Bartz, Hannes und Jerkovits, Thomas und Puchinger, Sven und Rosenkilde, Johan (2021) Fast Decoding of Codes in the Rank, Subspace, and Sum-Rank Metric. IEEE Transactions on Information Theory, Seite 1. IEEE - Institute of Electrical and Electronics Engineers. ISSN 0018-9448.
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Kurzfassung
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed–Solomon codes in the sum-rank metric. The speed-ups are achieved by new algorithms that reduce the cores of the underlying computational problems of the decoders to one common tool: computing left and right approximant bases of matrices over skew polynomial rings. To accomplish this, we describe a skew-analogue of the existing PM-Basis algorithm for matrices over ordinary polynomials. This captures the bulk of the work in multiplication of skew polynomials, and the complexity benefit comes from existing algorithms performing this faster than in classical quadratic complexity. The new algorithms for the various decoding-related computational problems are interesting in their own and have further applications, in particular parts of decoders of several other codes and foundational problems related to the remainder-evaluation of skew polynomials.
elib-URL des Eintrags: | https://elib.dlr.de/141924/ | ||||||||||||||||||||
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Dokumentart: | Zeitschriftenbeitrag | ||||||||||||||||||||
Titel: | Fast Decoding of Codes in the Rank, Subspace, and Sum-Rank Metric | ||||||||||||||||||||
Autoren: |
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Datum: | 2021 | ||||||||||||||||||||
Erschienen in: | IEEE Transactions on Information Theory | ||||||||||||||||||||
Referierte Publikation: | Ja | ||||||||||||||||||||
Open Access: | Nein | ||||||||||||||||||||
Gold Open Access: | Nein | ||||||||||||||||||||
In SCOPUS: | Ja | ||||||||||||||||||||
In ISI Web of Science: | Ja | ||||||||||||||||||||
Seitenbereich: | Seite 1 | ||||||||||||||||||||
Verlag: | IEEE - Institute of Electrical and Electronics Engineers | ||||||||||||||||||||
ISSN: | 0018-9448 | ||||||||||||||||||||
Status: | akzeptierter Beitrag | ||||||||||||||||||||
Stichwörter: | Gabidulin codes, skew polynomials, rank metric, sum-rank metric, Gabidulin codes | ||||||||||||||||||||
HGF - Forschungsbereich: | Luftfahrt, Raumfahrt und Verkehr | ||||||||||||||||||||
HGF - Programm: | Raumfahrt | ||||||||||||||||||||
HGF - Programmthema: | Kommunikation, Navigation, Quantentechnologien | ||||||||||||||||||||
DLR - Schwerpunkt: | Raumfahrt | ||||||||||||||||||||
DLR - Forschungsgebiet: | R KNQ - Kommunikation, Navigation, Quantentechnologie | ||||||||||||||||||||
DLR - Teilgebiet (Projekt, Vorhaben): | R - Projekt Cybersicherheit für autonome und vernetzte Systeme [KNQ] | ||||||||||||||||||||
Standort: | Oberpfaffenhofen | ||||||||||||||||||||
Institute & Einrichtungen: | Institut für Kommunikation und Navigation > Satellitennetze | ||||||||||||||||||||
Hinterlegt von: | Bartz, Hannes | ||||||||||||||||||||
Hinterlegt am: | 27 Apr 2021 15:46 | ||||||||||||||||||||
Letzte Änderung: | 27 Apr 2021 15:46 |
Verfügbare Versionen dieses Eintrags
- Fast Decoding of Codes in the Rank, Subspace, and Sum-Rank Metric. (deposited 27 Apr 2021 15:46) [Gegenwärtig angezeigt]
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