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Algebraic Network Coding Approach to Deterministic Wireless Relay Networks (2010)
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BibTeX
@MISC{Kim10algebraicnetwork,
author = {Minji Kim and Muriel Médard},
title = {Algebraic Network Coding Approach to Deterministic Wireless Relay Networks},
year = {2010}
}
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Abstract
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 Médard. 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). I.
Keyphrases
adt network deterministic wireless relay network algebraic network coding approach system matrix min-cut max-flow theorem adt network model general connection set bi-directional link non-multicast connection gaussian relay network multiple multicast random linear network coding two-level multicast adt network problem algebraic approach exponential number single unicast multicast connection algebraic network deterministic wireless relay network model wireless medium random erasure broadcast nature general set network code construction sufficiency condition capacity characterization single matrix disjoint multicast
