TY - JOUR
T1 - Snake-in-the-box codes for rank modulation
AU - Yehezkeally, Yonatan
AU - Schwartz, Moshe
N1 - Funding Information:
Manuscript received July 18, 2011; revised January 25, 2012 and April 16, 2012; accepted April 16, 2012. Date of publication April 27, 2012; date of current version July 10, 2012. This work was supported in part by the Israel Science Foundation under Grant 134/10. This paper was presented in part at the 2012 IEEE International Symposium on Information Theory.
PY - 2012/7/23
Y1 - 2012/7/23
N2 - 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.
AB - 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.
KW - Flash memory
KW - permutations
KW - rank modulation
KW - snake-in-the-box codes
UR - http://www.scopus.com/inward/record.url?scp=84863897273&partnerID=8YFLogxK
U2 - 10.1109/TIT.2012.2196755
DO - 10.1109/TIT.2012.2196755
M3 - Article
AN - SCOPUS:84863897273
SN - 0018-9448
VL - 58
SP - 5471
EP - 5483
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 8
M1 - 6191350
ER -