Abstract
Combining topology control with network coding has been recently noticed which provides essential advantages, such as lower energy consumption and higher lifetime. In this letter, we utilize optimization and graph theory to propose a mathematical perspective for combining network coding with transmission range adjustment in wireless sensor network (WSN). For this aim, we define an extended optimization problem based on two vectors of variables, including transmission range and network flow. In particular, it is proved that there is a coding solution if and only if the extended optimization problem has at least an optimal solution. Due to this theorem, a new objective function is provided which is more practical to prolong the lifetime of WSNs. Simulation results demonstrate that the proposed model could adjust transmission range efficiently to obtain the optimal lifetime for network-coding-based WSNs.
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