The Balanced Unicast and Multicast Capacity Regions of Large Wireless Networks

We consider the question of determining the scaling of the $n^2$-dimensional balanced unicast and the $n 2^n$-dimensional balanced multicast capacity regions of a wireless network with $n$ nodes placed uniformly at random in a square region of area $n$ and communicating over Gaussian fading channels. We identify this scaling of both the balanced unicast and multicast capacity regions in terms of $\Theta(n)$, out of $2^n$ total possible, cuts. These cuts only depend on the geometry of the locations of the source nodes and their destination nodes and the traffic demands between them, and thus can be readily evaluated. Our results are constructive and provide optimal (in the scaling sense) communication schemes.Comment: 37 pages, 7 figures, to appear in IEEE Transactions on Information Theor

On the utility of network coding in dynamic environments

Many wireless applications, such as ad-hoc networks and sensor networks, require decentralized operation in dynamically varying environments. We consider a distributed randomized network coding approach that enables efficient decentralized operation of multi-source multicast networks. We show that this approach provides substantial benefits over traditional routing methods in dynamically varying environments. We present a set of empirical trials measuring the performance of network coding versus an approximate online Steiner tree routing approach when connections vary dynamically. The results show that network coding achieves superior performance in a significant fraction of our randomly generated network examples. Such dynamic settings represent a substantially broader class of networking problems than previously recognized for which network coding shows promise of significant practical benefits compared to routing

On the Capacity Bounds of Undirected Networks

In this work we improve on the bounds presented by Li&Li for network coding gain in the undirected case. A tightened bound for the undirected multicast problem with three terminals is derived. An interesting result shows that with fractional routing, routing throughput can achieve at least 75% of the coding throughput. A tighter bound for the general multicast problem with any number of terminals shows that coding gain is strictly less than 2. Our derived bound depends on the number of terminals in the multicast network and approaches 2 for arbitrarily large number of terminals.Comment: 5 pages, 5 figures, ISIT 2007 conferenc

An asymptotically optimal push-pull method for multicasting over a random network

We consider allcast and multicast flow problems where either all of the nodes or only a subset of the nodes may be in session. Traffic from each node in the session has to be sent to every other node in the session. If the session does not consist of all the nodes, the remaining nodes act as relays. The nodes are connected by undirected links whose capacities are independent and identically distributed random variables. We study the asymptotics of the capacity region (with network coding) in the limit of a large number of nodes, and show that the normalized sum rate converges to a constant almost surely. We then provide a decentralized push-pull algorithm that asymptotically achieves this normalized sum rate without network coding.Comment: 13 pages, extended version of paper presented at the IEEE International Symposium on Information Theory (ISIT) 2012, minor revision to text to address review comments, to appear in IEEE Transactions in information theor

Content Distribution by Multiple Multicast Trees and Intersession Cooperation: Optimal Algorithms and Approximations

In traditional massive content distribution with multiple sessions, the sessions form separate overlay networks and operate independently, where some sessions may suffer from insufficient resources even though other sessions have excessive resources. To cope with this problem, we consider the universal swarming approach, which allows multiple sessions to cooperate with each other. We formulate the problem of finding the optimal resource allocation to maximize the sum of the session utilities and present a subgradient algorithm which converges to the optimal solution in the time-average sense. The solution involves an NP-hard subproblem of finding a minimum-cost Steiner tree. We cope with this difficulty by using a column generation method, which reduces the number of Steiner-tree computations. Furthermore, we allow the use of approximate solutions to the Steiner-tree subproblem. We show that the approximation ratio to the overall problem turns out to be no less than the reciprocal of the approximation ratio to the Steiner-tree subproblem. Simulation results demonstrate that universal swarming improves the performance of resource-poor sessions with negligible impact to resource-rich sessions. The proposed approach and algorithm are expected to be useful for infrastructure-based content distribution networks with long-lasting sessions and relatively stable network environment