  In an M x N interference network, there are M transmitters and N receivers
with each transmitter having independent messages for each of the 2^N -1
possible non-empty subsets of the receivers. We consider the 2 x 2 interference
network with 6 possible messages, of which the 2 x 2 interference channel and X
channel are special cases obtained by using only 2 and 4 messages respectively.
Starting from an achievable rate region similar to the Han-Kobayashi region, we
obtain an achievable sum rate. For the Gaussian interference network, we
determine which of the 6 messages are sufficient for maximizing the sum rate
within this rate region for the low, mixed, and strong interference conditions.
It is observed that 2 messages are sufficient in several cases.
