Markov Capacity for Factor Codes with an Unambiguous Symbol

In this paper, we first give a necessary and sufficient condition for a factor code with an unambiguous symbol to admit a subshift of finite type restricted to which it is one-to-one and onto. We then give a necessary and sufficient condition for the standard factor code on a spoke graph to admit a subshift of finite type restricted to which it is finite-to-one and onto. We also conjecture that for such a code, this finite-to-one property is equivalent to the existence of a stationary Markov chain that achieves the capacity of the corresponding deterministic channel.