At Every Corner: Determining Corner Points of Two-User Gaussian Interference Channels

TL;DR

This paper precisely characterizes the corner points of the capacity region for two-user Gaussian interference channels under various interference regimes, employing novel information-theoretic techniques that bypass complex integral and transportation methods.

Contribution

It introduces a new approach using almost Gaussian and almost linearly dependent vectors to determine corner points, avoiding traditional complex integral and transportation methods.

Findings

Exact determination of corner points for strong and weak interference regimes.

Novel proof techniques that simplify the analysis of interference channels.

Resolution of the 'missing' corner point problem without complex integrations.

Abstract

The corner points of the capacity region of the two-user Gaussian interference channel under strong or weak interference are determined using the notions of almost Gaussian random vectors, almost lossless addition of random vectors, and almost linearly dependent random vectors. In particular, the "missing" corner point problem is solved in a manner that differs from previous works in that it avoids the use of integration over a continuum of SNR values or of Monge-Kantorovitch transportation problems.