  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.
