Influence of Graph Properties of Peer-to-Peer Topologies on Video Streaming with Network Channel Coding

Network channel coding (NCC) distributes channel coding functions over network nodes participating in common or diverse communication sessions. A particular case of NCC is network embedded FEC (NEF), which has been shown to exhibit significant improvements in the performance of video streaming applications over multicast peer-to-peer (p2p) trees. The placement of NCC/NEF codecs and its utility in improving the throughput performance is in general a function of the underlying p2p graph topology. In this paper we consider two major forms of p2p topologies: (1) perfectly structured k-ary tree topologies that can be built from (virtually) ideal p2p graphs and (2) unstructured random tree topologies where new nodes randomly join as children to any of the existing peers. The two topologies represent an optimal low diameter structured p2p topology and a trivial randomly evolving sub-optimal topology, respectively. In this paper, we show the impact of key graph parameters, such as the maximum node-degree k and minimum tree-height D, on the performance of NCC in terms of NEF throughput as well as video quality for both structured and unstructured topologies. The utility of NCC/NEF for low-degree and/or less structured p2p topologies is especially highlighted by demonstrating that, embedding of additional codecs can render the performance of less structured topologies or higher diameter topologies to be almost as good as that of the very well structured low diameter topologies. We also investigate the impact of the graph properties on the placement of the NEF codecs