characterized within a constant gap in [@AvestimehrSezginTse]. These results were also extended to the larger network consisting of two pair of nodes in addition to the relay. The approximate capacity of the two-pair bi-directional relay network was obtained in [@SezginKhajehnejadAvestimehrHassibi] and [@SezginAvestimehrKhajehnejadHassibi].

If more than two nodes want to communicate via a relay in a bi-directional manner, we get the multi-way relay channel. The multi-way relay channel was studied in [@GunduzYenerGoldsmithPoor], where upper and lower bounds for the capacity of the Gaussian multi-way relay channel were given. In their setup, Gündüz et al. divided users into several clusters, where each user in a cluster has a single message intended to all other users in the same cluster. All users communicate simultaneously via a relay. A similar setup was considered in [@OngKellettJohnson], where all users belong to the same cluster and all channel gains are equal. The authors of [@OngKellettJohnson] obtained the sum-capacity of this Gaussian setup with more than 2 users.

In this paper, we consider a Gaussian 3-way relay channel, with a slight difference from the aforementioned multi-way relay channel. In our 3-way channel, 3 users communicate with each other simultaneously via a relay. However, each user has 2 