The Approximate Capacity Region of the Gaussian Y-Channel via the Deterministic Approach

A full-duplex wireless network with three users that want to establish full message exchange via a relay is considered. Thus, this network which is known as the Y-channel has a total of six messages, two outgoing, and two incoming at each user. The users are not physically connected, and thus the relay is essential for their communication. The deterministic Y-channel is considered first, its capacity region is characterized, and shown not to be given by the cut-set bounds. The capacity achieving scheme has three different components (strategies): 1) a bidirectional; 2) a cyclic; and 3) a unidirectional strategy. Network coding is used to realize the bidirectional and the cyclic strategies, and thus to prove the achievability of the capacity region. The result is then extended to the Gaussian Y-channel where the capacity region is characterized within a constant gap independent of the channel parameters.