An improvement to Levenshtein's upper bound on the cardinality of deletion correcting codes

Daniel Cullina, Negar Kiyavash

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

We consider deletion correcting codes over a q-ary alphabet. It is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions. To obtain asymptotic upper bounds on code size, we apply a packing argument to channels that perform different mixtures of insertions and deletions. Even though the set of codes is identical for all of these channels, the bounds that we obtain vary. Prior to this work, only the bounds corresponding to the all insertion case and the all deletion case were known. We recover these as special cases. The bound from the all deletion case, due to Levenshtein, has been the best known for more than forty five years. Our generalized bound is better than Levenshtein's bound whenever the number of deletions to be corrected is larger than the alphabet size.

Original languageEnglish (US)
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages699-703
Number of pages5
DOIs
StatePublished - Dec 19 2013
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: Jul 7 2013Jul 12 2013

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Other

Other2013 IEEE International Symposium on Information Theory, ISIT 2013
CountryTurkey
CityIstanbul
Period7/7/137/12/13

Fingerprint

Deletion
Cardinality
Upper bound
Case Deletion
Insertion
Packing
Vary

All Science Journal Classification (ASJC) codes

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

Cite this

Cullina, D., & Kiyavash, N. (2013). An improvement to Levenshtein's upper bound on the cardinality of deletion correcting codes. In 2013 IEEE International Symposium on Information Theory, ISIT 2013 (pp. 699-703). [6620316] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2013.6620316
Cullina, Daniel ; Kiyavash, Negar. / An improvement to Levenshtein's upper bound on the cardinality of deletion correcting codes. 2013 IEEE International Symposium on Information Theory, ISIT 2013. 2013. pp. 699-703 (IEEE International Symposium on Information Theory - Proceedings).
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Cullina, D & Kiyavash, N 2013, An improvement to Levenshtein's upper bound on the cardinality of deletion correcting codes. in 2013 IEEE International Symposium on Information Theory, ISIT 2013., 6620316, IEEE International Symposium on Information Theory - Proceedings, pp. 699-703, 2013 IEEE International Symposium on Information Theory, ISIT 2013, Istanbul, Turkey, 7/7/13. https://doi.org/10.1109/ISIT.2013.6620316

An improvement to Levenshtein's upper bound on the cardinality of deletion correcting codes. / Cullina, Daniel; Kiyavash, Negar.

2013 IEEE International Symposium on Information Theory, ISIT 2013. 2013. p. 699-703 6620316 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Cullina D, Kiyavash N. An improvement to Levenshtein's upper bound on the cardinality of deletion correcting codes. In 2013 IEEE International Symposium on Information Theory, ISIT 2013. 2013. p. 699-703. 6620316. (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2013.6620316