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. doi:10.1109/TIT.2013.2268534. 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.
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| 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. | ||||||||||||||||
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| Subject Keywords: | Flash memory; gray code; local rank modulation; permutations; rank modulation | ||||||||||||||||
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| Issue or Number: | 10 | ||||||||||||||||
| DOI: | 10.1109/TIT.2013.2268534 | ||||||||||||||||
| 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: | 10 Nov 2021 04:36 |
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