Abstract

In this paper, we report a novel mechanism to simultaneously provide secure connections for multiple users in indoor optical wireless communication systems by employing the time-slot coding scheme together with chaotic phase sequence. The chaotic phase sequence is generated according to the logistic map and applied to each symbol to secure the transmission. Proof-of-concept experiments are carried out for multiple system capacities based on both 4-QAM and 16-QAM modulation formats, i.e. 1.25 Gb/s, 2 Gb/s and 2.5 Gb/s for 4-QAM, and 2.5 Gb/s, 3.33 Gb/s and 4 Gb/s for 16-QAM. Experimental results show that in all cases the added chaotic phase does not degrade the legitimate user’s signal quality while the illegal user cannot detect the signal without the key.

© 2017 Optical Society of America

1. Introduction

In conjunction with today’s well-deployed fiber based broadband access networks, the optical wireless communications (OWC) system has emerged as a promising technique to provide high speed wireless connections for indoor applications. The optical band employed in OWC systems has a huge amount of unregulated bandwidth and is also immune to the interference from the radio frequency (RF) band [1, 2]. With these key enabling characteristics, OWC systems can be implemented not only in personal living and working spaces but also in areas where RF signal is forbidden, e.g. in hospitals and in airplanes [3].

High-speed OWC channel has been widely-studied where single user access exceeding 200 Gb/s can be achieved with the help of space division multiplexing (SDM) or wavelength division multiplexed (WDM) [1, 4, 5]. At the same time, multi-user scenario for practical OWC applications has also attracted considerable attention recently. Besides conventional multiple access techniques such as time-division multiple access (TDMA), code-division multiple access (CDMA) and frequency-division multiple access (FDMA) [6, 7], an effective multi-user access framework termed as time-slot coding (TSC) scheme has been proposed and experimentally shown to support multiple users simultaneously without sophisticated long-length codes or strict synchronization requirements [8].

However, communication security in OWC systems, especially those supporting multiple user access, has yet to be widely-studied. It is widely-known that OWC has the ability to offer secure communications physically since an optical wave with short wavelength cannot penetrate objects such as walls in its transmission path [9]. However, this assumption is only valid for immediate vicinity with very narrow optical beams. When multiple users are covered with the same beam, security issues arise, such as eavesdropping, tampering, imitation, forgery, etc [10]. Our focus in this paper is on alleviating eavesdropping, which is one of the most widely existing issues in multi-user telecommunication systems. For example, in the TSC-based multi-user OWC system, each active user has the opportunity to eavesdrop messages from other users simply by shifting the location of code bit “1’ in the time-slotted code. Hence, secure and private multiple access cannot be guaranteed.

In previous studies, nulling strategies have been proposed in [11] for free space optical communications whereby illegal interception is prevented by controlling both amplitude and phase from each element of a transmitter array to realize destructive interference at locations where potential eavesdroppers (Eve) may locate. To employ this null steering method, knowledge of locations of potential illegal users are required. Without the knowledge of an eavesdropper’s channel state information (CSI), artificial noise is added in the intended user’s null-space to degrade the received signal-to-noise ratio (SNR) of eavesdropper [12]. However, by using the methods mentioned above, users in the null area cannot be served while security problem still exists for users located in the constructive interference area. In [13], a chaotic-CDMA based visible light communication (VLC) system has been proposed for multiple access whereby spreading codes are generated using chaotic sequences and security can be further enhanced by employing advanced encryption standard (AES) to interleave the spread information. However, this technique incurs additional bandwidth and complex computations. Further, simulation results show degradation in BER performance with increasing number of users. The authors in [14] have employed a chaotic series of elements that locate between −1 and 1 and applied a sign function to this sequence to obtain a new sequence of discrete values with only −1 and 1. The new sequence is applied to I and Q components of each OFDM carrier in passive optical networks (PON). A power gain of 0.3 dB has been achieved with 16-QAM due to the coding gain, however, the coded symbol data can only have four possible patterns including its original version and it is relatively less resistive to brute force or exhaustive computation. Furthermore, some quantum based solutions including Quantum Key Distribution (QKD) methods are able to provide ultimate security due to the non-cloning theorem and the fact that any disturbance will results in quantum state collapse [15, 16]. However, quantum methods are much more complicated to implement in indoor OWC systems currently, and one of the reason is the challenge of realizing single photon source and single photon detector. At the time of writing, there are limited studies addressing the security issue for indoor OWC systems supporting multiple access.

In order to provide multi-user indoor OWC connectivity with secure connection from the transmitter (Alice) to the intended user (Bob), here we present an indoor OWC system employing the TSC scheme together with chaotic phase added to each user’s symbol data. In such a system, the TSC scheme is responsible for eliminating the multi-user interference and the chaotic phase, which is generated over the entire signal constellation plane using the logistic map with an initial value x1 and a constant parameter r, is employed to prevent illegal users’ eavesdropping. As importantly, our proposed secure system does not require additional bandwidth and has no performance degradation on the original symbol quality. In addition, blind equalization can be avoided as an option for the eavesdropper due to the chaotic manner, and the chaotic phase over the entire signal constellation plane makes the system more resistive to brute force or exhaustive computation compared to [14].

