In this paper, we introduce multi-link two-way relay channels where multiple two-way relay systems are interfering with each other. We study the capacity of this system by investigating the degree of freedom (DOF) with various message settings. Specifically, we consider two cases of two-way relay interference channels and two-way relay X channels. We show that the two-way relay interference channel where all nodes have M antennas obtains the DOF of 2M and compare with multipair two-way relay channels. Next, we introduce general message settings for two-way relay X channels. For the case where each user is equipped with 3 antennas and relays have 4 antennas, we prove that the DOF of 8 is achieved by employing network coding.
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