High-safety probability shaping method based on three-dimensional constellation joint shaping

Abstract

The invention discloses a high-safety probability shaping method based on three-dimensional constellation joint shaping, and the method comprises the steps: applying a BCPU-PS scheme based on a bit-level probability update strategy to a three-dimensional constellation after geometric shaping, and achieving the probability shaping through modifying the probability distribution of bits of a transmitting end. Coding and calculation complexity introduced by a traditional probability shaping technology is avoided. The combined shaping technology improves the bit error rate performance while improving the signal transmission rate. Besides, in order to prevent signals from being eavesdropped or tampered in transmission, a chaotic encryption technology is introduced in the scheme, and bits, symbols and time domain subcarriers of a sending end are subjected to multi-layer encryption by using a secret key generated by a three-dimensional chaotic system, so that high-safety, large-capacity and high-speed signal transmission is realized.

Description

Technical Field

[0001] The invention relates to a high-security probability shaping method based on three-dimensional constellation joint shaping, and belongs to the technical field of optical communication. Background Art

[0002] In recent years, with the rapid digitalization of society, global data traffic has risen sharply. Technologies such as 6G, blockchain, and the Internet of Things will incorporate more and more devices into data networks and continuously expand the boundaries of the network. This means that the development of social economy will put forward higher bandwidth and coverage requirements for existing communication networks. Orthogonal frequency division multiplexing (OFDM) has been widely studied due to its high spectral efficiency. OFDM can be implemented by inverse fast Fourier transform (IFFT). This IFFT-based multi-carrier multiplexing can improve the spectral efficiency of the system. However, the introduction of OFDM technology has also brought new problems, among which the more serious one is the high peak-to-average power ratio (PAPR) problem. PAPR refers to the ratio of the maximum power to the average power in an OFDM symbol. When multiple subcarrier signals are linearly superimposed, if the phases of each subcarrier at a certain moment are close to the same, the signal power at this moment will be much higher than the average value, resulting in a higher PAPR. High PAPR will cause the signal power to exceed the linear operating range of the communication system hardware, causing signal distortion and hardware loss.

[0003] In order to alleviate this problem, many scholars have conducted active research on it. From the perspective of technical principles, it is mainly divided into three categories: limiting technology, coding technology, and constellation expansion technology. Among them, the limiting technology limits the amplitude of the signal sample point to a fixed value to achieve the effect of PAPR suppression, which will inevitably introduce additional noise and increase the bit error rate. Coding technology avoids high peak signals by selecting codewords with low PAPR. When the modulation order becomes larger, its encoding and decoding complexity will increase rapidly. Constellation expansion technology reduces PAPR by changing the position of the constellation points. Compared with the first two technologies, constellation expansion not only avoids signal distortion, but also effectively reduces PAPR while maintaining relatively low complexity.

[0004] Although 3D OFDM can effectively improve the transmission performance of the system, in the face of the rapid development of future communication technology and the ever-changing application requirements, the transmission rate of the system needs to be further improved. Especially for 6G communication, improving the transmission rate is particularly important.

[0005] At the same time, as the transmission rate of optical networks increases, security issues become more prominent. High-speed data transmission allows a large amount of sensitive information to flow quickly in the network. This rapid transmission method increases the risk of data being intercepted, tampered with, and other malicious attacks. Therefore, it is particularly important to encrypt optical network signals. The main encryption methods at this stage include: Advanced Encryption Standard, RSA encryption, digital authentication, quantum confidentiality technology, and physical layer chaos encryption technology. However, traditional upper-layer encryption technology often exposes data header information during transmission, resulting in a decrease in the security of encrypted information.

[0006] Therefore, those skilled in the art urgently need to solve the problem of how to transmit signals more safely and efficiently in existing optical communications. Summary of the invention

[0007] Purpose: To overcome the problem that the traditional PS scheme in the prior art often introduces high complexity in terms of calculation, hardware requirements and overall system power consumption during encoding and decoding, especially when the two-dimensional space is expanded to three dimensions, this complexity will be further increased. And the problem that the signal in the prior art is easily eavesdropped or tampered during transmission, the present invention provides a high-security probability shaping method based on three-dimensional constellation joint shaping.