In this paper, we first investigate the impact of the initial value x1 and the constant parameter r on the noisy probability. We also evaluate the outage probability with the potential eavesdropper’s attack on the security key. The analytical result indicates that r dominates both the noisy probability and the outage probability. We also present results from a proof-of-concept experiment over 2-meter free space transmission distance and with 20 cm optical beam waist. Power penalty introduced by the chaotic phase for legitimate user is experimentally demonstrated with multiple data rates based on both 4-QAM and 16-QAM modulation formats. The results show that signal quality of each legitimate user is not degraded by the chaotic phase. Performances of 2.5 Gb/s 4-QAM and 4 Gb/s 16-QAM modulation formats without knowledge of key are evaluated, where the transmitted data cannot be recovered without the key and secure communication can be achieved by employing the chaotic phase.

2. Principle of secure multiple access with chaotic phase

The secure OWC in our work is provided by adding artificial phase noise to each symbol. In order to simplify the procedures for the end users to generate exactly the same phase as the transmitter, we employ a logistic map to build the chaotic sequence:

xi+1=rxi(1xi).r[0,4],x1(0,1).
where r is a constant parameter and x1 is the initial element. Since the chaotic manner of logistic map presents for r larger than 3.57 [17], the value of r ranging from 3.57 and 4 are considered in this paper. After multiplying by 360 degrees, phases over the entire I-Q plane are generated as:
θ[n]=360x[n],n=1,2,,N.
Each phase element is applied to the corresponding symbol by the transmitter, and then the original symbol sequence is encrypted. Since reference symbols in a general QAM modulation format have typical decision regions, in order to add phase noise, the chaotic phase sequence is expected to move the transmitted symbol outside the corresponding decision region of the reference symbol. Consequently, the feasibility of chaotic phase sequence in adding phase noise is further evaluated. As illustrated in Fig. 1, the phase range within the decision region for a reference symbol is described by the summation of β and γ.

 figure: Fig. 1

Fig. 1 Signal constellation for a general square QAM.

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Due to the symmetry of signal constellation, only the first quadrant is shown. For reference symbol (I, Q) in a general square 22l -ary QAM (l = 1, 2, 3 …) modulation format, β and γ are expressed as:

β(I,Q)={cos1I2I+QI2+Q2(I1)2I2+Q2,IQcos1Q2+Q+II2+Q2(Q+1)2I2+Q2,I>Qγ(I,Q)={cos1I2I+QI2+Q2(I+1)2I2+Q2,I<Qcos1Q2Q+II2+Q2(Q1)2I2+Q2,IQ
where in-phase (I) and quadrature (Q) components are generalized as:
I=2a12l,1a2l.Q=2b12l,1b2l.
The parameters a and b are natural numbers (1, 2, 3, etc.). In order to add phase noise, the added chaotic phase should satisfy:
β(I,Q)<θ[n]<360γ(I,Q).
As a result, the noisy probability is defined as the percentage of added phase elements that satisfy Eq. (5) and is expressed as:

Ρnoisy=14l1I,QP(β(I,Q)<θ[n]<360γ(I,Q)).

The numerical simulation results for 4-QAM and 16-QAM modulation formats are shown in Figs. 2(a) and 2(b) according to Eq. (6). It shows that the value of r dominates the noisy probability and the high noisy probability which is larger than 0.5 is always guaranteed for both 4-QAM and 16-QAM. As a result, it is feasible to add phase noise by employing the chaotic phase generated by the logistic map. Furthermore, the noisy probability for 16-QAM is higher than that for 4-QAM due to its higher complexity of signal constellation.

 figure: Fig. 2

Fig. 2 Noisy probability for (a) 4-QAM and (b) 16-QAM.

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At the receiver side, each user employs its dedicated key (r and x1) to generate the same phase sequence and decode the encrypted symbol data. Registered users within the coverage of OWC multiple access network are assigned with dedicated keys. Chaffing and winnowing technique, which provides confidentiality via authentication, can be employed by Alice to transmit keys. By employing the chaffing and winnowing technique, Eve has no ability to obtain other users’ keys with a satisfactory MAC algorithm [18]. Since the chaotic phase sequence generated by the logistic map is not periodic and is sensitive to the value of r and x1 [19], blind equalization at Eve’s side is not effective to extract the message, and hence each optical wireless connection can be secured.

However, since all users registered in OWC network know the security mechanism and the value of r and x1 has finite range, potential eavesdropper is able to scan all possible values and land on one set of r and x1 that minimizes SER to extract other’s message. Consequently, the sensitivity of key is further evaluated. The legitimate user (Bob) has the key of rb and x1b while Eve prepares to eavesdrop the message using re and x1e at the decoder side:

re=rb+δ,x1e=x1b+δ
where δ is the difference between keys of Bob and Eve. The chaotic phase sequence generated by Bob and Eve are denoted by θb[n] and θe[n] using Eqs. (1) and (2). The outage probability (Pout) is defined as the percentage of symbols that can be decoded correctly with Eve’s key:
Ρout=14l1I,QP(γ(I,Q)θb[n]θe[n]β(I,Q))
The numerical simulation results of the outage probability with δ = 1e-10 for 4-QAM and 16-QAM are illustrated in Figs. 3(a) and 3(b).

 figure: Fig. 3

Fig. 3 Outage probability with δ = 1e-10 for (a) 4-QAM and (b) 16-QAM.

