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Abstract
This paper proposes a high-security multi-level constellation shaping trellis-coded modulation (TCM) method based on clustering mapping rules, which is suitable for passive optical networks (PON) using three-dimensional (3D) carrier-less amplitude and phase modulation (CAP). This method combines the TCM mapping process with the constellation shaping and performs a multi-level mapping of the coded signal according to the classification label, so as to obtain better constellation shaping gain while expanding the coding gain of the TCM. The 3D constellation generated by the multi-level mapping adopts Chua’s chaotic model for rotation encryption, which improves the ability of the optical access network to resist malicious attacks at the physical layer. Experiments show that 70 Gb/s (7×10 Gb/s) transmission is achieved on a 2 km weakly coupled seven-core fiber using the scheme proposed in this paper. At a bit error rate (BER) of 1 × 10−3, the difference in receiver sensitivity between the best and worst-performing cores is about 0.7 dB. The difference in receiver sensitivity between the cubic constellation and the chaotic spherical constellation is about 0.1 dB. The sensitivity of the chaotic spherical constellation receiver is about 6.98 dB higher than that of the 2D shaping constellation receiver. The experimental results show that the scheme has reliable security performance while improving the short-reach transmission capacity. It has broad application prospects in future short-reach communication research.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the continuous advancement and development of communication technology, the society has entered a stage of rapid development of information construction. Technologies such as driverless cars, virtual reality, and whole-house connectivity have been applied from concept to real life. The use of intelligent technology means the rapid growth of broadband network users. Under the background of the increasingly mature and stable development of backbone network technology, the access network system for medium and short-reach communication has ushered in pressure and challenges. By 2023, nearly two-thirds of the world’s population will have Internet access, and the number of Internet users worldwide will reach 5.3 billion, which is much higher than the 3.9 billion in 2018. How to improve the transmission capacity of short-reach access networks has become a research hotspot in the development of communication networks [1]. Compared with the traditional electrical interconnection network, the optical interconnection network has many advantages such as better flexibility and scalability, higher bandwidth, and lower power consumption. Therefore, the optical interconnection network is considered to be an important development direction of the short-reach communication network in the future [2–4], in which PON has become the most widely used solution for large capacity optical transmission in access network systems due to its low cost, high reliability, transparency to formats, and flexibility to easily upgrade to higher bit rates [5].
Spatial division multiplexing (SDM) technology is considered to be an effective solution for improving the transmission capacity of optical communication networks. It uses space as the dimension of signal multiplexing to improve the transmission capacity of optical fibers, in particular, it can effectively break through the 100 Tb/s capacity estimation limit of traditional single-mode fiber [6], so the research on multi-core fiber, few-mode fiber, and corresponding multiplexing and demultiplexing devices based on SDM technology has received extensive attention. Reference [7] studies the use of a single broadband comb source in a 4-core multi-core fiber for multi-band transmission, using PDM-64QAM/256QAM signals to transmit 54 km over a 4-core multi-core fiber, the maximum decoding throughput is 610 Tb/s. The average throughput of each fiber core exceeds the performance of standard single-mode fiber broadband transmission, and the maximum information transmission capacity of a single fiber core is 155.1 Tb/s. Reference [8] is also based on a 4-core multi-core fiber link, and studies the performance of cyclic transmission in multi-core fibers in the S, C, and L bands. Experiments have confirmed that a multi-core fiber with the same diameter (125 $\mathrm {\mu }$m) as standard single-mode fiber can multiply the transmission capacity. Reference [9] conducted experimental research on high-capacity transmission in a coupled 3-core multi-core fiber and conducted two high-speed large-capacity long-distance transmission experiments in C and L-band bandwidths greater than 75 nm, and the experiment achieved a transmission rate of 172 Tb/s, a transmission distance of 2040 km, the transmission rate is still 81 Tb/s at a distance of more than 4080 km. The research shows that the coupling of multi-core fiber and the broadband optical signal has great potential in long-distance transmission. Reference [10] compares the performance of 3-mode few-mode fiber and 3-core coupled multi-core fiber in the cyclic transmission of space division multiplexing loop and studies the influence of wavelength and transmission distance on the transmission channel. The results show that the coupled multi-core fiber has a higher transmission rate than the few-mode fiber at a similar transmission distance. [11] achieved a large-capacity transmission of 13 km at a rate of 10.66 Pb/s in a 38-core 3-mode fiber, studied in detail the factors affecting the core data transmission rate, and explored the ability to use the same fiber for 65 km multi-span transmission. Reference [12] designed a 13 km 39-core 3-mode fiber and used cascaded spatial multiplexers at both ends of the fiber to construct a bidirectional space division multiplexing transmission device, which realized the simultaneous use of 228 spatial channels and most of the spatial channels have excellent transmission performance.
