Performance characterization of high-bit-rate optical ... - IEEE Xplore

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JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 21, NO. 3, MARCH 2003

Performance Characterization of High-Bit-Rate Optical Chaotic Communication Systems in a Back-to-Back Configuration Dimitris Kanakidis, Apostolos Argyris, and D. Syvridis

Abstract—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 -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 -factor is observed when the repetition bit-rate of the encoding message increases. In order to achieve as high -factor values as possible, a well-synchronized chaotic master–slave system is required. Index Terms—Chaotic communication systems, encoding methods, feedback, -factor value, semiconductor lasers, synchronization error.

I. INTRODUCTION

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IGH BIT-RATE data encryption in chaotic communications systems has been studied intensively during recent years [1], [2]. Several optoelectronics and all-optical systems based on fast chaotic dynamics have been proposed as possible alternatives to classical encryption techniques relying on numerical algorithms. The encryption in this case is performed in the physical layer rather than the application layer. The chaotic cryptography in the physical layer seems extremely attractive, since it exploits the deterministic nature of chaos, showing at the same time, a strong dependence on minimal variations of system’s parameter values. Communication systems utilizing chaotic carriers are an extension of the conventional communication systems used today. While in a conventional communication system the message is modulated in the transmitter upon a periodic carrier, in chaotic systems the message is modulated within the chaotic signal of the transmitter. The chaotic carrier in which data is encrypted can be either electronic or optical using corresponding electronic Manuscript received August 1, 2002; revised November 5, 2002. This work was supported by the European Commission Project IST-2000-29683– OCCULT. The authors are with the Department of Informatics and Telecommunications, University of Athens, Athens GR 15784, Greece. Digital Object Identifier 10.1109/JLT.2003.809575

Fig. 1. (a) The ML output is optically injected to the SL and forces it to synchronize. (b) CM encryption method. (c) CMS encryption method. (d) CSK encryption method.

[3], [4] or optic oscillators working in the chaotic regime. The optical oscillators can be either erbium-doped fiber lasers [5], [6] or semiconductor lasers [7]–[13]. In the case of the semiconductor laser-based oscillators, the operation in the chaotic regime can be achieved by applying optical feedback [8]–[10], optoelectronic feedback [2], [14], or optical injection [14], [15], and their chaotic behavior appears either in the amplitude or in the wavelength regime. Concerning the encoding of the information in the chaotic carrier, the schemes that have been proposed are the chaotic masking (CMS), chaotic modulation (CM), chaotic shift-keying (CSK), on–off shift keying (OOSK), and CSK using chaos in wavelength [1], [16]–[19]. The philosophy of the decoding process, however, is always the same, based on a very good synchronization between the transmitter and the receiver system. In this paper, we compare the performance of CM, CMS, and CSK encoding techniques

0733-8724/03$17.00 © 2003 IEEE

KANAKIDIS et al.: PERFORMANCE CHARACTERIZATION OF HIGH BIT-RATE OPTICAL CHAOTIC COMMUNICATION SYSTEMS

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TABLE I PARAMETERS SET IN THE NUMERICAL SIMULATIONS

in a chaotic transmission system based on optical feedback. In order to avoid any influence of the transmission medium and to concentrate only to the differences in the system performance induced by the different encoding techniques, we studied a back-to-back scheme by numerically measuring the -factor values extracted from the decoded and the recovered (after filtering) message. The simulations have been carried out for different bit-rates, from 1 to 20 Gb/s. A similar comparison of chaotic encoding techniques has been very recently published by Liu et al. [20] and seems to be in good agreement with our present results.

exactly same conditions as the ML [Fig. 1(a)]. This injection field forces the SL to synchronize with the ML. The above setup, referred to as a master–slave configuration, is described by the well-known Lang–Kobayashi equations [9], [10]

(1) II. THE MODEL Three different encryption methods have been considered: CM, CMS, and CSK encryption. All three schemes differ in the way the message is encoded within the chaotic carrier, although the decoding process is the same for all schemes, based on subtracting the output of the SL from the received signal. In the CM method, the message emerges by modulating the chaotic carrier of the ML [Fig. 1(b)] [9]. In the CMS method, the message is simply added at the output of the ML [Fig. 1(c)] [17]. Finally, in the CSK method, the bias current of the ML is modulated resulting two different states of the same attractor associated to the two levels of the injection current [Fig. 1(d)] [16]. The current , where of the ML is given by the equation (or 1/2) for a “1” (or a “0”) bit and , . The fact while the SL current is fixed to a single value that the ML is never biased with the same current as the SL, when the message is encoded, induces synchronization error in the system. However, the amount of this synchronization error is kept to a small value by modulating the ML current no more than 2%. In the last method, we use a CSK scheme that utilizes only one receiver laser rather than two (conventional CSK method) [16]. III. RESULTS AND DISCUSSION For our numerical analysis, the carrier wave is a chaotic signal generated by a Fabry–Perot semiconductor laser diode subjected to an external optical feedback [(master laser (ML)]. This chaotic waveform is optically injected into another semiconductor laser diode [slave laser (SL)] that operates at the

