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Abstract
A new optical transmitting scheme based on chaotic constant component distribution matcher (CCDM) and Polar coding was proposed. The data is first encrypted by Polar coding using a five-dimensional chaotic sequence. Then the encrypted data is divided into two paths to perform chaotic CCDM encryption operations with different schemes. Finally, the two channels are merged, and the subcarriers are scrambled. The transmission experiment of 16QAM-OFDM signal on 2 km seven-core fiber is conducted to verify the scheme's feasibility. The experimental results show that the received optical power of all ONUs is less than −15dBm when the BER of all ONUs is reduced to less than 10−3. In addition, the key space of the proposed system reaches 1085, and the security performance is further enhanced. The advantages of BER and safety performance make this two-path chaotic encrypted OFDM-PON with an optimistic application prospect in the current optical transmission systems.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the growth of large capacity communication requirements in the modern information society, the risk of illegal users eavesdropping on data transmission has gradually increased, and the importance of information transmission security has become increasingly prominent. Among the existing encryption technologies, physical layer encryption is oriented to optical fiber transmission channels, which can guarantee secured communication systems, including optical encryption [1], quantum encryption [2], and digital chaotic encryption [3]. Among them, digital chaotic encryption technology is compatible with existing technologies such as coding modulation and channel equalization algorithms [4]. With the improvement of high-speed digital signal processing capabilities, this technology is expected to improve system effectiveness, reliability, and security. Therefore, it has gradually become the research focus in various institutions recently.
Due to the increasing demand for large bandwidth in society, more and more users enjoy the convenience of optical communication technology. OFDM is widely used in optical access systems because of its high spectral efficiency and large capacity [5]. Due to the broadcast characteristics of OFDM-PON, all-optical network units (ONU) can quickly receive the single downlink point, and the security of transmission information is challenging to guarantee [6,7]. With the rapid development of optical communication, the demand for the security and reliability of optical communication systems will significantly increase. Therefore, under the existing technology, realizing the synchronous improvement of the overall security and reliability of the OFDM transmission system becomes the core scientific problem to be solved. In recent years, there have been many studies to improve the security of OFDM systems. For example, X. Liang [8] et al. proposed a novel security enhancement technique for physical layer secure orthogonal frequency division multiplexed-based passive optical network (OFDM-PON) using chaotic Hilbert motion. By using chaos to construct Hilbert motion, the traversal and the scrambling of two-dimensional (2D) symbol matrix are completed.
In optical communication systems, the loss and noise generated during transmission will significantly increase the BER of the received signal. In the existing technology, using error correction coding [such as soft detection forward error correction (FEC) coding] to encode and modulate the signal can improve this problem. Polar code is a new FEC coding method proposed in recent years [9]. This coding can effectively reduce the system's bit error rate (BER) and approach the Shannon limit with relatively low complexity. In addition, it has been proved [10] that polar codes decoded by list cyclic redundancy check (CRC) have excellent short-block length performance. In recent years, the research on Polar codes mainly focuses on decoding [11,12], while there are few studies on the security of Polar codes for encryption.
On the other hand, the research on chaotic encryption mainly includes encryption mechanisms such as frequency domain, time domain, and modulation format [13–18]. Research on joint chaotic encryption based on FEC coding is also relatively scarce. Considering that Polar codes have excellent BER performance for OFDM transmission systems, it is necessary to make Polar codes carry out more research on chaotic encryption.
On the other hand, the probabilistic shaping technology can significantly reduce the constellation's average power and obtain a certain degree of constellation figure of merit (CFM) gain under the condition of keeping the position of the constellation point unchanged [19]. The BER performance of the constellation will also be significantly improved. In recent years, there has been much research on the probabilistic shaping of chaotic encryption technology. For example, Y. Gu [20] et al. proposed a new carrier-free amplitude/phase modulation and probabilistic shaping scheme based on the Lorentz model and superposition method (LS-PS-CAP). The chaotic model is used to change the probability distribution of the constellation, and the constellation is superimposed to obtain LS-PS-16CAP. This scheme can increase modulation flexibility, improve the BER performance, and provide security for the transmission system. S. Han et al. [21] proposed a high-security dynamic probabilistic chaotic encryption method based on 16-carrier amplitude-free in-phase (CAP) PON by using a two-layer chaotic map based on feedforward neural network XOR operator (FNNXOR). Experiments show the scheme has a high anti-hacking ability and good performance under key leakage. If the probability shaping technology is combined with FEC technology, the channel capacity can significantly increase to approach the Shannon limit [22,23]. [24] demonstrated a probabilistic amplitude shaping (PAS) technique that combines PS with FEC coding to improve the BER performance of the system further. It connects the shaped outer code, the distributed matcher [25], with the FEC inner code.
