### Abstract

Shannonâ€™s coding theorem establishes conditions under which a given stochastic
source can be encoded by a given stochastic channel with zero probability of
error. One can also consider a deterministic channel, given by a function from
one space of sequences to another, and ask which sources can be transmitted by
that channel not just with zero error probability but in fact injectively.
Working with an existing formalization of this idea in symbolic dynamics, I
will present a characterization of the subshifts that can be transmitted
injectively by a given sliding block code on a mixing shift of finite type
(i.e. the space of sequences realizable by an ergodic Markov chain). The
result generalizes a classical embedding theorem of Krieger and answers a
question posed to me by Tom Meyerovitch.