Snake-in-the-Box Codes for Rank Modulation

Yonatan Yehezkeally; Moshe Schwartz

doi:10.1109/tit.2012.2196755

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arXiv · 1107.3372

Snake-in-the-Box Codes for Rank Modulation

Yonatan Yehezkeally·Moshe Schwartz

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Abstract

Motivated by the rank-modulation scheme with applications to flash memory, we consider Gray codes capable of detecting a single error, also known as snake-in-the-box codes. We study two error metrics: Kendall's $\tau$-metric, which applies to charge-constrained errors, and the $\ell_\infty$-metric, which is useful in the case of limited magnitude errors. In both cases we construct snake-in-the-box codes with rate asymptotically tending to 1. We also provide efficient successor-calculation functions, as well as ranking and unranking functions. Finally, we also study bounds on the parameters of such codes.

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Yonatan Yehezkeally, Moshe Schwartz. 2011-07-18. Snake-in-the-Box Codes for Rank Modulation. https://doi.org/10.1109/tit.2012.2196755

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