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Abstract
This paper proposes an encryption scheme for floating probabilistic shaping orthogonal frequency division multiplexing passive optical networks (FPS-OFDM-PON). Four chaotic sequences are generated by the 4D hyperchaotic model for floating probabilistic shaping (FPS) and bubble sort encryption scheme. An experiment is conducted to demonstrate the transmission of a 70Gb/s (7×10Gb/s) FPS-OFDM-PON signal across a 2km weakly coupled 7-core fiber. The keyspace of the 4D hyperchaotic model reaches 10120. The results show that a 1.82 dB gain in receiver sensitivity compared with the conventional uniform 16QAM-OFDM due to the introduction of FPS. When the system is assaulted by an unlawful receiver, the bit error rate (BER) can still remain at 0.49, successfully assuring the system's security. Due to its good transmission and security performance, the scheme has important application prospects in the future optical access network.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The exponential growth of network bandwidth is fueled by the constant creation of new network services such as digital twins, virtual reality/augmented reality, and the metaverse. To meet the technical difficulties of increasing transmission capacity, advanced coding and modulation techniques have begun to attract widespread attention. At present, probabilistic shaping (PS) technology has aroused great repercussions in the field of optical fiber communication [1–2]. PS technology is a coded modulation scheme that transmits non-equi-probable constellation points. Since the utilization rate of constellation points is improved, the nonlinear influence received by the signal can be effectively reduced, and the system capacity can be closer to the Shannon limit of the channel. At the same time, this technology can significantly reduce the average constellation power and surpass in the robustness against noise, thus improving the system performance [3–6]. Existing relatively mature PS use constant composition distribution matching (CCDM) [7–9], however, CCDM modules have high computational complexity. In the short-distance access network, how to reduce the complexity of coding and modulation has become the focus of our attention.
With the rapid development of optical communication technology, the communication capacity of traditional single-mode fiber is approaching the nonlinear Shannon limit, and space division multiplexing (SDM) technology has become the focus of our attention [10–12]. Multi-core fiber (MCF) is a promising SDM fiber, which can improve the transmission capacity of the fiber by increasing the number of fiber cores [13–15]. In addition, floating probabilistic shaping and SDM technology are compatible, because constellation mapping uses the coordinates of constellation points to represent the phase and amplitude of the signal, while PS only changes the occurrence probability of constellation points. An 11.3 km 6-mode 19-core fiber is used in the experiment to achieve ultra-dense SDM transmission [16]. In [17], the authors used 37 km of 7-core fiber to transmit 12 channels of 40Gb/s polarization division multiplexing quadrature phase-shift keying (PDM-QPSK) signals, using ultra-dense wavelength division multiplexing passive optical networks (WDM-PON). Similarly, a 3D carrier-free amplitude modulation phase (CAP) signal transmission of 25.45 Gb/s was successfully achieved on a 7-core fiber communication system [18]. In fact, using the spatial dimension can increase the capacity and splitting ratio of the access system, enabling it to meet the needs of more users.
Passive optical networks (PON) [19–21] are considered a promising candidate with advantages such as higher transmission rate, larger optical splitting ratio, and good expansion compatibility, capable of handling optical access networks with rapidly growing bandwidth and capacity demands. Orthogonal frequency division multiplexing (OFDM) has become a leading research and development area in the field of high-speed optical communications. OFDM is a highly spectrally efficient parallel transmission technique utilizing orthogonal overlapping sub-carriers [22–23]. Since each subcarrier is independent, channel effects can be easily equalized using a simple single-point equalizer. Meanwhile, OFDM can effectively combat the interference between signal waveforms and is suitable for high-speed data transmission in multipath environments and fading channels. In orthogonal frequency division multiple passive optical networks (OFDM-PON), by assigning subcarriers to different optical network units (ONUs), signal bandwidth can be simply allocated according to data requirements, making network resource management more flexible [24–27]. However, because the traditional PON system downstream data flow adopts broadcast technology, the downstream signal is broadcast to all-optical network units without any restriction, so higher requirements are put forward for the security of OFDM-PON [28–30].
