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

TL;DR

This paper introduces a new constraint-coding scheme tailored for correcting asymmetric magnitude-1 errors in multi-level memories, offering improved correction capabilities, low decoding complexity, and flexible parameter adjustments.

Contribution

The paper presents an algebraic formulation, necessary and sufficient conditions for correction, and a maximum-likelihood decoder with linear complexity, enhancing error correction in non-volatile memories.

Findings

Outperforms existing schemes in correction capability for large error numbers

Provides a low-complexity decoder with linear runtime

Offers flexible code parameter adjustments without major redesigns

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.