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.
|Title of host publication||2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||6|
|State||Published - 12 Jul 2021|
|Event||2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia|
Duration: 12 Jul 2021 → 20 Jul 2021
|Name||IEEE International Symposium on Information Theory - Proceedings|
|Conference||2021 IEEE International Symposium on Information Theory, ISIT 2021|
|Period||12/07/21 → 20/07/21|
Bibliographical noteFunding Information:
Michael Langberg is with the Department of Electrical Engineering, University at Buffalo (State University of New-York), Buffalo, NY 14260, USA (e-mail: firstname.lastname@example.org). Work supported in part by NSF grant 1909451.
© 2021 IEEE.