@inproceedings{38bea99cae824e3f8564129420176097,
title = "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 the hypergraph coloring problem.",
author = "Mira Gonen and Michael Langberg and Alex Sprintson",
note = "Publisher Copyright: {\textcopyright} 2021 IEEE.; 2021 IEEE International Symposium on Information Theory, ISIT 2021 ; Conference date: 12-07-2021 Through 20-07-2021",
year = "2021",
month = jul,
day = "12",
doi = "10.1109/ISIT45174.2021.9517761",
language = "الإنجليزيّة",
series = "IEEE International Symposium on Information Theory - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "940--945",
booktitle = "2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings",
address = "الولايات المتّحدة",
}