A Constrained Coding Scheme for Correcting Asymmetric Magnitude-$1$ Errors in $q$-ary Channels
Abstract
We present a constraint-coding scheme to correct asymmetric magnitude- 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 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.
Cite
@article{arxiv.1607.00762,
title = {A Constrained Coding Scheme for Correcting Asymmetric Magnitude-$1$ Errors in $q$-ary Channels},
author = {Evyatar Hemo and Yuval Cassuto},
journal= {arXiv preprint arXiv:1607.00762},
year = {2017}
}