  We investigate the optimal performance of dense sensor networks by studying
the joint source-channel coding problem. The overall goal of the sensor network
is to take measurements from an underlying random process, code and transmit
those measurement samples to a collector node in a cooperative multiple access
channel with feedback, and reconstruct the entire random process at the
collector node. We provide lower and upper bounds for the minimum achievable
expected distortion when the underlying random process is stationary and
Gaussian. In the case where the random process is also Markovian, we evaluate
the lower and upper bounds explicitly and show that they are of the same order
for a wide range of sum power constraints. Thus, for a Gauss-Markov random
process, under these sum power constraints, we determine the achievability
scheme that is order-optimal, and express the minimum achievable expected
distortion as a function of the sum power constraint.
