On Linear Information-Feedback Schemes for White Gaussian Channels

Abstract

For the transmission of a Gaussian information source over an additive white Gaussian-noise (AWGN) channel, several noiseless, linear-feedback 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 (MSE), but also possess identical system parameters. These equivalent schemes can be easily applied to solving the problem of optimally matching a colored Gaussian source with an AWGN channel. These equivalent schemes can further be employed to send messages from digital information sources over AWGN channels. It can be shown that any of these equivalent schemes as a decision-error probability which is the smallest among the class of all linear schemes. The condition of noiseless feedback can be relaxed to cover the more general noisy information-feedback case. A suboptimal scheme is proposed for transmitting data from a Gaussian source, whose output process has a power spectral density function which is uniform in some frequency range and zero elsewhere, over some AWGN channels to some destination. This suboptimal noisy feedback scheme can also be used to send data from a digital information source over an AWGN channel with better performance than can be achieved without noisy feedback.