Capacity of ThreeDimensional Erasure Networks
Abstract
In this paper, we introduce a largescale threedimensional (3D) erasure network, where $n$ wireless nodes are randomly distributed in a cuboid of $n^{\lambda}\times n^{\mu}\times n^{\nu}$ with $\lambda+\mu+\nu=1$ for $\lambda,\mu,\nu>0$, and completely characterize its capacity scaling laws. Two fundamental pathloss attenuation models (i.e., exponential and polynomial powerlaw models) are used to suitably model an erasure probability for packet transmission. Then, under the two erasure models, we introduce a routing protocol using percolation highway in 3D space, and then analyze its achievable throughput scaling laws. It is shown that, under the two erasure models, the aggregate throughput scaling $n^{\min\{1\lambda,1\mu,1\nu\}}$ can be achieved in the 3D erasure network. This implies that the aggregate throughput scaling $n^{2/3}$ can be achieved in 3D cubic erasure networks while $\sqrt{n}$ can be achieved in twodimensional (2D) square erasure networks. The gain comes from the fact that, compared to 2D space, more geographic diversity can be exploited via 3D space, which means that generating more simultaneous percolation highways is possible. In addition, cutset upper bounds on the capacity scaling are derived to verify that the achievable scheme based on the 3D percolation highway is orderoptimal within a polylogarithmic factor under certain practical operating regimes on the decay parameters.
 Publication:

arXiv eprints
 Pub Date:
 May 2016
 arXiv:
 arXiv:1605.03282
 Bibcode:
 2016arXiv160503282J
 Keywords:

 Computer Science  Information Theory;
 Computer Science  Networking and Internet Architecture
 EPrint:
 26 pages, 7 figures, To appear in IEEE Transactions on Communications