General non-asymptotic and asymptotic formulas in channel resolvability and identification capacity and their application to wire-tap channel

摘要

Several non-asymptotic formulas are established in channel resolvability andidentification capacity, and they are applied to wire-tap channel. By usingthese formulas, the $\epsilon$ capacities of the above three problems areconsidered in the most general setting, where no structural assumptions such asthe stationary memoryless property are made on a channel. As a result, we solvean open problem proposed in Han & Verdu and Han. Moreover, we obtain lowerbounds of the exponents of error probability and the wire-tapper's informationin wire-tap channel.