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

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Executive Summary

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. The authors 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.

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