  In this paper, we take a unified approach for network information theory and
prove a coding theorem, which can recover most of the achievability results in
network information theory that are based on random coding. The final
single-letter expression has a very simple form, which was made possible by
many novel elements such as a unified framework that represents various network
problems in a simple and unified way, a unified coding strategy that consists
of a few basic ingredients but can emulate many known coding techniques if
needed, and new proof techniques beyond the use of standard covering and
packing lemmas. For example, in our framework, sources, channels, states and
side information are treated in a unified way and various constraints such as
cost and distortion constraints are unified as a single joint-typicality
constraint.
  Our theorem can be useful in proving many new achievability results easily
and in some cases gives simpler rate expressions than those obtained using
conventional approaches. Furthermore, our unified coding can strictly
outperform existing schemes. For example, we obtain a generalized
decode-compress-amplify-and-forward bound as a simple corollary of our main
theorem and show it strictly outperforms previously known coding schemes. Using
our unified framework, we formally define and characterize three types of
network duality based on channel input-output reversal and network flow
reversal combined with packing-covering duality.
