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Abstract
The physical layer security of radio-over-fiber (RoF) system is a very important problem for future communication. In this paper, a novel probabilistic shaping (PS) based constellation encryption scheme is proposed in which two bit-level encryption operations are firstly performed according to chaotic sequences and hash values. The chaotic sequences are generated by hyperchaotic system and hash values are obtained by SHA-512. Then PS is applied to enhance transmission performance. After PS-16-quadrature amplitude modulation (QAM), constellation encryption is implemented aiming at maintaining overall shaping distribution unchanged and improving security. An encrypted PS-16-QAM orthogonal frequency division multiplexing (OFDM) signal is successfully transmitted over 50 km standard single-mode fiber (SSMF) and 5 m wireless channel in our experiment. The results demonstrate that the key space of 10121 is achieved to defend malicious attacks. Moreover, the proposed PS-based encryption scheme can obtain approximately 2.4 dB gain at a BER of 10−3 compared with traditional OFDM signal. Thus, the proposed scheme has a good application prospect in the future OFDM-RoF system due to the dominant BER and security performance.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As an emerging wireless access technology, radio-over-fiber (RoF) combines wireless and wired optical network technology. It has many distinguished characteristics such as high transmission bandwidth, long transmission distance, flexible deployment, low power consumption and low cost. Moreover, the simple structure of the remote base station and the centralized network management capabilities make it a very potential access network solution to solve the problem of “last mile” or “last meter” and ultra-fast optical signal connection [1,2]. On the other hand, orthogonal frequency division multiplexing (OFDM) has been widely used in RoF due to its high spectral efficiency, high flexibility, and robustness against dispersion [3–9]. Moreover, the signal from the central station (CS) is broadcast to each distributed base station (BS) in the same way. Then, each BS can share the same information, and the privacy of each BS may be easily leaked [10,11]. In terms of sophisticated network planning and provisioning, researches about the routing, modulation and spectrum assignments optimization scheme have been proposed [12,13]. In this paper, the main practical problem is how to enhance the physical layer security of OFDM-RoF system.
A large number of approaches have been developed over the last decade to improve the physical layer security in optical networks. With the help of convenient digital signal processing (DSP), chaotic encryption has become an alternative approach for physical layer security owing to the universality, ergodicity, pseudo-randomness and sensitivity to initial values [14]. Meanwhile, different encryption strategies have been proposed such as a security enhancement technique based on three-dimensional Brownian motion and chaos in cell [15], a fixed-point chaos algorithm by introducing the native randomness of the data [16], high rates transmission by deep-learning based chaos synchronization [17], permutation algorithms [18–20], DNA based methods [21–23], and quantum stream cipher [24]. In terms of constellation-based schemes, chaotic active constellation extension (ACE) [25], chaotic constellation transformation [26], and chaotic constellation mapping [27] have already been proposed. However, some of the existing encryption methods will bring about the deterioration of the signal error rate.
Recently, with a milestone development of the invention of probabilistic amplitude shaping, which contains a distribution matcher and a forward error correction inner code, probabilistic shaping (PS) becomes practical [28,29]. Subsequently, PS has aroused great attention due to its higher capacity and longer transmission distance in optical fiber communication system [30–32]. It has been proved that PS can improve signal-to-noise ratio and increase system capacity [33,34]. Researches about the encryption schemes combining with probabilistic shaping have attracted much attention in recent years. A chaos encryption with dynamic probability in 16-carrier-less amplitude/phase (CAP) PON system was proposed [35], which combines a feedforward neural network-based XOR operator for scrambling to improve the security of CAP-PON. And then a floating probabilistic shaping scheme in the PS-16-CAP system using chaotic mapping to disturb probability mass function (PMF) was proposed [36]. Afterwards, a four-dimensional chaos encryption scheme was proposed, in which PS and dimension coordination optimization were applied to improve the efficiency of the system [37]. In addition, a chaotic CCDM-based scrambling encryption was implemented in QAM mapping [38]. A symmetric encryption scheme for five dimensions before and after PS was proposed [39]. Nevertheless, some of the encryption algorithms may have changed the original distribution of PS symbol, which will weaken the effects of PS and have negative impacts on transmission performance.
