  A communication setup is considered where a transmitter wishes to
simultaneously sense its channel state and convey a message to a receiver. The
state is estimated at the transmitter by means of generalized feedback, i.e. a
strictly causal channel output that is observed at the transmitter. The
scenario is motivated by a joint radar and communication system where the radar
and data applications share the same frequency band. For the case of a
memoryless channel with i.i.d. state sequences, we characterize the
capacity-distortion tradeoff, defined as the best achievable rate below which a
message can be conveyed reliably while satisfying some distortion constraint on
state sensing. An iterative algorithm is proposed to optimize the input
probability distribution. Examples demonstrate the benefits of joint sensing
and communication as compared to a separation-based approach.