(2) is the slowly varying amplitude of the electric field where and the carrier density at the oscillation frequency refer to the within the cavity. The subscript symbols transmitter and the receiver system, respectively. In order to study a back-to-back system, we have taken the propagation time of the injection signal from the ML to the SL equal to zero. The two lasers were considered to be similar to each other and, therefore, most of the internal parameters are the same. The frequency detuning between the two lasers is set to zero, while the optical injection fraction is set to a moderate value. The above conditions correspond to a complete chaos synchronization process [21]. The feedback parameter for both ns , while the injection parameter for lasers is set to ns corresponding to only a few percent the SL is of the amplitude of the ML’s output electric field. The values of the rest of the parameters set in our numerical simulations are shown in Table I, and generally represent a typical set for a semiconductor laser. The relaxation frequency of the lasers, according to the parameters of the Table I, is estimated to be 4.5 GHz. The photon lifetime of the SL has been selected to be different from that of the ML (in our case smaller than the in order to simulate a real system where one of the ML) ( slightly different photon lifetimes of ML and SL are expected even with devices having the same structural characteristics. Therefore, the above mismatch can be compensated by properly

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Fig. 2. Time trace of the chaotic carrier wave of the ML.

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adjusting the injected optical power to the SL, an easily achievin able operation in a real setup [9], [16], [21]. The term (1) exists only for the SL. The bias current of both lasers is set mA ( mA). The spontaneous emission to process is taken into account through a complex Gaussian of zero mean value and correlation white noise term [9]. The time evolution of the chaotic carrier wave of the ML for the above set of parameters is shown in Fig. 2. In all three encoding methods, the message amplitude is set to a value equal to 2% of the amplitude of the solitary ML. As will be discussed later in this section, this small value ensures security (signal totally indistinguishable from the chaotic carrier of the ML), as well as limited distortion on the synchronization of the master–slave system. In order to characterize the performance of the above three encryption schemes, -factor values have been calculated for different repetition rates. It is well known that the -factor value is a parameter exhaustively used in evaluating the performance of communication systems, and is given by the expression (3) and are the average optical power of bits “1” where and “0”, respectively, and and are the corresponding stanpseudodard deviations. The encoded message was a 2 random nonreturn-to-zero (NRZ) bit sequence. The parameters for the master–slave configuration have the same values for all encoding systems and are properly selected in order to achieve a very small synchronization error. Without any message encrypted, the synchronization error varies in time, not exceeding a maximum value of 0.2%. However, after applying the message, the synchronization error is expected to increase due to the asymmetry between the master and SLs’ rate equations [20]. Fig. 3 shows the -factor values calculated for different repetition rates, for the three encryption methods. These values are taken for the decoded message, as well as after filtering the decoded message with a fifth order Butterworth low-pass filter. The filter is used to cut off all the high-frequency components of the chaotic carrier that remain after the decoding process. Without any usage of filters, the CM encryption method has

Fig. 3. Estimation of -factor values for different repetition bit-rates of the decoded message, employing: (a) the CM method; (b) the CMS method; and (c) the CSK method. The synchronization error of the master–slave system is set to 0.2%.