In this paper, a novel PS-based constellation encryption method for OFDM-RoF is put forward and experimentally demonstrated, which keeps the overall probability of the shaping distribution unchanged. Compared with single level encryption method for original data, two bit-level encryption operations including chaos encryption and hash encryption are applied to improve the security. A 4-D hyperchaotic system is used to generate key sequences for bit-level encryption and constellation scrambling. In addition, the hash value is related to original data and hash encryption can further enhance the security and increase the key space. Then, PS is applied in our scheme to improve the transmission performance. After PS-16-QAM, PS-based constellation scrambling is implemented, which can maintain the total probability of the shaping distribution unchanged simultaneously. Compared with the above-mentioned PS and constellation encryption methods, our proposed scheme not only guarantees the original characteristics of probabilistic shaping, but also improves the physical layer security of the system. The experimental results show that the PS-16-QAM encrypted signal has been successfully transmitted over 50 km SSMF in OFDM-RoF.
2. Principle
The principle of proposed encryption scheme is illustrated in Fig. 1. At the central station, the encrypted OFDM signals are processed in the offline DSP before loading to the optical modulation channel. Firstly, pseudo-random binary sequences (PRBSs) are applied as original data and hash values of data are calculated. In this step, two bit-level encryption operations are performed according to exclusive or (XOR). After the serial-to-parallel conversation (S/P), the input encrypted sequences are mapped onto the QAM subcarriers through PS encoder. Subsequently, PS-based constellation scrambling is implemented according to key sequences generated by hyperchaotic system. Finally, encrypted signals are processed by OFDM modulation and loaded to the transmission channel.
As shown in Fig. 1, a 4-D hyper chaotic system is employed to generate chaotic key sequences, which can be expressed as follows [21]:
According to Eq. (1), four chaotic sequences X, Y, Z and V can be generated. To obtain encryption sequences ${K_1}$ and H for XOR operations, X is post-processed by
where the function $fix(x)$ returns the nearest integer to zero and $(A > B)$ returns 0 when left value is smaller than right, or returns 1. Original sequence is expressed as S with the length of $N.$ Then, SHA-512 is applied to compute hash value of original data. The calculated values are converted to $H.$ Hence, two bit-level encryptions can be performed asSubsequently, the probabilistic shaping scheme is applied to improve the system performance [40]. Different from the uniform distribution of traditional constellation mapping, PS changes the distribution of constellation mapping, increasing the probability of low-power points and reducing the probability of high-power points. Therefore, the average transmission power can be reduced and the minimum Euclidean distance can be increased.
After bit-level encryption and serial-to-parallel conversion, every 16-QAM symbol can be represented by 4-bit binary. Based on the mapping rules [40], the probability distribution can be transformed by changing binary bits of each 16-QAM symbol. The shaping rules can be described as follows: 1) Every three symbols form a group. 2) Judge the first and second binary numbers of three symbols. If the probability of “1” greater than the probability of “0”, the three binary numbers in each symbol should be reversed. Otherwise, the three binary numbers remain the same. 3) Set the flag bit for the reverse of each group.
Figure 3 shows the non-uniform distribution constellation of PS-16QAM symbols. It can be seen that the size of corresponding probability can be divided into three parts which means three power levels signed first, second and third respectively. Constellation points of different power levels are marked in different colors as shown in Fig. 3(b).
Fig. 3. PS-16-QAM constellations (a) original, and (b) constellation divided into three levels with different color marks.
After QAM mapping, the proposed constellation encryption scheme with constant total shaping distribution probability is performed according to hyperchaotic sequences Y, Z and $V.$ Eq. (5) describes the post-process of chaotic sequences. Three different key sequences ${K_2}$, ${K_3}$ and ${K_4}$ are obtained, corresponding to the constellation scrambling of three different power levels (first, second and third levels respectively). The length of key sequences ${K_2}$, ${K_3}$ and ${K_4}$ is the same as the number of symbols. Thus, different constellation points belonging to the same power level are encrypted with different keys.
