On Joint Communication and Channel Discrimination

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.