Generalized gray codes for local rank modulation

Eyal En Gad, Michael Langberg, Moshe Schwartz, Jehoshua Bruck

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We consider the local rank-modulation scheme, in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. Local rank-modulation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory. We study gray codes for the local rank-modulation scheme in order to simulate conventional multilevel flash cells while retaining the benefits of rank modulation. Unlike the limited scope of previous works, we consider code constructions for the entire range of parameters including the code length, sliding-window size, and overlap between adjacent windows. We show that the presented codes have asymptotically optimal rate. We also provide efficient encoding, decoding, and next-state algorithms.

Original languageEnglish
Article number6531662
Pages (from-to)6664-6673
Number of pages10
JournalIEEE Transactions on Information Theory
Volume59
Issue number10
DOIs
StatePublished - 25 Sep 2013

Keywords

  • Flash memory
  • gray code
  • local rank modulation
  • permutations
  • rank modulation

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