In addition, it is also considered an effective means to improve the transmission performance of the communication system through advanced coding and modulation algorithms. According to Shannon’s Noisy Channel Coding Theorem, for a discrete memoryless stationary channel, when the transmission rate of the signal to be transmitted is less than the channel capacity, there must be a channel coding algorithm to achieve an arbitrarily small average error when the code length is large enough [13]. In response to this theorem, constellation shaping technology is proposed as a way to improve channel capacity. Constellation shaping technology includes probability shaping (PS) technology and geometric shaping (GS) technology. The PS technology reduces the average power of the constellation by optimizing the probability of signal points appearing on the constellation points, increasing the probability of the signal points appearing in the inner constellation, and reducing the probability of the outer constellation points appearing. The GS technique is to maximize the minimum Euclidean distance (MED) by optimizing the spatial position distribution of constellation points under the condition of constant constellation power. Both constellation shaping techniques can obtain shaping gain, improve the spectral efficiency of the system, and increase the transmission capacity of the system [14]. There are many studies combining the two shaping methods to obtain larger system shaping gains. In [15], a PS-PON system based on symbol-level marking and diamond modulation is proposed, combining both PS and GS, which significantly increases the transmission rate and capacity of the signal. In [16], a star-shaped PS-16/32 scheme based on a honeycomb shape decision area was proposed, which overall optimized the constellation diagram of the system and improved the BER performance of the system. For short-reach data communication scenarios, unlike long-reach backbone networks, coherent systems and complex digital signal processing (DSP) algorithms need to be used to compensate for damage during long-reach transmission. The method of intensity modulation/direct detection (IMDD) will have a simple structure, power consumption, and lower cost advantages. At present, there are many advanced modulation formats based on IMDD such as pulse amplitude modulation (PAM), discrete multi-tone (DMT), carrier-less amplitude phase (CAP), etc. [17]. CAP is a digital Quadrature Amplitude Modulation (QAM). Unlike other QAM modulation, which superimposes the signal modulated on the carrier through a multiplier, CAP modulation uses a band-pass pulse filter to modulate and demodulate the signal, which means that the use of CAP modulation can have multiple dimensions of operation space, which greatly increases the flexibility of the communication system and can support 3D and above signal modulation.
Research has consistently shown that if the system transmission capacity is improved only from the perspective of spatial multiplexing or the coding and modulation algorithm, problems such as reducing the channel spacing, increasing the crosstalk between channels, or reducing the power efficiency will occur, and the spectral efficiency and power spectral efficiency cannot be balanced. Obviously, we need to start from two angles at the same time to solve the problem and make the system get better performance. In this paper, TCM is adopted on the basis of research on multi-core fiber, TCM is considered to be a new type of error correction coding scheme that balances spectral efficiency and power spectral efficiency. It is an effective combination of channel error correction coding and constellation modulation process, which improves the spectral efficiency of the system and has robust error correction capabilities [18]. In [19], a PS-16QAM scheme based on TCM is proposed, which allows the uncoded bits in conventional TCM to generate non-uniform symbols through a probability distribution matcher (DM) to participate in the signal mapped to 16QAM to improve the performance of TCM. [20] proposed a PS-TCM scheme based on a generalized frequency division multiplexing (GFDM) system, which was experimentally verified to have significant coding gain and flexible spectral efficiency.
