Strong converse, feedback channel capacity and hypothesis testing

In light of recent results by Verdu and Han on channel capacity, we examine three problems: the strong converse condition to the channel coding.theorem, the capacity of arbitrary channels with feedback and the Neyman-Pearson hypothesis testing type-II error exponent. It is first remarked that the strong converse condition holds if and only if the sequence of normalized channel information densities converges in probability to a constant. Examples illustrating this condition are provided. A general formula for the capacity of arbitrary channels with output feedback is then obtained. Finally, a general expression for the Neyman-Pearson type-II error exponent based on arbitrary observations subject to a constant bound on the type-I error probability is derived.