Some inequalities for channel capacities, mutual informations and mean-squared errors

We derive some information-theoretic inequalities to evaluate the channel capacity and mean-squared error. We prove an inequality for the capacity of an additive-noise channel with feedback. We also prove an inequality for mutual information and mean-squared error. The inequality is applied to bound minimum mean-squared transmission errors. The results for the channel capacity and the mean-squared error are expressed in terms of the capacity of the related Gaussian channel, the distortion rate function of the related Gaussian process, the mutual information, and the relative entropy.