Encoding subshifts through sliding block codes

Abstract

We prove a generalization of Krieger's embedding theorem, in the spirit of zero-error information theory. Specifically, given a mixing shift of finite type $X$, a mixing sofic shift $Y$, and a surjective sliding block code $\pi :X\to Y$, we give necessary and sufficient conditions for a subshift $Z$ of topological entropy strictly lower than that of $Y$ to admit an embedding $\psi :Z\to X$ such that $\pi \circ \psi$ is injective.

13 pages, no figures. Typos corrected from previous version (results are unaffected)

References in corpus (1)

• Markov Capacity for Factor Codes with an Unambiguous Symbol