[0008] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is:

[0009] In a first aspect, a high-security probability shaping method based on three-dimensional constellation joint shaping specifically includes:

[0010] Step 1: Obtain a bit sequence to be transmitted, generate a first set of keys using a three-dimensional chaotic map, encrypt the bit sequence to be transmitted using the first set of keys, and obtain an encrypted bit sequence to be transmitted.

[0011] Step 2: Convert the encrypted bit sequence to be transmitted from serial to parallel and obtain an updated sequence through BCPU operation.

[0012] Step 3: Perform 3D-QPSK constellation mapping on the updated sequence to obtain the constellation points of the 3D-32QAM signal.

[0013] Step 4: Generate a second set of keys using a three-dimensional chaotic map, and encrypt the constellation points of the 3D-32QAM signal using the second set of keys to obtain an encrypted 3D-32QAM signal.

[0014] Step 5: Map the encrypted 3D-32QAM signal to each subcarrier in the OFDM system. After completing the subcarrier mapping, use the inverse frequency domain transform to convert the frequency domain 3D-OFDM signal into a time domain signal. Use the three-dimensional chaotic mapping to generate the third set of keys. Use the third set of keys to encrypt the time domain signal to obtain the encrypted 3D-32QAM signal time domain signal.

[0015] As a preferred solution, the step 1 specifically includes:

[0016] Step 1.1: Get the bit sequence t to be transmitted.

[0017] Step 1.2: Using the three-dimensional chaotic system, obtain the chaotic sequence x i+1 , where the three-dimensional chaotic system expression is as follows:

[0018]

[0019] Among them, xi +1 represents the chaotic sequence x after the i+1th iteration, yi +1 represents the chaotic sequence y after the i+1th iteration, z i+1 represents the chaotic sequence z after the i+1th iteration. i represents the chaotic sequence x after the i-th iteration, y i represents the chaotic sequence y after the i-th iteration, z i represents the chaotic sequence z after the i-th iteration. a, b, c represent the system parameters.

[0020] Step 1.3: According to the chaotic sequence x i+1 , calculate the key x corresponding to the chaotic sequence x i+1 '.

[0021] Among them, the key x corresponding to the chaotic sequence x i+1 'The calculation formula is as follows:

[0022] x i+1 '=floor(mod(x i+1 10 5 ,2))

[0023] Among them, floor(·) represents the downward integer function, and mod(·) represents the remainder function.

[0024] Step 1.4: According to the key x corresponding to the chaotic sequence x i+1 'Encrypt the bit sequence t to be transmitted to obtain the encrypted bit sequence T to be transmitted.

[0025] The calculation formula of the encrypted bit sequence T to be transmitted is as follows:

[0026] T=XOR(t,x i+1 ')

[0027] Among them, XOR represents the exclusive OR logic operation.

[0028] As a preferred solution, the step 2 specifically includes:

[0029] Step 2.1: Convert the encrypted bit sequence to be transmitted from serial to parallel to obtain five parallel sequences G1, G2, G3, G4 and G5. The lengths of G1, G2 and G3 are all (3 / 13)M, and the lengths of G4 and G5 are all (2 / 13)M, where M is the length of the encrypted bit sequence to be transmitted.

[0030] Step 2.2: Group the bit streams in groups of k bits each in G4 and add an extra bit EWB (R i ), add an extra bit EWB (H) before each bit group of G5 i ), where EWB(R i ) represents the effective weighted bit of the ith group in G4, EWB(H i ) represents the effective weighted bits of the i-th group in G5, and k is an integer greater than or equal to 2.

[0031] Step 2.3: If the number of "1"s in the bit group of G4 or G5 is less than k / 2, the corresponding EWB (R i ) and EWB(H i ) is set to "1", and the data in the bit group of G4 or G5 is bit-reversed. If the number of "1" in the bit group of G4 or G5 is greater than or equal to k / 2, the corresponding EWB (R i ) and EWB(H i ) is set to "0" and the data bits in the bit group of G4 or G5 remain unchanged.

[0032] Step 2.4: Remove all EWB (R i ) to form the effective weighted bit sequence of G4, and add the effective weighted bit sequence of G4 to the end of G4 to form the shaped G4, and add all EWB (H i ) to form a G5 effective weighted bit sequence, and add the G5 effective weighted bit sequence to the end of G5 to form a shaped G5, and perform parallel to serial (P / S) conversion on G1, G2, G3, the shaped G4 and the shaped G5 to obtain an updated sequence.