In this research, we propose and demonstrate a floating Probabilistic shaping orthogonal frequency division multiple passive optical networks (FPS-OFDM-PON) scheme in optical access networks, which is based on Floating Probabilistic Shaping (FPS) and bubble sort encryption scheme. The FPS scheme combined with the 4D hyperchaotic model reduces the complexity of traditional PS coding and modulation. The dynamic probability is generated for each symbol through the chaos model, and the dynamic chaos configuration is performed for the probability of each layer of constellation points. This scheme not only improves the utilization rate of constellation points but also enhances the anti-noise capability of the system. At the same time, the introduction of the chaos model enables high-security encryption of constellation points from the physical layer. In addition, the bubble sort encryption scheme is used to encrypt the frequency and time of the OFDM sub-carrier to realize double high-security signal transmission. In this scheme, the multi-dimensional information is scrambled at the same time through the 4D hyperchaotic model, which can provide a keyspace of 10120 that can effectively resist the attacks of illegal receivers. The experiment shows that an encrypted 16QAM-OFDM signal is transmitted across a 2km 7-core fiber in the FPS-OFDM-PON system to validate the scheme's security performance.
2. Principle
The block diagram of the whole algorithm is shown in Fig. 1. The pseudo-random binary sequence (PRBS) is used as original data. Firstly, the original bitstream is converted into multiple rows of data through serial to parallel (S/P) for constellation mapping, passes through the FPS constellation mapping, then enters the bubble sort encryption scheme, and finally enters the transmission system through Inverse Fast Fourier Transform (IFFT). Secondly, the receiving end is opposite the transmitting end, where the signal passing through the transmission system is first subjected to Fast Fourier Transform (FFT), then enters the OFDM demodulation module for descrambling, and then passes through the FPS constellation de-mapping module for decryption processing. Finally, parallel to serial (P/S) transform the exported data.
For the encryption module, the masking vector and disturbance factor are generated by the 4D hyperchaotic model. The masking vector is subjected to variable probabilistic shaping and encryption. The processed signal is perturbed in the OFDM modulation bubble sort encryption scheme. The masking vector and disturbance factor at the receiver are the same as those at the transmitter.
As shown in Eq. (1), where x, y, z and w are the state variables of the system; a, b, c and d are the parameters of the system, and the system is at a unique equilibrium point ${E_0} = (0,0,0,0)$. When the parameters take $a = 35$, $b = 3$, $c = 33$, $d = 8$, there is a typical hyperchaotic attractor in the system. The phase diagram of the 4D hyperchaotic is shown in Fig. 2.
The autocorrelation and cross-correlation of the 4D hyperchaotic model are investigated to further evaluate the system's safety performance. The autocorrelation and cross-correlation diagrams are shown in Fig. 3 when the initial parameter x1 is 5 and 5 + 10−16. When the correlation interval is 0, the maximum value of the autocorrelation function is 1, and the autocorrelation function at other positions is about 0. When the initial value is slightly changed by 10−16, the cross-correlation of the two sequences is almost zero, which indicates that our sequence has good randomness.
We offer a mechanism for FPS encryption in this section. The chaotic masking vector modifies the constellation mapping rule to achieve the constellation's uneven distribution. For data mapping, we use the uniform 16QAM constellation diagram, as illustrated in Fig. 4. We modify the probability distribution of constellation points under the premise of uniform 16QAM mapping. The 16QAM constellation points are divided into 3 power levels. Power level 1 is the constellation point whose first two bits are “00”, power level 2 is the constellation point whose first two bits are “01” or “10”, and power level 3 is the constellation point whose first two bits are “11”. Through the processing of this module, the occurrence probability of constellation points of different power levels in 16QAM is changed, and the transmission probability of the inner circle of constellation points is improved, that is, the occurrence probability of “00XX” is increased.
Specifically, three groups of chaotic sequences ${x_m}$, ${y_m}$ and ${z_m}$ are extracted from the above hyperchaotic model. Firstly, the remainder processing is performed on ${x_m}$, and the masking vector ${x_n}$ is obtained as in Eq. (2), which is employed to encrypt the constellation points of power level 3. When the value of ${x_n}$ is 0, the data keeps the original constellation point unchanged. When the value of ${x_n}$ is 1, the data is transferred from the constellation point “11XX” of power level 3 to the constellation point “01XX” of power level 2. When the value of ${x_n}$ is 2, the data is transferred from the constellation point “11XX” of power level 3 to the constellation point “10XX” of power level 2. The purpose of multiplying by 103 is to increase the randomness of the masking vector. If you replace it with another number, there will be a similar encryption effect.
