Noiseless Linear Feedback and Analog Data Tranmission

Abstract

It is well known that noiseless linear feedback achieves channel capacity for the additive Gaussian channel. It has also been shown that it can be used to achieve the rate-distortion bound on the mean squared error for an arbitrary Gaussian source sent over the infinite bandwidth white Gaussian channel. However, it is shown here that noiseless linear feedback by itself does not suffice when the channel is bandlimited. It is shown that, out of the more than countable variety of Gaussian sources that ordinarily exist, only a countable subset can be transmitted via the bandlimited noiseless feedback link at the theoretical efficiency predicted by Shannon's rate-distortion bound. Thus, some nonlinear operations are necessary in almost all cases even with feedback.