Effects of message encoding and decoding on synchronized chaotic optical communications

Chaotic optical communication at 2.5 Gb/s is experimentally investigated using three major encoding and decoding schemes, namely chaos shift keying (CSK), chaos masking (CMS), and additive chaos modulation (ACM). The effects of message encoding and decoding on the chaotic dynamics, the chaos synchronization, and the chaotic communication performance are compared among the three schemes. In the schemes of CSK and ACM, it is found that a small amount of message injected into the chaotic dynamics can increase the complexity of the chaotic state dramatically. In the CMS scheme, the chaotic dynamics are found not to be influenced by the encoded message. The synchronization quality deteriorates dramatically with an increase in the message strength in CSK and CMS. The ACM scheme is found to have the best synchronization quality among the three schemes when there is an encoded message. Message recovery is demonstrated for each of the three schemes. The ACM scheme is found to have the best communication performance.     

Performance characterization of high-bit-rate optical chaotic communication systems in a back-to-back configuration

A comparative study of three data-encoding techniques in optical chaotic communication systems is reported. The chaotic carrier is generated by a semiconductor laser subjected to optical feedback and the data are encoded on it by chaotic modulation (CM), chaotic masking (CMS), or chaotic shift keying (CSK) methods. In all cases, the receiver-which is directly connected to the transmitter-consists of a semiconductor laser similar to that of the transmitter subjected to the same optical feedback. The performance of this back to back configuration is numerically tested by calculating the Q-factor of the eye diagram of the received data for different bit rates from 1 to 20 Gb/s. The CM scheme appears to have the best performance relative to the CMS and CSK scheme, before and after filtering the residual high-frequency oscillations remaining due to nonperfect synchronization between the transmitter and receiver. Moreover, in all encoding methods, a decrease in the Q-factor is observed when the repetition bit-rate of the encoding message increases. In order to achieve as high Q-factor values as possible, a well-synchronized chaotic master-slave system is required.     

非相干光反馈的半导体激光器混沌保密通信性能分析及其仿真

首先研究了非相干光反馈同步系统内部参数失配对系统同步性能的影响,并与相干光反馈的完全同步系统以及广义同步系统进行了比较,其次研究了非相干光反馈采用三种不同的信号调制解调方式(CSK,CMS,ACM),对三种不同频率(250 MHz,2.5GHz和12.5GHz)的信号进行了调制解调。通过MATLAB仿真实验可知,非相干光反馈混沌同步系统相对于相干光反馈完全同步系统更易于实现,同时保留了一定的对参数失配的敏感特性,从而确保了该系统比相干光反馈广义同步具有更高的安全性;在信号解调时,CSK只能解调出250MHz信号,CMS能解调出2.5GHz信号,ACM能够解调出高达12.5GHz的信号。     

Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers

We numerically study the synchronization or entrainment of two unidirectional coupled single-mode semiconductor lasers in a master-slave configuration. The emitter laser is an external-cavity laser subject to optical feedback that operates in a chaotic regime. The receiver can either operate at a chaotic regime similar to the emitter (closed-loop configuration) or without optical feedback and consequently under continuous-wave conditions when it is uncoupled (open-loop configuration). We compute the degree of synchronization of the two lasers as a function of the emitter-receiver coupling constant, the feedback rate of the receiver, and the detuning. We find that the closed-loop scheme has, in general, a larger region of synchronization when compared with the open loop. We also study the possibility of message encoding and decoding in both open and closed loops and their robustness against parameter mismatch. Finally, we compute the time it takes the system to recover the synchronization or entrainment state when the coupling between the two subsystems is lost. We find that this time is much larger in the closed loop than in the open one.     

Numerical investigation of fiber transmission of a chaotic encrypted message using dispersion compensation schemes

A detailed numerical investigation of the transmission properties of all-optical chaotic communication systems is presented for two data-encoding techniques and for various dispersion compensation maps. A semiconductor laser subjected to optical feedback generates the chaotic carrier, and the data is encoded on it by chaotic modulation (CM) or chaotic-shift-keying (CSK) methods. The complete transmission module consists of different types of fiber, inline amplifiers, and Gaussian optical filters. Different dispersion maps based on either Nonzero dispersion-shifted fibers (NZ-DSFs) or combinations of single-mode fibers (SMF) along with dispersion-compensating fibers (DCF) were considered. The system's performance is numerically tested by calculating the Q factor of the eye diagram of the received data for 1 and 2.4 Gb/s. The influence of the optical power launched into fiber and the transmission distance to the quality of the decoded message has been investigated. The CSK scheme appears to have better performance relative to the CM scheme, while dispersion maps utilizing NZ-DSFs are superior to that employing DCF. In all encoding methods and transmission maps, a decrease in the Q factor is observed when the repetition bit rate of the encoding message and the transmission distance increases.     

