  The Wyner-Ahlswede-K\"orner (WAK) empirical-coordination problem where the
encoders cooperate via a finite-capacity one-sided link is considered. The
coordination-capacity region is derived by combining several source coding
techniques, such as Wyner-Ziv (WZ) coding, binning and superposition coding.
Furthermore, a semi-deterministic (SD) broadcast channel (BC) with one-sided
decoder cooperation is considered. Duality principles relating the two problems
are presented, and the capacity region for the SD-BC setting is derived. The
direct part follows from an achievable region for a general BC that is tight
for the SD scenario. A converse is established by using telescoping identities.
The SD-BC is shown to be operationally equivalent to a class of relay-BCs
(RBCs) and the correspondence between their capacity regions is established.
The capacity region of the SD-BC is transformed into an equivalent region that
is shown to be dual to the admissible region of the WAK problem in the sense
that the information measures defining the corner points of both regions
coincide. Achievability and converse proofs for the equivalent region are
provided. For the converse, we use a probabilistic construction of auxiliary
random variables that depends on the distribution induced by the codebook.
Several examples illustrate the results.