[0033] As a preferred solution, the step 4 specifically includes:

[0034] Step 4.1: Obtain the constellation point q of the 3D-32QAM signal.

[0035] Step 4.2: Using the three-dimensional chaotic system, obtain the chaotic sequence y i+1 , where the three-dimensional chaotic system expression is as follows:

[0036]

[0037] Among them, x i+1 represents the chaotic sequence x after the i+1th iteration, y i+1 represents the chaotic sequence y after the i+1th iteration, z i+1 represents the chaotic sequence z after the i+1th iteration. i represents the chaotic sequence x after the i-th iteration, y i represents the chaotic sequence y after the i-th iteration, z i represents the chaotic sequence z after the i-th iteration. a, b, c represent the system parameters.

[0038] Step 4.3: According to the chaotic sequence y i+1 , calculate the key y corresponding to the chaotic sequence y i+1 '.

[0039] Among them, the key y corresponding to the chaotic sequence y i+1 The calculation formula of ' is as follows:

[0040] y i+1 '=fix(mod(abs(y i+1 10 6 ),N))+1

[0041] Wherein, fix(·) represents an integer function, mod(·) represents a remainder function, abs(·) represents an absolute value function, and N represents the number of subcarriers of OFDM.

[0042] Step 4.4: According to the key y corresponding to the chaotic sequence y i+1 'Encrypt the constellation point q of the 3D-32QAM signal to obtain the encrypted 3D-32QAM signal Q.

[0043] Q=q·y i+1 '

[0044] Wherein, q represents the three-dimensional coordinate matrix of the constellation points of the 3D-32QAM signal, and Q represents the three-dimensional coordinate matrix of the encrypted constellation points.

[0045] As a preferred solution, the step 5 specifically includes:

[0046] Step 5.1: Map the encrypted 3D-32QAM signal to each subcarrier in the OFDM system. After completing the subcarrier mapping, use the inverse frequency domain transform to convert the frequency domain 3D-OFDM signal into a time domain signal s.

[0047] Step 5.2: Using the three-dimensional chaotic system, obtain the z chaotic sequence z i+1 , where the three-dimensional chaotic system expression is as follows:

[0048]

[0049] Among them, x i+1 represents the chaotic sequence x after the i+1th iteration, y i+1 represents the chaotic sequence y after the i+1th iteration, z i+1 represents the chaotic sequence z after the i+1th iteration. i represents the chaotic sequence x after the i-th iteration, y i represents the chaotic sequence y after the i-th iteration, z i represents the chaotic sequence z after the i-th iteration. a, b, c represent the system parameters.

[0050] Step 5.3: According to the chaotic sequence z i+1 , calculate the key z corresponding to the z chaotic sequence i+1 '.

[0051] Among them, the key z corresponding to the z chaotic sequence i+1 The calculation formula of ' is as follows:

[0052] z i+1 '=fix(mod(abs(z i+1 10 6 ),N))+1

[0053] Wherein, fix(·) represents an integer function, mod(·) represents a remainder function, abs(·) represents an absolute value function, and N represents the number of subcarriers of OFDM.

[0054] Step 5.4: According to the key z corresponding to the z chaotic sequence i+1 'Encrypt the time domain signal s to obtain the encrypted 3D-32QAM signal time domain signal S.

[0055] The calculation formula of the encrypted 3D-32QAM signal time domain signal S is as follows:

[0056] S=s·z i+1 '.

[0057] As a preferred solution, the system parameters are a=1, b=0.3, c=20 and the initial value of the three-dimensional chaotic system is x1=y1=z1=0.2.

[0058] In a second aspect, a transmitting end is provided, and the transmitting end is used to execute a high-security probability shaping method based on three-dimensional constellation joint shaping in the first aspect.

[0059] Beneficial effects: The present invention provides a high-security probabilistic shaping method based on three-dimensional constellation joint shaping, which applies the probabilistic shaping scheme based on the bit-level probability update strategy (BCPU-PS) to the three-dimensional constellation after geometric shaping, and realizes probabilistic shaping by modifying the probability distribution of the bits at the transmitting end, thereby avoiding the coding and computational complexity introduced by the traditional probabilistic shaping technology. The joint shaping technology improves the bit error rate performance while increasing the transmission rate of the signal. In addition, in order to prevent the signal from being eavesdropped or tampered with during transmission, the scheme introduces chaotic encryption technology, and uses the key generated by the three-dimensional chaotic system to perform multi-layer encryption on the bits, symbols and time-domain subcarriers at the transmitting end, thereby achieving high-security, large-capacity and high-speed signal transmission.

