A Characterization of the Number of Subsequences Obtained via the Deletion Channel

Yuvalal Liron, Michael Langberg

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by the study of deletion channels, this paper presents improved bounds on the number of subsequences obtained from a binary string X of length n under t deletions. It is known that the number of subsequences in this setting strongly depends on the number of runs in the string X; where a run is a maximal substring of the same character. Our improved bounds are obtained by a structural analysis of the family of r-run strings X, an analysis in which we identify the extremal strings with respect to the number of subsequences. Specifically, for every r, we present r-run strings with the minimum (respectively maximum) number of subsequences under any t deletions; we perform an exact analysis of the number of subsequences of these extremal strings; and show that this number can be calculated in polynomial time.

Original languageEnglish
Article number7061929
Pages (from-to)2300-2312
Number of pages13
JournalIEEE Transactions on Information Theory
Volume61
Issue number5
DOIs
StatePublished - 1 May 2015

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

  • Channel coding
  • binary codes
  • error correction codes

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