Correcting limited-magnitude errors in the rank-modulation scheme

Itzhak Tamo*, Moshe Schwartz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study error-correcting codes for permutations under the infinity norm, motivated by a novel storage scheme for flash memories called rank modulation. In this scheme, a set of n flash cells are combined to create a single virtual multilevel cell. Information is stored in the permutation induced by the cell charge levels. Spike errors, which are characterized by a limited-magnitude change in cell charge levels, correspond to a low-distance change under the infinity norm. We define codes protecting against spike errors, called limited-magnitude rank-modulation codes (LMRM codes), and present several constructions for these codes, some resulting in optimal codes. These codes admit simple recursive, and sometimes direct, encoding and decoding procedures.We also provide lower and upper bounds on the maximal size of LMRM codes both in the general case, and in the case where the codes form a subgroup of the symmetric group. In the asymptotic analysis, the codes we construct outperform the Gilbert-Varshamov-like bound estimate.

Original languageEnglish
Article number2046241
Pages (from-to)2551-2560
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Jun 2010
Externally publishedYes


  • Asymmetric channel
  • Flash memory
  • Infinity norm
  • Permutation arrays
  • Rank modulation
  • Subgroup codes


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