We introduce the notion of an `action' into two classical
Shannon-theoretic frameworks.

The first is the Wyner-Ziv problem of source coding with decoder
side information. We revisit and extend this problem to the case
where the decoder is allowed to choose actions that  affect the
nature and quality of the side information. Actions may have costs
that are commensurate with the quality of the side information they
yield, and  an overall per-symbol cost constraint may be imposed. We
characterize the achievable tradeoff between rate, distortion, and
cost.


The second is the Gelfand-Pinsker problem of communication with
transmitter state information. We revisit and extend this problem to
channels with action-dependent states:  Given the message to be
communicated, the transmitter chooses  actions  that affect the
formation of the channel states, and  then creates the channel input
sequence based on the state sequence. We characterize the capacity
of such  channels both for the case where the channel inputs are
allowed to depend non-causally on the state sequence and the case
where they are restricted to causal dependence, under cost
constraints on the actions and/or the channel inputs.


Among our findings is the fact that even in the absence of cost
constraints, both for the source coding and the channel coding
problem, greedily choosing the action associated with the `best'
side information/channel state is, in general, sub-optimal.
  Our results cover a variety of new coding scenarios such as source
  coding under a limited budget of measurements, and coding for  channels with a
`rewrite' option. A few examples are worked out in detail.

Parts of this talk are based on collaborations with Haim Permuter
and with Sergio Verd\'{u}.