  The interference channel achievable rate region is presented when the
interference is treated as noise. The formulation starts with the 2-user
channel, and then extends the results to the n-user case. The rate region is
found to be the convex hull of the union of n power control rate regions, where
each power control rate region is upperbounded by a (n-1)-dimensional
hyper-surface characterized by having one of the transmitters transmitting at
full power. The convex hull operation lends itself to a time-sharing operation
depending on the convexity behavior of those hyper-surfaces. In order to know
when to use time-sharing rather than power control, the paper studies the
hyper-surfaces convexity behavior in details for the 2-user channel with
specific results pertaining to the symmetric channel. It is observed that most
of the achievable rate region can be covered by using simple On/Off binary
power control in conjunction with time-sharing. The binary power control
creates several corner points in the n-dimensional space. The crystallized rate
region, named after its resulting crystal shape, is hence presented as the
time-sharing convex hull imposed onto those corner points; thereby offering a
viable new perspective of looking at the achievable rate region of the
interference channel.
