ملخص: We consider a scenario of broadcasting information over a network of nodes connected by noiseless communication links. A source node in the network has some data packets to broadcast. It encodes these data packets into n coded packets in such a way that any node in the network that receives any k out of the n coded packets will be able to retrieve all the original data packets. The source transmits the n coded packets 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 . We say that the information from the source undergoes a "near-broadcast" if 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. We study how, for a given k , this minimum forwarding probability and the associated expected total number of packet transmissions varies with n . We specifically analyze the probabilistic forwarding of coded packets on two 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, a judicious choice of n significantly reduces the expected total number of transmissions needed for a near-broadcast. Behaviour similar to that of the grid is also observed in other well-connected network topologies such as random geometric graphs and random regular graphs.

لغة: إنجليزية