Scalar-linear solvability of matroidal networks associated with representable matroids
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Medard_Scalar-linear solvability.pdf
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Author(s)
Kim, Anthony
Medard, Muriel
Date Issued
October 2010
Journal
Proceedings of the IEEE International Symposium on Turbo Codes and Iterative Information (ISTC), 2010
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Médard, Muriel, and Anthony Kim. "Scalar-linear solvability of matroidal networks associated with representable matroids." Proceedings of the IEEE International Symposium on Turbo Codes and Iterative Information (ISTC), 2010: 452-456. © 2010 IEEE.
Version
Final published version
Abstract
We study matroidal networks introduced by Dougherty et al., who showed that if a network is scalar-linearly solvable over some finite field, then the network is a matroidal network associated with a representable matroid over a finite field. In this paper, we prove the converse. It follows that a network is scalar-linearly solvable if and only if the network is a matroidal network associated with a representable matroid over a finite field and that determining scalar-linear solvability of a network is equivalent to finding a representable matroid over a finite field and a valid network-matroid mapping. As a consequence, we obtain a correspondence between scalar-linearly solvable networks and representable matroids over finite fields. We note that this result, combined with the construction method due to Dougherty et al., can generate potentially new scalar-linearly solvable networks.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1109/ISTC.2010.5613864
