ABSTRACT

We now turn to the more general question of identifying fundamental limits on the performance of a system being controlled across an analog erasure channel, and the design of encoders and decoders to achieve such limits as discussed, for example, in [7]. To proceed, we must define the class of encoders that we will consider. The information theoretic capacity of an analog erasure channel is infinite. Thus, the only constraints we impose on the encoder are that the transmitted vector is some causal (possibly time-varying) function of the measurements available to the encoder until time k and that the dimension of the vector is finite. The encoder is collocated with the sensor, while the decoder is located at the estimator/controller. We will sometimes refer to the encoder as an encoding algorithm.