A Constrained Coding Scheme for Correcting Asymmetric Magnitude-$1$ Errors in $q$-ary Channels

Evyatar Hemo, Yuval Cassuto

Research output: Working paperPreprint

Abstract

We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known alternatives, while admitting low-complexity of decoding. Our results include an algebraic formulation of the constraint, necessary and sufficient conditions for correctability, a maximum-likelihood decoder running in complexity linear in the alphabet size, and upper bounds on the probability of failing to correct $t$ errors. Besides the superior rate-correction tradeoff, another advantage of this scheme over standard error-correcting codes is the flexibility to vary the code parameters without significant modifications.
Original languageEnglish
StatePublished - 4 Jul 2016

Keywords

  • cs.IT
  • math.IT

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