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Abstract
With the development of 6 G network, the issue of information security is becoming more and more significant. In this paper, a secure RoF system based on key nested polar code and feedback neural network (FNN) is proposed. For the nested polar code, the original key is randomly selected from the constructed codebook and the index of key is encoded by inner polar code which is placed at the location with better channel quality bit of the frozen bit of outer polar code, for the other part of outer polar code, information bits are encrypted by chaotic sequence generated by 4-D cellular neural network. The polar coded sequence is mapped to the 16-QAM symbol for orthogonal frequency division multiplexing (OFDM) and then the OFDM signal is modulated to the optical pulse, which is delivered to users through 50 km standard single-mode fiber and 5 m wireless channel. In the receiver, successive cancellation list (SCL) decoder is used for decoding outer polar code and FNN is used for decoding inner polar code to reduce the latency. The experimental results show that, compared with the existing scheme, when the bit err rate is 10−3, the received optical power (ROP) gain of the proposed scheme with SCL2 decoder and SCL4 decoder is ∼1.2 dB and ∼1.6 dB, respectively. And compared with the traditional OFDM signal with polar code, when the bit err rate is 10−3, the ROP gain of the proposed scheme with SCL4 decoder is ∼1 dB. What’s more, the randomness of the chaotic key sequence, the ability to resist brute-force attacks and the ability to resist chosen-plaintext attacks are elaborated. Therefore, the proposed scheme can greatly improve the security of the system while ensuring the correct transmission of information.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
OFDM is widely used in various wireless communication system because of its high spectrum utilization, resistance to multipath interference, and it can resist the walk-off effect caused by dispersion in optical fiber system [1]. Millimeter-wave radio-over-fiber (MMW-RoF), which combines the large transmission bandwidth and low energy consumption of RoF, can simultaneously transmit millimeter-wave signal and optical signal with high-capacity, long-distance, low-cost and high-speed [2,3]. However, the broadcast characteristics of central station signal and the sharing structure of optical fiber make the communication system be vulnerable to hacker attacks and information leaks [4–6], so it is an important issue to enhance the physical layer security of MMW-RoF system.
In recent years, many researchers have studied how to improve the security of RoF system. At present, there are two kinds of chaotic encryption schemes: the improvement of chaotic system and the improvement of encryption method. For the former, a novel 3-D multi wings chaotic encryption scheme for pulse-amplitude-modulated discrete multitone is proposed [7]. Then, a secure transmission scheme for RoF system based on dynamic resource allocation is proposed, which enhances system security through 7-D CNN chaotic system [8], and the scheme based on manifold learning-assisted generative adversarial networks is proposed [9]. Also, an encryption scheme based on 3-D Jerk chaotic equation system is proposed [10], which is implemented based on phase ambiguity in a DMT system. These physical layer security enhancing schemes are all implemented by improving the chaotic system. For the latter, researchers encrypted signals by employing different encryption approaches, such as the encrypted scheme based on chaotic sequences and hash values [11], a physical layer chaotic encryption scheme by employing three independent pseudo-random sequences generated by the multi-scroll chaotic system [12], an encryption strategy based on diversity deoxyribonucleic acid (DNA) chaotic [13], a scheme combining dynamic and static keys [14], and a secure transmission system based on one dual-polarization in-phase and quadrature modulator [15], by using a nonlinear opto-electronic oscillator to generate broadband chaotic sequences for encrypting signal. There are also some key distribution schemes [16,17], which improve the system security by innovating the generation and distribution of keys. In some of the above schemes, only one type of key is shared between the receiver and the transmitter, which has the risk of information leakage, while in other schemes, there are multiple key forms, but the transmission performance of the system is not considered.
