Achieving Capacity Region of 2-users Weak GIC by Enlarging the Core in a Nested Set of Polymatroids (continuation of arXiv:2012.07820 "Optimality of Gaussian in Enlarging HK Rate Region, and its Overlap with ...")

TL;DR

This paper presents a novel approach to characterizing the capacity region of a 2-user weak Gaussian Interference Channel by enlarging a nested set of Polymatroids, demonstrating the optimality of Gaussian codes.

Contribution

It introduces a new formulation using nested Polymatroids and dummy private messages to achieve the capacity region, extending previous work on HK rate regions.

Findings

Enlarging the core in nested Polymatroids characterizes the capacity region.

Gaussian random code-books are proven to be optimal.

The approach achieves the boundary of Han-Kobayashi constraints.

Abstract

This article shows that achieving capacity region of a 2-users weak Gaussian Interference Channel (GIC) is equivalent to enlarging the core in a nested set of Polymatroids (each equivalent to capacity region of a multiple-access channel) through maximizing a minimum rate, then projecting along its orthogonal span and continuing recursively. This formulation relies on defining dummy private messages to capture the effect of interference in GIC. It follows that relying on independent Gaussian random code-books is optimum, and the corresponding solution corresponds to achieving the boundary in HK constraints.