Reduced complexity likelihood approximation for chaotic trajectory segments

Recently, statistically optimal detection methods for communication schemes based on chaos have been developed. The decision criterion is based on the well-known maximum likelihood criterion. Unfortunately, the calculation of the likelihoods is of exponential complexity in the block length $N$. Thus, an efficient implementation of the optimal detector is impossible for large $N$. In this work we propose a reduction of the complexity of the likelihood computation from exponential to linear by eliminating insignificant terms in the exact likelihood formula. This is in fact equivalent to eliminating certain paths in the tree of all possible symbolic sequences for a given trajectory of length $N$. The result is a viterbi decoder like method which can efficiently decode chaos based communication schemes like chaos shift keying (CSK) for any block length $N$. The reduction of complexity results in only minor increase of the bit error rate, which is shown using simulation results.