Duplication-correcting codes

Andreas Lenz, Antonia Wachter-Zeh, Eitan Yaakobi

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

In this work, we propose constructions that correct duplications of multiple consecutive symbols. These errors are known as tandem duplications, where a sequence of symbols is repeated; respectively as palindromic duplications, where a sequence is repeated in reversed order. We compare the redundancies of these constructions with code size upper bounds that are obtained from sphere packing arguments. Proving that an upper bound on the code cardinality for tandem deletions is also an upper bound for inserting tandem duplications, we derive the bounds based on this special tandem deletion error as this results in tighter bounds. Our upper bounds on the cardinality directly imply lower bounds on the redundancy which we compare with the redundancy of the best known construction correcting arbitrary burst insertions. Our results indicate that the correction of palindromic duplications requires more redundancy than the correction of tandem duplications and both significantly less than arbitrary burst insertions.

Original languageEnglish
Pages (from-to)277-298
Number of pages22
JournalDesigns, Codes, and Cryptography
Volume87
Issue number2-3
DOIs
StatePublished - 15 Mar 2019

Keywords

  • Burst insertions/deletions
  • Combinatorial channel
  • DNA storage
  • Duplication errors
  • Error-correcting codes
  • Generalized sphere packing bound

Fingerprint

Dive into the research topics of 'Duplication-correcting codes'. Together they form a unique fingerprint.

Cite this