Stabilization of Block-Type-Decodability Properties for Constrained Systems

We consider a class of encoders for constrained systems, which we call block-typedecodable encoders. For a constrained system presented by a deterministic graph, we design a blocktype-decodable encoder by selecting a subset of states of the graph to be used as encoder states. Such a subset is known as a set of principal states. Our goal is to find an optimal set of principal states, i.e., a set which yields the highest code rate. We study the relationship between optimal sets of principal states at finite block length and at asymptotically large block length. Specifically, we show that for a primitive constraint and a large enough block length, any optimal set of principal states is also asymptotically optimal. Moreover, we give bounds on the block length such that this relationship holds. We also characterize asymptotically optimal block-type-decodable encoders. Finally, we study the complexity of various problems related to block-type-decodable encoders.