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It can be seen that the constant parameter in Bob’s key (rb) dominates the outage probability while the initial value (x1b) has limited impact. With the tiny difference (1e-10) between keys for both modulation formats, the outage probability maintains lower than 0.5 for rb landing outside the islands of stability of logistic map. The islands of stability refer to some values of the constant parameter that make the system show non-chaotic manner [17, 20]. As a result, it is generally concluded that the outage probability can be well limited with the scanning accuracy of potential eavesdropper up to (1e-10)2 by carefully selecting the constant parameter for each user according to Eq. (8).

The architecture of the proposed indoor optical wireless system supporting secure multi-user access is described in Fig. 4. As illustrated, the data bits are firstly generated for k users and then are mapped into symbol patterns according to a specific QAM modulation format. In order to add phase noise to each symbol, the chaotic phase sequence is generated containing elements with the same number of symbols (N) for each user, respectively. After applying each phase element to the corresponding symbol, the ith user’s secured symbol sequence is multiplied with the unique k-bit time slotted code which is the ith row of the identity matrix with the size of k, where k is the number of users as shown in Eq. (9):

 figure: Fig. 4

Fig. 4 Block diagram of secure OWC with TSC and chaotic phase.

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Ck=[10000010000001000001]

By employing the dedicated time-slot code, each user occupies non-overlapping symbol slots to avoid inter-user interference. The coded symbol sequences are summed up before passing through a pulse shaping filter for upsampling. The baseband signal is then up-converted to a carrier frequency fc and is completed with the digital-to-analog conversion (DAC). The optical source is modulated by the electrical signal via an external modulator.

At the receiver side, the optical signal along with the background light is captured by the photodiode (PD) after free space transmission. The output of PD is converted to digital signal for post-processing. Each user receives the entire signal sequence which is firstly down-converted and passed through a matched filter for downsampling and filtering out of the baseband signal. The signature time slot code is then applied to extract intended symbols for each user. Next, the artificial phase noise is cancelled by employing the negative version of the same chaotic phase. Lastly, amplitude and phase changes introduced from transmission are recovered before baseband demodulation and symbol error rate (SER) are evaluated.

3. Experimental demonstration

Figure 5 illustrates the experimental setup employed for proof-of-concept demonstration. In the experiments, time-slot coded data with chaotic phases were generated off-line and sent to an arbitrary wave generator (AWG). After passing through an electrical amplifier (EA), the amplified electrical signal modulated a tunable laser centered at 1553.01 nm via a Mach-Zehnder modulator (MZM). A polarization controller (PC) was employed to control the polarization state at the input of the MZM. At the output of the MZM, the modulated optical signal was launched into a 5.6 km single-mode fiber to emulate the distribution process from the central office to the indoor transmitter. At the transmitter side, an adaptive lens system comprised of a fiber end and a lens was employed to expand the optical beam to cover multiple users. The optical power after the transmitter fiber end was set to be 7.5 dBm, chosen to comply with eye and skin safety regulations [21]. The distance between the fiber end and the lens can be adjusted to control the beam width after beam expansion. In our experiments, the beam width was set to ~20 cm at the receiver plane. The selection of beam width was restricted by the optical transmission power as well as the availability of lenses. After 2 m of free space transmission, a coupling system including a compound parabolic concentrator (CPC) and a series of lenses was placed to collect and focus light into the fiber end. Then a 2 GHz bandwidth photodiode integrated with a FET based transimpedance preamplifier was used to convert the optical signal to electrical signal. A digital storage oscilloscope (DSO) performed analog to digital conversion (A/D) for off-line processing.

 figure: Fig. 5

Fig. 5 Experimental setup

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For the post-processing part, each user firstly identified the message tag to differentiate the beginning of the message sequence and down-converted the signal from the carrier frequency. Then a raised-cosine filter was employed for downsampling and filtering out the baseband signal. Then the summed symbol sequence was multiplied with the corresponding time-slot code for each user to retrieve its own chaotic phase coded symbol sequence. Each user then employed its security key (r and x1) to generated the chaotic phase sequence according to Eq. (1) and Eq. (2) and applied the negative version to the coded symbol sequence to securely decode the message. The traditional baseband demodulator and SER calculator were applied after amplitude and phase recovery.

For the proof-of-concept demonstration, the five-user scenario was considered. Four users were provided with the secure connection with chaotic phase, and the connection of the remaining user was unsecured as a reference. We selected four typical constant parameters of r for the four secure users, i.e. 3.95, 3.78, 3.61, and 3.67, which contribute to a higher noisy probability successively according to the analytical results shown in Figs. 2(a) and 2(b). The initial value x1 was fixed as 0.35 as it has ignorable impact on the noise probability according to results shown in Figs. 2(a) and 2(b). Measurements were first carried out to test the power penalty by comparing the SER performances of the user without chaotic phase and the other four users with the chaotic phase. The secure capability of the proposed mechanism was then demonstrated by comparing SER performances with and without the knowledge of keys.