[0060] Compared with the prior art, the present invention has the following advantages:

[0061] 1. The present invention applies chaotic encryption technology and BCPU-PS technology to three-dimensional constellations.

[0062] 2. BCPU technology only performs probability adjustment in the bit dimension, effectively avoiding the complex calculation process of traditional probability shaping. By expanding the two-dimensional constellation to three dimensions and performing geometric shaping, it effectively improves the utilization of the constellation space and avoids the problem of sudden increase in bit error rate caused by the small spacing between constellation points in high-order modulation.

[0063] 3. In order to ensure the high density of the signal transmission process, the chaotic system is also used to perform multiple encryption operations on the signal, which provides efficient and low-complexity signal transmission while ensuring high security. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a schematic diagram of the process of the present invention.

[0065] Figure 2 For 2D 32QAM and 3D 32QAM constellation diagrams, Figure 2 The middle figure (a) is a 2D 32QAM constellation diagram. Figure 2 The middle figure (b) shows the traditional 3D 32QAM constellation diagram and the GS-3D 32QAM constellation diagram.

[0066] Figure 3 Schematic diagram of the BCPU-PS process in the present invention.

[0067] Figure 4 Schematic diagram of the distribution of 3D 32QAM constellation points after only bit probability shaping and 3D 32QAM constellation points after joint probability shaping. Figure 4 The middle figure (a) is a schematic diagram of the constellation point distribution after PS 3D 32QAM bit probability shaping. Figure 4 The middle figure (b) is a schematic diagram of the constellation point distribution after PS-GS 3D 32QAM bit probability shaping. Figure 4 The middle figure (c) is a schematic diagram of the probability of occurrence of each constellation point.

[0068] Figure 5 Schematic diagram of 3-D HICM cascade mapping, where: Figure 5 The middle figure (a) is the bifurcation diagram corresponding to the system parameter a. Figure 5 The middle figure (b) is the bifurcation diagram corresponding to the system parameter b. Figure 5 The middle figure (c) is the bifurcation diagram corresponding to the system parameter c.

[0069] Figure 6 Encryption diagram for constellations.

[0070] Figure 7 1 is a structural diagram of an experimental device corresponding to the method of the present invention.

[0071] Figure 8 The bit error rate curves of different 3D 32QAM schemes after passing through optical fiber. DETAILED DESCRIPTION

[0072] The following is a clear and complete description of the technical solutions in the examples of the present invention in conjunction with the accompanying drawings in the examples of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the protection scope of the present invention.

[0073] The present invention will be further described below in conjunction with specific embodiments.

[0074] Embodiment 1:

[0075] This embodiment introduces a high-security probability shaping method based on three-dimensional constellation joint shaping. Figure 1As shown, at the transmitting end, a key group is first generated through HICM (Ernon infinite cascade) three-dimensional chaotic mapping, and the first group of keys is selected to encrypt the input bits. The encrypted bits are adjusted through BCPU (based on bit-level probability update strategy) operation to adjust the bit probability. The probability of the bit "1" appearing in the adjusted bit stream will be much greater than the probability of the bit "0" appearing. Then, the adjusted bit stream is mapped to a 3D-32QAM signal that meets the probability shaping requirements through three-dimensional mapping. Then, the second group of keys is selected to perform the second encryption on the constellation after probability shaping. After encryption, the frequency domain signal is converted into a time domain signal through 2D IFFT transformation. Finally, the third group of keys is selected to scramble the time domain subcarriers to complete the third encryption.

[0076] The receiving end follows the reverse operation process of the sending end, gradually demodulates the signal and restores the original information, thereby achieving secure communication transmission.

[0077] Specifically, they include:

[0078] Step 1: Obtain a bit sequence to be transmitted, generate a first set of keys using a three-dimensional chaotic map, encrypt the bit sequence to be transmitted using the first set of keys, and obtain an encrypted bit sequence to be transmitted.

[0079] Step 2: Convert the encrypted bit sequence to be transmitted from serial to parallel and obtain an updated sequence through BCPU operation.

[0080] Step 3: Perform 3D-QPSK constellation mapping on the updated sequence to obtain the constellation points of the 3D-32QAM signal.

