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MRD rank metric convolutional codes


Napp, Diego; Pinto, Raquel; Rosenthal, Joachim; Vettori, Paolo (2017). MRD rank metric convolutional codes. In: IEEE International Symposium on Information Theory (ISIT), Aachen, 25 June 2017 - 30 June 2017, 2766-2770.

Abstract

So far, in the area of Random Linear Network Coding, attention has been given to the so-called one-shot network coding, meaning that the network is used just once to propagate the information. In contrast, one can use the network more than once to spread redundancy over different shots. In this paper, we propose rank metric convolutional codes for this purpose. The framework we present is slightly more general than the one which can be found in the literature. We introduce a rank distance, which is suitable for convolutional codes, and derive a new Singleton-like upper bound. Codes achieving this bound are called Maximum Rank Distance (MRD) convolutional codes. Finally, we prove that this bound is optimal by showing a concrete construction of a family of MRD convolutional codes.

Abstract

So far, in the area of Random Linear Network Coding, attention has been given to the so-called one-shot network coding, meaning that the network is used just once to propagate the information. In contrast, one can use the network more than once to spread redundancy over different shots. In this paper, we propose rank metric convolutional codes for this purpose. The framework we present is slightly more general than the one which can be found in the literature. We introduce a rank distance, which is suitable for convolutional codes, and derive a new Singleton-like upper bound. Codes achieving this bound are called Maximum Rank Distance (MRD) convolutional codes. Finally, we prove that this bound is optimal by showing a concrete construction of a family of MRD convolutional codes.

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Additional indexing

Item Type:Conference or Workshop Item (Paper), not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Event End Date:30 June 2017
Deposited On:31 Jan 2018 07:47
Last Modified:18 Apr 2018 11:49
ISBN:978-1-5090-4096-4
Funders:Schweizeriche Nationalfonds
OA Status:Closed
Publisher DOI:https://doi.org/10.1109/ISIT.2017.8007033
Project Information:
  • : FunderSNSF
  • : Grant ID
  • : Project TitleSchweizeriche Nationalfonds

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