To observe or not to observe the channel state

We consider the problem of optimal probing of communication channel at the encoder for discrete memoryless channels (DMC) with i.i.d. states. The encoder generates an action sequence dependent on the message with which it probes the channel and hence acquires partial state information. This is further used causally or non-causally to generate channel input symbols while decoder may or may not have partial channel state information. We call the maximum achievable rate for such systems as the `Probing Capacity'. In this paper we characterize this capacity when channel inputs are allowed to depend causally or non-causally on partially observed state sequence.We motivate the problem by addressing the issue of characterizing the essential trade-off between the capacity and the cost `to observe or not to observe' the channel states at the encoder.