Channel Capacity with Cost Constraint Allowing Cost Overrun

A channel coding problem with cost constraint for general channels is considered. Verdú and Han derived ε-capacity for general channels. Following the same lines of its proof, we can also derive ε-capacity with cost constraint. In this paper, we derive a formula for ε-capacity with cost constraint allowing overrun. In order to prove this theorem, a new variation of Feinstein's lemma is applied to select codewords satisfying cost constraint and codewords not satisfying cost constraint.