This paper proposes a new optical transmitting scheme based on chaotic CCDM and Polar coding. The five-dimensional chaotic model is utilized to encrypt the data. Firstly, Polar coding encryption is performed, and then chaotic CCDM encryption operations of different schemes are performed in two paths. Then the synchronization of transmission performance and security is effectively improved. The transmission experiment of 16QAM-OFDM signal on 2 km seven-core fiber is conducted to verify the scheme's feasibility. The experimental results show that the received optical power of all ONUs is less than −15dBm when the BER of all ONUs is reduced to less than 10−3. In addition, the key space of the proposed system reaches 1085, and the security performance is further enhanced. The advantages of BER and safety performance make this two-path chaotic encrypted OFDM-PON have an optimistic application prospect in the current optical transmission systems.
2. Principles
2.1 Overview
The diagrammatical presentation of the high-security transmission system based on chaotic CCDM and Polar coding hybrid encryption proposed in this paper is shown in Fig. 1. Firstly, the original data is transformed from serial to parallel to reduce the complexity. Then the parallel data stream is Polar coded, and the first set of chaotic sequences is used to encrypt the frozen bits. After the encryption, the data is divided into two paths using the second group of chaotic sequences. The two paths perform 16QAM chaotic CCDM operations of different schemes, respectively. The third and fourth groups of chaotic sequences determine the specific chaotic CCDM operation mode, and then the amplitude values after chaotic encryption are obtained. These amplitude values are divided into two channels of equal number-I channel and Q channel, and finally, constellation mapping is realized, respectively. Then, the two sets of data are merged into one path, and the subcarriers are sequentially scrambled using the fifth set of chaotic sequences to achieve the last encryption, and finally, the secure data after multiple rounds of encryption is obtained.
Fig. 1. The diagrammatic drawing of a high-security transmission system based on chaotic CCDM and Polar coding hybrid encryption.
2.2 Introduction to chaotic sequence
The traditional chaotic encryption model is generally three-dimensional and below. Due to the simple structure, few parameters, and high computational efficiency of low-dimensional chaotic systems, it has been widely used in data encryption. However, the security of low-dimensional chaotic systems is relatively weak in the case of violent attacks, and the high-dimensional chaotic model can generate more sets of chaotic sequences, so it can further improve the security performance. In this paper, based on the structure of a four-dimensional hyperchaotic system [26], a new state variable [27] is introduced to obtain a five-dimensional hyperchaotic system. Compared with the low-dimensional chaotic system, the five-dimensional chaotic system has a larger key space and better anti-attack ability. The five-dimensional chaotic model expression used is given by (1):
Among them, x, y, z, u, and w are chaotic sequences generated by chaotic systems, and a, b, c, d, and f are constants of the model. [27] shows that when a = 20, b = 8, c = 5, d = −20, f = −15, the five-dimensional hyperchaotic system has good randomness. The initial values (x0, y0, z0, u0, w0) were set to 1.81, 1.09, 0.97, 0.42, 0.03. The phase diagram of the model in different three-dimensional spaces is shown in Fig. 2. It can be seen that the five-dimensional chaotic system exhibits complex bifurcation dynamic characteristics and high-security chaotic characteristics.
