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1 results

Encoding subshifts through sliding block codes
Part of
- Topological dynamics
- Communication, information
SOPHIE MACDONALD
Journal:

Ergodic Theory and Dynamical Systems / Volume 44 / Issue 6 / June 2024

Published online by Cambridge University Press:

03 August 2023, pp. 1609-1628

Print publication:

June 2024
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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.