  A joint communication and channel state estimation problem is investigated,
in which reliable information transmission over a noisy channel, and
high-fidelity estimation of the channel state, are simultaneously sought. The
tradeoff between the achievable information rate and the estimation distortion
is quantified by formulating the problem as a constrained channel coding
problem, and the resulting capacity-distortion function characterizes the
fundamental limit of the joint communication and channel estimation problem.
The analytical results are illustrated through case studies, and further issues
such as multiple cost constraints, channel uncertainty, and capacity per unit
distortion are also briefly discussed.
