Sequence Reconstruction for Limited-Magnitude Errors

Hengjia Wei, Moshe Schwartz

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by applications to DNA storage, we study reconstruction and list-reconstruction schemes for integer vectors that suffer from limited-magnitude errors. We characterize the asymptotic size of the intersection of error balls in relation to the code’s minimum distance. We also devise efficient reconstruction algorithms for various limited-magnitude error parameter ranges. We then extend these algorithms to the list-reconstruction scheme, and show the trade-off between the asymptotic list size and the number of required channel outputs. These results apply to all codes, without any assumptions on the code structure. Finally, we also study linear reconstruction codes with small intersection, as well as show a connection to list-reconstruction codes for the tandem-duplication channel.

Original languageEnglish
JournalIEEE Transactions on Information Theory
DOIs
StateAccepted/In press - 1 Jan 2022

Keywords

  • Codes
  • DNA
  • Lattices
  • Noise measurement
  • Reconstruction algorithms
  • Reconstruction codes
  • Uncertainty
  • Upper bound
  • integer codes
  • limited-magnitude errors
  • list-reconstruction codes

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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