Capacity Results for Two Classes of Three-Way Channels

TL;DR

This paper derives the capacity of three-way channels in finite-field and phase-fading AWGN scenarios, demonstrating achievable schemes with and without feedback, and introduces cooperative strategies for optimal performance.

Contribution

It provides the first capacity results for finite-field three-way channels and proposes cooperative feedback schemes for phase-fading AWGN channels.

Findings

Finite-field three-way channel capacity derived and achievable without feedback.

Non-cooperative scheme achieves equal-rate capacity in sender-symmetrical phase-fading AWGN channels.

Cooperative feedback scheme with relaying and network coding achieves capacity in reciprocal phase-fading AWGN channels.

Abstract

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.