A shift space $(X, \sigma)$ is a *coded system* if there exist a countable collection of finite words $(\omega^n)_{n \in \mathbb{N}}$, called generators, such that $X$ is the closure of the set of sequences obtained by freely concatenating the generators.

In Lind and Marcus book *An introduction to symbolic dynamics and coding,* page 451 there is stated a nice topological equivalence: $(X,\sigma)$ is a coded system if and only if $X$ contain an increasing sequence of transitive subshifts of finite type whose union is dense in $X$.

It is mentioned that this equivalence is due to Krieger and it is cited on Blanchard and Hansel paper *Sofic constant-to-one extensions of subshifts of finite type*, Proc. Amer.Math. Soc. **112** (1991), 259-265. The given reference is a personal communication between W. Krieger and the authors.

I would like to know if there exist a reference where I can find the proof of this statement.