  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.
