Symbolic dynamics for processing chaotic signals - II: Communication and coding

The idea of using chaotic signals in different layers of communication syst ems attracted the attention of researchers as well as engineers and many en cryption, coding, and modulation schemes have been proposed in recent years . One promising application is to employ chaotic codes in broadband communi cation with the intention to achieve a better immunity to multipath degrada tion and self-interference, exploiting the nonperiodicity of chaotic signal s. The main drawback is that an optimum, coherent detection cannot be imple mented since a synchronized reference signal on the receiver side has been, so far, only realizable for a finite number of code-words. This paper prov ides the analysis and results (theoretic and numerical) regarding design an d optimization of chaos-based communication schemes, in particular: 1) perf ormance limits for optimum coding and decoding schemes are derived, that ar e based on an infinite number of finite-length chaotic sequences that are g enerated by a special class of chaotic systems; 2) identification of fundam ental differences between a finite set of conventional block codes and chao tic codes; and 3) development of optimization rules for chaotic codes. With the introduction of symbolic dynamics, the infinite number of finite-lengt h chaotic signals can be partitioned into a finite number of signals sets. The information symbol is then encoded by transmitting a chaotic codes sequ ence from a predefined signal set. The decoder determines the signal set wi th the maximum likelihood and retrieves the information symbol that corresp onds to this signal set. In this way, a decoder is devised that has the sam e properties as coherent receivers of conventional coding systems. It is de monstrated that the particular decomposition in signal sets does not only l ead to analytical performance upper bounds and estimates, it also allows th e appropriate comparison with conventional codes and the development of cod e optimization rules. Even though the analytical results presented here app ly only to the additive white Gaussian noise channel, suggestions are made in which channel environments the nonperiodicity of chaotic codes may be of advantage.