In order to improve the bit err rate (BER) performance while ensuring the security of system, researchers have proposed many strategies, including precoding and forward error correction (FEC) [18]. Polar code, as the most prominent in FEC code, is proposed by Arikan who proved that the polar code can reach Shannon limit capacity in binary discrete memoryless channel under a successive cancellation (SC) decoder, as the length of code goes infinity [19]. To further improve the performance of polar code, the SC list (SCL) decoder retains multiple paths and selects the best path, which can effectively solve the problem of error accumulation of SC decoder and improves the BER performance [20]. In 2019, researchers enhance security and reduced PAPR by combining polar codes and chaotic keys [21]. Later, a highly secure and reliable optical orthogonal frequency division multiplexing passive optical network (OFDM-PON) based on the chaos encryption inside polar code scheme is proposed [22]. Recently we have proposed and experimentally demonstrated one-time pad scheme, which combined with dynamic key embedding and multi-level chaotic encryption for RoF [23]. But they didn't consider how to ensure that the key would be correctly transmitted. What is more, SCL decoding will result in high latency, so many researchers have focused on decoding method using neural network (NN) for low latency.
In 2019, a deep learning (DL) based SCC-SCL decoding scheme has been proposed, by using a long short-term memory network replaces the error correction table to perform error correction [24]. Then, researchers proposed a DL method to optimize polar belief propagation (BP) decoding which significantly improves transmission performance [25]. After that, a neural successive cancellation decoder of polar code is investigated to reduce the decoding latency in free space optical communication system [26]. These show that NN is promising in the field of decoding.
In this paper, a secure RoF system based on key nested polar code and feedback neural network (FNN) is proposed. In the scheme, compared with our previous work [23], the one-time key is polar coded and placed in the frozen bit of outer polar code to realize the secret distribution of the key. And the reliability of the key is guaranteed by the key repeating mechanism, and the low-delay decoding of the key is realized by FNN. The key is first randomly selected as the initial value of the 4-D CNN system from the constructed codebook for obtaining the chaotic sequence, then the corresponding index of the key is encoded with low code-rate inner polar code, and the data are encrypted by the chaotic sequence, including exclusive or (XOR) operation, bit scrambling and frozen bits filling. Next, the polar-coded key index sequences are combined with the encrypted data for outer polar code. At the receiver, the codebook is shared with the transmitter. For the outer polar decode, the SCL decoder is used to decode the encrypted data and the encoded key by keeping multiple decoding paths and selecting the best path, while for the inner polar decode, the trained FNN is for decoding the key, which can reduce the decryption delay and its simple structure and the characteristic of easy training can facilitate its communication deployment. Since the key is constantly changed, the security of system is greatly strengthened, even if someone intercept the data, he cannot get any useful information without the correct key. We have experimentally demonstrated a 3.76Gb/s encrypted 16QAM-OFDM RoF link through 50 km standard single-mode fiber and 5 m wireless channel and achieve an error-free performance.
2. Principle
The block diagram of the proposed secure RoF system based on nested polar code and FNN is demonstrated in Fig. 1. The pseudo-random binary sequence (PRBS) is employed as the original data, and the key is randomly selected from the constructed codebook, which will be destroyed after using. The key is first randomly selected as the initial value of the 4-D CNN system from the constructed codebook for obtaining the chaotic sequence, as the initial value for 4-D CNN system to get chaotic sequences, part of which is dedicated to scrambling the original data. In the secure method, the used key will no longer be used in the subsequent encryption process. As for the key index, the inner polar code is performed for protecting and hiding information. Then, the polar-encoded key index is combined with the encrypted information for the outer polar encode, and another part of the chaotic sequences is employed for the frozen bit filling. Next, the output bits of outer polar encoder are mapped to 16 quadrature amplitude modulation (QAM) symbol, and then OFDM modulation is performed, including inverse fast Fourier transform (IFFT), adding cyclic prefix (CP) and training sequence (TS). After that, OFDM signal is transmitted to the receiver through the optical wireless channel. At the receiver, the reverse operations are performed to obtain the combined information, for the decode of outer polar code, the SCL decoder is employed, and for the inner polar decoding, the FNN is used to decode the key index, by which the corresponding key can be recovered from the codebook to decrypt the data.
