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Publication# Network-Coded Broadcast: from Canonical Networks to Random Topologies

Abstract

We consider the problem of finding the minimum number of transmissions in an ad-hoc network for all-to-all broadcasting using network coding. This work generalizes previous results for canonical topologies such as the circle and the wrap around grid to the finite-sized line, and non-wrap-around grid. The latter topologies better reflect network coding in random topologies, since the dissemination of information is "directional", in a sense that information usually arrives via the neighbors on the path to its originator instead of from all possible directions. We find that while the line topology requires a higher number of transmissions compared to the circle, this is interestingly not the case for the grid. We further present simulation results on a heuristic that estimates the required minimum number of transmissions in random wireless topologies and compare it to the optimum solution, as well as previously proposed heuristics.

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Linear network coding

In computer networking, linear network coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations.
Linear network coding may be use

Wireless ad hoc network

A wireless ad hoc network (WANET) or mobile ad hoc network (MANET) is a decentralized type of wireless network. The network is ad hoc because it does not rely on a pre-existing infrastructure, such

Network topology

Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. Network topology can be used to define or describe the arrangement of various types of telecommunic

Christina Fragouli, Jean-Yves Le Boudec, Jörg Widmer

We consider the problem of broadcasting in an ad-hoc wireless network, where all nodes of the network are sources that want to transmit information to all other nodes. Our figure of merit is energy efficiency, a critical design parameter for wireless networks since it directly affects battery life and thus network lifetime. We prove that applying ideas from network coding allows to realize significant benefits in terms of energy efficiency for the problem of broadcasting, and propose very simple algorithms that allow to realize these benefits in practice. In particular, our theoretical analysis shows that network coding improves performance by a constant factor in fixed networks. We calculate this factor exactly for some canonical configurations. We then show that in networks where the topology dynamically changes, for example due to mobility, and where operations are restricted to simple distributed algorithms, network coding can offer improvements of a factor of log n, where n is the number of nodes in the network. We use the insights gained from the theoretical analysis to propose low-complexity distributed algorithms for realistic wireless ad-hoc scenarios, discuss a number of practical considerations, and evaluate our algorithms through packet level simulation.

2008Christina Fragouli, Jean-Yves Le Boudec, Jörg Widmer

We consider the problem of broadcasting in an ad hoc wireless network, where all nodes of the network are sources that want to transmit information to all other nodes. Our figure of merit is energy efficiency, a critical design parameter for wireless net- works since it directly affects battery life and thus network life- time. We prove that applying ideas from network coding allows to realize significant benefits in terms of energy efficiency for the problem of broadcasting, and propose very simple algorithms that allow to realize these benefits in practice. In particular, our theo- retical analysis shows that network coding improves performance by a constant factor in fixed networks. We calculate this factor exactly for some canonical configurations. We then show that in networks where the topology dynamically changes, for example due to mobility, and where operations are restricted to simple dis- tributed algorithms, network coding can offer improvements of a factor of , where is the number of nodes in the network. We use the insights gained from the theoretical analysis to propose low-complexity distributed algorithms for realistic wireless ad hoc scenarios, discuss a number of practical considerations, and eval- uate our algorithms through packet level simulation.

2008