Study Of Information Transfer In Chaos Synchronization

The chaotic secure communication schems had been questioned for their unlimited channel capacity assumption. The OCCULT project (Optical Chaos Communications Using Laser-Diodes Transmitters) reported that, they have achieved the high-speed long-distance chaotic secure communication on commercial optical cables in 2005. Some other researchers have also reported their specific chaotic secure communication schemes based on limited channel capacity. Despite all this, the least channel capacity which is needed for attaining the complete chaos synchronization, which is the basis of the chaos-based communications, has not been well resolved.In 1997, Stojanovski etc. reported that, with the use of the symbolic dynamics, they had figured out the least channel capacity for the complete synchronization. However, Pethel and Fradkov etc. argued that, the idea of Stojanovski etc. was wrong, and they in fact showed that, a channel with capacity exceeding the Kolmogorov-Sinai entropy of chaotic systems (hKs) can sustain the synchronization error to arbitrarily small. More-over, Pethel etc. have given the tradeoff between the synchronization precision, drive signal precision and time difference between the synchronized systems.In this study, we give out the least channel capacity for attaining the complete synchronization with the use of the symbolic dynamics and the finite automaton. Only the complete synchronization with finite precision can be achieved through the finite channel capacity. For such a reason, we first use the symbolic dynamics and the finite automaton to describe the chaotic system and the synchronization with finite precision. Thus, when the states of the automata describing the drive and response systems are identical, the two systems are said to be synchronized to the given precision. And, when the identity is sustained, the synchronization between the two systems are said to be sustained. To investiagte whether the states of the two automata can be identical, we have also generalized the automaton reset sequence in this study.Then, the complete synchronizatoin can be sustained, if the transitions between the states of the drive automaton can be sent to the response side. On this basis, we show that, by using a non-generating partition, the complete synchronization can be sustained with the channel capacity hβ