A logistic map-based model for long-range correlated data and its application to encoding and decoding problems

Nonlinear processes are observed in many fields such as biology, ecology, mathematics, software etc. These processes may sometimes exhibit some surprising and complex effects. The principal reason for high nonlinearity considerations is the non Markov behavior. Markov processes are frequently assumed in the technical applications while no process in nature is truly Markov. In this thesis the symbolic dynamics of super stable period orbits generated by the nonlinear maps and logistic maps were explored. The grammar and its statistical properties that characterize the long-range correlations between the words of symbolic sequences are studied. The analysis and design of a system based on the nonlinear dynamics considerations is the main achievement of the thesis. Further, the turbo coding schemes are explored for the transmission of these long-range correlated sequences, and the results are observed by modifying the parameters at coders and decoder ends based on the correlation in the sequence being generated by the logistic maps.