Robust positioning patterns with low redundancy

• Main Authors: Chee, Yeow Meng, Dao, Duc Tu, Kiah, Han Mao, Ling, San, Wei, Hengjia
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2020
• Subjects: Science::Mathematics; Robust Positioning Patterns; Gray Codes
• Online Access: https://hdl.handle.net/10356/145046
• Institution: Nanyang Technological University

A robust positioning pattern is a large array that allows a mobile device to locate its position by reading a possibly corrupted small window around it. In this paper, we provide constructions of binary positioning patterns, equipped with efficient locating algorithms, that are robust to a constant number of errors and have redundancy within a constant factor of optimality. Furthermore, we modify our constructions to correct rank errors and obtain binary positioning patterns robust to any errors of rank less than a constant number. Additionally, we construct $q$-ary robust positioning sequences robust to a large number of errors, some of which have length attaining the upper bound. Our construction of binary positioning sequences that are robust to a constant number of errors has the least known redundancy among those explicit constructions with efficient locating algorithms. On the other hand, for binary robust positioning arrays, our construction is the first explicit construction whose redundancy is within a constant factor of optimality. The locating algorithms accompanying both constructions run in time cubic in sequence length or array dimension.