Then we perform remainder processing on ${y_m}$ and ${z_m}$ to obtain masking vectors ${y_n}$ and ${z_n}$ as shown in Eq. (3), mask the constellation points of power level 2. When the value of ${y_n}$ is 0, the data remains the same as the original constellation point. When the value of ${y_n}$ is 1, the data is transferred from the constellation point “XX01” of power level 2 to the constellation point “00XX” of power level 1. When the value of ${z_n}$ is 0, the data keeps the original constellation point unchanged. When the value of ${z_n}$ is 1, the data is transferred from the constellation point “01XX” of power level 2 to the constellation point “00XX” of power level 1.
After FPS, we map the signal onto OFDM subcarriers. Assuming the total number of subcarriers be M, the symbol duration is ${T_s}$, and ${f_k}$ is the frequency of the kth subcarrier, then the OFDM original signal after the first masking can be is represented by Eq. (4).
In digital signal processing (DSP), the data of one column and one row is modulated by OFDM to form a matrix with multiple rows and multiple columns. The number of subcarriers used in this paper is 512, and each subcarrier contains 120 symbols. We divide the data into 120 groups of 8×15 resource blocks combined. Then we extract a list of chaotic sequences ${w_m}$ from the above chaotic model. Similarly, multiply ${w_m}$ by 103 to increase the randomness of the disturbance factor, and perform rounding and remainder calculations on the extracted new sequence. At the same time, the unique function is used to exclude duplicate keys, and finally, the perturbation factor ${w_n}$ is generated by Eq. (5).
Then, each group of resource blocks is perturbed. The perturbation principle is shown in Fig. 5. The adjacent resource blocks from left to right are compared in sequence, and the resource block with the larger result after the comparison is replaced backward. In each round of comparison, the resource block with the largest disturbance factor will emerge from the far right and finally implement bubble sort encryption. Since the encryption schemes are all reversible, the original data can be recovered using the opposite algorithm at the receiving end.
Dual-physical layer high-security encrypted communication can be produced using the preceding techniques. FPS keeps the geometric position of the constellation points the same, but it reduces the likelihood of high-amplitude constellation point signals while increasing the probability of low-amplitude values. It not only improves the utilization rate of constellation points but also effectively reduces the nonlinear influence received by the signal, making the system capacity closer to the Shannon limit of the channel. Through the introduction of the chaotic model, the entire encryption process obtains higher security. At the same time, because the distribution probability of constellation points is optimized, the average power of the system can be effectively reduced, and the bit error rate of the system can be reduced under the same transmit power. In addition, we use the bubble sort encryption scheme to encrypt the OFDM sub-carriers from the physical layer, which further improves the security of the system.
3. Experimental setup and results
To verify the performance of the proposed encrypted FPS-OFDM-PON system, the experiment has been carried out, the experimental system is shown in Fig. 6. At the optical line terminal (OLT), the original data is mapped to 512 sub-carriers, each sub-carrier contains 120 symbols, and the IFFT point is 2048. The modulated data is encrypted by offline DSP. Then the encrypted data are imported into an arbitrary waveform generator (AWG, TekAWG70002A) and sent at a sampling rate of 10GSa/s. Then the RF signal amplified by the electronic amplifier (EA) is intensity-modulated by a Mach-Zehnder modulator (MZM). The gain of the electrical amplifier is 20 dB and the MZM is biased at the quadrature point. The wavelength of the light source used in the experiment was 1550 nm. After amplifying the adjusted optical signal through an erbium-doped fiber amplifier (EDFA), the optical signal is divided into 8 equal parts through a 1:8 power splitter. Finally, each component is fanned into the 7-core fiber (the average core insertion loss is about 1.5 dB, and the crosstalk between the adjacent cores is less than -50 dB). After 2 km of transmission, the transmitted 7 core signals are spatially demultiplexed into single-mode fibers through a fan-out device. To compensate for the transmission power loss, EDFA is used for amplification again. Before the optical signal enters the receiving end, the optical power is adjusted by a variable optical attenuator. Photodiode is used to receive optical signals and realize photoelectric conversion. Finally, the converted electrical signals were acquired by a mixed-signal oscilloscope (MSO, TekMS073304DX) with a sampling rate of 50GSa/s. Analog-to-digital conversion was realized, simultaneously. Finally, by offline processing, the correct key is used to restore the original data.
Fig. 6. Experimental setup (DSP: digital signal process; AWG: arbitrary waveform generator; MZM: Mach-Zehnder modulator; EDFA: Erbium-doped fiber amplifier; PS: power splitter; DL: delay line; VOA: variable optical attenuator; PD: photodiode; MSO: mixed-signal oscilloscope).
