3 for all values of channel coefficients, and approaches 1 bit as the transmit power increases.'
author:
- 
- '[^1]'
bibliography:
- '/home/chaaban/tex/myBib.bib'
title: 'On the Sum Capacity of the Y-Channel'
---

Multi-way relaying, sum-capacity, functional decode-and-forward, constant gap.

Introduction
============

A multi-way channel is a scenario where users communicate with each other in both directions. The smallest multi-way communication model is the two way channel [@Shannon_TWC] where 2 nodes communicate with each other, and each has a message to deliver to the other node. In this sense, each node is a source and a destination at the same time.

The two-way channel can be extended into a bi-directional relay channel by including a relay in the model. In the bi-directional relay channel, two nodes communicate with each other via a relay. This setup was introduced in [@RankovWittneben] where relaying protocols were analyzed. In [@KimDevroyeMitranTarokh], further relaying protocols were proposed, and their achievable rate regions were compared to previous work. Achievable schemes for this setup using decode-and-forward and compress-and-forward were studied in [@GunduzTuncelNayak] where rate regions were given and capacity was characterized within half a bit for the Gaussian setting. The capacity region of the two-way relay channel was also 