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The problem of reliably transmitting a real-valued random vector through a digital noisy channel is relevant for the design of distributed estimation and control techniques over networked systems. One important example consists in the remote state estimation under communication constraints. In this case, an anytime transmission scheme consists of an encoder—which maps the real vector into a sequence of channel inputs—and a decoder—which sequentially updates its estimate of the vector as more and more channel outputs are observed. The encoder performs both source and channel coding of the data. Assuming that no channel feedback is available at the transmitter, this paper studies the rates of convergence to zero of the mean squared error. Two coding strategies are analyzed: the first one has exponential convergence rate but is expensive in terms of its encoder/decoder computational complexity, while …