  In this paper, we show that the total Degrees-Of-Freedoms (DOF) of the
$K$-user Gaussian Interference Channel (GIC) can be achieved by incorporating a
new alignment technique known as \emph{real interference alignment}. This
technique compared to its ancestor \emph{vector interference alignment}
performs on a single real line and exploits the properties of real numbers to
provide optimal signaling. The real interference alignment relies on a new
coding scheme in which several data streams having fractional multiplexing
gains are sent by transmitters and interfering streams are aligned at
receivers. The coding scheme is backed up by a recent result in the field of
Diophantine approximation, which states that the convergence part of the
Khintchine-Groshev theorem holds for points on non-degenerate manifolds.