Multiple data rates for both 4-QAM and 16-QAM modulation formats were evaluated in our experiments, i.e. 1.25 Gb/s, 2 Gb/s and 2.5 Gb/s for 4-QAM, and 2.5 Gb/s, 3.33 Gb/s and 4 Gb/s for 16-QAM. The SER threshold is set according to the 7% FEC limit (BER≤3.8 × 10−3) and the relationship between SER and BER [22, 23]. As illustrated in Figs. 6(a) and 6(b), there is no significant difference in the SER performance amongst users with different r and x1 values. In addition, the users with and without the proposed chaotic phase for a specific system capacity also have similar performance. The reason is that the chaotic phase can be cancelled at the user terminal by applying the corresponding key (r and x1) as stated in the principle. Also, no superiority exists among users according to the rules of the TSC scheme

 figure: Fig. 6

Fig. 6 Power penalty results with different bit rates for (a) 4-QAM and (b) 16-QAM.

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In addition, we tested the SER performance without the knowledge of keys. The results of 2.5 Gb/s 4-QAM and 4 Gb/s 16-QAM scenarios are shown in Figs. 7(a) and 7(b). We can see from the figure that the SER without the knowledge of each key is always above the error-free threshold at any location, which means the transmitted data cannot be recovered and secure communication can be achieved. In addition, the key that contributes to higher noisy probability shown in Figs. 2(a) and 2(b) (i.e. 3.95, 3.78, 3.61, and 3.67, which contribute to a higher noisy probability successively) leads to higher SER without the knowledge of the corresponding key. For different locations, SER without knowledge of each key is almost flat as it is dominated by the phase noise added by the chaotic sequence rather than SNR.

 figure: Fig. 7

Fig. 7 SER performance and constellation with and without the key for (a) 2.5 Gb/s 4-QAM and (b) 4 Gb/s 16-QAM.

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4. Conclusion

We have proposed an effective mechanism to provide multiple secure connections in an indoor OWC system, whereby the TSC scheme is responsible for multiple access and the chaotic sequence generated based on the logistic map is employed to protect each connection from potential eavesdropping. Both analytical and experimental results have shown that it is feasible for the proposed mechanism to provide secure OWC. Our experiments indicate that SER without the knowledge of key always exceeds the 7% FEC limit, which means an illegal user cannot detect the signal without the key. What is more, our experimental results have shown that adding the chaotic phase does not affect the signal quality of each legitimate user.

Acknowledgments

This work is supported by Australian Research Council Discovery Project DP170100268. The authors would also like to acknowledge the Australian Commonwealth Government for providing Australian Research Training Program Scholarship.

References and links

1. A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015). [CrossRef]  

2. K. Wang, A. Nirmalathas, C. Lim, and E. Skafidas, “High-speed indoor optical wireless communication system with single channel imaging receiver,” Opt. Express 20(8), 8442–8456 (2012). [CrossRef]   [PubMed]  

3. E. Hanada, “The electromagnetic environment of hospitals: how it is affected by the strength of electromagnetic fields generated both inside and outside the hospital,” Ann. Ist. Super. Sanita 43(3), 208–217 (2007). [PubMed]  

4. M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, and A. E. Willner, “Demonstration of a 280 Gbit/s free-space space-division-multiplexing communications link utilizing plane-wave spatial multiplexing,” Opt. Lett. 41(5), 851–854 (2016). [CrossRef]   [PubMed]  

5. Z. Cao, L. Shen, Y. Jiao, X. Zhao, and T. Koonen, “200 Gbps OOK transmission over an indoor optical wireless link enabled by an integrated cascaded aperture optical receiver,” in Optical Fiber Communication Conference (2017), paper Th5A.6. [CrossRef]  

6. Y. Wang, N. Chi, Y. Wang, L. Tao, and J. Shi, “High-speed LED based visible light communication networks for beyond 10 Gb/s wireless access,” in Proceedings of IEEE 6th International Conference on Wireless Communications and Signal Processing (2014), pp. 1–6.

7. O. Gonzalez, J. A. Martin-Gonzalez, M. F. Guerra-Medina, F. J. Lopez-Hernandez, and F. A. Delgado-Rajo, “Cyclic code-shift extension keying for multi-user optical wireless communications,” Electron. Lett. 51(11), 847–849 (2015). [CrossRef]  

8. T. Liang, K. Wang, C. Lim, E. Wong, T. Song, and A. Nirmalathas, “Time-slot coding scheme for multiple access in indoor optical wireless communications,” Opt. Lett. 41(22), 5166–5169 (2016). [CrossRef]   [PubMed]  

9. J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997). [CrossRef]  

10. J. Li, Z. Feng, Z. Feng, and P. Zhang, “A survey of security issues in cognitive radio networks,” China Commun. 12(3), 132–150 (2015). [CrossRef]  

11. M. Agaskar and V. W. S. Chan, “Nulling strategies for preventing interference and interception of free space optical communication,” in Proceedings of IEEE International Conference on Communications (2013), pp. 3927–3932. [CrossRef]  

12. A. Mostafa and L. Lampe, “Physical-layer security for indoor visible light communications,” in Proceedings of IEEE International Conference on Communications (2014), pp. 3342–3347. [CrossRef]  

