Encoding subshifts through sliding block codes

10/15/2022

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by   Sophie MacDonald, et al.

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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 π: X → Y, we give necessary and sufficient conditions for a subshift Z of topological entropy strictly lower than that of Y to admit an embedding ψ: Z → X such that π∘ψ is injective.