Snake-in-the-Box Codes for Rank Modulation
Information Theory
2020-07-01 v1 math.IT
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 -metric, which applies to charge-constrained errors, and the -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.
Cite
@article{arxiv.1107.3372,
title = {Snake-in-the-Box Codes for Rank Modulation},
author = {Yonatan Yehezkeally and Moshe Schwartz},
journal= {arXiv preprint arXiv:1107.3372},
year = {2020}
}