Error-Erasure Decoding of Linearized Reed-Solomon Codes in the Sum-Rank Metric

Felicitas Hörmann, Hannes Bartz, Sven Puchinger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

Codes in the sum-rank metric have various applications in error control for multishot network coding, distributed storage and code-based cryptography. Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as subclasses and fulfill the Singleton-like bound in the sum-rank metric with equality. We propose the first known error-erasure decoder for LRS codes to unleash their full potential for multishot network coding by incorporating erasures into the known syndrome-based Berlekamp-Massey-like decoder. This allows to correct tF full errors, tR row erasures and tC column erasures up to 2tF + tR + tC ≤ n - k in the sum-rank metric requiring at most O(n2) operations in F qm, where n is the code's length and k its dimension. We show how the proposed decoder can be used to correct errors in the sum-subspace metric that occur in (noncoherent) multishot network coding.

Original languageEnglish
Title of host publication2022 IEEE International Symposium on Information Theory, ISIT 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7-12
Number of pages6
ISBN (Electronic)9781665421591
DOIs
StatePublished - 2022
Externally publishedYes
Event2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland
Duration: 26 Jun 20221 Jul 2022

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2022-June
ISSN (Print)2157-8095

Conference

Conference2022 IEEE International Symposium on Information Theory, ISIT 2022
Country/TerritoryFinland
CityEspoo
Period26/06/221/07/22

Keywords

  • error-erasure decoding
  • linearized Reed-Solomon codes
  • sum-rank metric
  • syndrome-based decoding

Fingerprint

Dive into the research topics of 'Error-Erasure Decoding of Linearized Reed-Solomon Codes in the Sum-Rank Metric'. Together they form a unique fingerprint.

Cite this