propose a non-adaptive QGT schemefor the underlying randomized model for defective items, which utilizes sparsegraph codes over irregular bipartite graphs with optimized degree profiles onthe left nodes of the graph as well as binary $t$-error-correcting BCH codes.We show that in the sub-linear regime, i.e., when the ratio $K/N$ vanishes as$N$ grows unbounded, the proposed scheme with ${m=c(t,d)K(t\log (\frac{\ellN}{c(t,d)K}+1)+1)}$ tests can identify all the defective items with probabilityapproaching $1$, where $d$ and $\ell$ are the maximum and average left degree,respectively, and $c(t,d)$ depends only on $t$ and $d$ (and does not depend on$K$ and $N$). For any $t\leq 4$, the testing and recovery algorithms of theproposed scheme have the computational complexity of $\mathcal{O}(N\log\frac{N}{K})$ and $\mathcal{O}(K\log \frac{N}{K})$, respectively. The proposedscheme outperforms two recently proposed non-adaptive QGT schemes for thesub-linear regime, including our scheme based on regular bipartite graphs andthe scheme of Gebhard et al., in terms of the number of tests required toidentify all defective items with high probability.

Non-adaptive Quantitative Group Testing Using Irregular Sparse Graph Codes