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Published June 2009 | Published
Journal Article Open

Rank Modulation for Flash Memories

Abstract

We explore a novel data representation scheme for multilevel flash memory cells, in which a set of n cells stores information in the permutation induced by the different charge levels of the individual cells. The only allowed charge-placement mechanism is a ldquopush-to-the-toprdquo operation, which takes a single cell of the set and makes it the top-charged cell. The resulting scheme eliminates the need for discrete cell levels, as well as overshoot errors, when programming cells. We present unrestricted Gray codes spanning all possible n-cell states and using only "push-to-the-top" operations, and also construct balanced Gray codes. One important application of the Gray codes is the realization of logic multilevel cells, which is useful in conventional storage solutions. We also investigate rewriting schemes for random data modification. We present both an optimal scheme for the worst case rewrite performance and an approximation scheme for the average-case rewrite performance.

Additional Information

© Copyright 2009 IEEE. Manuscript received September 18, 2008; revised January 28, 2009. Current version published May 20, 2009. This work was supported in part by the Caltech Lee Center for Advanced Networking, by the National Science Foundation (NSF) under Grant ECCS-0802107 and the NSF CAREER Award 0747415 , by the GIF under Grant 2179-1785.10/2007, by the NSF-NRI, and by a gift from Ross Brown. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Toronto, ON, Canada, July 2008. The authors would like to thank the anonymous reviewers, whose comments helped improve the presentation of the paper.

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