  The channel synthesis problem has been widely investigated over the last
decade. In this paper, we consider the sequential version in which the encoder
and the decoder work in a sequential way. Under a mild assumption on the target
joint distribution we provide a complete (single-letter) characterization of
the solution for the point-to-point case, which shows that the canonical
symbol-by-symbol mapping is not optimal in general, but is indeed optimal if we
make some additional assumptions on the encoder and decoder. We also extend
this result to the broadcast scenario and the interactive communication
scenario. We provide bounds in the broadcast setting and a complete
characterization of the solution under a mild condition on the target joint
distribution in the interactive communication case. Our proofs are based on a
R\'enyi entropy method.
