Sensitivity of Gaussian channel capacity and rate-distortionfunction to nonGaussian contamination

摘要

In some applications, channel noise is the sum of a Gaussian noiseand a relatively weak non-Gaussian contaminating noise. Although thecapacity of such channels cannot be evaluated in general, we analyze thedecrease in capacity, or sensitivity of the channel capacity to the weakcontaminating noise. We show that for a very large class ofcontaminating noise processes, explicit expressions for the sensitivityof a discrete-time channel capacity do exist. Sensitivity is shown todepend on the contaminating process distribution only through itsautocorrelation function and so it coincides with the sensitivity withrespect to a Gaussian contaminating noise with the same autocorrelationfunction. A key result is a formula for the derivative of thewater-filling capacity with respect to the contaminating noise power.Parallel results for the sensitivity of rate-distortion functionrelative to a mean-square-error criterion of almost Gaussian processesare obtained