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 with 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.
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