In this paper we examine coded modulations based on iterations of higher dimensional piece-wise linear maps(PWLM). Particulary, we study a generalization of the Bernoulli map in higher dimensions and its application to communications. In the proposed scheme we show that the transmitted information corresponds to the dynamics of the chaotic systems controlled by small perturbations. Minimum distance properties of the proposed class of codes are analyzed and it is pointed out that they perform much better comparing to one-dimensional systems.