  We consider discrete linear time invariant (LTI) channels satisfying the
phase independence (PI) assumption. We show that under the PI assumption the
capacity of LTI channels is positive. The main technical tool that we use to
establish the positivity of the capacity is the delocalisation theorem for
one-dimensional marginals of the product measure due to Ball and Nazarov. We
also prove two delocalisation results that can be seen as extensions of
Ball-Nazarov Theorem.
