Abstract-We present the first unified modeling framework for the computation of the throughput capacity of random wireless ad hoc networks in which information is disseminated by means of unicast routing, multicast routing, broadcasting, or different forms of anycasting. We introduce (n, m, k)-casting as a generalization of all forms of one-to-one, one-to-many and many-to-many information dissemination in wireless networks. In this context, n, m, and k denote the total number of nodes in the network, the number of destinations for each communication group, and the actual number of communication-group members that receive information (i.e., k ≤ m), respectively.We compute upper and lower bounds for the (n, m, k)-cast throughput capacity in random wireless networks. When m = k = Θ(1), the resulting capacity equals the well-known capacity result for multi-pair unicasting by Gupta and Kumar. We demonstrate that Θ(1/ √ mn log n) bits per second constitutes a tight bound for the capacity of multicasting (i.e., m = k < n) when m ≤ Θ (n/(log n)). We show that the multicast capacity of a wireless network equals its capacity for multi-pair unicasting when the number of destinations per multicast source is not a function of n. We also show that the multicast capacity of a random wireless ad hoc network is Θ (1/n), which is the broadcast capacity of the network, when m ≥ Θ(n/ log n). Furthermore, we show that Θ( √ m/(k √ n log n)), Θ(1/(k log n)) and Θ(1/n) bits per second constitutes a tight bound for the throughput capacity of multicasting (i.e., k < m < n) when Θ(1) ≤ m ≤ Θ (n/ log n), k ≤ Θ (n/ log n) ≤ m ≤ n and Θ (n/ log n) ≤ k ≤ m ≤ n respectively.
Abstract-We demonstrate that the gain attained by network coding (NC) on the multicast capacity of random wireless ad hoc networks is bounded by a constant factor. We consider a network with n nodes distributed uniformly in a unit square, with each node acting as a source for independent information to be sent to a multicast group consisting of m randomly chosen destinations. We show that, under the protocol model, the persession capacity in the presence of arbitrary NC has a tight). Our result follows from the fact that prior work has shown that the same order bounds are achievable with pure routing based only on traditional store-and-forward methods.
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