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In this paper, we propose a multi-lobe directional transmission for network coding in multi-rate ad hoc networks to improve throughput performance of XOR-based WNC. The proposed scheme uses directional antennas that can make antenna beam forms with multiple main lobes. In the proposed scheme, a node transmits uncoded packets with a beam form of one or multiple main lobes for realizing high-rate unicast transmissions. In addition, a node transmits XORed packets and native packets with a beam form of multiple main lobes with directional antenna to realize high-rate multicast transmissions. We evaluated and investigated the performance of the proposed scheme in terms of throughput via intensive computer simulations. The simulated results show that the proposed scheme can improve throughput performance of XOR-based WNC in some simple topologies such as 5 nodes straight line topology and X topology. In the fundamental evaluation, we have confirmed that the proposed scheme can achieve higher throughput than the conventional XOR-based WNC without using directional antennas in the same topologies. The proposed scheme is also applicable for other smart/directional antennas.