Sliding block codes between constrained channels

We continue the work of Karabed and Marcus on constructing finite-state codes between constrained systems called sofic systems. It S1 is a shift of finite type and S2 is a sofic system with E/q = h(S2)/h(S1), wnere h denotes entropy, there is a. non-catastrophic finite-state invertible code from S1 to S2 at rate p: q if: (1) S1 and S2 satisfy a. certain algebraic condition, and (2) S1 and S2 satisfy a certain condition on their periodic points. Moreover, if S2 is an almost finite type sofic system then the decoder can be sliding block.