Fig. 2. The partial space phase diagram of a five-dimensional chaotic system: (a) x-y-z space, (b) x-y-w space, (c) x-z-u space, (d) x-u-w space, (e) y-z-w space, (f) z-u-w space, (g) x-y plane, (h) x-z plane, (i) x-u plane
2.3 Polar coding encryption
The Polar coding is performed by passing the original data through serial and parallel transformations to obtain several sub-carriers. The generator matrix GN of Polar coding and the output sequence XN used in the scheme are defined as:
For traditional Polar codes, the freezing bit is usually the number 0. To improve the security of the transmission system, some freezing bits are changed from 0 to 1. The chaotic sequence x determines which block group's frozen bits will become 1. After encrypting the frozen bits during Polar coding, the security of the rectification and transmission system will be significantly higher than that of the traditional Polar coding scheme. The specific rules of the scheme are shown in (3):
Where lfrozon represents the freezing position, which is 0 or 1.The chaotic sequence y determines which path each subcarrier goes to after completing Polar encryption. The generating rule is shown in (4):
If k = 0, it leads to the first path; if k = 1, it leads to the second path.
The cyclic redundancy (CRC) and successive cancellation list (SCL) joint polar decoding method has excellent performance in short codes. SCL decoding list size (L) determines the performance of SCL decoder. With the increase of L, the system performance becomes better, but the complexity also increases. Therefore, considering the performance and complexity of the system, the SCL decoder is adopted, and L is set to 16.
2.4 Chaos CCDM process
These two paths of data prepared for 16QAM chaotic CCDM operation are divided into a group of 3 bits. For the PS-16QAM signal, there are two possible amplitude values of {1,3}. To meet the probability distribution characteristics of probability shaping to reduce its average power, the ideal distribution of the two amplitude values is P (1) = 3/4, P (3) = 1/4. At the same time, the input 3 bits have 8 possibilities of 000, 001, 010, 100, 011, 101, 110, and 111. The constellation mapping can be realized by corresponding these bits to different amplitude values; 8 different amplitude combinations are needed. To correspond to the 1/4 probability of the amplitude ‘3’ and the 3/4 probability of the amplitude ‘1’, the amplitude of each 2 symbols is divided into a group, which is divided into eight groups of amplitude combinations: {1,1}, {1,−1}, {−1,1}, {−1,−1}, {1,3}, {1,−3}, {−1,3}, {−1,3}, and the distribution probabilities of these amplitude combinations are equal in theory. Therefore, the probability of amplitude 1 is 3/4, and amplitude 3 is 1/4, corresponding to the probability of probability forming amplitude distribution. If the chaotic sequence is used to dynamically select the mapping rules because there are 8 groups of Bits and 8 groups of amplitude combinations, then a total of 8! = 40320 mapping possibilities. This scheme is too complex and not conducive to actual coding and experiment. Therefore, the original bits data and the amplitude data are divided into two large groups respectively, and four groups of data form one large group. For the bits combination, the group of 000, 001, 010, and 100 is named Group A, and the group of 110, 101, 011, and 111 is named Group B; for the amplitude combination, {1,1}, {1,−1}, {−1,1}, {−1,−1} group, named C group, for {1,3}, {1,−3}, {−1,3}, {−1,−3} group, named D group. Here, the first data uses A→C, B→D mapping rules, and the second data uses A→D, B→C mapping rules. Figure 3 is the mapping rule diagram of the scheme.
Then, the chaotic sequences z and u are used for selecting the bit-amplitude mapping rules of the first and second paths, respectively. In the proposed mothod, there are 4! = 24 corresponding methods of each path, the complexity is significantly reduced, and the feasibility is significantly improved. The specific mapping rules of bit-amplitude are as follows:
Where n1 represents the sequence generated by the chaotic sequence z, which is used to select the first mapping rule; n2 represents the sequence generated by the chaotic sequence u, which is used to select the second mapping rule. The values of n1 and n2 are integers between 1 and 24.Taking the first path A→C and B→D mapping rules as an example, Table 1 and Table 2 list the bit-amplitude mapping rules based on chaotic sequence z. Since the mapping rule of the second path is similar to this, it is not repeated.
Table 1. Intra-Group Chaotic CCDM Mapping Table (A→C)
Table 2. Intra-Group Chaotic CCDM Mapping Table (A→C)
After the chaotic CCDM generates the amplitude, the first half of the data is sent to the I road, and the second half of the data is sent to the Q road. The I-channel data will be used as the real part of the output data, and the Q-channel data will be used as the imaginary part of the output data. The QAM mapping converts the two-channel amplitude data into 16QAM symbols.
