The Deterministic Capacity of Relay Networks with Relay Private Messages

TL;DR

This paper characterizes the capacity region of a deterministic 4-node network where one node acts as a relay with private messages, using a novel upper bound and an achievable scheme combining broadcasting and detour strategies.

Contribution

It introduces a new capacity characterization for a deterministic relay network with private messages, employing a single-sided genie bound and a combined broadcasting and detour scheme.

Findings

Derived a tight upper bound on the capacity region.

Constructed an achievable scheme matching the upper bound.

Extended the understanding of relay networks with private messages.

Abstract

We study the capacity region of a deterministic 4-node network, where 3 nodes can only communicate via the fourth one. However, the fourth node is not merely a relay since it can exchange private messages with all other nodes. This situation resembles the case where a base station relays messages between users and delivers messages between the backbone system and the users. We assume an asymmetric scenario where the channel between any two nodes is not reciprocal. First, an upper bound on the capacity region is obtained based on the notion of single sided genie. Subsequently, we construct an achievable scheme that achieves this upper bound using a superposition of broadcasting node 4 messages and an achievable "detour" scheme for a reduced 3-user relay network.