Balanced de Bruijn Sequences

Sagi Marcovich, Tuvi Etzion, Eitan Yaakobi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The de Bruijn graph and its sequences have found many diverse applications in information theory as well as other areas of computer science and engineering such as interconnection networks, VLSI decomposition, and most recently in DNA storage. Binary balanced sequences have also been a subject to a large research during the last forty years with various applications and a lot of interest in information theory. There have been some works on classification of balanced sequences mainly based on their spectral-null order. This work generalizes the concept of de Bruijn sequences, based on the de Bruijn graph of order \ell, where each edge is multiplied to a fixed number of multiple edges. This implies that in the sequences derived from the generalized graph each l-tuple has the same multiplicity. Using this generalization we form an interesting hierarchy between balanced sequences. Furthermore, another hierarchy is given by the derivatives of balanced sequences. Enumeration for each such family of sequences and efficient encoding and decoding algorithms are also provided.

Original languageEnglish
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
Pages1528-1533
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - 12 Jul 2021
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: 12 Jul 202120 Jul 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2021-July

Conference

Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/TerritoryAustralia
CityVirtual, Melbourne
Period12/07/2120/07/21

All Science Journal Classification (ASJC) codes

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

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