  We consider a basic joint communication and sensing setup comprising a
transmitter, a receiver and a sensor. The transmitter sends a codeword to the
receiver through a discrete memoryless channel, and the receiver is interested
in retrieving the underlying encoded message. On the other hand, the sensor
picks up a noisy version of the transmitted codeword through one of two
possible discrete memoryless channels. The sensor knows the codeword 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
message coding rate against the two types of discrimination error exponents. We
characterize the optimal trade-off between the rate and the exponents for
general discrete memoryless channels with an input cost constraint.
