Systematic Codes for Rank Modulation

Creators: Buzaglo, Sarit; Yaakobi, Eitan; Etzion, Tuvi; Bruck, Jehosua

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Abstract

The goal of this paper is to construct systematic error-correcting codes for permutations and multi permutations in the Kendall's τ-metric. These codes are important in new applications such as rank modulation for flash memories. The construction is based on error-correcting codes for multi-permutations and a partition of the set of permutations into error-correcting codes. For a given large enough number of information symbols k, and for any integer t, we present a construction for (k + r, k) systematic t-error-correcting codes, for permutations from S_(k+r), with less redundancy symbols than the number of redundancy symbols in the codes of the known constructions. In particular, for a given t and for sufficiently large k we can obtain r = t+1. The same construction is also applied to obtain related systematic error-correcting codes for multi-permutations.

Additional Information

Submitted on 27 Nov 2013 (v1), last revised 20 Apr 2014 (this version, v3) The work of Sarit Buzaglo and Tuvi Etzion was supported in part by the U.S.-Israel Binational Science Foundation, Jerusalem, Israel, under Grant No. 2012016. The work of Eitan Yaakobi and Jehoshua Bruck was supported in part by Intellectual Ventures and an NSF grant CIF-1218005 and in part by the U.S.-Israel Binational Science Foundation, Jerusalem, Israel, under Grant No. 2010075. The work of Eitan Yaakobi was done while he was with the Electrical Engineering Department, California Institute of Technology, Pasadena, CA 91125, U.S.A.

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