Relay-aided multiuser communications are crucial for future 5G systems. In this paper, we consider the two-user multiple access relay channel (MARC), in which two users transmit messages to a common destination with the assistance of a half-duplex relay. The decode-and-forward (DF) based lattice coding was shown to be effective for the MARC in our previous work [1]. However when the links from the users to the relay are weak, DF protocol may fail to decode all users at the relay. Aiming to solve this problem, we propose a new lattice coding where the relay only needs to decode an integer-weighted-sum of users' lattice codewords, re-maps it with a modulo-based mapper and then forwards the corresponding codeword. Although the decoding at the relay is akin to the orthogonal compute-and-forward protocol, we relax the restriction imposed by previous works that the users have to be silent when the relay is transmitting to avoid interference. The key ingredient is the joint multi-user lattice decoding performed at the destination. This jointly decoding strategy not only complicates the corresponding code design but also the error analysis. To find the proper integer-weighted-sum at the relay for the destination's joint decoder, we also solve a non-convex integer problem by carefully transforming and relaxing it to a convex one. Simulation results show that the proposed non-orthogonal lattice coding can outperform existing schemes in a variety of channel settings.
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