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arXiv · 1311.7113

Systematic Codes for Rank Modulation

Sarit Buzaglo·Eitan Yaakobi·Tuvi Etzion·Jehoshua Bruck
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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.

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Sarit Buzaglo, Eitan Yaakobi, Tuvi Etzion, Jehoshua Bruck. 2014-04-20. Systematic Codes for Rank Modulation. https://arxiv.org/abs/1311.7113

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