2.1 Nested polar code
To improve BER performance, polar code is introduced. The $(N,K)$ polar code contains information set I and frozen set F, the former is composed of K most reliable sub-channel indexes, while the latter is composed of sub-channel indexes of $N - K$ frozen bits. The message word $u = \{ {u_0},{u_1},\ldots ,{u_{K - 1}}\}$ is encoded into x by linear transformation, codewords x of the length N is expressed as:
where G is the n-th Kronecker product of the matrix $G = [\begin{array}{{cccc}} 1&{0;}&1&1 \end{array}]$ and $n = \log _2^{}N$. $x$ consists of K-bit information bits and N-K-bit frozen bits. As for the positions of information bit and frozen bit, they are determined by Bhattacharyya parameter, which measures the quality of the channel. The Bhattacharyya parameter is defined as follow: where $W(y|x)$ expresses transition probability of channel W.The structure of nested polar code is shown in the Fig. 2, the Bhattacharyya parameter is getting larger from left to right, which means that the quality of channel is getting worse. There are two-layer structure in nested polar code, for the inner layer, it is $(N^{\prime},K^{\prime})$ polar code, whose information set and frozen set are $I^{\prime}$ and $F^{\prime}$ respectively, while the outer layer is $(N,K)$ polar code, and its information set and frozen set and key set are I, F and E respectively. The locations with better channel quality in the frozen set are selected to form the key set.
Assuming $m = \textrm{\{ }{m_0},{m_1},\ldots ,{m_{K^{\prime} - 1}}\textrm{\} }$ is a sequence of key index that needs to be protected and hidden, $u = \{ {u_0},{u_1},\ldots ,{u_{K - 1}}\}$ is the sequence of information. m can be used as information bit to construct the inner polar code M, which is expressed as:
where $n^{\prime} = {\log _2}{N^{\prime}}$. For the outer polar code, M is placed in the frozen position where the channel quality is better, that is set E. The encoding process of outer polar code is as follows:2.2 Chaotic sequences generation and encryption
In this paper, a 4-D CNN system is adopted to obtained chaotic sequences, which is represented as:
The chaotic sequences X, $Y$, $Z$ and $W$ can be obtained by Eq. (5,6) by using the Runge-Kutta method. In order to implement XOR encryption operation, X is first processed by:
where the function $floor(x)$ returns the largest integer less or equal to x. Assuming the PRBS are expressed as I, the XOR operation can be expressed as: and the scrambling operation can be processed by:The sequence F consists of “0” or “1”. According to Eq. (3,4), the outer polar code can be completed. The sequence after encryption will be mapped to 16QAM symbol. Then OFDM modulation is performed, including inverse fast Fourier transform (IFFT), adding cyclic prefix (CP) and training sequence (TS). Next, the OFDM signal is transmitted to the receiver through the optical wireless channel.
2.3 Key repeating mechanism
Since the transmission quality of frozen bits is relatively low, the reliable transmission of keys also needs to be considered, a key repeating mechanism is introduced to ensure the reliable transmission of key, which is shown in Fig. 3. The same key index is placed in multiple frames of the OFDM signal, the exact number of frames is determined by the channel quality, for example, they are $m - k$, m and $m + k$ three frames, the value of k is shared between the receiver and the transmitter. This means that even in the case of poor channel quality, the correct key can be obtained to decrypt the message as long as there is no error in one of these frames.
2.4 Feedback neural network decoder
After the receiver receives the signal, the FNN decoder is used for decoding the key index. The structure of FNN is shown in Fig. 4 and the decode method is shown as Algorithm 1.
Firstly, the neural network is initialized to determine the number of layers and the number of nodes per layer, and the activation functions of the hidden and output layers are defined as follows:
After epochs, the adjustment of neural network parameters is gradually completed, and after training, the code word to be decoded can be input, and the neural network will output the corresponding decoding result. By the FNN, the decoding latency can be significantly reduced.
