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Correcting Charge-Constrained Errors in the Rank-Modulation Scheme

Jiang, Anxiao (Andrew) and Bruck, Jehoshua and Schwartz, Moshe (2010) Correcting Charge-Constrained Errors in the Rank-Modulation Scheme. IEEE Transactions on Information Theory, 56 (5). pp. 2112-2120. ISSN 0018-9448.

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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 one—a 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.

Item Type:Article
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Bruck, Jehoshua0000-0001-8474-0812
Schwartz, Moshe0000-0002-1449-0026
Additional Information:© 2010 IEEE. Manuscript received April 12, 2009; revised October 07, 2009. Current version published April 21, 2010. This work was supported in part by the NSF CAREER Award CCF-0747415, in part by the NSF Grant ECCS-0802107, in part by the GIF Grant 2179-1785.10/2007, in part by the Caltech Lee Center for Advanced Networking, and in part by an NSF-NRI award. The material in this paper was presented in part at the 2008 IEEE International Symposium on Information Theory, Toronto, Canada, July 2008. The authors would like to thank the anonymous reviewers, who pointed out important previous work, and whose comments helped improve the presentation of the paper.
Funding AgencyGrant Number
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
NSF- Nanoelectronics Research Initiative (NRI)UNSPECIFIED
Subject Keywords:Error-correcting codes; flash memory; Kendall's tau-metric; metric embeddings; permutations; rank modulation
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INSPEC Accession Number11256641
Issue or Number:5
Record Number:CaltechAUTHORS:20100617-092653362
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18718
Deposited By: Tony Diaz
Deposited On:29 Jun 2010 18:28
Last Modified:09 Mar 2020 13:19

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