13. J. Qiu, L. Zhang, D. Li, and X. Liu, “High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving,” Opt. Eng. 55(6), 066121 (2016). [CrossRef]  

14. W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014). [CrossRef]  

15. C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002). [CrossRef]   [PubMed]  

16. A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate,” Opt. Express 16(23), 18790–18797 (2008). [CrossRef]   [PubMed]  

17. J. C. Sprott, Chaos and Time-Series Analysis (Oxford University, 2003), Chap.2.

18. R. L. Rivest, “Chaffing and winnowing: confidentiality without encryption,” Crypto Bytes 4(1), 12–17 (1998).

19. J. C. Sprott, Chaos and Time-Series Analysis (Oxford University, 2003), Chap.5.

20. C. Zhang, “Period three begins,” Math. Mag. 83(4), 295–297 (2010). [CrossRef]  

21. AS/NZS 2211.1:2004, Safety of laser products (Standards Australia International Ltd and Standards New Zealand, 2004).

22. K. Cho and D. Yoon, “On the general BER expression of one-and-two-dimensional amplitude modulations,” IEEE Trans. Commun. 50(7), 1074–1080 (2002). [CrossRef]  

23. J. G. Proakis, Digital Communications (McGraw-Hill, 2000), Chap. 5.

References

  • View by:

  1. A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015).
    [Crossref]
  2. K. Wang, A. Nirmalathas, C. Lim, and E. Skafidas, “High-speed indoor optical wireless communication system with single channel imaging receiver,” Opt. Express 20(8), 8442–8456 (2012).
    [Crossref] [PubMed]
  3. E. Hanada, “The electromagnetic environment of hospitals: how it is affected by the strength of electromagnetic fields generated both inside and outside the hospital,” Ann. Ist. Super. Sanita 43(3), 208–217 (2007).
    [PubMed]
  4. M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, and A. E. Willner, “Demonstration of a 280 Gbit/s free-space space-division-multiplexing communications link utilizing plane-wave spatial multiplexing,” Opt. Lett. 41(5), 851–854 (2016).
    [Crossref] [PubMed]
  5. Z. Cao, L. Shen, Y. Jiao, X. Zhao, and T. Koonen, “200 Gbps OOK transmission over an indoor optical wireless link enabled by an integrated cascaded aperture optical receiver,” in Optical Fiber Communication Conference (2017), paper Th5A.6.
    [Crossref]
  6. Y. Wang, N. Chi, Y. Wang, L. Tao, and J. Shi, “High-speed LED based visible light communication networks for beyond 10 Gb/s wireless access,” in Proceedings of IEEE 6th International Conference on Wireless Communications and Signal Processing (2014), pp. 1–6.
  7. O. Gonzalez, J. A. Martin-Gonzalez, M. F. Guerra-Medina, F. J. Lopez-Hernandez, and F. A. Delgado-Rajo, “Cyclic code-shift extension keying for multi-user optical wireless communications,” Electron. Lett. 51(11), 847–849 (2015).
    [Crossref]
  8. T. Liang, K. Wang, C. Lim, E. Wong, T. Song, and A. Nirmalathas, “Time-slot coding scheme for multiple access in indoor optical wireless communications,” Opt. Lett. 41(22), 5166–5169 (2016).
    [Crossref] [PubMed]
  9. J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
    [Crossref]
  10. J. Li, Z. Feng, Z. Feng, and P. Zhang, “A survey of security issues in cognitive radio networks,” China Commun. 12(3), 132–150 (2015).
    [Crossref]
  11. M. Agaskar and V. W. S. Chan, “Nulling strategies for preventing interference and interception of free space optical communication,” in Proceedings of IEEE International Conference on Communications (2013), pp. 3927–3932.
    [Crossref]
  12. A. Mostafa and L. Lampe, “Physical-layer security for indoor visible light communications,” in Proceedings of IEEE International Conference on Communications (2014), pp. 3342–3347.
    [Crossref]
  13. J. Qiu, L. Zhang, D. Li, and X. Liu, “High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving,” Opt. Eng. 55(6), 066121 (2016).
    [Crossref]
  14. W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014).
    [Crossref]
  15. C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002).
    [Crossref] [PubMed]
  16. A. R. Dixon, Z. L. Yuan, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate,” Opt. Express 16(23), 18790–18797 (2008).
    [Crossref] [PubMed]
  17. J. C. Sprott, Chaos and Time-Series Analysis (Oxford University, 2003), Chap.2.
  18. R. L. Rivest, “Chaffing and winnowing: confidentiality without encryption,” Crypto Bytes 4(1), 12–17 (1998).
  19. J. C. Sprott, Chaos and Time-Series Analysis (Oxford University, 2003), Chap.5.
  20. C. Zhang, “Period three begins,” Math. Mag. 83(4), 295–297 (2010).
    [Crossref]
  21. AS/NZS 2211.1:2004, Safety of laser products (Standards Australia International Ltd and Standards New Zealand, 2004).
  22. K. Cho and D. Yoon, “On the general BER expression of one-and-two-dimensional amplitude modulations,” IEEE Trans. Commun. 50(7), 1074–1080 (2002).
    [Crossref]
  23. J. G. Proakis, Digital Communications (McGraw-Hill, 2000), Chap. 5.

