The state splitting algorithm of Adler, Coppersmith, and Hassner for graphs with edges of fixed length is extended to graphs with edges of variable lengths. This has the potential to improve modulation code construction techniques. Although the ideas of state splitting come from dynamical systems, completely graph-theoretic terms are used.

Ideas which have origins in Shannon's work in information theory have arisen independently in a mathematical discipline called symbolic dynamics. These ideas have been refined and developed in recent years to a point where they yield general algorithms for constructing practical coding schemes with engineering applications. In this work we prove an extension of a coding theorem of Marcus and trace a line of mathematics from abstract topological dynamics to concrete logic network diagrams.