Maximum Length of Robust Positioning Sequences

Duc Tu Dao; Han Mao Kiah; Hengjia Wei

doi:10.1109/ISIT44484.2020.9174454

Maximum Length of Robust Positioning Sequences

Duc Tu Dao, Han Mao Kiah, Hengjia Wei

Department of Electrical & Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

An (n,d)-robust positioning sequence (RPS) is a binary sequence where every pair of length-n subwords is distance d apart. In this paper, we study the quantity P(n,d), which denotes maximum length of an (n,d)-RPS, and provide tight estimates in the range n/2 < d ≤ n. First, we show that the usual Plotkin bound cannot be attained when certain divisibility conditions hold. Next, using the concept of differences, we construct an infinite family of RPSs that attain a modified Plotkin bound. Finally, except for 16 cases, we determine the exact values of P(n,d) for δ(n) ≤ d ≤ n ≤ 50, where δ(n) = ⌈n/2⌉ if n ≢ 0(mod 4) and δ(n) = (n +2)/2 if n ≡ 0(mod 4).

Original language	English
Title of host publication	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers
Pages	108-113
Number of pages	6
ISBN (Electronic)	9781728164328
DOIs	https://doi.org/10.1109/ISIT44484.2020.9174454
State	Published - 1 Jun 2020
Event	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2020-June
ISSN (Print)	2157-8095

Conference

Conference	2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/Territory	United States
City	Los Angeles
Period	21/07/20 → 26/07/20

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT44484.2020.9174454

Cite this

Dao, D. T., Mao Kiah, H., & Wei, H. (2020). Maximum Length of Robust Positioning Sequences. In 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings (pp. 108-113). Article 9174454 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT44484.2020.9174454

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abstract = "An (n,d)-robust positioning sequence (RPS) is a binary sequence where every pair of length-n subwords is distance d apart. In this paper, we study the quantity P(n,d), which denotes maximum length of an (n,d)-RPS, and provide tight estimates in the range n/2 < d ≤ n. First, we show that the usual Plotkin bound cannot be attained when certain divisibility conditions hold. Next, using the concept of differences, we construct an infinite family of RPSs that attain a modified Plotkin bound. Finally, except for 16 cases, we determine the exact values of P(n,d) for δ(n) ≤ d ≤ n ≤ 50, where δ(n) = ⌈n/2⌉ if n ≢ 0(mod 4) and δ(n) = (n +2)/2 if n ≡ 0(mod 4).",

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Dao, DT, Mao Kiah, H & Wei, H 2020, Maximum Length of Robust Positioning Sequences. in 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings., 9174454, IEEE International Symposium on Information Theory - Proceedings, vol. 2020-June, Institute of Electrical and Electronics Engineers, pp. 108-113, 2020 IEEE International Symposium on Information Theory, ISIT 2020, Los Angeles, United States, 21/07/20. https://doi.org/10.1109/ISIT44484.2020.9174454

Maximum Length of Robust Positioning Sequences. / Dao, Duc Tu; Mao Kiah, Han; Wei, Hengjia.
2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. Institute of Electrical and Electronics Engineers, 2020. p. 108-113 9174454 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Mao Kiah, Han

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N2 - An (n,d)-robust positioning sequence (RPS) is a binary sequence where every pair of length-n subwords is distance d apart. In this paper, we study the quantity P(n,d), which denotes maximum length of an (n,d)-RPS, and provide tight estimates in the range n/2 < d ≤ n. First, we show that the usual Plotkin bound cannot be attained when certain divisibility conditions hold. Next, using the concept of differences, we construct an infinite family of RPSs that attain a modified Plotkin bound. Finally, except for 16 cases, we determine the exact values of P(n,d) for δ(n) ≤ d ≤ n ≤ 50, where δ(n) = ⌈n/2⌉ if n ≢ 0(mod 4) and δ(n) = (n +2)/2 if n ≡ 0(mod 4).

AB - An (n,d)-robust positioning sequence (RPS) is a binary sequence where every pair of length-n subwords is distance d apart. In this paper, we study the quantity P(n,d), which denotes maximum length of an (n,d)-RPS, and provide tight estimates in the range n/2 < d ≤ n. First, we show that the usual Plotkin bound cannot be attained when certain divisibility conditions hold. Next, using the concept of differences, we construct an infinite family of RPSs that attain a modified Plotkin bound. Finally, except for 16 cases, we determine the exact values of P(n,d) for δ(n) ≤ d ≤ n ≤ 50, where δ(n) = ⌈n/2⌉ if n ≢ 0(mod 4) and δ(n) = (n +2)/2 if n ≡ 0(mod 4).

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Maximum Length of Robust Positioning Sequences

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