After completing the previous two-paths encryption, the two-paths 16QAM symbol data is merged. Then the last step of the encryption process is carried out, and the order of subcarriers is scrambled and encrypted by chaotic sequence w. (7) represents the rule that chaotic sequence w generates disturbance sequence:
Among them, subcarriersnew represent subcarrier sequences, fw{} is the rule for generating scrambling sequences, the generated perturbation sequences are integers between 1-m, and m represents the number of subcarriers. The order of subcarriers is rearranged according to the newly generated perturbation sequence.
3. Experimental setup and result
3.1 Experimental setup
The transmission BER performance and safety capability of the presented 16QAM-OFDM transmission system based on Polar code and chaotic CCDM are experimentally verified. Since the multi-core fiber has the advantages of low average optical channel cost, high integration, and large transmission capacity, and the single-core fiber can no longer meet the increasing communication capacity requirements, the seven-core fiber is used for transmission in the experiment. Figure 4 shows the schematic drawing of the experimental device. The computer generates the encrypted 16QAM-OFDM signal. The number of subcarriers is 64, and the IFFT is 256. The transmitted signal is first digital-to-analog converted by a 12.5GSa/s arbitrary waveform generator (AWG, TekAWG70002A). The laser generates light of wavelength 1550 nm. Subsequently, the 16QAM-OFDM signal and laser that have undergone digital-to-analog conversion are intensity modulated by a Mach-Zehnder modulator (MZM) to generate a modulated optical signal for 2 km seven-core fiber transmission. Then the optical signal is amplified by EDFA, and then the power splitting (PS) is performed. The encrypted 16QAM signal is sent to the seven-core fiber through the fan-in device. At the ONU end, the variable optical attenuator (VOA) is connected to the fiber channel to adjust the received optical power so that the photodiode (PD) can further detect the optical signal. After the PD detects the received optical signal with a bandwidth of 40 GHz, the mixed signal oscilloscope (MSO) (the highest sampling rate is 100GSa/s) is used to sample the detected electrical signal. After the sampling, the data information from the receiving end can be obtained. If the correct key is obtained, the original data can be recovered by performing an offline decryption and demodulation process opposite to the sender. The experiment uses the above platform to transmit 70Gb/s (10Gb/s × 7) encrypted 16QAM-OFDM signals to test the performance of the proposed scheme.
Fig. 4. Diagram of the experimental device (AWG: arbitrary waveform generator; MZM: Mach-Zehnder modulator; PS: power splitter; VOA: variable optical attenuator; PD: photodiode; MSO: mixed signal oscilloscope)
3.2 Experimental result
Figure 5 shows the BER curve of each fiber after passing through the seven-core fiber and the constellation diagram when the received power is −15dBm for the proposed OFDM-PON transmission system based on Polar code and chaotic CCDM encryption. According to the curve, it can be concluded that due to the difference in the transmission loss of each fiber, the BER of different fibers at the same receiving power is also different, but the BER of all ONUs decreases with the increase of the receiving optical power. When the receiving optical power is greater than −15dBm, the BER of the legal ONUs with over-encoded encryption is reduced to less than 10−3, and when the receiving optical power reaches −14dBm, the BER of all ONUs is reduced to 0. The experimental results illustrate that the propounded encryption program has excellent BER performance.
Fig. 5. The BER curves of each fiber of the seven-core fiber after the proposed transmission scheme is transmitted by 2 km.
Figure 6 compares the BER performance of the proposed 16QAM-OFDM based on Polar code and chaotic CCDM two-paths encryption and two-paths chaotic CCDM coded encryption without Polar coding in the same fiber. The total bit rate for OFDM signals is equal to ‘ subcarrier number × entropy × AWG sampling rate / IFT size / (1 + CP)’. Due to the different information entropy of different modulation systems (the information entropy of the transmission system with Polar coding and the transmission system without Polar coding is 1.5 and 3, respectively), to ensure the fairness of the comparison, the AWG sampling rate of each modulation system is adjusted in the experiment (set to 20GS/s and 10GS/s, respectively), so that their bit rates are equal, both 6Gb/s. The curve shows that the BER of the two-path chaotic CCDM transmission system after Polar coding is much lower than that of the transmission system without Polar coding. When the BER is 10−3, the received optical power of the transmission system with Polar coding is about 1.5dBm lower than that of the transmission system without Polar coding. The results show that Polar coding has a very obvious improvement effect on the BER performance of the transmission system.
