Spatial information and coding theory

Bar code systems, magnetic storage on tape or disc and CD ROMs are each means of recording information on the surface of a substrate with binary recording polarities. Each of these systems can be viewed as constituting a spatial channel. Because of the differences on working environment many of the theoretical results used to study closed systems such as magnetic/optical systems cannot be transferred to open systems such as bar code systems. In this thesis we present a theoretical framework for the analysis of open spatial channels. We introduce a general channel model which is able to unify the analysis of a number of spatial recording systems. While our primary concern is applying this model to open systems, the model is relevant to the analysis of closed systems as well. In the new theory we discuss the topic of error detection/correction by introducing a new error distance, called the diagonal distance. Since the field spanned by the diagonal distance is not a Galois field, a new method is introduced for studying the properties of this new coding space. In coding theory the design problem is usually posed in the form of finding the highest density codes for a given undetectable error tolerance. We give equations for solving this optimum design problem. At the end of the thesis, we discuss a particular example of two-dimensional bar code design. This section demonstrates how the concepts and tools introduced in the thesis may be applied.