To maintain the overall shaping distribution probability, independent encryption of constellation symbols located in three power level regions is put forward. According to Eq. (5), key sequences ${K_2}$ and ${K_4}$ are in the range of $[0,3].$ K3 is in the range of $[0,7].$ The number of constellation symbol region is 4 or 8 in different power levels. As shown in Fig. 3(b), the numbers of constellation symbol regions in first and third levels are both 4, and the number in second level is 8. Before scrambling, three power level regions are randomly numbered with $[0,3]$ or $[0,7]$ correspondingly. After that, PS-16-QAM symbols are firstly distinguished which region the points located in, and then scrambled into the region corresponding to the key values according to the key sequences. That is, if the symbol is located in the first power level and key value in the key sequence ${K_2}$ is 0, this symbol will be scrambled into the region that numbered “0” in the first power level. It is worth mentioning that the scrambling operation only changes the sign of the symbol.
The detailed pseudo-code of constellation encryption algorithm is as follows:
Figure 4 illustrates PS-16-QAM constellations after three different power levels scrambling. It indicates that the symbols are disturbed randomly after scrambling, which enhance the security of the transmission data, and the overall probability distribution of constellation points has not been changed.
3. Experimental setup and results
The experimental setup of proposed secure OFDM-RoF system is shown in Fig. 5. At CS, the frame number is 50, and the IFFT size is 1024, including 256 real 16-QAM data and another 256 complex conjugate of real part for Hermitian symmetry. In addition, the rest of carriers are zero padded. The cyclic prefix (CP) is 1/8 of the OFDM symbol duration. For initial conditions, ${x_0}$, ${y_0}$, ${z_0}$ and ${v_0}$ are randomly generated. At the end of the OFDM modulation, the training sequences are inserted for synchronization. After above offline MATLAB process, OFDM signals are loaded on a commercial arbitrary waveform generator (AWG, Tektronix, 7122C). Two continuous wave (CW) light waves with spaced at 100 GHz are generated from two external cavity lasers (ECL1 and ECL2), operating at 1553.65 nm and 1554.45 nm respectively. The output powers of ECL1 and ECL2 are 14.5 dBm and 10 dBm. After passing through a polarization controller (PC), the CW from ECL1 is modulated with encrypted OFDM signal by a Mach–Zehnder Modulator (MZM) with bandwidth of 10 GHz and with the bias voltage of 2.1 V. The inset figure of Fig. 5 shows the optical spectrum after a 3 dB optical coupler (OC). Subsequently, the optical signal is launched into 50 km SSMF with the loss of 0.19 dB/km. After fiber transmission, an Erbium-doped fiber amplifier (EDFA) with fixed gain is applied to amplify the optical signal and a variable optical attenuator (VOA) is utilized to adjust the power of received optical OFDM signal. In this step, the received optical power (ROP) can be swept by adjusting VOA, and the point that ROP is measured is shown in the Fig. 5. In the experiment, the maximum received optical power is fixed at 0 dBm before being injected into the photodiode (PD). After captured by a PD with bandwidth of 100 GHz, the signal is sent to wireless transmitter. At the wireless receiver, the encrypted OFDM signal is delivered over 5 m radio channel by a pair of horn antennas (HAs) with 25 dBi gain. Finally, after passing through 10 GHz electrical amplifier (EA), the signal is captured by a digital sampling oscilloscope (DSO, DSA72004B, 12 GSa/s).
First of all, the peak-to-average power ratio (PAPR) is a non-negligible point in OFDM which will cause nonlinear distortion. The complementary cumulative distribution function (CCDF) represents the statistical characteristics of the PAPR in OFDM system, which is defined as the probability that the peak-to-average value exceeds a certain threshold. Assuming the time domain signal can be obtained and expressed as $x(t)$ after inverse fast Fourier transform (IFFT), the PAPR of the signal can be calculated as:
Fig. 6. CCDF curves of the PAPR with the proposed encrypted OFDM signal and traditional OFDM signal.
To verify the anti-attack capability of the proposed chaotic PS-based encryption scheme, the sensitivity of hyperchaotic system responding to initial value is elaborated. Figure 7 shows the bit error ratio (BER) curves of signals decrypted by chaotic sequences with a tiny change of initial values. According to Eq. (1), there are four initial key values $\{{{x_0},{y_0},{z_0},{v_0}} \}$ and four system parameter key values $\{{a,b,c,d} \}$. The system parameter keys are set as $a = 10$, $b = 8/3$, $c = 28$ and $d ={-} 1$, and initial sequence keys ${x_0}$, ${y_0}$, ${z_0}$ and ${v_0}$ are randomly generated.
