Maximum Energy Benefit of Compute-and-Forward for Multiple Unicast Sessions
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Abstract
In this thesis, we investigate the maximum energy benefit of compute-and-forward applying on general networks. The energy benefit is defined as the ratio of the minimum energy consumption in network when a symbol is communicated successfully for every session when the network is in traditional routing mode, and the minimum energy consumption in network when a symbol is communicated successfully for every session when the network is in compute-and-forward mode. The upper bound of the energy benefit is derived by proving the upper bound of the minimum energy consumption when applying traditional routing scheme, and the lower bound of the minimum energy consumption when applying compute-and-forward. We give theorems and proofs about the energy benefit on general wireless networks and on some special wireless networks. Before that we give the model set-up for wireless networks. In general networks, we get the conclusion that for the benefit of energy consumption when applying compute-and-forward is upper bounded by the average distance of all sessions in the network. It is also upper bounded by the larger one of the maximum distance between each source node to the destination set, and the maximum distance between the source set and each destination node. For some special networks, we start by giving definitions of them, then we give upper bounds of the energy benefit on these special networks. We present the idea that applying compute-and-forward in a network does not make any benefit if the network is a single source network where the source node needs to transmit independent information to each destination node, or it is a single destination network where the destination node needs to receive independent information from each source node. In networks with non-collated source nodes and destination nods, the energy benefit is upper bounded by $2K$, where $K$ is the number of sessions in the network. Upper bounds of energy benefit on other special networks, e.g. line networks, 2D/3D rectangular lattice networks are studied in this thesis. We get the conclusion that in these special networks, the upper bounds of energy benefit are constants factors.