3. Experimental setup
The experimental setup and the system parameters of the proposed scheme is shown in Fig. 5 and Table 1, respectively. At the transmitter, the initial key is selected from the shared codebook, the code length of outer polar code is 1024, while the code length of inner polar code is 128, 64, 32, the code rate of outer polar code is 1/2, and the code rate of inner polar code is set to 1/8, 1/4, 1/2, respectively. The size of IFFT/FFT is 1024, including 256 real 16-QAM symbols and 256 real part complex conjugation for Hermite symmetry. The size of CP is 64 symbols. After adding the synchronization sequence (SS) and TS, the OFDM frame is assembled, which also means that offline processing is completed. The OFDM signal is loaded into a commercial arbitrary waveform generator (AWG, Tektronix, 7122C), which converts it into an electrical signal. Two external cavity lasers (ECL1 and ECL2) are utilized to generate continuous wave (CW) with an interval of 100 GHz and they operate at 1547.52 nm and 1546.72 nm with output power of 15.5 dBm and 12 dBm, respectively. After the polarization controller (PC), the CW signal form ECL1 is modulated with the encrypted 16QAM-OFDM signal via Mach-Zehnder modulator (MZM) to obtain the modulated optical signal. After the optical coupler (OC) with the gain of 2 dB, the coupled optical signal is transmitted over 50 km SSMF. At receiver, the optical signal is amplified by erbium-doped fiber amplifier (EDFA).
Table 1. System Parameters
In the experiment, the maximum received optical power (ROP) is 4 dBm. By variable optical attenuator (VOA), the power of optical signal before photodetector (PD) can be flexibly adjusted and the electrical signal can be obtained by a PD. Then electrical signal is transmitted through a horn antenna (HA) and 5 m wireless channel and received by another HA. After the envelope detector (ED) and electrical amplifier (EA), the digital sampling oscilloscope (DSO, DSA72004B) is used to collect signal for offline digital signal processing.
As shown in Table 2, the three-layer (1500-1200-1000) FNN for decoding inner polar code is trained through the GeForce GTX TITAN V graphic processing unit (GPU) on the Pycharm platform. The training set consist of 128,000 data, of which 80% is used as the training set and the remaining 20% is used as the validation set, the epoch is set to 1024.
Table 2. Parameters Of the FNN
4. Results and discussions
In this section, the performance of system is analyzed from two aspects, security and reliability, where the security focuses on the size of key space and the initial value sensitivity of system. As for reliability, the BER curve are analyzed, which are affected by the code length, code rate of the inner polar code, the decoding method of outer polar code, and whether a repeating mechanism is used. In order to explore the security of the proposed scheme, the sensitivity of chaotic systems to initial values is first discussed. When the ROP is 2.0 dBm and the inner polar code is P(32,8), and the decoder is SCL4, the effect of tiny changes on BER is experimentally tested for 16 initial values of the 4-D CNN chaotic system.
4.1 Security analysis
In this section, the security of the RoF system is analyzed firstly. Then, in the case of ensuring the security of the system, three aspects are considered, namely randomness analysis, resistance to brute-force attacks, and resistance to chosen-plaintext attack analysis.
4.1.1 Randomness analysis
The randomness of the chaotic key sequence with the data volume of ${10^6}$ is analyzed, which is measured by statistical test of NIST SP 800-22 suit. NIST SP 800-22 suit contains 15 sub-tests, and each sub-test gives a measure of whether the test sequence reaches the P-value. If the P-value corresponding to the sequence in the test is greater than 0.01, it is considered that the sequence has passed the sub-test. As shown in Fig. 6, the minimum P-value of subtest is 0.043, which is greater than 0.01, which shows that the chaotic key sequence generated by the system has good randomness.
4.1.2 Resistance to brute-force attacks
Brute force attacks are the simplest of password attacks, the attacker only needs to attempt to decrypt the message by guessing the key, so a sufficiently long keys are required to prevent brute force attacks. As shown in Fig. 7, which abscissa indicates the fineness of change of the initial value, the computational accuracy of the parameters y, ${S_{11}}$, ${S_{21}}$, ${S_{23}}$ and ${S_{33}}$ are $1 \times {10^{ - 16}}$, x, z, v, ${S_{13}}$, ${S_{14}}$, ${S_{22}}$, ${S_{31}}$ and ${S_{32}}$ are $1 \times {10^{ - 15}}$, ${S_{41}}$ and ${S_{44}}$ are $1 \times {10^{ - 14}}$, and a is $1 \times {10^{ - 13}}$, respectively. From the figure, if these parameters change more than the accuracy range, the BER performance of system will drop dramatically, with BER value approaching 0.5, and the encrypted signal cannot be recovered. As for the size of key space, a key space of at least is ${10^{217}}$,which will take $7.17 \times {10^{208}}$ years to crack the encrypted data by the supercomputer FuYue, whose operating speed is $4.42 \times {10^{17}}$ FLOPS. Considering that the key is chosen randomly from the codebook, the key space gets larger actually. Without sufficient time and computing resources, brute force attacks can’t definitely find the correct key.