an obvious advantage over the other two methods. As shown in Fig. 3(a), the CM method exhibits very high -factor values ( 18) at low values of bit-rate (1 Gb/s), while for higher bitrates that end up to 20 Gb/s, the -factor value gradually decreases to 5. On the contrary, CMS method exhibits very low -factor values ( 1.5), which remain practically constant as the bit-rate increases [Fig. 3(b)]. The slight increase observed in the -factor values in Fig. 3(b) (without filtering) are caused by the statistical error of the simulation process, as in all cases a -factor of less than 2 corresponds to extremely noisy eye diagrams. Finally, in the CSK method the -factor degrades in respect to the bit-rate increase, with values remaining below 4 in all cases. The higher -factor values extracted from the CM method in comparison to the other two methods can be explained by the nature of the encoding process. For the optical feedback system under investigation, complete synchronization entails not only synchronization of the laser field amplitude waveform, but also the synchronization of the laser field phase [16], [17]. In the CM method, the message is being applied by modulating the transmitter’s chaotic carrier itself, according to , resembling the typthe expression ical coherent amplitude modulation (AM) scheme. Therefore, the phase of the chaotic carrier with the message encoded on it, which is injected to the receiver, is the same with that of the chaotic carrier without any information. Thus, the presence of signal on the chaotic carrier does not cause a significant perturbation in the synchronization process of the system. On the contrary, in the CMS method, the message is a totally independent electric field, which is added to the chaotic carrier, according to . Therefore, the the expression phase of the total electric field injected now to the receiver consists of two independent components. The phase of the message acts, in this case, as a perturbation in the phase-matching condition of a well-synchronized system, and thus, the phase difference between the transmitter and the receiver diverges from zero. The above phase mismatch in the CMS method results in a much larger perturbation in the synchronization process of the


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Fig. 4. Spectra of 1-GHz decoded messages as they emerge from (a) CM, (b) CMS, (c) CSK encoding methods.

Fig. 5. Spectra of 10-GHz decoded messages as they emerge from (a) CM, (b) CMS, (c) CSK encoding methods.

system [22]. In the CSK scheme with one receiver, although the phase exhibits the same behavior as in the CM method, the -factor values are degraded due to the synchronization error of the system, induced by the different injection currents between the ML and the SL. An additional drawback of the CSK method is that the laser cannot be modulated properly for frequencies higher than the relaxation oscillation frequency. This constraint imposes certain limitations to the high-frequency performance of the CSK method, as will be discussed later. The above conclusions are also supported by observing the spectra of the decoded message in each encryption scheme. Fig. 4(a)–(c) shows these spectra for 1-Gb/s bit-rate decoded message, for the three encoding schemes. The spectrum of the decoded message in CM method [Fig. 4(a)] has one clear difference with respect to the corresponding spectra of the other two methods [Fig. 4(b) and (c)]. The high-frequency oscillations are much more suppressed in the CM method due to the reduced sensitivity of the synchronization process to this encoding scheme. However, in all methods the Fourier spectrum of the 1-GHz decoded message is distinguishable from the high-frequency oscillations, since the latter appear to become more significant in higher frequencies. When the bit-rate of the message is increased to 10 Gb/s, the -factor value of the CM method is reduced to less than half its initial value, being always higher than the corresponding -factor values of the other methods, both of which remain at levels as low as 1.5. The explanation of the above behavior can also be deduced from the corresponding spectra of the 10-Gb/s decoded messages for the three schemes shown in Fig. 5(a)–(c). For the 10-Gb/s bit rate, the spectral components of the message extend to higher frequencies where also chaotic high-frequency oscillations exist. Therefore, even for minor synchronization errors, the power level of the residual chaotic oscillations at these high frequencies is comparable with that of the message, resulting in the observed reduced -factors relative to lower bit-rate messages. In the CMS and CSK encoding schemes, the corresponding spectra [Fig. 5(b) and (c)] exhibit extremely high-frequency oscillations, which almost cover the spectral components of the decoded message, resulting in the observed very low -factors. On the contrary, when high-frequency oscillations are suppressed, as in the CM method [Fig. 5(a)], the

spectral product of the decoded message is clearer, giving rise to a higher -factor value. It is worth mentioning that the frequency range of interest in the above spectra extends up to 30 GHz where the spectral components of the 10-Gb/s modulation appear. Therefore, the performance of the CM method relative to that of the CMS and CSK methods is not affected by the higher noise level of its spectrum at very high frequencies. In order to improve the efficiency of the studied encoding schemes, a fifth-order Butterworth low-pass filter is employed. The role of this filter is to cut off the high-frequency oscillations. The cutoff frequency of the filter is optimized for the different repetition bit-rate values of the encoding message. As can be seen from Fig. 3, for the 1-Gb/s bit-rate message all methods exhibit a similar behavior, providing a very high -factor value (17 to 19), since the high-frequency oscillations have been removed entirely. This improvement can be seen from the eye diagrams extracted for the three encoding schemes before and after filtering [Fig. 6(a)–(f)]. However, by increasing the repetition bit rate, the effectiveness of the filter usage becomes poorer. This is due to the fact that the message now includes a part of the high-frequency oscillation spectrum. The -factor values become worse as the repetition bit rate of the message increases, for all encoding schemes. Even now, by comparing the -factor values, the CM method exhibits a better behavior than the CMS method and a much better behavior than the CSK method. This can be confirmed by the eye diagrams extracted for 10 Gb/s bit-rate encoding message, before and after filtering, for all encoding schemes [Fig. 7(a)–(f)]. From the comparison of the -factor values of the three methods before and after filtering (Fig. 3), it is noticed that the CM scheme is not affected significantly by the filtering. This comes about by the fact that the very good synchronization achieved in this scheme causes the high-frequency oscillations to be minimized. In real systems, however, the existence of noise and the slightly different parameters between the master and the SL, produce a synchronization error that is well above the value considered (0.2%). In order to approximate a real system, to 35 ns and the we change the injection parameter photon lifetime of the SL to 1.98 ps. The chaotic system is now characterized by worse synchronization, with an error of