Figure 7 is a schematic diagram of the BER curve of the FPS-OFDM-PON signal after 2km transmission in 7 fiber cores. It can be found that at the legal ONU, bit errors start to appear from the received optical power -16dBm, which indicates that the FPS can effectively improve the performance of the system. And with the continuous increase of optical power, the BER of each fiber core has dropped significantly. In addition, the BER curves of each fiber core almost overlap, indicating that the transmission effect of the seven fiber cores has strong stability. As shown in the figure, when the system BER is 1×10−3, the optical power difference between the best core and the worst core is 0.54dB, which confirms that the 7-core fiber used in this experiment has good uniformity. For the illegal receiver, due to the lack of the correct key, the original information cannot be decrypted correctly. With the increase of optical power, the bit error rate of the illegal receiver remains around 0.49, which indicates that the encryption scheme proposed in this paper can effectively improve the security performance of the system.
A channel is randomly selected to do a comparison group experiment, respectively transmitting the FPS-16QAM-OFDM signal and the uniform 16QAM-OFDM signal. It can be seen from the curve change in Fig. 8 that the transmission effect of the FPS-16QAM-OFDM signal is better than that of the traditional 16QAM-OFDM signal. The FPS-16QAM-OFDM signal has obvious bit errors at the optical power of -17dBm, while the uniform 16QAM-OFDM signal has obvious bit errors at the optical power of -15dBm. When the optical power is -15.81dBm, the system BER of the uniform 16QAM-OFDM signal is 1×10−3. And the system bit error rate of FPS-16QAM-OFDM signal is 1×10−3 when the optical power is -17.62dBm. It shows that the receiver sensitivity of the FPS scheme is increased by 1.82 dB compared with the traditional uniform 16QAM-OFDM. The received constellations of the FPS-16QAM-OFDM signal and uniform 16QAM-OFDM signal at the received optical power of -17 dBm are also embedded in Fig. 8, of which the former one is more clearly viewed and displays an optimized probability distribution pattern where the inner points have higher transmitting chances. It can be concluded that due to the introduction of FPS, the bit error performance of the system is effectively improved.
Fig. 8. BER curves of encrypted FPS-16QAM-OFDM and uniform 16QAM-OFDM at the same bit rate in 7-core fiber.
The parameters of the 4D hyperchaotic model are altered significantly in order to validate the sensitivity of the initial value, as shown in Fig. 9, and the BER after each adjustment with different measurements is recorded. As an example, consider the third core, which has a receiving optical power of -17dBm. The abscissa in the figure is the change of the initial value. For example, -19 means that the parameter is disturbed by 1 × 10−19, and the ordinate corresponds to the BER. When the precision is -17, the distribution of the constellation diagram is clear, the BER is low, and it can’t affect the BER. When the precision is -16, the bit error rate rises sharply and exceeds the FEC threshold, making it impossible for an illegal receiver to get the right information. This shows that our chaotic model is highly sensitive to the initial value. Even if the parameters and initial values of the chaotic model are changed very little at the illegal receiving end, it is difficult to crack. The keyspace of the 4D hyperchaotic model can reach ${({10^{15}})^8} = {10^{120}}$. Therefore, the keyspace is sufficient to resist brute force cracking.
In addition, to study the encryption performance of the proposed encryption scheme on images, we use a cute dog as a transmission instance for verification. At the legal ONU, the image is recovered normally due to the correct key decryption, and the grayscale histogram is regularly distributed. The image and histogram are shown in Fig. 10 (a)-(b). However, the images and histograms received at the illegal ONU are shown in Fig. 10 (c)-(d), the images are blurred and the gray-scale histogram distribution is scattered, indicating that no useful information can be obtained.
Fig. 10. (a) image before encryption; (b) histogram before encryption; (c) image after encryption; (d) histogram after encryption.
4. Conclusion
This paper proposes and demonstrates an FPS-OFDM-PON scheme based on FPS and bubble sort encryption scheme in the optical access network. Four chaotic sequences are generated by using the four-dimensional hyperchaotic model, and the uniform 16QAM constellation diagram is encrypted with floating probability. The frequency and time of OFDM sub-carriers are encrypted by chaotic sequence to realize a double-high security encryption scheme. The experiment uses a 2km weakly coupled 7-core fiber, which increases the transmission capacity by 7 times. The experiments show that OFDM signals encrypted at 70Gb/s can be transmitted across a 2km 7-core fiber. The results support the scheme's effective high-security performance and improved transmission. In terms of security, the system can achieve a keyspace of 10120 while being less complex.
