Position Coding

Abstract: A position coding pattern is an array of symbols in which subarrays of a certain fixed size appear at most once. So, each subarray uniquely identifies a location in the larger array, which means there is a bijection of some sort from this set of subarrays to a set of coordinates. The key to Fly Pentop Computer paper and other examples of position codes is a method to read the subarray and then convert it to coordinates. Position coding makes use of ideas from discrete mathematics and number theory. In this paper, we will describe the underlying mathematics of two position codes, one being the Anoto code that is the basis of "Fly paper". Then, we will present two new codes, one which uses binary wavelets as part of the bijection.