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Fig. 6. Eye diagrams for 1-GHz decoded messages, without filtering, of the (a) CM, (b) CMS, and (c) CSK methods, and after filtering, of the (d) CM, (e) CMS, and (f) CSK methods.

approximately 2% (increased ten times that previously). The -factor values extracted for the three encoding methods before and after filtering are illustrated in Fig. 8(a)–(c). Without any filtering, the CMS and CSK method behave exactly in the same way as in the case of the well-synchronized system discussed above. In the CM method, though, the larger synchronization error affects the decoded message by the enhancement of the high-frequency oscillations, therefore reducing the corresponding -factor values. After filtering, the methods exhibit almost the same behavior with the 0.2%-synchronized system. When the synchronization error increases to even higher values, the -factor is minimized in all three methods, even at low repetition bit-rates. The improvement caused by the filter

usage is now limited. For example, 5% synchronization error gives a -factor value of almost 6, in the CM method after filtering, while 30% error limits further the -factor value to only 2.5. The above behavior proves a relative transparency of the recovered message with respect to the quality of synchronization, when the synchronization error is very low. On the contrary, by increasing the synchronization error, the message cannot be recovered at all. Thus, it is crucial to maintain the system well synchronized in order to achieve a fully recovered message with a high -factor value. In the analysis that has been made so far, the set of parameters that describe the lasers’ operation correspond to a relaxation frequency of about 4.5 GHz [23]. Thus, in the above comparison,


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Fig. 7. Eye diagrams for 10-GHz decoded messages, without filtering, of the (a) CM, (b) CMS, and (c) CSK methods, and after filtering, of the (d) CM, (e) CMS, and (f) CSK methods.

the CSK method has an inherent handicap relative to the other two, as the laser cannot respond to direct modulation bit rates higher than 6 Gb/s [23]. According to our calculations in the 5-Gb/s case, which is approximately the upper boundary for the direct modulation bit rate of the laser, the CSK method appears to have the lowest -factor value among the three methods, confirming the conclusions extracted for lower bit-rates. In order to extend these conclusions to the range of a 10-Gb/s bit rate and compare the three encoding techniques more accurately, a laser with parameters corresponding to 10-GHz relaxation frequency was chosen. The two lasers were driven to a similar to the previous simulations chaotic regime, and a synchronization error of the same level as before ( 0.2%) was established. The -factor values calculated, the CM, CMS, and CSK methods were 9.8,

3.3, and 2.1, respectively. It is obvious from the above results that, even without the relaxation frequency limiting factor, the CSK method performs worse than the other two indicating that the dominant factor affecting the quality of the decoded message is the nature of the encoding process. The dependence of the -factor from the codeword length of the NRZ pseudorandom bit sequence has been also investigated. The results are shown in Fig. 9, where the -factor values are plotted versus the pseudorandom codeword length at a bit rate of 10 Gb/s and for the three encoding schemes. By to , the increasing the codeword length from -factor value remains practically constant with a tendency to increase as the codeword length increases. The small increase is attributed to the fact that longer pseudorandom codeword se-

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Fig. 8. Estimation of -factor values for different repetition bit-rates of the decoded message, employing the (a) CM method, (b) CMS method, and (c) CSK method. The synchronization error of the master–slave system is set now to 2%.

Fig. 10. Chaotic spectra of the transmitter output (a) without any encrypted message and (b) after 1-Gb/s message encoding, and (c) the decoded message after subtracting the chaotic carrier, for the CM method.

Fig. 11. Chaotic spectra of the transmitter output (a) without any encrypted message and (b) after 1-Gb/s message encoding, and (c) the decoded message after subtracting the chaotic carrier, for the CMS method.

