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 nearbroadcast. 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.Index Terms-Broadcast, ad-hoc networks, probabilistic forwarding, coded packets, site percolation.
I. MOTIVATIONA N AD-HOC network is a network of nodes which communicate with each other without relying on any centralized infrastructure. A classical example of ad-hoc networks is wireless sensor networks (WSNs) which have sensors measuring temperature, humidity etc. connected with each other. The Internet of Things (IoT) network, which involves different types of physical devices-sensors, actuators, routers, mobiles etc.-communicating with each other over a network can be thought of as an ad-hoc network.Broadcast mechanisms on such distributed networks are crucial in order to disburse key network-related information throughout the network. In the applications mentioned above,