Anytime reliable transmission of real-valued information through digital noisy channels

Motivated by distributed sensor networks scenarios, we consider a problem of state estimation under communication constraints, in which a real-valued random vector needs to be reliably transmitted through a digital noisy channel. Estimations are sequentially updated by the receiver, as more and more channel outputs are observed. Assuming that no channel feedback is available at the transmitter, we study the rates at which the mean squared error of the estimation can be made to converge to zero with time. First, simple low-complexity schemes are considered, and trade-offs between performance and encoder/decoder complexity are found. Then, information-theoretic bounds on the best achievable error exponent are obtained.