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Previous researches regard the signals from other users as interfereces to be avoided in wireless ad-hoc network systems (e.g, IEEE 802.11/16). However, if the purpose of ad-hoc communications is relaying information from one node to another node through the third node, we can apply the network coding (NC) at the physical layer to increase a capacity by regarding a received signal from different nodes as one added signal. In this papar, we combine NC for MIMO relay systems with a linear pre-equalizer. For examples, zero-forcing (ZF) or lattice reduction-aided ZF pre-equalizers is used at each transmitter. We have evaluated the proposed system by comparing uncoded BER performance with those of several one-way relaying scheme focused on phase 1 mainly, because the overall performance is upperbounded by that of phase 1. The proposed system increases a multiplexing gain twice, maintaining a same diversity order, compared to one-way relaying. Finally, we combine the lattice encoder and the decoder to achieve an optimal capacity of the proposed scheme.