[0081] Step 4: Generate a second set of keys using a three-dimensional chaotic map, and encrypt the constellation points of the 3D-32QAM signal using the second set of keys to obtain an encrypted 3D-32QAM signal.

[0082] Step 5: Map the encrypted 3D-32QAM signal to each subcarrier in the OFDM system. After completing the subcarrier mapping, use the inverse frequency domain transform to convert the frequency domain 3D-OFDM signal into a time domain signal. Use the three-dimensional chaotic mapping to generate the third set of keys. Use the third set of keys to encrypt the time domain signal to obtain the encrypted 3D-32QAM signal time domain signal.

[0083] Furthermore, the step 1 specifically includes:

[0084] Step 1.1: Get the bit sequence t to be transmitted.

[0085] Step 1.2: Using the three-dimensional chaotic system, obtain the chaotic sequence x i+1 , where the three-dimensional chaotic system expression is as follows:

[0086]

[0087] Among them, x i+1 represents the chaotic sequence x after the i+1th iteration, y i+1 represents the chaotic sequence y after the i+1th iteration, z i+1 represents the chaotic sequence z after the i+1th iteration. i represents the chaotic sequence x after the i-th iteration, y i represents the chaotic sequence y after the i-th iteration, z i represents the chaotic sequence z after the i-th iteration. a, b, c represent the system parameters.

[0088] Step 1.3: According to the chaotic sequence x i+1 , calculate the key x corresponding to the chaotic sequence x i+1 '.

[0089] Among them, the key x corresponding to the chaotic sequence x i+1 'The calculation formula is as follows:

[0090] x i+1 '=floor(mod(x i+1 10 5 ,2))

[0091] Among them, floor(·) represents the downward integer function, and mod(·) represents the remainder function.

[0092] Step 1.4: According to the key x corresponding to the chaotic sequence x i+1 'Encrypt the bit sequence t to be transmitted to obtain the encrypted bit sequence T to be transmitted.

[0093] The calculation formula of the encrypted bit sequence T to be transmitted is as follows:

[0094] T=XOR(t,x i+1 ')

[0095] Among them, XOR represents the exclusive OR logic operation.

[0096] Furthermore, the step 2 specifically includes:

[0097] Step 2.1: Convert the encrypted bit sequence to be transmitted from serial to parallel to obtain five parallel sequences G1, G2, G3, G4 and G5. The lengths of G1, G2 and G3 are all (3 / 13)M, and the lengths of G4 and G5 are all (2 / 13)M, where M is the length of the encrypted bit sequence to be transmitted.

[0098] Step 2.2: Group the bit streams in groups of k bits each in G4 and add an extra bit EWB (R i ), add an extra bit EWB (H) before each bit group of G5 i ), where EWB(R i ) represents the effective weighted bit of the ith group in G4, EWB(H i ) represents the effective weighted bits of the i-th group in G5, and k is an integer greater than or equal to 2.

[0099] Step 2.3: If the number of "1"s in the bit group of G4 or G5 is less than k / 2, the corresponding EWB (R i ) and EWB(H i ) is set to "1", and the data in the bit group of G4 or G5 is bit-reversed. If the number of "1" in the bit group of G4 or G5 is greater than or equal to k / 2, the corresponding EWB (R i ) and EWB(H i ) is set to "0" and the data bits in the bit group of G4 or G5 remain unchanged.

[0100] Step 2.4: Remove all EWB (R i ) to form the effective weighted bit sequence of G4, and add the effective weighted bit sequence of G4 to the end of G4 to form the shaped G4, and add all EWB (H i ) to form a G5 effective weighted bit sequence, and add the G5 effective weighted bit sequence to the end of G5 to form a shaped G5, and perform parallel to serial (P / S) conversion on G1, G2, G3, the shaped G4 and the shaped G5 to obtain an updated sequence.

[0101] Furthermore, the step 4 specifically includes:

[0102] Step 4.1: Obtain the constellation point q of the 3D-32QAM signal.

[0103] Step 4.2: Using the three-dimensional chaotic system, obtain the chaotic sequence y i+1 , where the three-dimensional chaotic system expression is as follows:

[0104]

[0105] Among them, xi +1 represents the chaotic sequence x after the i+1th iteration, yi +1 represents the chaotic sequence y after the i+1th iteration, z i+1 represents the chaotic sequence z after the i+1th iteration. i represents the chaotic sequence x after the i-th iteration, yi represents the chaotic sequence y after the i-th iteration, z i represents the chaotic sequence z after the i-th iteration. a, b, c represent the system parameters.