In addition, for PON networks, security issues cannot be ignored after the number of access users increases. Illegal optical network units (ONUs) will disguise as legal ONUs. When optical line terminals (OLTs) transmit downlink data in broadcast form, all ONUs can receive downstream data from the connected OLT. At this time, the illegal ONU will steal or tamper with the downstream data signal, so it is necessary to apply a security encryption scheme to the PON at the physical layer. At present, chaotic encryption communication technology has been widely studied in the field of communication security. The chaotic model has initial value sensitivity and uncertainty, non-repeatability, and unpredictability. Therefore, the use of chaotic model-based encryption technology is an efficient and convenient encryption scheme for PON [21].
In this paper, to the best of our knowledge, a high-security multi-level constellation shaping TCM method based on clustering mapping rules is proposed for the first time. The multi-level GS mapping is designed for the constellation diagram after TCM, which realizes the improvement of the constellation diagram from 2D to 3D after TCM, which significantly expands the constellation shaping gain. The 3D constellation is rotated and encrypted by Chua’s chaotic model to generate a chaotic spherical constellation. Compared with the 2D constellation diagram using PS combined with GS, this method effectively improves the spectral rate, bit error performance, and transmission security performance of the system. When 64QAM modulation is used at the transmitter, the experiment successfully demonstrated that the proposed 3D-2GS-TCM-CAP has more advantages than 2D-PS-GS-TCM-CAP on a 2 km seven-core multiplexed fiber link.
2. Principle
2.1 Principles of the system model
The schematic diagram of the transmission system model structure is shown in Fig. 1, including the TCM-64QAM encoder on transmitter, the multi-level constellation shaping and mapping under the clustering mapping rule, the security constellation rotation encryption, the seven-core multiplexed fiber of the transmission link and constellation rotation decryption at the receiver, the constellation de-mapping module and the TCM Viterbi decoder, each module will be described in detail in the following subsections.
2.2 Principle of TCM-64QAM
The principle of TCM-64QAM encoder is shown in Fig. 2. The serial-to-parallel conversion is performed on the original input bitstream, and the original serial bit stream is converted into a 3-line parallel bit stream branch $x_1, x_2, x_3$, select the 2nd and 3rd branches of the parallel bitstream branch as the coded bits ($x_2, x_3$ in the figure) for the input of the 8-state convolutional encoder, the first branch of the parallel bitstream ($x_1$ in the figure) is sent directly to the symbol mapper as uncoded bits. We use an 8-state convolutional encoder with a code rate of 2/3 to generate 3 encoder outputs $y_2, y_3, y_4$ and enter the TCM signal mapper, which includes a redundancy check bit $y_4$. The key conditions for the TCM technique to achieve coding gain are:
This condition indicates that the system has coding gain when the free distance of the encoded signal sequence needs to be greater than the MED between the signal points of the unencoded constellation, therefore, after the bitstream enters the signal mapper, the mapping by set-partitioning (MSP) technique is used to map the bitstream into symbol data. The MSP process of 64QAM is shown in Fig. 3. Divide the constellation into 8 subsets, the convolutional encoder output bits $y_2, y_3, y_4$ are used to select the subsets, and the uncoded bits $x_1$ ($y_1$ in the symbol mapper) are used to select specific signal points from the selected subsets. The MSP technology makes the mapped constellation points have the largest Euclidean Distance and does not add extra bandwidth at the same time. At the receiving end of the system, the TCM decoder selects the Viterbi algorithm for decoding to complete the whole process of TCM [22,23].
The constellation modulation process of the standard TCM-64QAM is to map the signal into a standard 64QAM constellation diagram. In [19,20], the combination of PS technology and TCM can improve the performance of the system. In this paper, from the perspective of GS, the GS and TCM processes are combined. Combined and further seek greater coding gain by designing the geometric distribution of constellation points. The performance advantage of TCM comes from the fact that TCM uses the extended constellation to accommodate the redundant bits contained in the output of the convolutional encoder, but when the modulation order increases to 64QAM or 128QAM, the coding gain obtained by TCM will gradually approach the loss caused by the extended constellation, which will lead to the deterioration of the BER of the system and the degradation of the system performance. In order to make the system obtain a higher rate, this paper adopts the method of hierarchical mapping to enlarge the gap between the coding gain and the constellation expansion loss and further improves the performance of the system based on the GS technology.