4.1.3 Resistance to chosen-plaintext attacks
It is obvious that the most difficult attack to resist is chosen plaintext attack. In one case, it is assumed that the decipherer temporarily gains access to the encryption machine, but the encryption key is safely embedded in the device, and the decipherer cannot get the key. At this time, a large number of chosen-plaintexts can be encrypted, and then the key can be inferred by using the generated ciphertext. Hence, we study a cryptosystem’s ability to resisting chosen plaintext attack to deduce its ability to resisting all types of attacks. In the secure method, the key for each encryption is randomly selected from the constructed codebook, which act as the initial value, and the used key will no longer be used in the subsequent encryption process, every encryption in the encryption system is the chaotic sequences generated by using different keys. Then, for the decipherer, this encryption system is time-varying, even if the chosen-plaintext attack is adopted, the decipherer cannot guess the encryption algorithm by the change of plaintext and ciphertext. Figure 8 shows the number of bit changes on each subcarrier of the ciphertext when only one-bit in the plaintext is changed. It is not hard to find that when one-bit of plaintext is changed, the change of ciphertext is considerable, which indicates that it is difficult for attackers to guess the ciphertext corresponding to new plaintext, even if there is only one-bit change in plaintext. Also, the correlation coefficient between the two ciphertexts is 0.0330, which means that the correlation between the ciphertexts is extremely weak. If the sequence length becomes large enough, the correlation will tend to 0. Therefore, the scheme can resist chosen-plaintext attacks.
4.2 BER performance analysis
In order to investigate the BER effect of different inner polar code lengths and code rates, seven signals with different structure are experimentally tested. In this test, the structure of outer polar code is P(1024,512), the decoder is successive cancellation list 2 (SCL2), and the structures of inner polar code for different schemes are denoted as P(32,8), P(32,16), P(64,16), P(64,32), P(128,16), P(128,32). For the traditional scheme without encryption, only the polar code is used. Figure 9 shows BER curve of the proposed scheme under different inner polar code structures over 50-km SSMF, it can be found that the performance of the scheme P(32,8) is the best, when the BER is ${10^{ - 3}}$, compared with the scheme P(32,16) and the scheme proposed in Ref. [23], the received optical power (ROP) gain of the scheme P(32,8) with SCL2 decoder is ∼0.4 dB and ∼1.2 dB, respectively. The BER of scheme P(32,16) reach ${10^{ - 3}}$ when ROP is 2.5 dBm, compared with traditional OFDM scheme with polar code, it can get a power gain of ∼0.6 dB and the scheme can realize error-free transmission when ROP continues to increase. For P(64,16) and P(64,32), the BER of the former is slightly lower than that of the latter, which is caused by the reduction of the code rate. Similarly, P(128,16) is also able to reach the BER performance of P(64,32) and P(64,16) because of its low bit rate of 1/8. However, the performance of scheme P(128,32) is the worst, which is due to its excessive resource utilization of frozen bits. Overall, when ROP is greater than 2.5 dBm, all schemes except scheme P(128,32) can achieve error-free transmission. It can be seen that the schemes P(32,8), P(32,16) and P(64,16) have better BER performance than the traditional scheme, and the scheme P(64,32) have similar performance to the traditional one. And for illegal users without keys, the BER is 0.5, which means that the useful information cannot be obtained.
The BER curve of P(32,8) under different decoders over 50-km SSMF is demonstrated in Fig. 10. Compared with SC decoder, SCL decoder has L alternative paths for the best decoding result, so the BER performance of the scheme will be better as the decoding list L increases, which brings a larger decoding latency. From this figure, it can be seen that when ROP is 2 dBm, the BER of SCL4 or SCL8 decoding scheme has reached ${10^{ - 4}}$. When the BER is ${10^{ - 3}}$, the SCL4 decoding scheme can get a power gain of ∼0.4 dB, ∼1 dB and ∼1.6 dB compared with SCL2 decoding scheme, the traditional OFDM scheme with polar code and the scheme in the Ref. [23], respectively. Also, when L is greater than 2, the performance of the scheme has been greatly improved compared with the traditional scheme. SCL4 is undoubtedly the best choice considering trade-off between the complexity and performance of decode.