[0106] Step 4.3: According to the chaotic sequence y i+1 , calculate the key y corresponding to the chaotic sequence y i+1 '.

[0107] Among them, the key y corresponding to the chaotic sequence y i+1 The calculation formula of ' is as follows:

[0108] y i+1 '=fix(mod(abs(y i+1 10 6 ),N))+1

[0109] Wherein, fix(·) represents an integer function, mod(·) represents a remainder function, abs(·) represents an absolute value function, and N represents the number of subcarriers of OFDM.

[0110] Step 4.4: According to the key y corresponding to the chaotic sequence y i+1 'Encrypt the constellation point q of the 3D-32QAM signal to obtain the encrypted 3D-32QAM signal Q.

[0111] Q=q·y i+1 '

[0112] Wherein, q represents the three-dimensional coordinate matrix of the constellation points of the 3D-32QAM signal, and Q represents the three-dimensional coordinate matrix of the encrypted constellation points.

[0113] Furthermore, the step 5 specifically includes:

[0114] Step 5.1: Map the encrypted 3D-32QAM signal to each subcarrier in the OFDM system. After completing the subcarrier mapping, use the inverse frequency domain transform to convert the frequency domain 3D-OFDM signal into a time domain signal s.

[0115] Step 5.2: Using the three-dimensional chaotic system, obtain the z chaotic sequence z i+1 , where the three-dimensional chaotic system expression is as follows:

[0116]

[0117] Among them, xi +1 represents the chaotic sequence x after the i+1th iteration, yi +1 represents the chaotic sequence y after the i+1th iteration, z i+1 represents the chaotic sequence z after the i+1th iteration. irepresents the chaotic sequence x after the i-th iteration, y i represents the chaotic sequence y after the i-th iteration, z i represents the chaotic sequence z after the i-th iteration. a, b, c represent the system parameters.

[0118] Step 5.3: According to the chaotic sequence z i+1 , calculate the key z corresponding to the z chaotic sequence i+1 '.

[0119] Among them, the key z corresponding to the z chaotic sequence i+1 The calculation formula of ' is as follows:

[0120] z i+1 '=fix(mod(abs(z i+1 10 6 ),N))+1

[0121] Wherein, fix(·) represents an integer function, mod(·) represents a remainder function, abs(·) represents an absolute value function, and N represents the number of subcarriers of OFDM.

[0122] Step 5.4: According to the key z corresponding to the z chaotic sequence i+1 'Encrypt the time domain signal s to obtain the encrypted 3D-32QAM signal time domain signal S.

[0123] The calculation formula of the encrypted 3D-32QAM signal time domain signal S is as follows:

[0124] S=s·z i+1 '.

[0125] Furthermore, the system parameters are a=1, b=0.3, c=20 and the initial value of the three-dimensional chaotic system is x1=y1=z1=0.2.

[0126] Embodiment 2:

[0127] This embodiment introduces a transmitting end, which is used to execute a high-security probability shaping method based on three-dimensional constellation joint shaping in Embodiment 1.

[0128] Embodiment 3:

[0129] This embodiment introduces the working principle of a high-security probability shaping method based on three-dimensional constellation joint shaping. The three-dimensional space utilization rate is significantly improved, which alleviates the problem of reduced Euclidean distance between constellation points under high-order modulation. However, the traditional cubic expansion Figure 2As shown in (a), the constellation points are arranged as two 16QAM structures distributed on both sides of the y axis. This symmetry limits the full utilization of the three-dimensional space. In order to overcome this limitation and maximize the spatial utilization efficiency of the constellation diagram, the present invention proposes a geometrically shaped 3D 32QAM (GS-3D-32QAM) constellation design. The design effectively increases the minimum Euclidean distance between constellation points by redistributing the constellation points so that they extend outward in six different directions in the three-dimensional space.

[0130] To further improve system performance, the BCPU probability shaping technology is combined with the 3D-32QAM constellation after geometric shaping to achieve higher system gain.

