Minimizing the alphabet size in codes with restricted error sets
Abstract
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In many such settings, a smaller field size is achievable than that offered by MDS and other standard codes. We establish a connection between the minimum alphabet size for this generalized setting and the combinatorial properties of a hypergraph that represents the prespecified collection of error patterns. We also show a connection between error and erasure correcting codes in this specialized setting. This allows us to establish bounds on the minimum alphabet size and show an advantage of non-linear codes over linear codes in a generalized setting. We also consider a variation of the problem which allows a small probability of decoding error and relate it to an approximate version of hypergraph coloring.
Cite
@article{arxiv.2102.02608,
title = {Minimizing the alphabet size in codes with restricted error sets},
author = {Mira Gonen and Michael Langberg and Alex Sprintson},
journal= {arXiv preprint arXiv:2102.02608},
year = {2021}
}