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Numerical Results for Gaussian Networks

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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

This chapter presents some numerical results for Gaussian networks. The goal is to provide some numerical evidence on the essential role played by submodularity for efficient computation of bounds and approximations on the multicast capacity region.

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Notes

  1. 1.

    The latter bound holds only if both source-terminal nodes are assigned sufficient rate by the loosened outer bound, see Sect. 7.1.5, which holds except for some unusual special cases.

  2. 2.

    The gap for bidirectional communication in single-antenna Gaussian networks with regular channel matrices can be derived from the results in [3] as \(\log _2e+2\log _2(1+|N|)\) by choosing the quantization noise variance parameter \(Q=|N|\), which corresponds to our parameter \(\rho =(1+Q)^{-1}=(1+|N|^{-1})\).

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Authors and Affiliations

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

    Maximilian Riemensberger

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  1. Maximilian Riemensberger
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Correspondence to Maximilian Riemensberger .

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Riemensberger, M. (2018). Numerical Results for Gaussian Networks. 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_8

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  • DOI: https://doi.org/10.1007/978-3-319-65232-0_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-65231-3

  • Online ISBN: 978-3-319-65232-0

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