  We consider a basic communication and sensing setup comprising a transmitter,
a receiver and a sensor. The transmitter sends an encoded sequence to the
receiver through a discrete memoryless channel, and the receiver is interested
in decoding the sequence. On the other hand, the sensor picks up a noisy
version of the transmitted sequence through one of two possible discrete
memoryless channels. The sensor knows the transmitted sequence and wishes to
discriminate between the two possible channels, i.e. to identify the channel
that has generated the output given the input. We study the trade-off between
communication and sensing in the asymptotic regime, captured in terms of the
coding rate to the receiver against the discrimination error exponent at the
sensor. We characterize the optimal rate-exponent trade-off for general
discrete memoryless channels with an input cost constraint.
