Correcting charge-constrained errors in the rank-modulation scheme

Anxiao Jiang, Moshe Schwartz, Jehoshua Bruck

Research output: Contribution to journalArticlepeer-review

86 Scopus citations


We investigate error-correcting codes for a the rank-modulation scheme with an application to flash memory devices. In this scheme, a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The resulting scheme eliminates the need for discrete cell levels, overcomes overshoot errors when programming cells (a serious problem that reduces the writing speed), and mitigates the problem of asymmetric errors. In this paper, we study the properties of error-correcting codes for charge-constrained errors in the rank-modulation scheme. In this error model the number of errors corresponds to the minimal number of adjacent transpositions required to change a given stored permutation to another erroneous onea distance measure known as Kendall's τ -distance. We show bounds on the size of such codes, and use metric-embedding techniques to give constructions which translate a wealth of knowledge of codes in the Lee metric to codes over permutations in Kendall's τ-metric. Specifically, the one-error-correcting codes we construct are at least half the ball-packing upper bound.

Original languageEnglish
Article number8
Pages (from-to)2112-2120
Number of pages9
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - 1 May 2010


  • Error-correcting codes
  • Flash memory
  • Kendall's τ-metric
  • Metric embeddings
  • Permutations
  • Rank modulation

ASJC Scopus subject areas

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


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