Gaussian Interference Networks: Sum Capacity in the Low Interference Regime and New Outer Bounds on the Capacity Region

TL;DR

This paper improves understanding of Gaussian interference networks by deriving new outer bounds and showing that treating interference as noise is optimal in low interference regimes, with results extending to networks with many users.

Contribution

The paper introduces improved outer bounds on the capacity region and generalizes the low interference regime results to multi-user Gaussian interference networks.

Findings

Treating interference as noise achieves sum capacity in low interference regimes.

New outer bounds tighten the capacity region estimates.

Interference threshold for optimality increases with number of users.

Abstract

Establishing the capacity region of a Gaussian interference network is an open problem in information theory. Recent progress on this problem has led to the characterization of the capacity region of a general two user Gaussian interference channel within one bit. In this paper, we develop new, improved outer bounds on the capacity region. Using these bounds, we show that treating interference as noise achieves the sum capacity of the two user Gaussian interference channel in a low interference regime, where the interference parameters are below certain thresholds. We then generalize our techniques and results to Gaussian interference networks with more than two users. In particular, we demonstrate that the total interference threshold, below which treating interference as noise achieves the sum capacity, increases with the number of users.