On the capacity of channels with additive non-gaussian noise

We give upper and lower bounds of the capacity C(X) of a channel with additive noise X under a constraint on input signals in terms of the second order moments. It is proved that C(X0)⩽C(X)⩽C(X0)+HX0(X), where C(X0) is the capacity of the channel with additive Gaussian noise X0 with same covariance as that of X and HX0(X) is the entropy of the measure induced by X in the functional space with respect to that induced by X0