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

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English
Pages (from-to)	571-586
Number of pages	16
Journal	Designs, Codes, and Cryptography
Volume	73
Issue number	2
DOIs	https://doi.org/10.1007/s10623-014-9954-4
State	Published - Nov 2014
Externally published	Yes

Keywords

Decoding
Error and erasure correction
Gabidulin codes
Interleaved codes
Transform-domain

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10.1007/s10623-014-9954-4

Cite this

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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 - Sidorenko, Vladimir

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

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Keywords

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