Linear Transmission of Gaussian Messages over a Nonstationary Gaussian Channel with Feedback

Necessary and sufficient existence conditions are found for linear transmission of a Gaussian message over a discrete (in time) memoryless Gaussian channel with complete feedback, under the condition that the transmitted and reproduced messages have a specified covariance function. An algorithm for this transmission is given; a transmission algorithm that minimizes the mean-square error (MSE) is indicated, and the value of this error is written out.