We consider broadcasting in multi-hop wireless networks, in which one source transmits information to all the nodes in the networks. We focus on energy efficiency, or minimizing the total number of transmissions. Our main result is the proof that, from the energy-efficiency perspective, network coding may essentially operate in an optimal way in the core of the network for uniform wireless networks in Euclidean spaces with idealized communication. In such networks, one corollary is that network coding is expected to outperform routing. We prove that the asymptotic network coding gain is comprised between 1.642 and 1.684 for networks of the plane, and comprised between 1.432 and 2.035 for networks in 3-dimensional space.
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