In this thesis, a new class of codes on graphs based on chaotic dynamical systems are proposed. In particular, trellis coded modulation and iteratively decodable codes on graphs are studied. The codes are designed by controlling symbolic dynamics of chaotic systems and using linear convolutional codes. The relation between symbolic dynamics of chaotic systems and trellis aspects to minimum distance properties of coded modulations is explained. Our arguments are supported by computer simulations and results of search procedures for more powerful modulations. Ensembles of codes in systematic forms based on high dimensional (couple of hundreds and thousands) are developed generalizing lower dimensional systems. Analyzing the complex structure of chaotic systems a particular kind of factor graphs is developed. A forward-backward decoding method based on belief propagation on factor graphs of codes based on chaotic systems is proposed. The communication performance with signaling over additive white Gaussian noise (AWGN) channel and 8- and 16-PSK modulations is studied and convergence analysis of iterative decoding system is presented. An important property of our schemes relies in their low encoding complexity. Hence, comparison and some advantages over Low Density Generator Matrix (LDGM) block codes in terms of encoding complexity and bit error rate (BER) performance are described and possible applications of our codes are discussed.