DLR-Logo -> http://www.dlr.de
DLR Portal Home | Imprint | Privacy Policy | Contact | Deutsch
Fontsize: [-] Text [+]

Interpolation-Based Decoding of Folded Variants of Linearized and Skew Reed-Solomon Codes

Hörmann, Felicitas and Bartz, Hannes (2023) Interpolation-Based Decoding of Folded Variants of Linearized and Skew Reed-Solomon Codes. Designs, Codes and Cryptography. Springer. doi: 10.1007/s10623-023-01214-8. ISSN 0925-1022.

[img] PDF - Preprint version (submitted draft)
[img] PDF - Published version

Official URL: https://link.springer.com/article/10.1007/s10623-023-01214-8


The sum-rank metric is a hybrid between the Hamming metric and the rank metric and suitable for error correction in multishot network coding and distributed storage as well as for the design of quantum-resistant cryptosystems. In this work, we consider the construction and decoding of folded linearized Reed-Solomon (FLRS) codes, which are shown to be maximum sum-rank distance (MSRD) for appropriate parameter choices. We derive an efficient interpolation-based decoding algorithm for FLRS codes that can be used as a list decoder or as a probabilistic unique decoder. The proposed decoding scheme can correct sum-rank errors beyond the unique decoding radius with a computational complexity that is quadratic in the length of the unfolded code. We show how the error-correction capability can be optimized for high-rate codes by an alternative choice of interpolation points. We derive a heuristic upper bound on the decoding failure probability of the probabilistic unique decoder and verify its tightness by Monte Carlo simulations. Further, we study the construction and decoding of folded skew Reed-Solomon codes in the skew metric. Up to our knowledge, FLRS codes are the first MSRD codes with different block sizes that come along with an efficient decoding algorithm.

Item URL in elib:https://elib.dlr.de/189224/
Document Type:Article
Additional Information:F. Hörmann and H. Bartz acknowledge the financial support by the Federal Ministry of Education and Research of Germany in the programme of “Souverän. Digital. Vernetzt.” Joint project 6 G-RIC, Project Identification Number 16KISK022.
Title:Interpolation-Based Decoding of Folded Variants of Linearized and Skew Reed-Solomon Codes
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Hörmann, FelicitasUNSPECIFIEDhttps://orcid.org/0000-0003-2217-9753UNSPECIFIED
Bartz, HannesUNSPECIFIEDhttps://orcid.org/0000-0001-7767-1513UNSPECIFIED
Date:6 May 2023
Journal or Publication Title:Designs, Codes and Cryptography
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
Keywords:folded linearized Reed–Solomon codes, folded skew Reed–Solomon codes, interpolation-based decoding, sum-rank metric, skew metric
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Communication, Navigation, Quantum Technology
DLR - Research area:Raumfahrt
DLR - Program:R KNQ - Communication, Navigation, Quantum Technology
DLR - Research theme (Project):R - Project Cybersecurity for Autonomous and Networked Systems [KNQ]
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation > Satellite Networks
Deposited By: Hörmann, Felicitas
Deposited On:28 Jul 2023 11:29
Last Modified:21 Aug 2023 12:43

Repository Staff Only: item control page

Help & Contact
electronic library is running on EPrints 3.3.12
Website and database design: Copyright © German Aerospace Center (DLR). All rights reserved.