Minimum distance properties of coded modulations based on iterated chaotic maps

In this paper we introduce a method for analyzing the performance of coded modulation schemes based on iterated chaotic maps. In particular, it is known from coding theory that the minimum distance plays an important role, defining the behavior of the error probability performance at sufficiently high signal to noise ratios. We introduce the method and illustrate it for two examples of chaotic maps, the Bernoulli shift map and the tent map. We emphasize that the performance of the map can not be understood by a reasoning in terms of ergodic behavior of the map. The given simulation results confirm the relevance of the minimum distance for describing the performance of such a system.