On the Optimality of Treating Interference as Noise

TL;DR

This paper proves that in certain interference channels, treating interference as noise with simple coding schemes is near-optimal, achieving the capacity region within a constant gap under specific signal strength conditions.

Contribution

It establishes conditions under which treating interference as noise is optimal, characterizes the GDoF region as a polyhedron, and proves the scheme's optimality without time-sharing.

Findings

TIN scheme achieves all capacity points within a constant gap under specified conditions.

The GDoF region is a polyhedron fully achieved by TIN without time-sharing.

Theoretical proof of TIN's optimality in the described regime.

Abstract

It is shown that in the K-user interference channel, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in dB scale), then the simple scheme of using point to point Gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise at every receiver (in short, TIN scheme) achieves all points in the capacity region to within a constant gap. The generalized degrees of freedom (GDoF) region under this condition is a polyhedron, which is shown to be fully achieved by the same scheme, without the need for time-sharing. The results are proved by first deriving a polyhedral relaxation of the GDoF region achieved by TIN, then providing a dual characterization of this polyhedral region via the use of potential functions, and finally proving the optimality of this region in the desired regime.