  We present a case for the use of codes possessing algebraic closure
properties - coset codes - in developing coding techniques and characterizing
achievable rate regions for generic multi-terminal channels. In particular, we
consider three diverse communication scenarios - $3-$user interference channel
(many-to-many), $3-$user broadcast channel (one-to-many), and multiple access
with distributed states (many-to-one) - and identify non-additive examples for
which coset codes are analytically proven to yield strictly larger achievable
rate regions than those achievable using iid codes. On the one hand, our
findings motivate the need for multi-terminal information theory to step beyond
iid codes. On the other, it encourages current research of linear code-based
techniques to go beyond particular additive communication channels. Detailed
proofs of our results are available in [1]-[3].