2.3 2D constellation mapping module
The standard 64QAM constellation diagram obtained based on TCM is shown in Fig. 4(a). The 64QAM standard constellation diagram is transformed into an 8QAM constellation diagram by 2D-GS mapping. Fig. 4(b) shows the designed 2D geometrically shaped 8QAM constellation diagram, which has good anti-noise performance. According to the different amplitudes of the constellation points, the constellation points are clustered and mapped to realize the mapping transformation from the constellation diagram (a) to the constellation diagram (b). The specific rules are as follows: The orange constellation points in the red box are mapped to the four green constellation points in the inner circle of the 8QAM constellation diagram. For the blue constellation points in the red box, one type is mapped to the four green points on the inner circle of the 8QAM constellation diagram according to the positive and negative amplitudes, and the other type is mapped to the four purple constellation points on the outer circle of the constellation diagram. The brown constellation points outside the red frame are all mapped to the purple constellation points on the outer circle of 8QAM, this completes the 2D constellation mapping transformation process from 64QAM to 8QAM.
2.4 3D mapping transformation process
Compared with 2D constellation modulation, 3D constellation modulation has a higher transmission rate and transmission capacity. In [18], a 3D-9QAM mapping based on PS is proposed, adding a set of parallel convolutional encoders, the outputs of the two groups of convolutional encoders with different code rates and the uncoded bits are subjected to non-equal-probability mapping by a 3D signal mapper to generate a 3D-9QAM constellation map. In [24], a novel OFDM technique based on a 3D signal mapper and a 2D inverse Fourier transform is proposed, the signal is directly mapped onto a 3D Poincaré sphere and a 2D IDFT is used to generate OFDM symbols. Under the condition of maintaining the same average power, the 3D constellation has a larger MED than the 2D constellation, so the system will have better BER. However, the design of these schemes is cumbersome. For example, in [18], an additional convolutional encoder needs to be added for non-equal-probability mapping, which increases the decoding complexity correspondingly in the Viterbi decoding process.
After completing the 2D constellation mapping transformation in the previous step, this paper proposes a 3D mapping scheme based on clustering mapping, which does not require complex coding methods in the coding part, avoids increasing the difficulty of decoding, and can improve the transmission rate and system error code performance. As shown in Fig. 5, after the TCM and 2D constellation mapping transformation, the 2D-8QAM constellation diagram contains two random parallel symbol data. According to the design, the symbol data of the green marked constellation point in the inner circle of 8QAM is selected and mapped to the upper green constellation point of the cube, select the symbol data of the purple constellation points in the outer circle of 8QAM to map to the lower purple constellation points of the cube, After the data distribution is determined, the amplitude of the two-way symbol data is taken, the data is classified and judged according to the amplitude of the 2D constellation symbol data, and the data of the same vertex of the cube is classified together. Because the 2D constellation does not have z-axis, it is necessary to assign the z-axis coordinates of the corresponding constellation points according to the designed position distribution to increase the spatial dimension. According to the structure of the cube, the coordinates of the z-axis of the four vertices of the upper layer of the cube are all assigned as 1. Similarly, the z-axis of the four vertices of the lower layer is assigned -1, and the classified data is mapped to the 3D cubic constellation space in turn. Flexible mapping transformation from 2D constellation to 3D constellation, at the receiving end of the system, restoring the 3D constellation diagram to 2D is an inverse process, which can obtain considerable shaping gain without increasing the decoding complexity of the system.
2.5 3D constellation rotation encryption
After completing the GS of the 3D constellation under the clustering mapping rule, in order to prevent the data from being stolen or tampered with by illegal ONUs, as shown in Fig. 6, the 3D cube constellation is encrypted by using Chua’s chaotic model, Chua’s chaotic circuit model is:
where ($\alpha$, $\beta$,a,b) are constants whose values are 10, 14.87, -1.27, and -0.65, respectively. $x_1,y_1,z_1,t$ are variables, the initial value is set to (0.5, -0.2, 0.5), the range of the generated chaotic sequence is $x_1$(-3,3), $y_1$(-0.8,0.8), $z_1$(-5,5), the phase of Chua’s circuit model is shown in Fig. 7, the phase diagram has a double rolling attractor, which reflects that the Chua’s chaotic system has complex chaotic characteristics. In order to improve the randomness of the chaotic sequence, a sampling factor L=1 is introduced, and the initially formed chaotic sequence is sampled.
