Analyzing Network Coding (Gossip) Made Easy

Abstract

We introduce projection analysis—a new technique to analyze the stopping time of protocols that are based on random linear network coding (RLNC). Projection analysis drastically simplifies, extends, and strengthens previous results on RLNC gossip protocols. We analyze RLNC gossip in a general framework for network and communication models that encompasses and unifies the models used previously in this context. We show, in most settings for the first time, that the RLNC gossip converges with high probability in optimal time. Most stopping times are of the form O ( k + T ), where k is the number of messages to be distributed and T is the time it takes to disseminate one message. This means RLNC gossip achieves “perfect pipelining.” Our analysis directly extends to highly dynamic networks in which the topology can change completely at any time. This remains true, even if the network dynamics are controlled by a fully adaptive adversary that knows the complete network state. Virtually nothing besides simple O ( kT ) sequential flooding protocols was previously known for such a setting. While RLNC gossip works in this wide variety of networks our analysis remains the same and extremely simple. This contrasts with more complex proofs that were put forward to give less strong results for various special cases.