On transform-domain error and erasure correction by Gabidulin codes

Wenhui Li; Vladimir Sidorenko; Danilo Silva

doi:10.1007/s10623-014-9954-4

On transform-domain error and erasure correction by Gabidulin codes

Wenhui Li, Vladimir Sidorenko, Danilo Silva

Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

11 Zitate (Scopus)

Abstract

Gabidulin codes are the rank metric analogues of Reed-Solomon codes and have found many applications including network coding. In this paper, we propose a transform-domain algorithm correcting both errors and erasures with Gabidulin codes. Interleaving or the direct sum of Gabidulin codes allows both decreasing the redundancy and increasing the error correcting capability for network coding. We generalize the proposed decoding algorithm for interleaved Gabidulin codes. The transform-domain approach allows to simplify derivations and proofs and also simplifies finding the error vector after solving the key equation.

Originalsprache	Englisch
Seiten (von - bis)	571-586
Seitenumfang	16
Fachzeitschrift	Designs, Codes, and Cryptography
Jahrgang	73
Ausgabenummer	2
DOIs	https://doi.org/10.1007/s10623-014-9954-4
Publikationsstatus	Veröffentlicht - Nov. 2014
Extern publiziert	Ja

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10.1007/s10623-014-9954-4

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abstract = "Gabidulin codes are the rank metric analogues of Reed-Solomon codes and have found many applications including network coding. In this paper, we propose a transform-domain algorithm correcting both errors and erasures with Gabidulin codes. Interleaving or the direct sum of Gabidulin codes allows both decreasing the redundancy and increasing the error correcting capability for network coding. We generalize the proposed decoding algorithm for interleaved Gabidulin codes. The transform-domain approach allows to simplify derivations and proofs and also simplifies finding the error vector after solving the key equation.",

keywords = "Decoding, Error and erasure correction, Gabidulin codes, Interleaved codes, Transform-domain",

author = "Wenhui Li and Vladimir Sidorenko and Danilo Silva",

note = "Funding Information: Acknowledgments The authors would like to thank Antonia Wachter-Zeh and Di Chen for helpful discussions and the anonymous reviewers for very useful comments and suggestions to improve the paper. This work has been supported by DFG (German Research Council) under Grant BO 867/22. These results were partially presented at the International Workshop on Coding and Cryptography (WCC 2013) [23].",

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doi = "10.1007/s10623-014-9954-4",

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AU - Silva, Danilo

N1 - Funding Information: Acknowledgments The authors would like to thank Antonia Wachter-Zeh and Di Chen for helpful discussions and the anonymous reviewers for very useful comments and suggestions to improve the paper. This work has been supported by DFG (German Research Council) under Grant BO 867/22. These results were partially presented at the International Workshop on Coding and Cryptography (WCC 2013) [23].

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N2 - Gabidulin codes are the rank metric analogues of Reed-Solomon codes and have found many applications including network coding. In this paper, we propose a transform-domain algorithm correcting both errors and erasures with Gabidulin codes. Interleaving or the direct sum of Gabidulin codes allows both decreasing the redundancy and increasing the error correcting capability for network coding. We generalize the proposed decoding algorithm for interleaved Gabidulin codes. The transform-domain approach allows to simplify derivations and proofs and also simplifies finding the error vector after solving the key equation.

AB - Gabidulin codes are the rank metric analogues of Reed-Solomon codes and have found many applications including network coding. In this paper, we propose a transform-domain algorithm correcting both errors and erasures with Gabidulin codes. Interleaving or the direct sum of Gabidulin codes allows both decreasing the redundancy and increasing the error correcting capability for network coding. We generalize the proposed decoding algorithm for interleaved Gabidulin codes. The transform-domain approach allows to simplify derivations and proofs and also simplifies finding the error vector after solving the key equation.

KW - Decoding

KW - Error and erasure correction

KW - Gabidulin codes

KW - Interleaved codes

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On transform-domain error and erasure correction by Gabidulin codes

Abstract

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