Rank modulation for flash memories

Anxiao Jiang, Robert Mateescu, Mosche Schwartz, Jehoshua Bruck

Research output: Contribution to journalArticlepeer-review

196 Scopus citations


We explore a novel data representation scheme for multilevel flash memory cells, in which a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The only allowed charge-placement mechanism is a "push-to-the-top"operation, which takes a single cell of the set and makes it the top-charged cell. The resulting scheme eliminates the need for discrete cell levels, as well as overshoot errors, when programming cells. We present unrestricted Gray codes spanning all possible n-cell states and using only "push-to-the-top" operations, and also construct balanced Gray codes. One important application of the Gray codes is the realization of logic multilevel cells, which is useful in conventional storage solutions. We also investigate rewriting schemes for random data modification.We present both an optimal scheme for the worst case rewrite performance and an approximation scheme for the average-case rewrite performance.

Original languageEnglish
Pages (from-to)2659-2673
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - 17 Jun 2009


  • Asymmetric channel
  • Flash memory
  • Gray codes
  • Permutations
  • Rank modulation

ASJC Scopus subject areas

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


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