TY - GEN

T1 - Maximum Length of Robust Positioning Sequences

AU - Dao, Duc Tu

AU - Mao Kiah, Han

AU - Wei, Hengjia

N1 - Publisher Copyright:
© 2020 IEEE.

PY - 2020/6/1

Y1 - 2020/6/1

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).

UR - http://www.scopus.com/inward/record.url?scp=85090400405&partnerID=8YFLogxK

U2 - 10.1109/ISIT44484.2020.9174454

DO - 10.1109/ISIT44484.2020.9174454

M3 - Conference contribution

AN - SCOPUS:85090400405

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 108

EP - 113

BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings

PB - Institute of Electrical and Electronics Engineers

T2 - 2020 IEEE International Symposium on Information Theory, ISIT 2020

Y2 - 21 July 2020 through 26 July 2020

ER -