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Submodular Rate Region Models for Multicast Communication in Wireless Networks

Part of the book series: Foundations in Signal Processing, Communications and Networking ((SIGNAL,volume 14))

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Abstract

Multicast communication refers to one or multiple information sources transmitting data to one or multiple information sinks such that all sinks can recover the information from all sources. Network coding, introduced by Ahlswede et al. (IEEE Trans Inf Theory 46(4):1204–1216, 2000, [1]) for graphical networks, has revolutionized multicast communication in wired and wireless networks by shifting the paradigm from communication in a store-and-forward manner to coded communication where the network itself acts as a distributed encoding entity with all nodes being encoder parts. Traditional graph models for wireless networks typically ignore the wireless broadcast advantage, i.e., some receivers may also be able to get messages that are actually intended for other receivers. This chapter provides a literature survey on how the wireless broadcast advantage has been modeled and outlines the structure and results of the book.

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Notes

  1. 1.

    Ralf Kötter coined the simple phrase “A bit is not a car!” to highlight why network coding outperforms store-and-forward in most kinds of wired and wireless communication networks, see ITW 2006 tutorial slides: [online] http://www.ee.cityu.edu.hk/~itw06/static/ITW06_KeynotePPT_RalfKoetter.pdf.

  2. 2.

    This analogy is due to the Lovász extension [26], which associates a unique polyhedral convex function with each submodular set function and relates submodular function minimization to a particular type of polyhedral convex function minimization.

  3. 3.

    For surveys on submodular set function minimization see also [29, 30].

  4. 4.

    The standard notation for the distribution represented by its probability mass or density function is \(p_{X,Y|Z}(x,y|z)\). However, for brevity of notation and to avoid notation conflicts with flows x and auxiliary rates y, the short hand p(X, Y|Z) is used throughout this book to abstractly represent the distribution and, if applicable, its factorization properties.

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  1. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität München, Munich, Germany

    Maximilian Riemensberger

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Riemensberger, M. (2018). Introduction. In: Submodular Rate Region Models for Multicast Communication in Wireless Networks. Foundations in Signal Processing, Communications and Networking, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-65232-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-65232-0_1

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