Fig. 7. BER curves of encrypted signals with tiny changes of different initial values in hyperchaotic system.
As depicted in Fig. 7, the BER curves are measured when the received optical power is 0 dBm. The abscissa represents the magnitude of change of the initial value, for example, ${10^{ - 18}}$ means that the initial value has been changed by plus (or minus) $\textrm{1} \times {10^{ - 18}}$. From the figure, it can be seen that after x and y changed by $\textrm{1} \times {10^{ - 16}}$, z, v, a, b and d changed by $\textrm{1} \times {10^{ - 15}}$, and c changed by $\textrm{1} \times {10^{ - 14}}$, the BER will ascent rapidly to approximately 0.5, which indicates the signal cannot be recovered. The total key space of the proposed encryption system can be calculated as ${({10^{16}})^2} \times {({10^{15}})^5} \times ({10^{14}}) = {10^{121}}$, which will take $\textrm{7}\textrm{.17} \times {10^{\textrm{95}}}$ years to crack the encrypted data by the fastest supercomputer FuYue today, whose operating speed is $\textrm{4}\textrm{.42} \times {10^{\textrm{17}}}$ FLOPS. Furthermore, if hash keys are taken into consideration, the key space of the system will be greater. Therefore, it is huge enough to effectively prevent brute-force attacks. Although the two constellations inset the picture seem to be similar, it is still impossible for illegal users to decrypt the original signal correctly.
The BER performance of the conventional OFDM signal and OFDM signal after encrypted by proposed scheme is demonstrated in Fig. 8. It can be seen that, compared with traditional OFDM signal, the BER performance of the proposed encrypted OFDM signal has been improved by approximately 2.4 dB and 2 dB for 50 km SSMF and BTB transmission at a BER of ${10^{ - 3}}$ respectively. Whereas in terms of illegal user without correct key, the BER is fluctuating towards 0.5, which states the original signal cannot be recovered in spite of the similar constellation. Therefore, the results demonstrate that PS-based encrypted OFDM signal can effectively enhance the BER performance of system.
The main noise in the transmission process should be: channel noise in optical fiber and wireless link, and the noise of the instruments. The signal-to-noise ratio (SNR) is defined as the ratio of signal power to noise power, and it can be calculated as:
where ${P_{signal}}$ and ${P_{noise}}$ represent signal power and noise power respectively.The BER performance of the traditional OFDM signal and the proposed encrypted OFDM signal versus SNR is analyzed in Fig. 9. It can be seen that compared with traditional OFDM signal, the SNR of the proposed encrypted OFDM signal has been reduced by approximately 1.1 dB and 1.4 dB for 50 km SSMF and BTB transmission at a BER of ${10^{ - 3}}$ respectively. From another point of view, the BER of the proposed encrypted OFDM signal is lower than that of the traditional OFDM signal under the same SNR, which can be attributed to the increasing of Euclidean distance by PS. Therefore, the results demonstrate that PS-based encrypted OFDM signal can effectively enhance the transmission performance of system.
Figure 10 shows a comparison of the BER performance of proposed encrypted OFDM signal, PS-only OFDM signal and encryption-only OFDM signal over 50 km SSMF. It can be noted that, compared with the encryption-only signal, the BER performance of the proposed encryption scheme has improved by about 1.5 dB at a BER of ${10^{ - 3}}$. Moreover, the BER performance of the proposed is similar to the PS-only signal, which indicates that our proposed scheme has no deterioration in PS. Thus, the proposed PS-based constellation encryption method enhances the transmission performance and security of system simultaneously.
4. Conclusion
In this paper, a novel PS based encryption scheme combined with two bit-level encryption operations is proposed. PS is applied to improve transmission performance of the system. Based on hyperchaotic system and hash values, chaos-hash scrambling and constellation encryption are performed during offline processing. And the proposed constellation encryption scheme can maintain overall shaping distribution unchanged. In this way, the proposed scheme can achieve an enormous key space of ${10^{121}}$ to prevent brute-force attacks. In the experiment, a PS-16-QAM OFDM signal has been successfully transmitted over 50-km SSMF and 5-m wireless channel. The results demonstrate that PS-based OFDM signal can effectively improve the BER performance of OFDM-RoF system. Moreover, PS-only and encryption-only methods are also measured to make a comparison and further prove system transmission performance. Therefore, taking into account both BER performance and transmission security in OFDM-RoF, it would be a better solution when combining PS and PS-based encryption. It is convinced that the proposed scheme has great application prospects for future optical communication and wireless communication security.