Additive mixing modulation for public key encryption based on distributed dynamics

We introduce a public key encryption scheme that is based on additive mixing of a message with chaotic nonlinear dynamics. A high-dimensional dissipative nonlinear dynamical system is distributed between transmitter and receiver. The transmitter dynamics is public (known to all) and the receiver dynamics is private (known only to the authorized receiver). Bidirectional signals that couple transmitter and receiver are transmitted over a public channel. Once the chaotic dynamics which is initialized with a random state converges to the attractor, a message is mixed with the chaotic dynamics at the transmitter. The authorized receiver who knows the entire dynamics can use a simple algorithm to decode the message. An unauthorized receiver does not know the receiver dynamics and needs to use computationally unfeasible algorithms in order to decode the message. Security is maintained by altering the private receiver dynamics during transmission. We show that using additive mixing modulation is more efficient than the attractor position modulation distributed dynamics encryption scheme. We demonstrate the concept of this new scheme by simulating a simple coupled map lattice.     

GHz Bandwidth Message Transmission Using Chaotic Vertical-Cavity Surface-Emitting Lasers

Chaotic message encoding and decoding in unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs) with polarization-preserved and polarization-selected optical injection has been studied experimentally. A GHz message has been successfully encoded in the chaotic transmitter and decoded from the receiver with polarization-preserved optical injection. In contrast decoding using polarization-selected optical injection was achieved at only 330 MHz. It has also been demonstrated that GHz message extraction can be achieved using both normal and inverse chaos synchronization thus providing an opportunity for exploiting polarization properties of VCSELs for duplexed chaotic message transmission.     

Enhancing Chaotic Communication Performances by Manchester Coding

A numerical analysis of an optical chaotic transmission system, based on the synchronization of two chaotic lasers, in a master-slave closed loop configuration is presented. At the transmitter, the master chaotic wave is superposed on the information message; at the receiver, the message is recovered by subtracting the synchronized slave chaotic wave from the received signal. The performances are analyzed in terms of the Q-factor, considering two different message modulation formats: the nonreturn-to-zero and the Manchester coding. The Manchester coding shows enhanced performances due to the shift of the signal spectrum to higher frequencies.     

Performance of a new decoding method used in open-loop all-optical chaotic communication system

A new decoding method with decoder is used in open-loop all-optical chaotic communi-cation system under strong injection condition. The performance of the new decoding method is nu-merically investigated by comparing it with the common decoding method without decoder. For new decoding method, two cases are analyzed, including whether or not the output of the decoder is ad-justed by its input to receiver. The results indicate the decoding quality can be improved by adjusting for the new decoding method. Meanwhile, the injection strength of decoder can be restricted in a certain range. The adjusted new decoding method with decoder can achieve better decoding quality than decoding method without decoder when the bit rate of message is under 5 Gb/s. However, a stronger injection for receiver is needed. Moreover, the new decoding method can broaden the range of injection strength acceptable for good decoding quality. Different message encryption techniques are tested, and the result is similar to that of the common decoding method, indicative of the fact that the message encoded by using Chaotic Modulation (CM) can be best recovered by the new decoding method owning to the essence of this encryption technique.     

Synchronization of chaotic injected-laser systems and itsapplication to optical cryptography

We demonstrate that two chaotic systems, each made by two coupled semiconductor lasers, can be synchronized using direct-optical feedback. The robustness of the proposed synchronization scheme against mismatch of source parameters and difference in starting conditions is tested by numerical simulations. Applications to secure data transmission are proposed, namely chaotic masking and chaotic shift keying (CSK)     

Security Implications of Open- and Closed-Loop Receivers in All-Optical Chaos-Based Communications

We numerically find that higher privacy and security in all-optical chaos-based communication systems can be achieved when the closed-loop scheme is used in the receiver architecture, instead of the more traditional open-loop scheme. Our results show that the extraction of the encoded message demands a larger amplitude of the message when the open-loop receiver is used than when the closed loop is implemented. A large amplitude of the encoded message compromises the performance and security of the system.      

Demultiplexing chaos from multimode semiconductor lasers

We show numerically that the injection of two chaotic modes of a multimode semiconductor laser with optical feedback into two single-mode stand-alone semiconductor lasers leads to chaotic synchronization between the respective intensities. The effect of parameter mismatch between the transmitter and receiver lasers is examined, and it is concluded that the observed synchronization is a consequence of injection locking. Under these conditions, the possibility of using this demultiplexing scheme for message transmission is examined.     

混沌时间序列降噪在数字通信中的一个应用

根据对非线性时间序列降噪的理论,本文采用Gradient Descent方法在CSK(Chaos shift Keying)系统的接收端对混沌时间序列进行降噪,获得一条比原来时间序列噪声更小的时间序列轨道,然后采用非相干检测技术对发射端传输的符号进行判断,理论分析和计算机仿真结果基本一致.     

