Channel capacity and state estimation for state-dependent Gaussian channels
Arak Sutivong, Mung Chiang, Thomas M. Cover, and Young-Han Kim
IEEE Transactions on Information Theory, vol. 51, no. 4, pp. 1486–1495, April 2005.
One-page abstract appeared in Proceedings of IEEE International Symposium on Information Theory, p. 226, Lausanne, Switzerland, June/July 2002.
We formulate a problem of state information transmission over a
state-dependent channel with states known at the transmitter. In
particular, we solve a problem of minimizing the mean-squared channel
state estimation error 
for a state-dependent
additive Gaussian channel 
with an independent
and identically distributed (i.i.d.) Gaussian state sequence 
known at the transmitter and an unknown
i.i.d. additive Gaussian noise 
. We show that a simple technique
of direct state amplification (i.e., 
), where the
transmitter uses its entire power budget to amplify the channel state,
yields the minimum mean-squared state estimation error. This same
channel can also be used to send additional independent information at
the expense of a higher channel state estimation error. We
characterize the optimal tradeoff between the rate R of the
independent information that can be reliably transmitted and the
mean-squared state estimation error D. We show that any optimal (R, D)
tradeoff pair can be achieved via a simple power-sharing technique,
whereby the transmitter power is appropriately allocated between pure
information transmission and state amplification.