Set-Codes with Small Intersections and Small Discrepancies

Ryan Gabrys, H. Dau, C. J. Colbourn, O. Milenkovic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We are concerned with the problem of designing large families of subsets over a common labeled ground set that have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the sets is less than or equal to one. Our results, based on transversal designs, factorizations of packings and Latin rectangles, show that by jointly constructing the sets and labeling scheme, one can achieve optimal family sizes for many parameter choices. Probabilistic arguments akin to those used for pseudorandom generators lead to significantly suboptimal results when compared to the proposed combinatorial methods. The design problem considered is motivated by applications in molecular data storage.

Original languageEnglish (US)
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2359-2363
Number of pages5
ISBN (Electronic)9781538692912
DOIs
StatePublished - Jul 2019
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: Jul 7 2019Jul 12 2019

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
CountryFrance
CityParis
Period7/7/197/12/19

Fingerprint

Discrepancy
Intersection
Transversal Design
Factorization
Labeling
Labeling Scheme
Pseudorandom Generator
Labels
Data Storage
Less than or equal to
Data storage equipment
Rectangle
Packing
Pairwise
Subset
Family
Design

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

Cite this

Gabrys, R., Dau, H., Colbourn, C. J., & Milenkovic, O. (2019). Set-Codes with Small Intersections and Small Discrepancies. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 2359-2363). [8849651] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849651

Set-Codes with Small Intersections and Small Discrepancies. / Gabrys, Ryan; Dau, H.; Colbourn, C. J.; Milenkovic, O.

2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 2359-2363 8849651 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Gabrys, R, Dau, H, Colbourn, CJ & Milenkovic, O 2019, Set-Codes with Small Intersections and Small Discrepancies. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849651, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 2359-2363, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 7/7/19. https://doi.org/10.1109/ISIT.2019.8849651
Gabrys R, Dau H, Colbourn CJ, Milenkovic O. Set-Codes with Small Intersections and Small Discrepancies. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 2359-2363. 8849651. (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2019.8849651
Gabrys, Ryan ; Dau, H. ; Colbourn, C. J. ; Milenkovic, O. / Set-Codes with Small Intersections and Small Discrepancies. 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 2359-2363 (IEEE International Symposium on Information Theory - Proceedings).
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