Correcting Limited-Magnitude Errors in the Rank-Modulation Scheme

Itzhak Tamo, Moshe Schwartz

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We study error-correcting codes for permutations under the infinity norm, motivated the rank-modulation scheme for flash memories. In this scheme, a set of n flash cells are combined to create a single virtual multi-level 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 out-perform the Gilbert-Varshamov- like bound estimate.

Original languageEnglish
Title of host publication2010 Information Theory and Applications Workshop, ITA 2010 - Conference Proceedings
Number of pages2
StatePublished - 31 May 2010
Event2010 Information Theory and Applications Workshop, ITA 2010 - San Diego, CA, United States
Duration: 31 Jan 20105 Feb 2010


Conference2010 Information Theory and Applications Workshop, ITA 2010
Country/TerritoryUnited States
CitySan Diego, CA

ASJC Scopus subject areas

  • Computer Science Applications
  • Information Systems


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