On the Capacity of Network Coding for Random Networks

Abstract

Abstract-We study the maximum flow possible between a single-source and multiple terminals in a weighted random graph (modeling a wired network) and a weighted random geometric graph (modeling an ad-hoc wireless network) using network coding. For the weighted random graph model, we show that the network coding capacity concentrates around the expected number of nearest neighbors of the source and the terminals. Specifically, for a network with a single source, terminals, and relay nodes such that the link capacities between any two nodes is independent and identically distributed (i.i.d.), the maximum flow between the source and the terminals is approximately [ ] with high probability. For the weighted random geometric graph model where two nodes are connected if they are within a certain distance of each other we show that with high probability the network coding capacity is greater than or equal to the expected number of nearest neighbors of the node with the least coverage area.

Separating distributed source coding from network coding

“…Moreover, random linear network coding, which is an efficient distributed strategy, achieves this capacity with high probability [9], [10]. The multicast capacity of large random networks is considered in [11]. Variants of this problem involving multiple sources and multiple receivers are significantly harder and far less is known about them.…”

Network Coding-Aware Routing in Wireless Networks

“…In the context of wireless networks, Lun et al [16], [17] studied the problem of minimum-cost (energy) multicast involving a single session with a single source node. Ramamoorthy et al [19] derived results for maximum flow achievable in random wireless networks (modeled as geometric random graphs) for a similar single multicast session with a single source.…”

Video-aware opportunistic network coding over wireless networks

“…This breakthrough idea inspired significant effort in several directions [3]- [6], including practical application of network coding, studying topologies beyond multicast, such as unicast [21]- [23] and broadcast scenarios. The broadcast nature of the wireless medium offers an opportunity for exploiting the throughput benefits of network coding [24], [25]. The recent work in [7], [8] applied these ideas from the network coding community in the context of wireless mesh networks.…”