Sensitivity of channel capacity

Abstract

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.

Sensitivity of Quadratic Gaussian Matching to Interference

“…A surprising result in [14], however is that the sensitivity is actually equal to the upper bound for any contamination noise that is drawn i.i.d. Thus we can approximate the channel capacity for a wide class of interference noise distributions as…”

“…Before proceeding with the analysis, we review some results of Pinsker, Prelov, and Verdú on the sensitivity of channel capacity to weak additive interference [14].…”

“…This approximation involves two stages of linearization, first the capacity is linearized using the results of [14], and then the distortion is linearized using the chain rule of differentiation. Alternatively, we can get a better approximation of the distortion function if we use only one stage of linearization.…”

Maximin performance of binary-input channels with uncertain noise distributions

“…The closed intervals in (17) are validated by the continuity Lemma 6, which further determines that (19) ( 20) The constraint (4) and Lemma 2 in turn determine that (21) Straightforward computation yields for divergence the expression (22) and for the second moment of the expression (23) Finally, the constants and are determined, respectively, by the relationships via Lemma 4 and via the following result.…”

“…Such a specification encompasses models incorporating an ambient Gaussian noise channel subject to interference, jamming, or any general contamination satisfying a proximity (divergence) bound. In this case, the divergence-fromGaussian constraint provides a measure of "non-Gaussianness" as defined in [17] and [22].…”