In this paper, in order to reduce the decoding latency and improve the accuracy of key, an FNN is used for decoding and a key repeating mechanism is employed, and the effect of key repeating mechanism is discussed in Fig. 11. Figure 11(a) and Fig. 11(b) illustrate the BER of key without repeating mechanism and with repeating mechanism, respectively. By comparison, it can be seen that the BER of key with repeating mechanism is significantly reduced. Only ROP greater than 1 dBm is required to ensure the correctness of key in schemes P(32,8) and P(64,16) with repeating mechanism, and a power gain of ∼1 dB can be obtained compared to that without repeating mechanism. To achieve error-free key transmission, only ROP greater than 1.5 dBm is required for the schemes P(32,16) and P(64,32), and only ROP greater than 2 dBm is required for scheme P(128,16). This means that the repeating mechanism can greatly improve the reliability of transmission.
Fig. 11. Key BER over 50-km SSMF transmission (a) without repeating mechanism and (b) with repeating mechanism.
5. Conclusion
In this paper, a secure RoF system based on key nested polar code and FNN is proposed. The system can ensure the correct transmission by nested polar code and repeating mechanism. Encrypting the transmitted information with these random multiple keys can increase the security of system. Experimental results show that the proposed scheme successfully obtains a key space of ${10^{\textrm{217}}}$, which can resist brute force attacks by illegal users, and P(32,8) scheme with SCL4 decoder has better transmission performance than the traditional polar-OFDM scheme. Based on the tradeoff of reliability, complexity and security, the proposed scheme with the outer polar code of 1024 code length, 1/2 code rate SCL4 decoder, and the inner polar code of 32 code length, 1/4 code rate, FNN decoder has better overall performance and better deploy ability.
Funding
National Natural Science Foundation of China (61975054); Natural Science Foundation of Hunan Province (2022JJ30170).
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. J. Armstrong, “OFDM for Optical Communications,” J. Lightwave Technol. 27(3), 189–204 (2009). [CrossRef]
2. K. Wang, W. Zhou, L. Zhao, et al., “Bi-Directional OFDM Truncated PS-4096QAM Signals Transmission in a Full-Duplex MMW-RoF System at E-Band,” J. Lightwave Technol. 39(11), 3412–3419 (2021). [CrossRef]
3. W. Wang, F. Li, Z. Li, et al., “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]
4. F. Chen, M. Song, F. Zhou, et al., “Security-Aware Planning of Packet-Over-Optical Networks in Consideration of OTN Encryption,” IEEE Trans. Netw. Service Manag. 18(3), 3209–3220 (2021). [CrossRef]
5. Q. Lv and Z. Zhu, “On the Multilayer Planning of Filterless Optical Networks with OTN Encryption,” IEEE/ACM Trans. Networking 1, 1–16 (2023). [CrossRef]
6. X. Wang, H. Huang, C. Zhang, et al., “Optical True Time Delay-Based Hybrid Beamforming for Limited-Feedback Millimeter-Wave Massive MIMO Systems,” IEEE Commun. Lett. 25(7), 2405–2409 (2021). [CrossRef]
7. Y. Chen, Y. Huang, J. Fu, et al., “Multi Wings Chaotic Encryption Scheme for PAM-DMT-Based Optical Access Network,” IEEE Photonics J. 13(1), 1–8 (2021). [CrossRef]
8. Y. Xiao, Y. Chen, and Z. Wang, “Secure transmission of W-band millimeter-wave based on CNN and dynamic resource allocation,” Opt. Lett. 46(22), 5583–5586 (2021). [CrossRef]
