Rate-information-optimal Gaussian channel output compression

We study the maximum rate achievable over a Gaussian channel with Gaussian input under channel output compression. This problem is relevant to receive signal quantization in practical communication systems. We use the Gaussian information bottleneck to provide closed-form expressions for the information-rate function and the rate-information function, which quantify the optimal trade-off between the compression rate and the corresponding end-to-end mutual information. We furthermore show that mean-square error optimal compression of the channel output achieves the optimal trade-off, thereby greatly facilitating the design of channel output quantizers.