This talk investigates the value of interaction for two-terminal source coding
with reconstruction constraints. Communication consists of multiple rounds that
either take place sequentially among the terminals or simultaneously. In the
first case considered, each terminal wants to estimate the other source with
constrained reconstruction constraints at both ends. The next case involves
computation of a general function of the two sources with common reconstruction
constraint.  In both cases, an exact characterization of the rate region is
provided. To gain more insight, the rate region for jointly Gaussian sources
with common reconstruction constraint is computed and it is observed that for
certain functions the same sum rate can be achieved irrespective of the order of
communication.