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Linear Fractional Network Coding and Representable Discrete Polymatroids

Muralidharan, Vijayvaradharaj T and Rajan, Sundar B (2013) Linear Fractional Network Coding and Representable Discrete Polymatroids. In: IEEE GLOBAL COMMUNICATIONS CONFERENCE (GLOBECOM), DEC 09-13, 2013, Atlanta, GA, pp. 1979-1984.

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Official URL: http://dx.doi.org/10.1109/GLOCOM.2013.6831365


A linear Fractional Network Coding (FNC) solution over F-q is a linear network coding solution over F-q in which the message dimensions need not necessarily be the same and need not be the same as the edge vector dimension. Scalar linear network coding, vector linear network coding are special cases of linear FNC. In this paper, we establish the connection between the existence of a linear FNC solution for a network over F-q and the representability over F-q of discrete polymatroids, which are the multi-set analogue of matroids. All previously known results on the connection between the scalar and vector linear solvability of networks and representations of matroids and discrete polymatroids follow as special cases. An algorithm is provided to construct networks which admit FNC solution over F-q, from discrete polymatroids representable over F-q. Example networks constructed from discrete polymatroids using the algorithm are provided, which do not admit any scalar and vector solution, and for which FNC solutions with the message dimensions being different provide a larger throughput than FNC solutions with the message dimensions being equal.

Item Type: Conference Paper
Series.: IEEE Global Telecommunications Conference (Globecom)
Publisher: IEEE
Additional Information: Copy right for this article belongs to the IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 25 Aug 2016 05:02
Last Modified: 25 Aug 2016 05:02
URI: http://eprints.iisc.ac.in/id/eprint/54358

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