Secure Communication via Synchronization of Lur’e Systems Using Sampled-Data Controller

In this paper, synchronization of chaotic Lur’e systems using sampled-data control is applied to the secure communication problem. The message is transmitted and masked by the techniques of n-cipher and a public key obtained by the chaotic Lur’e system. The decryption of the transmitted encrypted message to recover the original message at the receiver can be achieved by synchronizing the transmitter and receiver chaotic systems. Sampled-data feedback control is used for synchronization, and a sufficient condition for obtaining feedback gain is derived in terms of linear matrix inequalities using a discontinuous Lyapunov functional. The secure communication system is simulated via Matlab along with the Chua system to show the effectiveness of the proposed result.     

基于混沌参数调制的数字通信方式

提出一种基于混沌参数调制的数字通信方式。即将一个由非线性映射所产生的混沌序列作为载波,将待发送的有用信号（数字信号）作为调制信号,对非线性映射的某一参数在其混沌区域内进行调制。在接收端,利用混沌序列的发生规则从接收信号中提取混沌载波,并经过简单的信号处理运算恢复出原来的有用信号。分析和计算机模拟表明,本文所提出的这种混沌通信系统具有一定的保密性且实现方便、性能可靠     

Optical Chaotic Communication Using Generalized and Complete Synchronization

We propose a secure optical communication system based on the principles of generalized and complete chaotic synchronization. A transmitter and a receiver both composed by two chaotic external-cavity semiconductor lasers are coupled in a master-slave configuration to provide generalized synchronization, while the master lasers in the transmitter and in the receiver are completely synchronized through the synchronization channel via an optical fiber. A message is added to the transmitter slave laser and sent to the receiver through the information channel to be compared with the output of the receiver slave laser. The system is robust to a small mismatch of the laser parameters or of the coupling between the master and slave lasers, unavoidable in a real system, and can even enable a good communication up to a 5 Gb/s transmission rate using the chaos masking encryption method, when the master laseres are coupled bidirectionally.      

Message encoding and decoding using chaotic external-cavity diodelasers

Synchronization of chaotic external-cavity diode lasers has been studied in a master-slave configuration. A message is encoded into the chaotic master laser by amplitude modulation and transmitted to the slave laser. A scheme for decoding the message at the slave is demonstrated     

Performance of open-loop all-optical chaotic communication systems under strong injection condition

A numerical investigation of the performance of an open-loop optical chaotic communication system for the isochronous synchronization solution has been carried out, under strong optical injection conditions achieved using antireflective coating at the input facet of the receiver laser in combination with an optical erbium-doped fiber amplifier (EDFA). Different message encoding techniques have been considered and tested at multigigabit rates and for different levels of optical injection to the receiver. The effects induced by the amplified spontaneous emission (ASE) noise of the EDFA to the performance of the chaotic communication system have also been studied. The performance of all the examined encryption methods for the 1 Gb/s bit-rate messages was quite satisfactory and was characterized by Q-factor values that exceeded 10, after synchronizing in the strong injection regime. For higher message bit rates, the Q-factor values for all methods decrease considerably due to the residual frequency components of the chaotic carrier that are now more significant in the message spectral region. The effect of the amplifier's ASE noise to the system's performance was deteriorated as long as the EDFA chaotic input was kept in relatively high power levels.     

Private Message Transmission by Common Driving of Two Chaotic Lasers

In this paper, we numerically demonstrate private data transmission using twin semiconductor lasers in which chaotic dynamics and synchronization are achieved by optical injection into the laser pair of a common, chaotic driving-signal, generated by a third laser subject to delayed optical feedback. This laser is selected with different parameters with respect to the twin pair, so that the emissions of the synchronized, matched lasers are highly correlated, whereas their correlation with the driver is low. The digital message modulates the emission of the transmitter, as in a standard CM scheme. Message recovery is then obtained by subtracting, from the transmitted chaos-masked message, the chaos, locally generated by the synchronized receiver laser. Simulations have been performed with the Lang–Kobayashi model, keeping into account both laser and photodetector noise. Private transmission has been demonstrated by investigating the effect of the parameter mismatch, between transmitter and receiver, on synchronization and message recovery.      

Feasibility of Analog Realization of a Sliding-Mode Observer: Application to Data Transmission

One of the main contributions of this paper is to highlight the feasibility of analog realization of a chaotic observer-based communication system. The system is composed of a chaotic Colpitts oscillator considered as transmitter and a sliding-mode observer used as receiver. The method used in this realization is based on the synchronization of two chaotic systems (transmitter-receiver). Moreover, another originality of this work is the application of a sliding-mode observer to a Colpitts oscillator, which has a totally different structure with respect to it. Nevertheless, the proposed structure of the observer is designed particularly for this type of oscillator. Only one of the states of the transmitter (chosen according to theoretical criteria) is sent to the receiver which is designed to reconstruct all of the states of the transmitter knowing only the transmitted state. In order to show an application of this work, a message signal is injected into the transmitter using the so-called inclusion method. The message is then recovered by the receiver once all of the transmitter states are reconstructed. Thus, the so-called left inversion problem is resolved experimentally. The whole system (transmitter-observer) is realized using simple and standard analog components, and practical results close to simulations are obtained.