Unification of linear information feedback schemes for additive white Gaussian noise channels (Corresp.)

Abstract

For the transmission of a Gaussian information source over an additive white Gaussian noise channel, several noiseless-feedback linear estimation schemes are shown to be the same in the sense that they not only achieve the rate-distortion bound on the minimum attainable mean-square error, but also possess identical system parameters. Moreover, Butman's noiseless-linear-feedback scheme for the transmission of a digital information source with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> possible messages over additive white Gaussian noise channels can, in fact, easily be obtained from any of these equivalent schemes by simply imposing a decision structure on it and by using the error probability criterion.