2016 (3)

2015 (3)

O. Gonzalez, J. A. Martin-Gonzalez, M. F. Guerra-Medina, F. J. Lopez-Hernandez, and F. A. Delgado-Rajo, “Cyclic code-shift extension keying for multi-user optical wireless communications,” Electron. Lett. 51(11), 847–849 (2015).
[Crossref]

A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015).
[Crossref]

J. Li, Z. Feng, Z. Feng, and P. Zhang, “A survey of security issues in cognitive radio networks,” China Commun. 12(3), 132–150 (2015).
[Crossref]

2014 (1)

W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014).
[Crossref]

2012 (1)

2010 (1)

C. Zhang, “Period three begins,” Math. Mag. 83(4), 295–297 (2010).
[Crossref]

2008 (1)

2007 (1)

E. Hanada, “The electromagnetic environment of hospitals: how it is affected by the strength of electromagnetic fields generated both inside and outside the hospital,” Ann. Ist. Super. Sanita 43(3), 208–217 (2007).
[PubMed]

2002 (2)

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002).
[Crossref] [PubMed]

K. Cho and D. Yoon, “On the general BER expression of one-and-two-dimensional amplitude modulations,” IEEE Trans. Commun. 50(7), 1074–1080 (2002).
[Crossref]

1998 (1)

R. L. Rivest, “Chaffing and winnowing: confidentiality without encryption,” Crypto Bytes 4(1), 12–17 (1998).

1997 (1)

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[Crossref]

Agaskar, M.

M. Agaskar and V. W. S. Chan, “Nulling strategies for preventing interference and interception of free space optical communication,” in Proceedings of IEEE International Conference on Communications (2013), pp. 3927–3932.
[Crossref]

Barry, J. R.

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[Crossref]

Chan, V. W. S.

M. Agaskar and V. W. S. Chan, “Nulling strategies for preventing interference and interception of free space optical communication,” in Proceedings of IEEE International Conference on Communications (2013), pp. 3927–3932.
[Crossref]

Chen, C.

W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014).
[Crossref]

Chi, N.

Y. Wang, N. Chi, Y. Wang, L. Tao, and J. Shi, “High-speed LED based visible light communication networks for beyond 10 Gb/s wireless access,” in Proceedings of IEEE 6th International Conference on Wireless Communications and Signal Processing (2014), pp. 1–6.

Cho, K.

K. Cho and D. Yoon, “On the general BER expression of one-and-two-dimensional amplitude modulations,” IEEE Trans. Commun. 50(7), 1074–1080 (2002).
[Crossref]

Delgado-Rajo, F. A.

O. Gonzalez, J. A. Martin-Gonzalez, M. F. Guerra-Medina, F. J. Lopez-Hernandez, and F. A. Delgado-Rajo, “Cyclic code-shift extension keying for multi-user optical wireless communications,” Electron. Lett. 51(11), 847–849 (2015).
[Crossref]

Dixon, A. R.

Dynes, J. F.

Faulkner, G.

A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015).
[Crossref]

Feng, Z.

J. Li, Z. Feng, Z. Feng, and P. Zhang, “A survey of security issues in cognitive radio networks,” China Commun. 12(3), 132–150 (2015).
[Crossref]

J. Li, Z. Feng, Z. Feng, and P. Zhang, “A survey of security issues in cognitive radio networks,” China Commun. 12(3), 132–150 (2015).
[Crossref]

Gomez, A.

A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015).
[Crossref]

Gonzalez, O.

O. Gonzalez, J. A. Martin-Gonzalez, M. F. Guerra-Medina, F. J. Lopez-Hernandez, and F. A. Delgado-Rajo, “Cyclic code-shift extension keying for multi-user optical wireless communications,” Electron. Lett. 51(11), 847–849 (2015).
[Crossref]

Gorman, P. M.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002).
[Crossref] [PubMed]

Guerra-Medina, M. F.

O. Gonzalez, J. A. Martin-Gonzalez, M. F. Guerra-Medina, F. J. Lopez-Hernandez, and F. A. Delgado-Rajo, “Cyclic code-shift extension keying for multi-user optical wireless communications,” Electron. Lett. 51(11), 847–849 (2015).
[Crossref]

Halder, M.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002).
[Crossref] [PubMed]

Hanada, E.

E. Hanada, “The electromagnetic environment of hospitals: how it is affected by the strength of electromagnetic fields generated both inside and outside the hospital,” Ann. Ist. Super. Sanita 43(3), 208–217 (2007).
[PubMed]

Huang, H.

Jiang, N.

W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014).
[Crossref]

Jin, W.

W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014).
[Crossref]

Kahn, J. M.

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[Crossref]

Kurtsiefer, C.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002).
[Crossref] [PubMed]

Lampe, L.

A. Mostafa and L. Lampe, “Physical-layer security for indoor visible light communications,” in Proceedings of IEEE International Conference on Communications (2014), pp. 3342–3347.
[Crossref]

Lavery, M. P. J.

Li, D.

J. Qiu, L. Zhang, D. Li, and X. Liu, “High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving,” Opt. Eng. 55(6), 066121 (2016).
[Crossref]

Li, J.

