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Generalized Gray Codes for Local Rank Modulation

En Gad, Eyal and Langberg, Michael and Schwartz, Moshe and Bruck, Jehoshua (2013) Generalized Gray Codes for Local Rank Modulation. IEEE Transactions on Information Theory, 59 (10). pp. 6664-6673. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:20131017-105937816

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Abstract

We consider the local rank-modulation scheme, in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. Local rank-modulation is a generalization of the rank-modulation scheme, which has been recently suggested as a way of storing information in flash memory. We study gray codes for the local rank-modulation scheme in order to simulate conventional multilevel flash cells while retaining the benefits of rank modulation. Unlike the limited scope of previous works, we consider code constructions for the entire range of parameters including the code length, sliding-window size, and overlap between adjacent windows. We show that the presented codes have asymptotically optimal rate. We also provide efficient encoding, decoding, and next-state algorithms.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/TIT.2013.2268534 DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6531662PublisherArticle
http://arxiv.org/abs/1103.0317arXivDiscussion Paper
ORCID:
AuthorORCID
Langberg, Michael0000-0002-7470-0718
Schwartz, Moshe0000-0002-1449-0026
Bruck, Jehoshua0000-0001-8474-0812
Additional Information:© 2013 IEEE. Manuscript received February 17, 2013; revised June 09, 2013; accepted June 11, 2013. Date of publication June 13, 2013; date of current version September 11, 2013. This work was supported in part by the ISF Grant 134/10, in part by the ISF Grant 480/08, in part by the Open University of Israel’s Research Fund under Grant 46114, in part by the NSF under Grant ECCS-0802107, in part by the NSF under Grant CIF-1218005, in part by the United States–Israel Binational Science Foundation (BSF) under Grant 2010075, and in part by a gift from Northrop Grumman. The authors would like to thank the Associate Editor and the anonymous reviewers, whose comments helped improve the presentation of this paper.
Funders:
Funding AgencyGrant Number
Israeli Science Foundation134/10
Israeli Science Foundation480/08
Open University of Israel46114
NSFECCS-0802107
NSFCIF-1218005
Binational Science Foundation (USA-Israel)2010075
Northrop GrummanUNSPECIFIED
Subject Keywords:Flash memory; gray code; local rank modulation; permutations; rank modulation
Other Numbering System:
Other Numbering System NameOther Numbering System ID
INSPEC Accession Number13767515
Issue or Number:10
Record Number:CaltechAUTHORS:20131017-105937816
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20131017-105937816
Official Citation:En Gad, E.; Langberg, M.; Schwartz, M.; Bruck, J., "Generalized Gray Codes for Local Rank Modulation," Information Theory, IEEE Transactions on , vol.59, no.10, pp.6664,6673, Oct. 2013 doi: 10.1109/TIT.2013.2268534
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41969
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Oct 2013 21:05
Last Modified:09 Mar 2020 13:19

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