Abstract-In some channels subject to crosstalk or other types of additive interference, the noise is the sum of a dominant 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. The main result of this paper is that for a very large class of contaminating noise processes, explicit expressions for the sensitivity of a discrete-time channel capacity do exist. Moreover, in those cases the sensitivity depends 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.

Abstract-The thinnest coverings of ellipsoids are studied in the Euclidean spaces of an arbitrary dimension . Given any ellipsoid, the main goal is to find its -entropy, which is the logarithm of the minimum number of the balls of radius needed to cover this ellipsoid. A tight asymptotic bound on the -entropy is obtained for all but the most oblong ellipsoids, which have very high eccentricity. This bound depends only on the volume of the sub-ellipsoid spanned over all the axes of the original ellipsoid, whose length (diameter) exceeds 2 .The results can be applied to vector quantization performed when data streams from different sources are bundled together in one block.

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