Analyzing Communication Schemes Using Methods from Nonlinear Filtering

The perfomance of a class of communication systems is investigated in a probabilistic framework. We investigate the bit error probability of the optimal as well as approximately optimal receivers. In general the latter turn out to be unavoidable due to the computational complexity of the former. We investigate a certain class of communication schemes including chaotic systems. Nonlinear filtering theory is employed to obtain a representation of the optimal receiver. Using known results on the filtering process we investigate the bit error probability. It is well known that in general there is no closed form expression of the nonlinear filter. Therefore, in practice approximations are necessary for the nonlinear filter in general and the optimal receiver in particular. We obtain bounds on the approximation error using stability properties of the filter. These bounds also apply to approximations of the optimal receiver.