Young-Han Kim, Arak Sutivong, and Thomas M. Cover
IEEE Transactions on Information Theory, vol. 54, no. 5, pp. 1850–1859, May 2008.
Preliminary results appeared in Proceedings of IEEE International Symposium on Information Theory, pp. 916–920, Nice, France, June 2007.
We consider the problem of transmitting data at rate over a
state-dependent channel
with state information available at
the sender and at the same time conveying the information about the
channel state itself to the receiver. The amount of state information
that can be learned at the receiver is captured by the mutual
information
between the state sequence
and the
channel output
. The optimal tradeoff is characterized between
the information transmission rate
and the state uncertainty
reduction rate
, when the state information is either causally
or noncausally available at the sender. In particular, when state
transmission is the only goal, the maximum uncertainty reduction rate
is given by
. This result is
closely related and in a sense dual to a recent study by Merhav and
Shamai, which solves the problem of masking the state
information from the receiver rather than conveying it.