To verify the impact of chaotic encryption Polar coding on the BER of the transmission system, the OFDM-PON with chaotic encryption Polar coding and without chaotic encryption Polar coding are transmitted by computer simulation. The simulation results are shown in Fig. 7. The results show that the two curves almost coincide, and the BER levels of the two schemes are very close. It shows that Polar coding with chaotic encryption does not significantly affect the performance of Polar codes.
Fig. 7. The BER curve of Polar coding with chaotic encryption and the original Polar coding after simulation transmission
Then, we further verify the security of this OFDM-PON based on Polar code and chaotic CCDM. Figure 8 shows the BER curve of the illegal ONU as well as the received constellation when the received optical power becomes −14dBm when one of the initial values in {x, y, z, u, w} is slightly disturbed (only 10−15 different from the correct value). The results show that the constellations received by all illegal ONUs are still clearly visible, but their BERs fluctuate around 0.5, indicating that even if the initial value of the chaotic sequence is very close to the correct value, the original information cannot be deciphered.
Based on the proposed chaotic encryption system, this paper uses computer simulation to transmit a landscape photo (Fig. 9(a)), and sets the signal-to-noise ratio (SNR) to 8. Figure 9(b) and 9(c) show the pictures received by the legitimate ONU and the illegal ONU, respectively. The key obtained by the illegal ONU is that only the difference between the initial value and the correct value of x is 10−15, and the other four variables’ initial values are all correct. It can be seen that the wallpaper images received by the legitimate ONU are very clear, and the information originally conveyed by the image is restored. Even if the illegal ONU only loses one key, it cannot receive the correct information. The pixels in the picture are disorderly, and no information is seen from the original picture. The above two experimental results show that the security performance of the proposed encryption scheme is well guaranteed.
Fig. 9. The images received by the original image (a), the legal ONU (b), and the illegal ONU (c) are compared.
For the five-dimensional chaotic system used in this paper, there are five dimensions of the initial value. After calculation, the five initial values of x, y, z, u, and w of the chaotic model are roughly (−47,42), (−50,48), (0,58), (−182,112), (−86,85). If only five initial values are taken into account, and the key space is calculated conservatively, the key space of the propounded system can be obtained to be about (89 × 1015) × (98 × 1015) × (58 × 1015) × (294 × 1015) × (171 × 1015) = 2.54 × 1085. Such a large key space can effectively ensure that illegal ONUs can hardly crack the correct key by a violent attack.
4. Conclusion
A new high-security and high-reliability optical transmission system is proposed based on two-paths encryption of chaotic CCDM and Polar coding. The experiment results show improved optical transmission security and BER performance. The 16QAM-OFDM signal is transmitted on a 2 km seven-core fiber. The experimental results show that the received optical power of all ONUs is less than −15dBm when the BER of all ONUs is reduced to less than 10−3. Compared with 16-QAM OFDM without FEC coding, the received optical power is reduced by about 1.5dBm when the BER is 10−3. In addition, the key space of the proposed system reaches 1085, and the security performance is further enhanced. The results illustrate that this scheme can efficiently prevent the transmission signal from being stolen by illegal ONUs and improve the optical access system's security and BER performance. The advantages of BER and safety performance make this two-path chaotic encrypted OFDM-PON have an optimistic application prospect in the current optical transmission systems.
Funding
National Key Research and Development Program of China (2021YFB2800903); National Natural Science Foundation of China (62171227, 62225503, 61835005, 62205151, 62275127, U2001601, 61935005); Jiangsu Provincial Key Research and Development Program (BE2022079, BE2022055-2); Natural Science Research of Jiangsu Higher Education Institutions of China (22KJB510031); Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology.
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.
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