Funding
National Key Research and Development Program of China (2018YFB1800901); National Natural Science Foundation of China (61720106015, 61727817, 61835005, 61875248, 61935005, 61935011, 61975084, 62035018, 62171227, U2001601); Jiangsu team of innovation and entrepreneurship; The Startup Foundation for Introducing Talent of NUIST.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. C. Pan and F. Kschischang, “Probabilistic 16-QAM Shaping in WDM Systems,” J. Lightwave Technol. 34(18), 4285–4292 (2016). [CrossRef]
2. G. Böcherer, F. Steiner, and P. Schulte, “Bandwidth Efficient and Rate-Matched Low-Density Parity-Check Coded Modulation,” IEEE Trans. Commun. 63(12), 4651–4665 (2015). [CrossRef]
3. G. Böcherer, P. Schulte, and F. Steiner, “Probabilistic Shaping and Forward Error Correction for Fiber-Optic Communication Systems,” J. Lightwave Technol. 37(2), 230–244 (2019). [CrossRef]
4. J. Ren, B. Liu, X. Xu, L. Zhang, Y. Mao, X. Wu, Y. Zhang, L. Jiang, and X. Xin, “A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions,” Opt. Express 27(3), 2732–2746 (2019). [CrossRef]
5. J. Ren, B. Liu, X. Wu, L. Zhang, Y. Mao, X. Xn, Y. Zhang, L. Jiang, J. Zhang, and X. Xin, “Three-Dimensional Probabilistically Shaped CAP Modulation Based on Constellation Design Using Regular Tetrahedron Cells,” J. Lightwave Technol. 38(7), 1728–1734 (2020). [CrossRef]
6. S. Zhang and F. Yaman, “Constellation design with geometric and probabilistic shaping,” Opt. Commun. 409, 7–12 (2018). [CrossRef]
7. P. Schulte and G. Böcherer, “Constant Composition Distribution Matching,” IEEE Trans. Inf. Theory 62(1), 430–434 (2016). [CrossRef]
8. J. Ma, M. Chen, K. Wu, and J. He, “Performance Enhancement of Probabilistically Shaped OFDM Enabled by Precoding Technique in an IM-DD System,” J. Lightwave Technol. 37(24), 6063–6071 (2019). [CrossRef]
9. M. Fu, Q. Liu, H. Lun, H. Jiang, Y. Wu, X. Liu, Z. Yang, L. Yi, W. Hu, and Q. Zhuge, “Parallel Bisection-based Distribution Matching for Nonlinearity-tolerant Probabilistic Shaping in Coherent Optical Communication Systems,” J. Lightwave Technol. 39(20), 6459–6469 (2021). [CrossRef]
10. R. J. Essiambre, R. Ryf, N. K. Fontaine, and S. Randel, “Breakthroughs in Photonics 2012: Space-Division Multiplexing in Multimode and Multicore Fibers for High-Capacity Optical Communication,” IEEE Photonics J. 5(2), 0701307 (2013). [CrossRef]
11. L. Zhang, J. Chen, E. Agrell, R. Lin, and L. Wosinska, “Enabling Technologies for Optical Data Center Networks: Spatial Division Multiplexing,” J. Lightwave Technol. 38(1), 18–30 (2020). [CrossRef]
12. R. S. Luís, G. Rademacher, B. J. Puttnam, Y. Awaji, and N. Wada, “Long distance crosstalk-supported transmission using homogeneous multicore fibers and SDM-MIMO demultiplexing,” Opt. Express 26(18), 24044–24053 (2018). [CrossRef]
13. F. Bao, Y. Ding, M. Nooruzzaman, Y. Amma, Y. Sasaki, L. K. Oxenløwe, H. Hu, and T. Morioka, “DSP-free single-wavelength 100 Gbps SDM-PON with increased splitting ratio using 10G-class DML,” Opt. Express 27(23), 33915–33925 (2019). [CrossRef]
14. T. Sakamoto, K. Saitoh, S. Saitoh, Y. Abe, K. Takenaga, A. Urushibara, M. Wada, T. Matsui, K. Aikawa, and K. Nakajima, “Spatial Density and Splicing Characteristic Optimized Few-Mode Multi-Core Fiber,” J. Lightwave Technol. 38(16), 4490–4496 (2020). [CrossRef]
