Multicast Throughput Order of Network Coding in Wireless Ad-hoc Networks

• Published in: IEEE transactions on communications Vol. 59; no. 2; pp. 497 - 506
• Main Authors: Karande, S S, Zheng Wang, Sadjadpour, Hamid R, Garcia-Luna-Aceves, J J
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2011; Institute of Electrical and Electronics Engineers
• Subjects: Ad hoc networks; Applied sciences; Business and industry local networks; Capacity; Coding, codes; Exact sciences and technology; Information, signal and communications theory; multicast; Network coding; Networks and services in france and abroad; Protocols; Receivers; Signal and communications theory; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Throughput; Transmission and modulation (techniques and equipments); Unicast; Wireless networks; Multicast; network coding; Coding; Capacity; Wireless telecommunication; Information rate; Wireless network; Ad hoc network; Information transmission; Data broadcast; Information dissemination; Nodes
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2011.121410.090368

We consider a network with n nodes distributed uniformly in a unit square. We show that, under the protocol model, when n s = Ω (log(n) 1+α ) out of the n nodes, each act as source of independent information for a multicast group consisting of m randomly chosen destinations, the per-session capacity in the presence of network coding (NC) has a tight bound of Θ(√n/n s √mlog(n)) when m = O(n/log(n)) and Θ(1/n s ) when m = Ω(n/log(n)). In the case of the physical model, we consider n s = n and show that the per-session capacity under the physical model has a tight bound of Θ(1/√mn) when m = O(n/(log(n)) 3 ), and Θ(1/n) when m = Ω(n/log(n)). Prior work has shown that these same order bounds are achievable utilizing only traditional store-and-forward methods. Consequently, our work implies that the network coding gain is bounded by a constant for all values of m. For the physical model we have an exception to the above conclusion when m is bounded by O(n/(log(n)) 3 ) and Ω(n/log(n)). In this range, the network coding gain is bounded by O((log(n)) 1/2 ).