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Constant-Weight Gray Codes for Local Rank Modulation

En Gad, Eyal and Langberg, Michael and Schwartz, Moshe and Bruck, Jehoshua (2010) Constant-Weight Gray Codes for Local Rank Modulation. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechPARADISE:2010.ETR105

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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 constant-weight Gray codes for the local rank- modulation scheme in order to simulate conventional multi-level flash cells while retaining the benefits of rank modulation. We provide necessary conditions for the existence of cyclic and cyclic optimal Gray codes. We then specifically study codes of weight 2 and upper bound their efficiency, thus proving that there are no such asymptotically-optimal cyclic codes. In contrast, we study codes of weight 3 and efficiently construct codes which are asymptotically-optimal. We conclude with a construction of codes with asymptotically-optimal rate and weight asymptotically half the length, thus having an asymptotically-optimal charge difference between adjacent cells.


Item Type:Report or Paper (Technical Report)
Additional Information:The material in this paper was presented in part at the IEEE International Symposium on Information Theory (ISIT 2010), Austin, TX, U.S.A., June 2010, and at the 26-th IEEE Convention of Electrical ans Electronics Engineers in Israel (IEEEI 2010), Eilat, Israel, November 2010. This work was supported in part by ISF grant 134/10, ISF grant 480/08, the Open University of Israel's research fund (grant no. 46114), the NSF grant ECCS-0802107, and an NSF-NRI award.
Group:Parallel and Distributed Systems Group
Subject Keywords:Gray code, rank modulation, local rank modulation, permutations, flash memory
Record Number:CaltechPARADISE:2010.ETR105
Persistent URL:http://resolver.caltech.edu/CaltechPARADISE:2010.ETR105
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:26136
Collection:CaltechPARADISE
Deposited By: Imported from CaltechPARADISE
Deposited On:04 Jan 2011
Last Modified:26 Dec 2012 13:54

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