Capacity Results for Two Classes of Three-Way Channels

This paper considers the three-way channel, consisting of three nodes, where each node broadcasts a message to the two other nodes. The capacity of the finite-field three-way channel is derived, and is shown to be achievable using a non-cooperative scheme without feedback. The same scheme is also shown to achieve the equal-rate capacity (when all nodes transmit at the same rate) of the sender-symmetrical (each node receives the same SNR from the other two nodes) phase-fading AWGN channel. In the light that the non-cooperative scheme is not optimal in general, a cooperative feedback scheme that utilizes relaying and network coding is proposed and is shown to achieve the equal-rate capacity of the reciprocal (each pair of nodes has the same forward and backward SNR) phase-fading AWGN three-way channel.