Exact Capacity Scaling of Extended Wireless Networks

Abstract

n source and destination pairs randomly located in an area extending linearly with n want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power attenuation of r-and random phase changes. Classical multihop architectures that decode and forward packets can deliver a n-scaling of the aggregate throughput, while recently proposed hierarchical cooperation achieves n2-,/2-scaling, which is superior to multi-hop for a < 3.The study of information theoretic upper bounds has revealed the optimality of multi-hop for av > 4, while the moderateattenuation regime (2 < av < 4) remains uncharacterized. We close this gap by deriving a tight upper bound on the scaling of the aggregate throughput, valid for all c > 2. Our result shows that the mentioned schemes are scaling-optimal, namely that no other scheme can beat hierarchical cooperation when av < 3, nor can it beat classical multi-hop when av > 3. The key ingredient is a careful evaluation of the scaling of the cut-set bound.

Routing versus Network Coding in Erasure Networks with Broadcast and Interference Constraints

“…As in [3], we consider a cut that divides the area of the network in half, through the middle, into L and R = L C . For any positive δ, with high probability, between (1 − δ)/4 and (1 + δ)/4 of the sourcedestination pairs will have s l ∈ S and t l ∈ S C .…”

“…(7) by assuming that there are log n nodes in each squarelet, and that they are all located at the minimum source-destination distance possible for each pair of squarelets under consideration ( Figure 7 on page 32 in [3]. We consider the rate achievable with just two nodes in each squarelet, and multiply it by the two log n terms.…”

“…That is, we establish an upper bound on the total throughput of the network that increases as Θ( √ n) within a poly-log factor, and that Θ( √ n) throughput growth is achievable using a routing-only strategy. The upper-bounding technique that we use to do so is similar to that of [3], where we use the fact that nodes and sourcedestination are uniformly randomly located in order to upper-bound the number of nodes that are in a sense "close" to one another, and can therefore achieve a greater throughput than nodes that are situated further away from each other.…”

Computational Modeling of Transmission Capacity With Outage Constraints in Ad-Hoc Networks

“…After their research, a number of studies (Xie and Kumar, 2004, Leveque and Telator, 2005, Ozqur, Leveque and Tse, 2007 have emerged. These studies focus on the behaviour of the end-to-end network capacity, growing within the node limit, under a variety of models of node interaction and fading conditions.…”