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

Delocalisation of one-dimensional marginals of product measures and the capacity of LTI discrete channels