Kumar, BRV and Kashyap, N (2021) Probabilistic Forwarding of Coded Packets on Networks. In: IEEE/ACM Transactions on Networking, 29 (1). pp. 234247.

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Abstract
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 onehop 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 'nearbroadcast' 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 nearbroadcast. Behaviour similar to that of the grid is also observed in other wellconnected network topologies such as random geometric graphs and random regular graphs. Â© 19932012 IEEE.
Item Type:  Journal Article 

Publication:  IEEE/ACM Transactions on Networking 
Publisher:  Institute of Electrical and Electronics Engineers Inc. 
Additional Information:  The copyright of this article belongs to Institute of Electrical and Electronics Engineers Inc. 
Keywords:  Binary trees; Network coding; Packet networks; Probability; Topology, Connected networks; Forwarding probabilities; Network topology; Number of transmissions; Packet transmissions; Probabilistic forwarding; Random geometric graphs; Random regular graph, Broadcasting 
Department/Centre:  Division of Electrical Sciences > Electrical Communication Engineering 
Date Deposited:  11 Mar 2021 09:32 
Last Modified:  11 Mar 2021 09:32 
URI:  http://eprints.iisc.ac.in/id/eprint/68197 
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