Codes in permutations and error correction for rank modulation

Authors:
Alexander Barg;Arya Mazumdar
Affiliations:
Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD and Institute for Problems of Information Transmission, Moscow, Russi ...;Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of n elements equipped with the Kendall tau distance. We derive several lower and upper bounds on the size of codes. These bounds enable us to establish the exact scaling of the size of optimal codes for large values of n. We also show the existence of codes whose size is within a constant factor of the sphere packing bound for any fixed number of errors.