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Codes for Asymmetric Limited-Magnitude Errors with Application to Multi-Level Flash Memories

Cassuto, Yuval and Schwartz, Moshe and Bohossian, Vasken and Bruck, Jehoshua (2008) Codes for Asymmetric Limited-Magnitude Errors with Application to Multi-Level Flash Memories. California Institute of Technology , Pasadena, CA. (Unpublished)

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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 ࡁ. 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:Report or Paper (Technical Report)
Cassuto, Yuval0000-0001-6369-6699
Schwartz, Moshe0000-0002-1449-0026
Bruck, Jehoshua0000-0001-8474-0812
Additional Information:This work was supported in part by the Caltech Lee Center for Advanced Networking. Also available
Group:Parallel and Distributed Systems Group
Subject Keywords:error-correcting codes; asymmetric limited-magnitude errors
Record Number:CaltechPARADISE:2008.ETR088
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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:26119
Deposited By: Imported from CaltechPARADISE
Deposited On:08 Sep 2008
Last Modified:18 Aug 2021 01:36

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