  Since the publication of Shannon's theory of one terminal source coding, a
number of interesting extensions have been derived by researchers such as
Slepian-Wolf, Wyner, Ahlswede-K\"{o}rner, Wyner-Ziv and Berger-Yeung.
Specifically, the achievable rate or rate-distortion region has been described
by a first order information-theoretic functional of the source statistics in
each of the above cases. At the same time several problems have also remained
unsolved. Notable two terminal examples include the joint distortion problem,
where both sources are reconstructed under a combined distortion criterion, as
well as the partial side information problem, where one source is reconstructed
under a distortion criterion using information about the other (side
information) available at a certain rate (partially). In this paper we solve
both of these open problems. Specifically, we give an infinite order
description of the achievable rate-distortion region in each case. In our
analysis we set the above problems in a general framework and formulate a
unified methodology that solves not only the problems at hand but any two
terminal problem with noncooperative encoding. The key to such unification is
held by a fundamental source coding principle which we derive by extending the
typicality arguments of Shannon and Wyner-Ziv. Finally, we demonstrate the
expansive scope of our technique by re-deriving known coding theorems. We shall
observe that our infinite order descriptions simplify to the expected first
order in the known special cases.
