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This letter investigates rate adaptation of network coding (NC) in a wireless network. In the network, two independent data flows intersect at a relay and a receiver can overhear the data flow of which it is not the intended destination. We propose NC schemes which actively exploit the overhearing channels by adapting the transmission rate to the direct- and overhearing-channel conditions. The proposed schemes allow a receiver to overhear only part of the data-flow by rate splitting, thus significantly improving the throughput in poor overhearing-channel conditions.