Codes for asymmetric limited-magnitude errors with application to multilevel flash memories

Yuval Cassuto, Moshe Schwartz, Vasken Bohossian, Jehoshua Bruck

Research output: Contribution to journalArticlepeer-review

104 Scopus citations


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.

Original languageEnglish
Article number5437412
Pages (from-to)1582-1595
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - 1 Apr 2010


  • Asymmetric limited-magnitude errors
  • Error-correcting codes
  • Flash memory codes
  • Q-ary codes
  • Systematic codes

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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