On Encoding Semiconstrained Systems

Semiconstrained systems (SCSs) were recently suggested as a generalization of constrained systems, commonly used in communication and data-storage applications that require certain offending subsequences be avoided. In an attempt to apply the techniques from constrained systems, we study the sequences of constrained systems that are contained in, or contain, a given SCS, while approaching its capacity. In the former case, we describe two such sequences resulting in constant-to-constant bit-rate block encoders and finite-state encoders. Perhaps surprisingly, we show in the latter case, under commonly made assumptions, that the only constrained system that contains a given SCS is the entire space. A refinement to this result is also provided, in which semiconstraints and zero constraints are mixed together.