15. G. Rademacher, R. S. Luis, B. J. Puttnam, R. Ryf, S. v. d. Heide, T. A. Eriksson, N. K. Fontaine, H. Chen, R. Essiambre, Y. Awaji, and H. Furukawa, “A Comparative Study of Few-Mode Fiber and Coupled-Core Multi-Core Fiber Transmission,” J. Lightwave Technol. 40(6), 1590–1596 (2022). [CrossRef]
16. D. Soma, Y. Wakayama, S. Beppu, S. Sumita, T. Tsuritani, T. Hayashi, T. Nagashima, M. Suzuki, M. Yoshida, K. Kasai, M. Nakazawa, H. Takahashi, K. Igarashi, I. Morita, and M. Suzuki, “10.16-Peta-B/s Dense SDM/WDM Transmission Over 6-Mode 19-Core Fiber Across the C + L Band,” J. Lightwave Technol. 36(6), 1375–1381 (2018). [CrossRef]
17. C. Xiong, M. Tang, C. Ke, Z. Feng, Q. Wu, L. Xu, S. Fu, W. Tong, P. P. Shum, and D. Liu, “Experimental Demonstration of Ultra-Dense WDM-PON With Seven-Core MCF-Enabled Self-Homodyne Coherent Detection,” IEEE Photonics J. 9(2), 1–7 (2017). [CrossRef]
18. C. Ni, B. Liu, J. Ren, Y. Mao, S. Chen, R. Ullah, X. Song, Y. Han, X. Wu, and F. Tian, “Three-dimensional constellation diagram with a hierarchical level design for multi-core transmission,” Opt. Express 30(2), 2877–2887 (2022). [CrossRef]
19. F. Effenberger, D. Cleary, O. Haran, R. Li, M. Oron, and T. Pfeiffer, “An introduction to PON technologies,” IEEE Commun. Mags. 45(3), (S17–S25) 2007. [CrossRef]
20. K. Suzuki, Y. Fukada, D. Nesset, and R. Davey, “Amplified gigabit PON systems [Invited],” J. Opt. Commun. Netw. 6(5), 422–433 (2007). [CrossRef]
21. R. Ullah, B. Liu, S. Ullah, Y. Mao, T. Feng, M. K. Khan, and X. Xin, “Flattened Optical Multicarrier Generation Technique for Optical Line Terminal Side in Next Generation WDM-PON Supporting High Data Rate Transmission,” IEEE Access 6, 6183–6193 (2018). [CrossRef]
22. I. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006). [CrossRef]
23. J. Armstrong and A. Lowery, “Power efficient optical OFDM,” Electron. Lett. 42(6), 370–372 (2006). [CrossRef]
24. M. Chen, X. Xiao, Z. R. Huang, J. Yu, F. Li, Q. Chen, and L. Chen, “Experimental Demonstration of an IFFT/FFT Size Efficient DFT-Spread OFDM for Short Reach Optical Transmission Systems,” J. Lightwave Technol. 34(9), 2100–2105 (2016). [CrossRef]
25. S. Jung, C. Kim, S. Jung, and S. Han, “Optical pulse division multiplexing-based OBI reduction for single wavelength uplink multiple access in IM/DD OFDMA-PON,” Opt. Express 24(25), 29198–29209 (2016). [CrossRef]
26. N. Cvijetic, “OFDM for Next-Generation Optical Access Networks,” J. Lightwave Technol. 30(4), 384–398 (2012). [CrossRef]
27. N. Cvijetic, M. Cvijetic, M.-F. Huang, E. Ip, Y.-K. Huang, and T. Wang, “Terabit Optical Access Networks Based on WDM-OFDMA-PON,” J. Lightwave Technol. 30(4), 493–503 (2012). [CrossRef]
28. T. Wu, C. Zhang, H. Wei, and K. Qiu, “PAPR and security in OFDM-PON via optimum block dividing with dynamic key and 2D-LASM,” Opt. Express 27(20), 27946–27961 (2019). [CrossRef]
29. M. Bi, X. Fu, X. Zhou, L. Zhang, G. Yang, X. Yang, S. Xiao, and W. Hu, “A Key Space Enhanced Chaotic Encryption Scheme for Physical Layer Security in OFDM-PON,” IEEE Photonics J. 9(1), 1–10 (2017). [CrossRef]
30. A. Sultan, X. Yang, A. Hajomer, and W. Hu, “Chaotic Constellation Mapping for Physical-Layer Data Encryption in OFDM-PON,” IEEE Photon. Technol. Lett. 30(4), 339–342 (2018). [CrossRef]
