  We consider the problem of optimal probing of states of a channel by
transmitter and receiver for maximizing rate of reliable communication. The
channel is discrete memoryless (DMC) with i.i.d. states. The encoder takes
probing actions dependent on the message. It then uses the state information
obtained from probing causally or non-causally to generate channel input
symbols. The decoder may also take channel probing actions as a function of the
observed channel output and use the channel state information thus acquired,
along with the channel output, to estimate the message. We refer to the maximum
achievable rate for reliable communication for such systems as the 'Probing
Capacity'. We characterize this capacity when the encoder and decoder actions
are cost constrained. To motivate the problem, we begin by characterizing the
trade-off between the capacity and fraction of channel states the encoder is
allowed to observe, while the decoder is aware of channel states. In this
setting of 'to observe or not to observe' state at the encoder, we compute
certain numerical examples and note a pleasing phenomenon, where encoder can
observe a relatively small fraction of states and yet communicate at maximum
rate, i.e. rate when observing states at encoder is not cost constrained.
