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This article shows that achieving capacity region of a 2-users weak GaussianInterference Channel (GIC) is equivalent to enlarging the core in a nested setof Polymatroids (each equivalent to capacity region of a multiple-accesschannel) through maximizing a minimum rate, then projecting along itsorthogonal span and continuing recursively. This formulation relies on definingdummy private messages to capture the effect of interference in GIC. It followsthat relying on independent Gaussian random code-books is optimum, and thecorresponding solution corresponds to achieving the boundary in HK constraints.

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 ...")