Iterated function system models of digital channels

This paper introduces a new class of models of digital communications channels. Physically, these models take account of the digital nature of the input. Mathematically, they are iterated function systems. As a consequence of making explicit assumptions about the role of discreteness in the models, it is possible to make general statements about the behaviour of these channels without needing to assume that they are linear. We provide the mathematical background necessary to understand the behaviour of these models and prove a number of results about their observability. We also provide a number of examples intended to demonstrate their connection with linear state-space models, and to suggest how the nonlinear theory might be developed towards applications.