Funding
National Natural Science Foundation of China (61775054, 61975054); the Open Fund of IPOC (BUPT).
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. Wang, X. Li, M. Zhao, K. Wang, J. Zhang, M. Kong, W. Zhou, J. Xiao, and J. Yu, “Delivery of 138.88Gpbs Signal in a RoF Network with real-time processing based on heterodyne detection,” in Optical Fiber Communication Conference (OFC) 2020, OSA Technical Digest (Optical Society of America, 2020), paper W2A.42.
2. Y. Hung, J. Yan, H. Huang, C. Tseng, K. Feng, and S. Hwang, “First Demonstration of Doppler Compensation Technique Using Period-one Nonlinear Semiconductor Laser Dynamics for OFDM-RoF Coherent Detection,” in Optical Fiber Communication Conference (OFC) 2018, OSA Technical Digest (online) (Optical Society of America, 2018), paper Th3G.4.
3. F. Wang, B. Zhu, K. Wang, M. Zhao, L. Zhao, and J. Yu, “Physical Layer Encryption in DMT Based on Digital Multi-Scroll Chaotic System,” IEEE Photonics Technol. Lett. 32(20), 1 (2020). [CrossRef]
4. F. Li, J. Yu, Z. Cao, J. Zhang, M. Chen, and X. Li, “Experimental Demonstration of Four-Channel WDM 560 Gbit/s 128QAM-DMT Using IM/DD for 2-km Optical Interconnect,” J. Lightwave Technol. 35(4), 941–948 (2017). [CrossRef]
5. L. Gong, X. Zhou, X. Liu, W. Zhao, W. Lu, and Z. Zhu, “Efficient resource allocation for all-optical multicasting over spectrum-sliced elastic optical networks,” J. Opt. Commun. Netw. 5(8), 836–847 (2013). [CrossRef]
6. W. Wang, F. Li, Z. Li, Q. Sui, and Z. Li, “Dual-Drive Mach-Zehnder Modulator-Based Single Side-Band Modulation Direct Detection System Without Signal-to-Signal Beating Interference,” J. Lightwave Technol. 38(16), 4341–4351 (2020). [CrossRef]
7. J. Zhang, K. Wang, Y. Wei, L. Zhao, W. Zhou, J. Xiao, B. Liu, X. Xin, and J. Yu, “Symmetrical 50-Gb/s/λ PAM-4 TDM-PON at O-band Supporting 26 dB+ Loss Budget using Low-bandwidth Optics and Semiconductor Optical Amplifier,” in Optical Fiber Communication Conference (OFC) 2020, OSA Technical Digest (Optical Society of America, 2020), paper Th1B.3.
