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.
Bibliographical noteFunding Information:
Manuscript received August 27, 2009; revised March 27, 2010. Current version published June 16, 2010. Research supported in part by NSF grants CCF0830699, CCF0635271, and DMS0807411. A. Barg is with the Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20742 USA, and also with the Institute for Problems of Information Transmission, Moscow, Russia (e-mail: email@example.com). A. Mazumdar is with the Department of Electrical and Computer Engineering and Institute for Systems Research, University of Maryland, College Park, MD 20742 USA (e-mail firstname.lastname@example.org). Communicated by M. Blaum, Associate Editor for Coding Theory. Digital Object Identifier 10.1109/TIT.2010.2048455
- Bose-Chowla theorem
- Flash memory
- Kendall tau distance
- Permutation codes