Codes in permutations and error correction for rank modulation

Alexander Barg, Arya Mazumdar

Research output: Contribution to journalArticlepeer-review

96 Scopus citations

Abstract

Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of n elements equipped with the Kendall tau distance. We derive several lower and upper bounds on the size of codes. These bounds enable us to establish the exact scaling of the size of optimal codes for large values of n. We also show the existence of codes whose size is within a constant factor of the sphere packing bound for any fixed number of errors.

Original languageEnglish (US)
Article number5485013
Pages (from-to)3158-3165
Number of pages8
JournalIEEE Transactions on Information Theory
Volume56
Issue number7
DOIs
StatePublished - Jul 1 2010

Keywords

  • Bose-Chowla theorem
  • Flash memory
  • Inversion
  • Kendall tau distance
  • Permutation codes

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