The Capacity of a Class of Multi-Way Relay Channels

TL;DR

This paper derives the capacity of a specific multi-way relay channel model where users communicate through a relay, demonstrating that the cut-set bound is achievable with advanced coding strategies, including joint source-channel coding.

Contribution

The paper provides a capacity characterization for multi-way relay channels with modular sum outputs, using novel coding schemes to achieve capacity at different user rates.

Findings

Capacity is achieved using rate splitting, functional-decode-forward, and joint source-channel coding.

The cut-set upper bound is tight and achievable for this channel class.

Joint source-channel coding is essential for capacity when users transmit at different rates.

Abstract

The capacity of a class of multi-way relay channels, where L users communicate via a relay (at possibly different rates), is derived for the case where the channel outputs are modular sums of the channel inputs and the receiver noise. The cut-set upper bound to the capacity is shown to be achievable. More specifically, the capacity is achieved using (i) rate splitting, (ii) functional-decode-forward, and (iii) joint source-channel coding. We note that while separate source-channel coding can achieve the common-rate capacity, joint source-channel coding is used to achieve the capacity for the general case where the users are transmitting at different rates.