Continue to process the sampled chaotic sequence M to generate a rotation masking vector of 0-360 degrees, select the classical theoretical quaternion rotation matrix of 3D space rotation, and convert the constellation rotation masking vector into a quaternion matrix. The 3D constellation data is disturbed, and the chaotic spherical constellation diagram generated by rotation is shown in Fig. 8, which realizes the effect of secure communication.
2.6 Principle of CAP mapping
The modulation principle of 3D-CAP is shown in Fig. 9. The masked 3D spherical constellation data is up-sampled according to the spatial dimension, and after the up-sampling is passed through digital filters, the 3D signal satisfies the orthogonal relationship, and the 3D constellation information is converted to a 3D-CAP signal. Likewise, the data stream at the receiving end first separates the 3D signal through matched filters and then performs down-sampling to separate the original 3D constellation data.
3. Experimental setup and results
The experimental diagram of the high-security multi-core optical transmission system based on TCM is shown in Fig. 10. To verify the actual effect of our proposed system, the intensity modulation/direct detection (IM/DD) based on 2 km weakly coupled seven-core optical fiber is used. Use MATLAB offline to complete the TCM module, the 2D constellation mapping module, the 3D constellation mapping module, and the 3D constellation rotation encryption module described in the previous chapters to generate three sets of offline signals to be sent, then the three groups of data are up-sampled, and the sampled data is sent to three orthogonal filters to obtain a digital 3D-CAP signal.
Use an arbitrary waveform generator (AWG) with a maximum sampling rate of 25 GSa/s to convert the digital 3D signal into an analog radio frequency (RF) signal. In this experiment, a continuous wave laser (CW) with a wavelength of 1550 nm is used as the light source, and an electronic amplifier (EA) drives the Mach-Zehnder modulator (MZM), modulates the RF signal sent by the arbitrary waveform generator (AWG), the modulated signal is then connected to a seven-core fiber fan-in device through an erbium-doped fiber amplifier (EDFA) and a 1:8 power splitter (PS), so the signal can be sent to a multi-core fiber link (MCF) for transmission. At the receiver, the fan-out device demultiplexes the seven-core multiplexed fiber into seven single-mode fibers. At the end of each single-mode fiber, a variable optical attenuator (VOA) is used to adjust the received optical power, and then the received optical signal is detected by a photodiode (PD) with a bandwidth of 40 Ghz. The received optical signal is sent to a mixed-signal oscilloscope (Tektronix, MSO73304DX), the signal is converted back to a digital signal, the DSP processing at the receiver is performed in the MATLAB program, and the 3D-CAP signal is subjected to matched filtering, down-sampling, equalization, and 3D constellation de-mapping, Viterbi decoding of the 2D constellation to obtain the received data.
Figure 11 describes the BER performance of different cores on the seven-core multiplexed fiber system. Each core is from -15 dBm to -24 dBm in a total of 10 groups of experiments, as shown in Fig. 11, when the optical power is greater than -19 dBm, the transmission scheme proposed in this paper is all 0-bit error rate in the system. The BER curve shows a downward trend between -24 dBm and -19 dBm as the optical power of the receiver increases. When the BER is $1\times 10^{-3}$, the received optical power of the seven-core multiplexed fiber is about -20.02, -20.11, -19.82, -20.39, -20.40, -20.53, -20.42 dBm, respectively. In terms of receiver sensitivity, the difference between the best performing core 6 and the worst performing core 3 is about 0.7 dB. Experiments show that the weakly coupled seven-core multiplexed fiber used in this paper has stable transmission performance and the effectiveness of the multi-level constellation shaping TCM method based on the clustering mapping rule, which provides a meaningful reference for the use of multi-core fiber transmission systems to improve transmission capacity.
