Sensitivity of Gaussian channel capacity and rate-distortion function to nonGaussian contamination

In some applications, channel noise is the sum of a Gaussian noise and a relatively weak non-Gaussian contaminating noise. Although the capacity of such channels cannot be evaluated in general, we analyze the decrease in capacity, or sensitivity of the channel capacity to the weak contaminating noise. We show that for a very large class of contaminating noise processes, explicit expressions for the sensitivity of a discrete-time channel capacity do exist. Sensitivity is shown to depend on the contaminating process distribution only through its autocorrelation function and so it coincides with the sensitivity with respect to a Gaussian contaminating noise with the same autocorrelation function. A key result is a formula for the derivative of the water-filling capacity with respect to the contaminating noise power. Parallel results for the sensitivity of rate-distortion function relative to a mean-square-error criterion of almost Gaussian processes are obtained.