In this paper, we aim to find a robust network formation strategy that can adaptively evolve the network topology against network dynamics in a distributed manner. We consider a network coding deployed wireless ad hoc network where source nodes are connected to terminal nodes with the help of intermediate nodes. We show that mixing operations in network coding can induce packet anonymity that allows the inter-connections in a network to be decoupled. This enables each intermediate node to consider complex network inter-connections as a node-environment interaction such that the Markov decision process (MDP) can be employed at each intermediate node. The optimal policy that can be obtained by solving the MDP provides each node with optimal amount of changes in transmission range given network dynamics (e.g., the number of nodes in the range and channel condition). Hence, the network can be adaptively and optimally evolved by responding to the network dynamics. The proposed strategy is used to maximize long-term utility, which is achieved by considering both current network conditions and future network dynamics. We define the utility of an action to include network throughput gain and the cost of transmission power. We show that the resulting network of the proposed strategy eventually converges to stationary networks, which maintain the states of the nodes. Moreover, we propose to determine initial transmission ranges and initial network topology that can expedite the convergence of the proposed algorithm. Our simulation results confirm that the proposed strategy builds a network which adaptively changes its topology in the presence of network dynamics. Moreover, the proposed strategy outperforms existing strategies in terms of system goodput and successful connectivity ratio.
The max-flow min-cut bound is a fundamental result in the theory of communication networks, which characterizes the optimal throughput for a point-to-point communication network. The recent work of extended it to single-source multisink multicast networks and proved that this bound can be achieved by linear codes. Following this line, Erez and Feder as well as Ngai and Yeung proved that the max-flow min-cut bound remains tight in single-source two-sink nonmulticast networks. But the max-flow min-cut bound is in general quite loose (see Yeung, 2002). On the other hand, the admissible rate region of communication networks has been studied by Yeung and Zhang as well as Song and Yeung, but the bounds obtained by these authors are not explicit. In this work, we prove a new explicit outer bound for arbitrary multisource multisink networks and demonstrate its relation with the minimum cost network coding problem. We also determine the capacity region for a special class of three-layer networks.  In this paper we consider the application of network coding to a multiple unicast setup. Wbe present two suboptimal, yet practical code construction techniques. One consists of a linear program and the other of an integer program with fewer variables and constraints. We discuss the performance of the proposed techniques as well as their complexity. In this letter, we propose a distributed network formation solution for network coding deployed wireless networks which includes multisource multicast flows. This is an attempt to solve an open problem of network coding based multisource multicast flow design based on a game theoretic approach, which can eventually form a network in a distributed way. The network is in particular constructed by individual decision makings of the nodes, while taking advantages of network coding techniques. The decisions made by the nodes include the transmission powers and the use of network coding operations. In each stage game, nodes update the parameters based on feedbacks such as rewards, penalties, and evaluate their prior actions, which enables the nodes to make best responses in the next stage game. Our simulations confirm that the resulting network can reduce overall power consumption compared to direct transmission, and improve system throughput with less power consumption compared to no coding strategy.