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Fig. 9. -factor values for the CM, CMS, and CSK encryption methods versus different pseudorandom codeword lengths.

quences are more likely to contain many low-frequency spectral components where the chaotic high-frequency oscillations are suppressed. Consequently, a slight increase of the power level of the message in the lower frequencies gives rise to a slightly improved -factor value. The codeword length could not be ex, due to the limited computational tended further than 2 power available. The successful encryption of the information within the chaotic carrier has been investigated through the comparison of the chaotic spectra of the transmitter without and with the encrypted information. Obviously, this is only a qualitative approach and much thorough quantitative techniques based on complicated mathematical methods would be required in order to have a quantitative figure on the security level of the system under investigation. Nevertheless, the comparison of the spectra of the chaotic carrier with and without information encoded on it, gives a sufficiently informative picture on the security of the studied encoding schemes. Parts (a)–(c) of Figs. 10–12 show the chaotic spectra of (a) the transmitter output without

Fig. 12. Chaotic spectra of the transmitter output (a) without any current modulation and (b) after 1-Gb/s message encoding, and (c) the decoded message after subtracting the chaotic carrier, for the CSK method.

any encrypted message [point A of Fig. 1(b) and (c)], (b) the transmitter output after 1-Gb/s message encoding [point B of Fig. 1(b)–(d)], and (c) the decoded message after subtracting


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is noted that in the CSK method, the message is produced together with the chaotic carrier, so in order to produce the spectra of the chaotic carrier itself [point B of Fig. 1(d)], the current modulation amplitude is set to zero. By comparing the (a) and (b) spectra of the above figures, it appears that the message is well hidden within the chaotic carrier in all encryption techniques and the extraction of information with the conventional methods (e.g., spectral filtering), is practically impossible. IV. CONCLUSION

Fig. 13. Chaotic spectra of the transmitter output (a) without any encrypted message and (b) after 10-Gb/s message encoding, and (c) the decoded message after subtracting the chaotic carrier, for the CM method.

Fig. 14. Chaotic spectra of the transmitter output (a) without any encrypted message and (b) after 10-Gb/s message encoding and (c) the decoded message after subtracting the chaotic carrier, for the CMS method.

A performance comparison by means of -factor calculations between the three encoding methods was demonstrated in the above analysis. It has been shown that the CM method has an obvious advantage over the other two methods, due to the fact that the message carries the phase of the chaotic carrier. The above conclusion is in good agreement with [20]. However, after filtering the chaotic high-frequency oscillations, all methods result in satisfactory -factor values for low-repetition bit rates up to 2.4 Gb/s. In this case, all schemes prove to be adequate in data encoding in chaotic communications systems. By increasing the bit rate, the -factor values are reduced independently of the encoding method. Thus, at 10 Gb/s, only the CM method could be characterized as a sufficient encoding scheme, while at 20 Gb/s, the best -factor value extracted is almost 5 and is referred to the CM method, also. An important parameter in the effectiveness of the encoding schemes is the synchronization quality of the master–slave chaotic system. The performance of all encoding schemes does not get affected significantly for a synchronization error less than few percent. When this error increases further, it becomes very difficult for the message to be recovered, even at very low bit rates. Therefore, a well-synchronized chaotic system is required to perform a sufficient message-encoding process, from which a fully recovered message can be extracted. REFERENCES

Fig. 15. Chaotic spectra of (a) the transmitter output without any current modulation and (b) after 10 Gb/s message encoding, and (c) the decoded message after subtracting the chaotic carrier, for the CSK method.

the chaotic carrier, for the CM, CMS, and CSK methods, respectively. Figs. 13–15 show the same chaotic spectra as above, with an encoded message now of 10-Gb/s bit rate. It

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Dimitris Kanakidis was born in Athens, Greece, in 1976. He received the B.S. degree in physics in 1999 and the M.S. degree in 2001, both from the National University of Athens, Athens, Greece, where he is currently working toward the Ph.D. degree. His research interests include semiconductor lasers dynamics and optical cryptography.

Apostolos Argyris was born in Thessaloniki, Greece, in 1976. He received the B.S. degree in physics from the Aristotle University of Thessaloniki, Thessaloniki, Greece, in 1999 and the M.S. degree from the University of Crete, Crete, Greece, in 2001. He is currently working toward the Ph.D. degree at the National University of Athens, Athens, Greece. He was with the Foundation of Research and Technology Hellas, Crete, working on fiber Bragg gratings (FGB) fabrication. His research interests include semiconductor lasers dynamics, four-wave mixing, FBGs, and optical cryptography.

D. Syvridis, photograph and biography not available at the time of publication.