A Study on the Problem of Channel Resolvability for Channels with Countable Input Alphabet

The problem of channel resolvability for channels with countably infinite input alphabet is considered. In particular, Hayashi’s lower bound (i.e., converse part) on the optimal rate of channel resolvability, which was proved under the assumption of the finiteness of the input alphabet of the channel, is revisited. Our motivation is to prove the bound without the finiteness of the input alphabet. Although we cannot accomplish the final goal, we introduce a slight modification into the problem of channel resolvability and establish a coding theorem (particularly converse coding theorem) corresponding to Hayashi’s result without the assumption of the finiteness of the input alphabet.