J. Li, Z. Feng, Z. Feng, and P. Zhang, “A survey of security issues in cognitive radio networks,” China Commun. 12(3), 132–150 (2015).
[Crossref]

Liang, T.

Lim, C.

Liu, X.

J. Qiu, L. Zhang, D. Li, and X. Liu, “High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving,” Opt. Eng. 55(6), 066121 (2016).
[Crossref]

Lopez-Hernandez, F. J.

O. Gonzalez, J. A. Martin-Gonzalez, M. F. Guerra-Medina, F. J. Lopez-Hernandez, and F. A. Delgado-Rajo, “Cyclic code-shift extension keying for multi-user optical wireless communications,” Electron. Lett. 51(11), 847–849 (2015).
[Crossref]

Martin-Gonzalez, J. A.

O. Gonzalez, J. A. Martin-Gonzalez, M. F. Guerra-Medina, F. J. Lopez-Hernandez, and F. A. Delgado-Rajo, “Cyclic code-shift extension keying for multi-user optical wireless communications,” Electron. Lett. 51(11), 847–849 (2015).
[Crossref]

Mostafa, A.

A. Mostafa and L. Lampe, “Physical-layer security for indoor visible light communications,” in Proceedings of IEEE International Conference on Communications (2014), pp. 3342–3347.
[Crossref]

Nirmalathas, A.

O’Brien, D.

A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015).
[Crossref]

Qiu, J.

J. Qiu, L. Zhang, D. Li, and X. Liu, “High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving,” Opt. Eng. 55(6), 066121 (2016).
[Crossref]

Qiu, K.

W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014).
[Crossref]

Quintana, C.

A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015).
[Crossref]

Rarity, J. G.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002).
[Crossref] [PubMed]

Ren, Y.

Rivest, R. L.

R. L. Rivest, “Chaffing and winnowing: confidentiality without encryption,” Crypto Bytes 4(1), 12–17 (1998).

Sato, M.

A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015).
[Crossref]

Sharpe, A. W.

Shi, J.

Y. Wang, N. Chi, Y. Wang, L. Tao, and J. Shi, “High-speed LED based visible light communication networks for beyond 10 Gb/s wireless access,” in Proceedings of IEEE 6th International Conference on Wireless Communications and Signal Processing (2014), pp. 1–6.

Shi, K.

A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015).
[Crossref]

Shields, A. J.

Skafidas, E.

Song, T.

Tao, L.

Y. Wang, N. Chi, Y. Wang, L. Tao, and J. Shi, “High-speed LED based visible light communication networks for beyond 10 Gb/s wireless access,” in Proceedings of IEEE 6th International Conference on Wireless Communications and Signal Processing (2014), pp. 1–6.

Tapster, P. R.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002).
[Crossref] [PubMed]

Thomsen, B. C.

A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015).
[Crossref]

Wang, K.

Wang, Y.

Y. Wang, N. Chi, Y. Wang, L. Tao, and J. Shi, “High-speed LED based visible light communication networks for beyond 10 Gb/s wireless access,” in Proceedings of IEEE 6th International Conference on Wireless Communications and Signal Processing (2014), pp. 1–6.

Y. Wang, N. Chi, Y. Wang, L. Tao, and J. Shi, “High-speed LED based visible light communication networks for beyond 10 Gb/s wireless access,” in Proceedings of IEEE 6th International Conference on Wireless Communications and Signal Processing (2014), pp. 1–6.

Weinfurter, H.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002).
[Crossref] [PubMed]

Willner, A. E.

Wong, E.

Xie, G.

Yoon, D.

K. Cho and D. Yoon, “On the general BER expression of one-and-two-dimensional amplitude modulations,” IEEE Trans. Commun. 50(7), 1074–1080 (2002).
[Crossref]

Yuan, Z. L.

Zarda, P.

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002).
[Crossref] [PubMed]

Zhang, C.

W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014).
[Crossref]

C. Zhang, “Period three begins,” Math. Mag. 83(4), 295–297 (2010).
[Crossref]

Zhang, L.

J. Qiu, L. Zhang, D. Li, and X. Liu, “High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving,” Opt. Eng. 55(6), 066121 (2016).
[Crossref]

Zhang, P.

J. Li, Z. Feng, Z. Feng, and P. Zhang, “A survey of security issues in cognitive radio networks,” China Commun. 12(3), 132–150 (2015).
[Crossref]

Zhang, W.

W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014).
[Crossref]

Ann. Ist. Super. Sanita (1)

E. Hanada, “The electromagnetic environment of hospitals: how it is affected by the strength of electromagnetic fields generated both inside and outside the hospital,” Ann. Ist. Super. Sanita 43(3), 208–217 (2007).
[PubMed]

China Commun. (1)

J. Li, Z. Feng, Z. Feng, and P. Zhang, “A survey of security issues in cognitive radio networks,” China Commun. 12(3), 132–150 (2015).
[Crossref]

Crypto Bytes (1)

R. L. Rivest, “Chaffing and winnowing: confidentiality without encryption,” Crypto Bytes 4(1), 12–17 (1998).

Electron. Lett. (1)

