An Optimal Coding Strategy for the Binary Multi-Way Relay Channel

TL;DR

This paper determines the maximum achievable data exchange rate in a binary multi-way relay channel using a new coding method where the relay decodes functions of messages rather than individual messages, enabling efficient multi-user communication.

Contribution

It introduces a novel functional-decode-forward coding strategy that achieves the capacity of the binary multi-way relay channel, a significant advancement over previous methods.

Findings

Capacity of the binary multi-way relay channel is derived.

Functional-decode-forward coding strategy achieves capacity.

Relay decodes functions of messages, not individual messages.

Abstract

We derive the capacity of the binary multi-way relay channel, in which multiple users exchange messages at a common rate through a relay. The capacity is achieved using a novel functional-decode-forward coding strategy. In the functional-decode-forward coding strategy, the relay decodes functions of the users' messages without needing to decode individual messages. The functions to be decoded by the relay are defined such that when the relay broadcasts the functions back to the users, every user is able to decode the messages of all other users.