On the relation between the Gaussian information bottleneck and MSE-optimal rate-distortion quantization

We use the Gaussian information bottleneck (GIB) to investigate the optimal rate-information trade-off for signal compression in linear Gaussian models and we provide a novel interpretation of the GIB in terms of the eigendecomposition of the Wiener filter. We further study mean-square-error-optimal rate-distortion compression preceded by a linear filter. Choosing this filter as square root of the Wiener filter is shown to be rate-information optimal. Finally, we extend our results to jointly stationary Gaussian random processes.