9. X. Zhu, J. Ren, X. Zhu, et al., “Chaotic physical security strategy based on manifold learning-assisted GANs for SDM-OFDM-PONs,” Opt. Lett. 47(7), 1834–1837 (2022). [CrossRef]
10. X. Wang, Z. Li, Q. Zhang, et al., “Chaotic physical layer encryption scheme based on phase ambiguity for a DMT system,” Opt. Express 30(9), 14782–14797 (2022). [CrossRef]
11. M. Chen, L. Wang, D. Xi, et al., “Comparison of Different Precoding Techniques for Unbalanced Impairments Compensation in Short-Reach DMT Transmission Systems,” J. Lightwave Technol. 38(22), 6202–6213 (2020). [CrossRef]
12. F. Wang, B. Zhu, K. Wang, et al., “Physical Layer Encryption in DMT Based on Digital Multi-Scroll Chaotic System,” IEEE Photonics Technol. Lett. 32(20), 1303–1306 (2020). [CrossRef]
13. R. Tang, B. Liu, J. Ren, et al., “FBMC/OQAM Security Strategy Based on Diversity DNA Encryption,” IEEE Photonics J. 13(1), 1–11 (2021). [CrossRef]
14. Y. Zhou, M. Bi, X. Zhou, et al., “Physical Layer Dynamic Key Encryption in OFDM-PON System Based on Cellular Neural Network,” IEEE Photonics J. 13(2), 1–14 (2021). [CrossRef]
15. Y. Wu, H. Luo, L. Deng, et al., “60 Gb/s coherent optical secure communication over 100 km with hybrid chaotic encryption using one dual-polarization IQ modulator,” Opt. Lett. 47(20), 5285–5288 (2022). [CrossRef]
16. X. Liang, C. Zhang, Y. Luo, et al., “Secure key distribution and synchronization method in an OFDM-PON based on chaos,” Opt. Express 30(11), 18310–18319 (2022). [CrossRef]
17. X. Liang, C. Zhang, Y. Luo, et al., “Secure Encryption and Key Management for OFDM-PON Based on Chaotic Hilbert Motion,” J. Lightwave Technol. 41(6), 1619–1625 (2023). [CrossRef]
18. Z. Wang, Y. Xiao, S. Wang, et al., “Probabilistic shaping based constellation encryption for physical layer security in OFDM RoF system,” Opt. Express 29(12), 17890–17901 (2021). [CrossRef]
19. E. Arikan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels,” IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009). [CrossRef]
20. K. Niu and K. Chen, “CRC-Aided Decoding of Polar Codes,” IEEE Commun. Lett. 16(10), 1668–1671 (2012). [CrossRef]
21. X. Lu, Y. Shi, W. Li, et al., “A Joint Physical Layer Encryption and PAPR Reduction Scheme Based on Polar Codes and Chaotic Sequences in OFDM System,” IEEE Access. 7, 73036–73045 (2019). [CrossRef]
22. Y. Bai, B. Liu, J. Ren, et al., “Highly Secure and Reliable 7-Core Fiber Optical OFDM Access System Based on Chaos Encryption Inside Polar Code,” IEEE Photonics J. 14(1), 1–6 (2022). [CrossRef]
23. Y. Xiao, B. Wang, Z. Wang, et al., “One-Time Pad Strategy Combined with Dynamic Key Embedding and Multi-Level Chaotic Encryption for RoF,” J. Lightwave Technol. 41(1), 41–47 (2023). [CrossRef]
24. X. Liu, S. Wu, Y. Wang, et al., “Exploiting Error-Correction-CRC for Polar SCL Decoding: A Deep Learning-Based Approach,” IEEE Trans. Cogn. 6(2), 817–828 (2020). [CrossRef]
25. W. Xu, X. Tian, Y. Be’ery, et al., “Deep Learning-Aided Belief Propagation Decoder for Polar Codes,” IEEE J. Emerg. 10(2), 189–203 (2020). [CrossRef]
26. J. Fang, M. Bi, S. Xiao, et al., “Neural Successive Cancellation Polar Decoder with Tanh-Based Modified LLR Over FSO Turbulence Channel,” IEEE Photonics J. 12(6), 1–10 (2020). [CrossRef]
27. G. Jiang and S. Wang, “Synchronization of hyperchaos of cellular neural network with applications to secure communication,” J. Commun. 21(9), 4040–4044 (2000).