O. Gonzalez, J. A. Martin-Gonzalez, M. F. Guerra-Medina, F. J. Lopez-Hernandez, and F. A. Delgado-Rajo, “Cyclic code-shift extension keying for multi-user optical wireless communications,” Electron. Lett. 51(11), 847–849 (2015).
[Crossref]

IEEE Photonics Technol. Lett. (2)

A. Gomez, K. Shi, C. Quintana, M. Sato, G. Faulkner, B. C. Thomsen, and D. O’Brien, “Beyond 100 Gb/s indoor wire field-of-view optical wireless communications,” IEEE Photonics Technol. Lett. 27(4), 367–370 (2015).
[Crossref]

W. Zhang, C. Zhang, W. Jin, C. Chen, N. Jiang, and K. Qiu, “Chaos coding based QAM IQ-encryption for improved security in OFDMA-PON,” IEEE Photonics Technol. Lett. 26(19), 1964–1967 (2014).
[Crossref]

IEEE Trans. Commun. (1)

K. Cho and D. Yoon, “On the general BER expression of one-and-two-dimensional amplitude modulations,” IEEE Trans. Commun. 50(7), 1074–1080 (2002).
[Crossref]

Math. Mag. (1)

C. Zhang, “Period three begins,” Math. Mag. 83(4), 295–297 (2010).
[Crossref]

Nature (1)

C. Kurtsiefer, P. Zarda, M. Halder, H. Weinfurter, P. M. Gorman, P. R. Tapster, and J. G. Rarity, “Quantum cryptography: a step towards global key distribution,” Nature 419(6906), 450 (2002).
[Crossref] [PubMed]

Opt. Eng. (1)

J. Qiu, L. Zhang, D. Li, and X. Liu, “High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving,” Opt. Eng. 55(6), 066121 (2016).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Proc. IEEE (1)

J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proc. IEEE 85(2), 265–298 (1997).
[Crossref]

Other (8)

Z. Cao, L. Shen, Y. Jiao, X. Zhao, and T. Koonen, “200 Gbps OOK transmission over an indoor optical wireless link enabled by an integrated cascaded aperture optical receiver,” in Optical Fiber Communication Conference (2017), paper Th5A.6.
[Crossref]

Y. Wang, N. Chi, Y. Wang, L. Tao, and J. Shi, “High-speed LED based visible light communication networks for beyond 10 Gb/s wireless access,” in Proceedings of IEEE 6th International Conference on Wireless Communications and Signal Processing (2014), pp. 1–6.

J. C. Sprott, Chaos and Time-Series Analysis (Oxford University, 2003), Chap.2.

J. C. Sprott, Chaos and Time-Series Analysis (Oxford University, 2003), Chap.5.

M. Agaskar and V. W. S. Chan, “Nulling strategies for preventing interference and interception of free space optical communication,” in Proceedings of IEEE International Conference on Communications (2013), pp. 3927–3932.
[Crossref]

A. Mostafa and L. Lampe, “Physical-layer security for indoor visible light communications,” in Proceedings of IEEE International Conference on Communications (2014), pp. 3342–3347.
[Crossref]

AS/NZS 2211.1:2004, Safety of laser products (Standards Australia International Ltd and Standards New Zealand, 2004).

J. G. Proakis, Digital Communications (McGraw-Hill, 2000), Chap. 5.

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Figures (7)

Fig. 1
Fig. 1 Signal constellation for a general square QAM.
Fig. 2
Fig. 2 Noisy probability for (a) 4-QAM and (b) 16-QAM.
Fig. 3
Fig. 3 Outage probability with δ = 1e-10 for (a) 4-QAM and (b) 16-QAM.
Fig. 4
Fig. 4 Block diagram of secure OWC with TSC and chaotic phase.
Fig. 5
Fig. 5 Experimental setup
Fig. 6
Fig. 6 Power penalty results with different bit rates for (a) 4-QAM and (b) 16-QAM.
Fig. 7
Fig. 7 SER performance and constellation with and without the key for (a) 2.5 Gb/s 4-QAM and (b) 4 Gb/s 16-QAM.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

x i+1 =r x i (1 x i ). r[ 0,4 ], x 1 (0,1).
θ[ n ]=360x[ n ], n=1,2,,N .
β( I,Q )={ cos 1 I 2 I+Q I 2 + Q 2 ( I1 ) 2 I 2 + Q 2 , IQ cos 1 Q 2 +Q+I I 2 + Q 2 ( Q+1 ) 2 I 2 + Q 2 , I>Q γ( I,Q )={ cos 1 I 2 I+Q I 2 + Q 2 ( I+1 ) 2 I 2 + Q 2 , I<Q cos 1 Q 2 Q+I I 2 + Q 2 ( Q1 ) 2 I 2 + Q 2 , IQ
I=2a1 2 l , 1a 2 l . Q=2b1 2 l , 1b 2 l .
β( I,Q )<θ[ n ]< 360 γ( I,Q ).
Ρ noisy = 1 4 l1 I,Q P( β( I,Q )<θ[ n ]< 360 γ( I,Q ) ) .
r e = r b +δ, x 1 e = x 1 b +δ
Ρ out = 1 4 l1 I,Q P( γ( I,Q ) θ b [ n ] θ e [ n ]β( I,Q ) )
C k =[ 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 ]

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