{'fraction_non_alphanumeric': 0.028931750741839762, 'fraction_numerical': 0.008160237388724036, 'mean_word_length': 5.1880733944954125, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The performance of chaos shift keying: synchronization versus symbolic backtracking

Since Chaos Shift Keying (CSK) has been proposed by Herve Dedieu et al. (see IEEE Trans. Circuits Syst., vol. CAS-40, no. 10, p. 634 et seq., 1993) there has been a number of papers published, dealing with different variations of CSK. However, there is also a deficiency of work devoted to determine the performance of such systems, mainly due to a difficult parameterization. We suggest in this paper the use of discrete-time piecewise linear chaotic systems for performance comparisons of CSK. Synchronization of chaotic systems with an average diverging vector field is in general more sensitive to noise than with a passive system, possessing a converging vector field. We propose therefore a CSK implementation that we term "symbolic backtracking". Symbolic backtracking is an algorithm that uses the ideas of symbolic dynamics to estimate the initial condition of a finite-length, noise perturbed chaotic trajectory. By "tracking" the signal backwards in time the vector field along the trajectory becomes convergent and we expect therefore better performance measures than for a "forward-oriented" synchronization technique. We compare finally the performance of CSK with conventional error feedback synchronization against CSK using symbolic backtracking.