research-article

Communication over finite-field matrix channels

Authors:

Frank R. Kschischang,

Ralf KötterAuthors Info & Claims

IEEE Transactions on Information Theory, Volume 56, Issue 3

Pages 1296 - 1305

https://doi.org/10.1109/TIT.2009.2039167

Published: 01 March 2010 Publication History

Abstract

This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random network coding. The model assumes that n packets of length m are transmitted over the network, and up to t erroneous packets are randomly chosen and injected into the network. Upper and lower bounds on capacity are obtained for any channel parameters, and asymptotic expressions are provided in the limit of large field or matrix size. A simple coding scheme is presented that achieves capacity in both limiting cases. The scheme has decoding complexity O(n²m) and a probability of error that decreases exponentially both in the packet length and in the field size in bits. Extensions of these results for coherent network coding are also presented.

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Cited By

Duc PLoidreau P(2021)On the decoding of the sum of Gabidulin codes2021 IEEE International Symposium on Information Theory (ISIT)10.1109/ISIT45174.2021.9517869(166-171)Online publication date: 12-Jul-2021
https://dl.acm.org/doi/10.1109/ISIT45174.2021.9517869
Kamche HMouaha C(2019)Rank-Metric Codes Over Finite Principal Ideal Rings and ApplicationsIEEE Transactions on Information Theory10.1109/TIT.2019.293352065:12(7718-7735)Online publication date: 19-Nov-2019
https://dl.acm.org/doi/10.1109/TIT.2019.2933520

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cover image IEEE Transactions on Information Theory

IEEE Transactions on Information Theory Volume 56, Issue 3

March 2010

529 pages

ISSN:0018-9448

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Copyright © 2010.

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IEEE Press

Publication History

Published: 01 March 2010

Revised: 01 June 2009

Received: 09 July 2008

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Cited By

Duc PLoidreau P(2021)On the decoding of the sum of Gabidulin codes2021 IEEE International Symposium on Information Theory (ISIT)10.1109/ISIT45174.2021.9517869(166-171)Online publication date: 12-Jul-2021
https://dl.acm.org/doi/10.1109/ISIT45174.2021.9517869
Kamche HMouaha C(2019)Rank-Metric Codes Over Finite Principal Ideal Rings and ApplicationsIEEE Transactions on Information Theory10.1109/TIT.2019.293352065:12(7718-7735)Online publication date: 19-Nov-2019
https://dl.acm.org/doi/10.1109/TIT.2019.2933520

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