Sliding block codes between constrained systems

The construction of finite-state codes between constrained systems called sofic systems introduced by R. Karabed and B. Marcus (1988) is continued. It is shown that if Σ is a shift of finite type and S is a sofic system with k/n=h(S )/h(Σ), where h denotes entropy, there is a noncatastrophic finite-state invertible code from Σ to S at rate k:n if Σ and S satisfy a certain algebraic condition involving dimension groups, and Σ and S satisfy a certain condition on their periodic points. Moreover, if S is an almost finite type sofic system, then the decoder can be sliding block