Lower bounds on the anticipation of encoders for input-constrained channels

Lower bounds are derived on the anticipation of encoders for constrained systems, while strengthening the universality of the state-splitting algorithm. It is shown that every irreducible (S,n)-encoder with anticipation A can be constructed by applying A splitting rounds on some deterministic presentation of S, followed by deleting excess edges and merging equivalent states. Furthermore, by specifying certain properties of those splitting rounds, we obtain lower bounds on the anticipation of (S,n)-encoders. Our lower bounds improve on previous known bounds and, in particular, they are tight for several constrained systems, such as the (1,7)-RLL, (2,7)-RLL, and (2,18,2)-RLL constraints. Input constrained channels are models for magnetic or optical disk storage