Topology Affects the Efficiency of Network Coding in Peer-to-Peer Networks

With network coding, intermediate nodes between the source and the receivers of an end-to-end communication session are not only capable of relaying and replicating data messages, but also of coding incoming messages to produce coded outgoing ones. It has been the traditional wisdom in information theory that network coding improves the capacity of multicast sessions in directed networks. Studies have also shown that network coding is beneficial for content distribution in peer-to-peer networks, since it resolves the "last block" problem, and eliminates content reconciliation. In this paper, we show that such benefits of network coding does not come without costs and trade-offs. In particular, we refute the previous claim that peers receive linearly independent coded blocks with very high probabilities. Using example scenarios and extensive simulations, we show that it is very likely for peers to receive linearly dependent non-innovative blocks, thus decreasing their efficiency as these redundant blocks consume bandwidth. We observe that such redundancy of network coding is critically dependent on the randomness and sparsity of the P2P topology. We conclude with suggestions on topologies of certain characteristics that are preferred over others, in order to minimize the network coding redundancy, the time to distribute data, and the server cost.