8. Z. Zhu, W. Lu, L. Zhang, and N. Ansari, “Dynamic Service Provisioning in Elastic Optical Networks with Hybrid Single-/Multi-Path Routing,” J. Lightwave Technol. 31(1), 15–22 (2013). [CrossRef]
9. P. Lu, L. Zhang, X. Liu, J. Yao, and Z. Zhu, “Highly efficient data migration and backup for big data applications in elastic optical inter-data-center networks,” IEEE Netw. 29(5), 36–42 (2015). [CrossRef]
10. F. Lin and M. Tsai, “Chaotic communication in radio-over-fiber transmission based on optoelectronic feedback semiconductor lasers,” Opt. Express 15(2), 302–311 (2007). [CrossRef]
11. C. Zhang, C. Chen, W. Zhang, J. Wei, K. Qiu, C. Li, and J. Ning, “Inter-BSs virtual private network for privacy and security enhanced 60 GHz radio-over-fiber system,” Opt. Fiber Technol. 19(3), 236–241 (2013). [CrossRef]
12. L. Gong, X. Zhou, W. Lu, and Z. Zhu, “A Two-Population Based Evolutionary Approach for Optimizing Routing, Modulation and Spectrum Assignments (RMSA) in O-OFDM Networks,” IEEE Commun. Lett. 16(9), 1520–1523 (2012). [CrossRef]
13. Y. Yin, H. Zhang, M. Zhang, M. Xia, Z. Zhu, S. Dahlfort, and S. J. B. Yoo, “Spectral and spatial 2D fragmentation-aware routing and spectrum assignment algorithms in elastic optical networks,” J. Opt. Commun. Netw. 5(10), A100–A106 (2013). [CrossRef]
14. Y. Xiao, Z. Wang, J. Cao, R. Deng, Y. Liu, J. He, and L. Chen, “Time–frequency domain encryption with SLM scheme for physical-layer security in an OFDM-PON system,” J. Opt. Commun. Netw. 10(1), 46–51 (2018). [CrossRef]
15. T. Wu, C. Zhang, C. Chen, H. Hou, H. Wei, S. Hu, and K. Qiu, “Security enhancement for OFDM-PON using Brownian motion and chaos in cell,” Opt. Express 26(18), 22857–22865 (2018). [CrossRef]
16. S. Li, M. Cheng, L. Deng, S. Fu, M. Zhang, M. Tang, P. Shum, and D. Liu, “Secure Strategy for OFDM-PON Using Digital Chaos Algorithm with Fixed-Point Implementation,” J. Lightwave Technol. 36(20), 4826–4833 (2018). [CrossRef]
17. J. Ke, L. Yi, Z. Yang, Y. Yang, Q. Zhuge, Y. Chen, and W. Hu, “32 Gb/s chaotic optical communications by deep-learning-based chaos synchronization,” Opt. Lett. 44(23), 5776–5779 (2019). [CrossRef]
18. B. Zhu, F. Wang, and J. Yu, “A Chaotic Encryption Scheme in DMT for IM/DD Intra-Datacenter Interconnects,” IEEE Photonics Technol. Lett. 33(8), 383–386 (2021). [CrossRef]
19. B. Liu, L. Zhang, X. Xin, and N. Liu, “Piecewise Chaotic Permutation Method for Physical Layer Security in OFDM-PON,” IEEE Photonics Technol. Lett. 28(21), 2359–2362 (2016). [CrossRef]
20. Y. Chen, Y. Huang, J. Fu, Y. Han, K. Li, and J. Yu, “Multi Wings Chaotic Encryption Scheme for PAM-DMT-Based Optical Access Network,” IEEE Photonics J. 13(1), 1–8 (2021). [CrossRef]
21. C. Zhang, W. Zhang, C. Chen, X. He, and K. Qiu, “Physical-enhanced secure strategy for OFDMA-PON using chaos and deoxyribonucleic acid encoding,” J. Lightwave Technol. 36(9), 1706–1712 (2018). [CrossRef]
22. Y. Xiao, Y. Chen, C. Long, J. Shi, J. Ma, and J. He, “A novel hybrid secure method based on DNA encoding encryption and spiral scrambling in chaotic OFDM-PON,” IEEE Photonics J. 12(3), 1–15 (2020). [CrossRef]
23. X. Song, B. Liu, H. Zhang, R. Ullah, Y. Mao, J. Ren, S. Chen, J. Zhang, J. Zhao, S. Han, X. Liu, D. Zhao, and X. Xin, “Security-enhanced OFDM-PON with two-level coordinated encryption strategy at the bit-level and symbol-level,” Opt. Express 28(23), 35061–35073 (2020). [CrossRef]
24. X. Chen, K. Tanizawa, P. Winzer, P. Dong, J. Cho, F. Futami, K. Kato, A. Melikyan, and K. W. Kim, “Experimental demonstration of a 4,294,967,296-QAM-based Y-00 quantum stream cipher template carrying 160-Gb/s 16-QAM signals,” Opt. Express 29(4), 5658–5664 (2021). [CrossRef]
25. J. Zhong, X. Yang, and W. Hu, “Performance-Improved Secure OFDM Transmission Using Chaotic Active Constellation Extension,” IEEE Photonics Technol. Lett. 29(12), 991–994 (2017). [CrossRef]
26. W. Zhang, C. Zhang, C. Chen, and K. Qiu, “Experimental Demonstration of Security-Enhanced OFDMA-PON Using Chaotic Constellation Transformation and Pilot-Aided Secure Key Agreement,” J. Lightwave Technol. 35(9), 1524–1530 (2017). [CrossRef]
27. A. Sultan, X. Yang, A. A. E. Hajomer, and W. Hu, “Chaotic Constellation Mapping for Physical-Layer Data Encryption in OFDM-PON,” IEEE Photonics Technol. Lett. 30(4), 339–342 (2018). [CrossRef]
28. G. Bocherer, 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]
29. X. Chen, J. Cho, G. Raybon, D. Che, K. W. Kim, E. Burrows, P. Kharel, C. Reimer, K. Luke, L. He, and M. Zhang, “Single-Wavelength and Single-Photodiode 700 Gb/s Entropy-Loaded PS-256-QAM and 200-GBaud PS-PAM-16 Transmission over 10-km SMF,” in Proceedings of IEEE European Conference on Optical Communications (IEEE, 2020), pp. 1–4.
