Bartz, Hannes und Wachter-Zeh, Antonia (2018) Efficient Decoding of Interleaved Subspace and Gabidulin Codes beyond their Unique Decoding Radius Using Gröbner Bases. Advances in Mathematics of Communications. American Institute of Mathematical Sciences. ISSN 1930-5346.
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Kurzfassung
An interpolation-based decoding scheme for L-interleaved subspace codes is presented. The scheme can be used as a (not necessarily polynomial-time) list decoder as well as a polynomial-time probabilistic unique decoder. Both interpretations allow to decode interleaved subspace codes beyond half the minimum subspace distance. Both schemes can decode γ insertions and δ deletions up to γ + Lδ ≤ L(nt − k), where nt is the dimension of the transmitted subspace and k is the number of data symbols from the field Fqm. Further, a complementary decoding approach is presented which corrects γ insertions and δ deletions up to Lγ +δ ≤ L(nt −k). Both schemes use properties of minimal Gr¨obner bases for the interpolation module that allow predicting the worst-case list size right after the interpolation step. An efficient procedure for constructing the required minimal Gr¨obner basis using the general K¨otter interpolation is presented. A computationally- and memory-efficient root-finding algorithm for the probabilistic unique decoder is proposed. The overall complexity of the decoding algorithm is at most O(L2n2 r) operations in F qm where nr is the dimension of the received subspace and L is the interleaving order. The analysis as well as the efficient algorithms can also be applied for accelerating the decoding of interleaved Gabidulin codes.
elib-URL des Eintrags: | https://elib.dlr.de/120785/ | ||||||||||||
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Dokumentart: | Zeitschriftenbeitrag | ||||||||||||
Titel: | Efficient Decoding of Interleaved Subspace and Gabidulin Codes beyond their Unique Decoding Radius Using Gröbner Bases | ||||||||||||
Autoren: |
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Datum: | 2018 | ||||||||||||
Erschienen in: | Advances in Mathematics of Communications | ||||||||||||
Referierte Publikation: | Ja | ||||||||||||
Open Access: | Nein | ||||||||||||
Gold Open Access: | Nein | ||||||||||||
In SCOPUS: | Ja | ||||||||||||
In ISI Web of Science: | Ja | ||||||||||||
Herausgeber: |
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Verlag: | American Institute of Mathematical Sciences | ||||||||||||
Name der Reihe: | Advances in Mathematics of Communications | ||||||||||||
ISSN: | 1930-5346 | ||||||||||||
Status: | akzeptierter Beitrag | ||||||||||||
Stichwörter: | Subspace Codes, Rank-metric Codes, Interleaved Gabidulin Codes, Probabilistic Unique Decoding, Interpolation-Based Decoding. | ||||||||||||
HGF - Forschungsbereich: | Luftfahrt, Raumfahrt und Verkehr | ||||||||||||
HGF - Programm: | Luftfahrt | ||||||||||||
HGF - Programmthema: | Luftverkehrsmanagement und Flugbetrieb | ||||||||||||
DLR - Schwerpunkt: | Luftfahrt | ||||||||||||
DLR - Forschungsgebiet: | L AO - Air Traffic Management and Operation | ||||||||||||
DLR - Teilgebiet (Projekt, Vorhaben): | L - Kommunikation, Navigation und Überwachung (alt) | ||||||||||||
Standort: | Oberpfaffenhofen | ||||||||||||
Institute & Einrichtungen: | Institut für Kommunikation und Navigation > Satellitennetze | ||||||||||||
Hinterlegt von: | Bartz, Hannes | ||||||||||||
Hinterlegt am: | 03 Jul 2018 13:01 | ||||||||||||
Letzte Änderung: | 03 Jul 2018 13:01 |
Verfügbare Versionen dieses Eintrags
- Efficient Decoding of Interleaved Subspace and Gabidulin Codes beyond their Unique Decoding Radius Using Gröbner Bases. (deposited 03 Jul 2018 13:01) [Gegenwärtig angezeigt]
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