On the Capacity Region of the Deterministic Y-Channel with Common and Private Messages

TL;DR

This paper analyzes the capacity region of a deterministic Y-channel with private and common messages, proposing bounds and achievable schemes, but notes the bounds are not tight enough for full characterization.

Contribution

It introduces outer bounds and a greedy achievable scheme for the deterministic Y-channel with mixed messages, advancing understanding of its capacity limits.

Findings

Outer bounds on the rate region are established.

A greedy scheme achieves the outer bounds at certain relay levels.

Bounds are insufficient for complete capacity characterization.

Abstract

In multi user Gaussian relay networks, it is desirable to transmit private information to each user as well as common information to all of them. However, the capacity region of such networks with both kinds of information is not easy to characterize. The prior art used simple linear deterministic models in order to approximate the capacities of these Gaussian networks. This paper discusses the capacity region of the deterministic Y-channel with private and common messages. In this channel, each user aims at delivering two private messages to the other two users in addition to a common message directed towards both of them. As there is no direct link between the users, all messages must pass through an intermediate relay. We present outer-bounds on the rate region using genie aided and cut-set bounds. Then, we develop a greedy scheme to define an achievable region and show that at a certain number of levels at the relay, our achievable region coincides with the upper bound. Finally, we argue that these bounds for this setup are not sufficient to characterize the capacity region.