30. G. Bocherer, 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]
31. R. Zhang, Y. Chen, S. Shen, Q. Zhou, S. Yao, S. -J. Su, Y. Alfadhli, and G. Chang, “Joint Optimization of Processing Complexity and Rate Allocation through Entropy Tunability for 64-/256-QAM Based Radio Fronthauling with LDPC and PAS-OFDM,” in Optical Fiber Communication Conference (OFC) 2020, OSA Technical Digest (Optical Society of America, 2020), paper M2F.2.
32. X. Xu, B. Liu, X. Wu, L. Zhang, Y. Mao, J. Ren, Y. Zhang, L. Jiang, and X. Xin, “A robust probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation,” Opt. Express 26(20), 26576–26589 (2018). [CrossRef]
33. C. Pan and F. R. Kschischang, “Probabilistic 16-QAM shaping in WDM systems,” J. Lightwave Technol. 34(18), 4285–4292 (2016). [CrossRef]
34. B. Liu, X. Li, Y. Zhang, X. Xin, and J. Yu, “Probabilistic shaping for ROF system with heterodyne coherent detection,” APL Photonics 2(5), 056104 (2017). [CrossRef]
35. S. Han, B. Liu, Y. Mao, J. Ren, X. Wu, X. Xu, L. Jiang, and J. Zhang, “High-Security Multi-Slot Chaos Encryption with Dynamic Probability for 16-CAP PON,” IEEE Photonics J. 12(3), 1–10 (2020). [CrossRef]
36. J. Zhao, B. Liu, Y. Mao, J. Ren, X. Xu, X. Wu, L. Jiang, S. Han, and J. Zhang, “High-Security Physical Layer in CAP-PON System Based on Floating Probability Disturbance,” IEEE Photonics Technol. Lett. 32(7), 367–370 (2020). [CrossRef]
37. J. Zhao, B. Liu, Y. Mao, R. Ullah, J. Ren, S. Chen, L. Jiang, S. Han, J. Zhang, and J. Shen, “High security OFDM-PON of physical layer based on 4D-hyperchaos and dimension coordination optimization,” Opt. Express 28(14), 21236–21246 (2020). [CrossRef]
38. J. Ren, B. Liu, D. Zhao, S. Han, S. Chen, Y. Mao, Y. Wu, X. Song, J. Zhao, X. Liu, and X. Xin, “Chaotic constant composition distribution matching for physical layer security in a PS-OFDM-PON,” Opt. Express 28(26), 39266–39276 (2020). [CrossRef]
39. M. Li, B. Liu, R. Ullah, J. Ren, Y. Mao, S. Han, J. Zhao, R. Tang, S. Chen, and J. Ling, “5D data iteration in a multi-wavelength OFDM-PON using the hyperchaotic system,” Opt. Lett. 45(17), 4960–4963 (2020). [CrossRef]
40. Q. Xu, L. Wang, D. Wang, X. Chen, and S. Sun, “Probabilistic Shaping QC-LDPC Coded Modulation Scheme for Optical Fiber Systems,” in CLEO Pacific Rim Conference 2018, OSA Technical Digest (Optical Society of America, 2018), paper Th1I.4.