As shown in Fig. 12, the optical power at the receiver is from -13 dBm to -24 dBm. The experiment compares the BER performance of three schemes: cubic constellation, chaotic spherical constellation and 2D constellation shaping constellation diagram before and after transmission of 2 km in core 5. It can be seen that the difference in transmission performance between the cubic constellation and the chaotic spherical constellation encrypted with the chaotic model is very small. When the BER is $1\times 10^{-3}$, the receiver sensitivity difference between the cubic constellation and the chaotic spherical constellation is about 0.1 dB. Experiments have confirmed that when the chaotic model encrypts and protects the cubic constellation, it enhances the security of the system and does not lose too much power to affect the transmission performance of the method itself. Then compare the chaotic spherical constellation with the 2D constellation shaping constellation. The 2D constellation shaping constellation is the constellation map generated by the combination of PS and GS in the 2D plane. It can be clearly seen that the overall BER of the 2D constellation shaping receiver shows a downward trend, but the transmission performance is far worse than that of the chaotic spherical constellation. When the optical power of the receiver is -21 dBm, the shape of the chaotic spherical constellation and the cubic constellation is clear and stable, but the 2D shaping constellation is already chaotic and disordered. When the BER is $1\times 10^{-3}$, the sensitivity of the chaotic spherical constellation receiver is about 6.98 dB higher than that of the 2D constellation shaping receiver, and the experiment proves that the method has better transmission performance under high security.
Fig. 12. BER curves of Cubic Shaping constellation, Chaotic Spherical Constellation and 2D Shaping Constellation.
Figure 13 compares the BER curve between the legal receiver and the illegal receiver. For the legal receiver, the BER curve is consistent with that in Fig. 12. As the optical power increases, the BER continues to decrease. The BER of the illegal receiver has been stably maintained at about 0.5. If there is no correct key information, the illegal access machine cannot obtain the correct information. In this paper, when the optical power of the receiver is -20dBm, the sensitivity of the security implementation in this paper to small changes is tested. As shown in Fig. 14, changing the initial value of the encryption scheme (0.5, -0.2, 0.5), when the initial value increases by $10^{-18}$,the system’s BER still maintains the original BER, When the initial value increases by $10^{-17}$,the BER of the system increases sharply to about 0.5. When the initial value increases by a larger amount of change, the BER of the system still remains at about 0.5, which shows that the encryption method adopted in this paper has a very good performance of high initial value sensitivity, seven key parameters can be used to expand the key space to $2^{31}\times 2^{31}\times 2^{31}\times 2^{31}\times 10^{17}\times 10^{17}\times 10^{17}=2.12\times 10^{88}$,which has an effective ability to resist illegal intrusion.
4. Conclusion
We propose a high-security multi-level constellation shaping TCM method based on clustering mapping rules. After TCM, multi-level GS constellation mapping is performed to generate 3D cubic constellations, and Chua’s chaotic model is used to generate chaotic sequences. According to the quaternion theory, the masking vector is generated to rotate the cubic constellation to generate the chaotic spherical constellation. The key space is $2.12\times 10^{88}$, which can effectively resist illegal attacks on the physical layer without affecting the transmission performance of the system itself. We successfully experimented on 2 km weakly coupled seven-core multiplexed fiber and verified the stable transmission performance of the seven-core multiplexed fiber used in this paper. When the BER is $1\times 10^{-3}$, the difference between the receiving sensitivity of the best performing core 6 and the worst performing core 3 is about 0.7 dB, the sensitivity of the chaotic spherical constellation receiver proposed in this paper is about 6.98 dB higher than that of the 2D shaping constellation receiver. Under the support of TCM, when the optical power of the receiver is greater than -20 dBm, compared with the 2D shaping constellation, the method proposed in this paper has achieved error-free transmission. It shows that the scheme is an effective combination of advanced error correction coding scheme and constellation shaping technology, which can enhance the security performance of the physical layer without affecting the transmission performance. It is a promising solution in the study of improving short-reach transmission capacity.
Funding
National Key Research and Development Program of China (2020YFB1805801); National Natural Science Foundation of China (61935005, 61835005, 62171227, 61727817, U2001601, 62035018, 61875248, 61935011, 61720106015, 61975084); Jiangsu team of innovation and entrepreneurship; 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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