Are Generalized Cut-Set Bounds Tight for the Deterministic Interference Channel?

TL;DR

This paper introduces extended networks and applies the generalized cut-set bound to establish tight capacity bounds for two- and three-user deterministic interference channels, advancing understanding of their fundamental limits.

Contribution

It proposes a novel method of extended networks combined with the GCS bound to derive tight capacity bounds for multi-user deterministic interference channels.

Findings

Tight capacity bounds for two-user DIC established.

Extended networks enable precise capacity analysis.

Method extends to symmetric three-user DIC.

Abstract

We propose the idea of extended networks, which is constructed by replicating the users in the two-user deterministic interference channel (DIC) and designing the interference structure among them, such that any rate that can be achieved by each user in the original network can also be achieved simultaneously by all replicas of that user in the extended network. We demonstrate that by carefully designing extended networks and applying the generalized cut-set (GCS) bound to them, we can derive a tight converse for the two-user DIC. Furthermore, we generalize our techniques to the three-user DIC, and demonstrate that the proposed approach also results in deriving a tight converse for the three-user DIC in the symmetric case.