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Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories

Cassuto, Yuval and Schwartz, Moshe and Bohossian, Vasken and Bruck, Jehoshua (2010) Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories. IEEE Transactions on Information Theory, 56 (4). pp. 1582-1595. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:20100415-101346040

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Abstract

Several physical effects that limit the reliability and performance of multilevel flash memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by ℓ. The constructions utilize known codes for symmetric errors, over small alphabets, to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown to exceed the sizes of known codes (for related error models), and asymptotic rate-optimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/TIT.2010.2040971DOIUNSPECIFIED
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5437412&tag=1PublisherUNSPECIFIED
Additional Information:© 2010 IEEE. Manuscript received August 26, 2008; revised November 12, 2009. Current version published March 17, 2010. Communicated by G. Seroussi, Associate Editor for Coding Theory. This work was supported in part by the Caltech Lee Center for Advanced Networking and by the GIF under Grant 2179- 1785.10/2007. The material in paper was presented in part at the IEEE International Symposium on Information Theory, Nice, France, June 2007. The authors wish to thank Anxiao Jiang for insightful comments and suggestions. In addition, the authors acknowledge the anonymous reviewers’ contributions to the paper’s quality of presentation.
Funders:
Funding AgencyGrant Number
GIF 2179-1785.10/2007
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
Subject Keywords:Asymmetric limited-magnitude errors; error-correcting codes; flash memory codes; q-ary codes; systematic codes
Record Number:CaltechAUTHORS:20100415-101346040
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100415-101346040
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17989
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:30 Apr 2010 02:39
Last Modified:26 Dec 2012 11:58

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