In this paper a class of discretized piecewise linear chaotic maps of a very high dimensions are used for communication over a noisy channel. An information payload that is sent over a channel is controlled in the transmitter and is related to the symbolic sequences of chaotic trajectory. Such chaotic systems are used for generating new ensembles of nonlinear codes. The proposed decoding method is based on belief propagation principle, such that a complete link to modern coding theory is established. The transmission of information using chaotic systems, usually showing mediocre performance, here on contrary, have a very good performance with a threshold for a certain level of signal-to-noise ratio (SNR).