Probabilistic Forwarding of Coded Packets on Networks

We consider a scenario of broadcasting information over a network of nodes connected by noiseless communication links. A source node in the network has k data packets to broadcast, and it suffices that a large fraction of the network nodes receives the broadcast. The source encodes the k data packets into n≥k coded packets using a maximum distance separable (MDS) code, and transmits them to its one-hop neighbours. Every other node in the network follows a probabilistic forwarding protocol, in which it forwards a previously unreceived packet to all its neighbours with a certain probability p. A "near-broadcast" is when the expected fraction of nodes that receive at least k of the n coded packets is close to 1. The forwarding probability p is chosen so as to minimize the expected total number of transmissions needed for a near-broadcast. In this paper, we analyze the probabilistic forwarding of coded packets on two specific network topologies: binary trees and square grids. For trees, our analysis shows that for fixed k, the expected total number of transmissions increases with n. On the other hand, on grids, we use ideas from percolation theory to show that a judicious choice of n will significantly reduce the expected total number of transmissions needed for a near-broadcast.