  In multi-terminal communication systems, signals carrying messages meant for
different destinations are often observed together at any given destination
receiver. Han and Kobayashi (1981) proposed a receiving strategy which performs
a joint unique decoding of messages of interest along with a subset of messages
which are not of interest. It is now well-known that this provides an
achievable region which is, in general, larger than if the receiver treats all
messages not of interest as noise. Nair and El Gamal (2009) and Chong, Motani,
Garg, and El Gamal (2008) independently proposed a generalization called
indirect or non-unique decoding where the receiver uses the codebook structure
of the messages to uniquely decode only its messages of interest. Non-unique
decoding has since been used in various scenarios.
  The main result in this paper is to provide an interpretation and a
systematic proof technique for why non-unique decoding, in all known cases
where it has been employed, can be replaced by a particularly designed joint
unique decoding strategy, without any penalty from a rate region viewpoint.
