Algebraic network coding approach to deterministic wireless relay networks
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Medard_Algebraic network.pdf
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Author(s)
Kim, MinJi
Medard, Muriel
Date Issued
October 2010
Journal
Proceedings of the 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2010
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Kim, MinJi, and Muriel Medard. “Algebraic Network Coding Approach to Deterministic Wireless Relay Networks.” 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2010. 1518–1525. © Copyright 2010 IEEE
Version
Final published version
Abstract
The deterministic wireless relay network model, introduced by Avestimehr et al., has been proposed for approximating Gaussian relay networks. This model, known as the ADT network model, takes into account the broadcast nature of wireless medium and interference. Avestimehr et al. showed that the Min-cut Max-flow theorem holds in the ADT network. In this paper, we show that the ADT network model can be described within the algebraic network coding framework introduced by Koetter and Medard. We prove that the ADT network problem can be captured by a single matrix, called the system matrix. We show that the min-cut of an ADT network is the rank of the system matrix; thus, eliminating the need to optimize over exponential number of cuts between two nodes to compute the min-cut of an ADT network. We extend the capacity characterization for ADT networks to a more general set of connections. Our algebraic approach not only provides the Min-cut Max-flow theorem for a single unicast/multicast connection, but also extends to non-multicast connections such as multiple multicast, disjoint multicast, and two-level multicast. We also provide sufficiency conditions for achievability in ADT networks for any general connection set. In addition, we show that the random linear network coding, a randomized distributed algorithm for network code construction, achieves capacity for the connections listed above. Finally, we extend the ADT networks to those with random erasures and cycles (thus, allowing bi-directional links).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
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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
http://dx.doi.org/10.1109/ALLERTON.2010.5707093
