TY - GEN
T1 - Semiquantitative Group Testing in at Most Two Rounds
AU - Cheraghchi, Mahdi
AU - Gabrys, Ryan
AU - Milenkovic, Olgica
N1 - Funding Information:
|Cp2q| ě 2qm and Cp1q ě 2qm ` 1, it folloˇws that |Cp1q X Cˇp2q| ě 1.Lettingc˚PCp1qXCp2q wehaveˇˇyPI:x˚“y˚(ˇˇď ˇ(ˇcc 4γ ´ 1 and ˇ y P I yc˚ ˇ “ 0. By Claim 12, we conclude that x R I. Open Problems. Although only a small gap remains between the lower bound and the actual constructions for the saturation model, many other problems remain open and include: ‚ Extending the nonadaptive and two-round constructions for general quantization thresholds under the SQGT model; ‚ Deriving bounds and test strategies for consecutive de-fective models [26], [27], as these capture the order of arrivals into testing queues; ‚ Addressing generalized binomial SQGT algorithms [28]. Acknowledgment: The work was supported by the NSF grants No. CCF-2006455 and 2107344.
Publisher Copyright:
© 2021 IEEE.
PY - 2021/7/12
Y1 - 2021/7/12
N2 - Semiquantitative group testing (SQGT) is a pooling method in which the test outcomes represent bounded intervals for the number of defectives. Alternatively, it may be viewed as an adder channel with quantized outputs. SQGT represents a natural choice for Covid-19 group testing as it allows for a straightforward interpretation of the cycle threshold values produced by polymerase chain reactions (PCR). Prior work on SQGT did not address the need for adaptive testing with a small number of rounds as required in practice. We propose conceptually simple methods for two-round and nonadaptive SQGT that significantly improve upon existing schemes by using ideas on nonbinary measurement matrices based on expander graphs and list-disjunct matrices.
AB - Semiquantitative group testing (SQGT) is a pooling method in which the test outcomes represent bounded intervals for the number of defectives. Alternatively, it may be viewed as an adder channel with quantized outputs. SQGT represents a natural choice for Covid-19 group testing as it allows for a straightforward interpretation of the cycle threshold values produced by polymerase chain reactions (PCR). Prior work on SQGT did not address the need for adaptive testing with a small number of rounds as required in practice. We propose conceptually simple methods for two-round and nonadaptive SQGT that significantly improve upon existing schemes by using ideas on nonbinary measurement matrices based on expander graphs and list-disjunct matrices.
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U2 - 10.1109/ISIT45174.2021.9518270
DO - 10.1109/ISIT45174.2021.9518270
M3 - Conference contribution
AN - SCOPUS:85115114736
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1973
EP - 1978
BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021
Y2 - 12 July 2021 through 20 July 2021
ER -