Optimal estimation for chaotic sequences using the Viterbi algorithm

Many communications algorithms based on chaos have been proposed previously. However, the performance of these proposed algorithms has been limited by noise. In this paper, a novel, computationally efficient, optimal estimation algorithm for chaotic sequences is presented. First, a symbolic dynamics representation of the chaotic system is exploited to enable the representation of the chaotic dynamics by an equivalent trellis diagram. Then, the Viterbi algorithm is used to reduce the noise from the corrupted chaotic sequence. This algorithm yields the minimum mean square error estimate. The performance of the algorithm in terms of improvement versus signal-to-noise ratio (SNR) is simulated for popular chaotic maps, including sawtooth, tent, and logistic maps. The algorithm is also incorporated into a chaotic communication system, and the resulting bit-error rate (BER) performance is presented.