  We consider the problem of coding over the multi-user Interference Channel
(IC). It is well-known that aligning the interfering signals results in
improved achievable rates in certain setups involving more than two users. We
argue that in the general interference problem, senders face a tradeoff between
communicating their message to their corresponding decoder or cooperating with
other users by aligning their signals. Traditionally, interference alignment is
carried out using structured codes such as linear codes and group codes. We
show through an example that the usual structured coding schemes used for
interference neutralization lack the necessary flexibility to optimize this
tradeoff. Based on this intuition, we propose a new class of codes for this
problem. We use the example to show that the application of these codes gives
strict improvements in terms of achievable rates. Finally, we derive a new
achievable region for the three user IC which strictly improves upon the
previously known inner bounds for this problem.
