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A multi-way communication network with three nodes and a relay is considered. The three nodes in this so-called Y-channel, communicate with each other in a bi-directional manner via the relay. Studying this setup is important due to its being an important milestone for characterizing the capacity of larger networks. A transmit strategy for the Gaussian Y-channel is proposed, which mimics a previously considered scheme for the deterministic approximation of the Y-channel. Namely, a scheme which uses nested-lattice codes and lattice alignment is used, to perform network coding. A new mode of operation is introduced, named `cyclic communication', which interestingly turns out to be an important component for achieving the capacity region of the Gaussian Y-channel within a constant gap.

Signal space alignment for the Gaussian Y-channel