A constraint scheme for correcting massive asymmetric magnitude-1 errors in multi-level NVMs

We present a constraint-coding scheme to correct large numbers of asymmetric magnitude-1 errors in multi-level non-volatile memories. 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 lower bounds on the probability 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.