  Motivated by computer networks and machine-to-machine communication
applications, a bidirectional link is studied in which two nodes, Node 1 and
Node 2, communicate to fulfill generally conflicting informational
requirements. Node 2 is able to acquire information from the environment, e.g.,
via access to a remote data base or via sensing. Information acquisition is
expensive in terms of system resources, e.g., time, bandwidth and energy and
thus should be done efficiently by adapting the acquisition process to the
needs of the application. As a result of the forward communication from Node 1
to Node 2, the latter wishes to compute some function, such as a suitable
average, of the data available at Node 1 and of the data obtained from the
environment. The forward link is also used by Node 1 to query Node 2 with the
aim of retrieving suitable information from the environment on the backward
link. The problem is formulated in the context of multi-terminal
rate-distortion theory and the optimal trade-off between communication rates,
distortions of the information produced at the two nodes and costs for
information acquisition at Node 2 is derived. The issue of robustness to
possible malfunctioning of the data acquisition process at Node 2 is also
investigated. The results are illustrated via an example that demonstrates the
different roles played by the forward communication, namely data exchange,
query and control.