[0131] Figure 3 The PS process based on BCPU is shown when the bit grouping is 2. First, the M bits of the serial transmission end are divided into five parallel sequences (G1, G2, G3, G4 and G5). The lengths of G1, G2 and G3 are all (3 / 13)M, and the lengths of G4 and G5 are both (2 / 13)M. Then, G4 and G5 are divided into i groups by bit, and an extra weight bit (EWB) is assigned to each bit group. In the bit weighting decision process, if the number of "1" in the bit group is less than k / 2, the corresponding EWB (Ri) and EWB (Hi) are defined as "1" and the bit inversion of the group is triggered. Otherwise, EWB will be set to "0" and the group bit remains unchanged. As a key step of BCPU-PS, the bit inversion operation is used to amplify the probability of bit "1" in sequences G4 and G5 before 3D-32QAM mapping. After the inversion operation is completed, the data stream of the tag bit will be appended to the end of the corresponding sequence, and then the parallel-to-serial (P / S) conversion will be performed to generate the final data stream. Finally, the data stream after the BCPU-PS operation is modulated into 32QAM-OFDM.

[0132] Figure 4 (a) and (b) show the distribution of 3D 32QAM constellation points after bit probability shaping only and after joint probability shaping, respectively. The probability of "1" in the bit data stream after BCPU-PS is significantly higher than that of "0", so the more "1" the last two bits of the symbol contain, the greater the probability of its occurrence. When mapping the constellation, the symbols with the last two bits of "11" are selectively placed closest to the origin of the coordinates, while the symbols with the last two bits of "00" are placed at the outermost circle of the constellation. Figure 4(c) shows the probability of occurrence of each constellation point after the simulation experiment. The average probability of the last two digits of the symbol "11", "10 / 01" and "00" are 0.070401, 0.023827 and 0.0073457 respectively. The simulation results further verify the probability shaping effect of BCPU and successfully realize the probability shaping of 3D-32QAM constellation.

[0133] The chaotic system used in the present invention is a three-dimensional HICM cascade mapping, which couples the Henon mapping and the ICMIC (one-dimensional infinite folding mapping) mapping, increasing the address space of the chaotic sequence. The complexity of the mapping structure can be increased by cascading. The definition of the three-dimensional HICM cascade mapping is:

[0134]

[0135] Among them, xi +1 represents the chaotic sequence x after the i+1th iteration, yi +1 represents the chaotic sequence y after the i+1th iteration, z i+1 represents the chaotic sequence z after the i+1th iteration. i represents the chaotic sequence x after the i-th iteration, y i represents the chaotic sequence y after the i-th iteration, z i represents the chaotic sequence z after the i-th iteration. a, b, c represent the system parameters.

[0136] Take the system parameters a = 1, b = 0.3, c = 20 and the initial value of the chaotic system x1 = y1 = z1 = 0.2. The bifurcation diagram of the three-dimensional HICM cascade chaotic map is shown in Figure 5 The characteristics of the chaotic dynamic system are directly observed through the bifurcation diagram of the three-dimensional HICM cascade mapping, and it can be seen that the system exhibits extremely complex chaotic behavior.

[0137] The 3D-32QAM signal is encrypted in three layers to improve security. The encryption process proposed by the present invention is as follows: Figure 6 As shown. The encryption system is divided into three layers: bit, constellation and time domain subcarrier. Bit encryption uses MATLAB to randomly generate a bit stream. Then, the bit stream and the key group are encrypted through an XOR operation. The specific process is as follows:

[0138]

[0139] Where floor(·) represents a downward integer function, and mod(·) represents a remainder function. t is the original bit stream to be modulated, and T is the encrypted bit stream. i+1 ' represents the key corresponding to the chaotic sequence x.

[0140] After using 3D-32QAM for signal mapping, the location information of the symbols is disturbed by disrupting their location distribution to achieve encryption of the constellation points. The specific process is as follows:

[0141]

[0142] Where, fix(·) represents an integer function, abs(·) represents an absolute value function. q represents the three-dimensional coordinate matrix of the initial 3D-32QAM, Q represents the encrypted three-dimensional coordinate matrix, and N represents the number of subcarriers of OFDM. i+1 ' represents the key corresponding to the y chaotic sequence.

[0143] After bit and constellation encryption, the 3D-32QAM data enters the OFDM module and is processed by 2D-IFFT to generate a time domain signal. Subsequently, the time domain signal is scrambled using a third set of keys, further enhancing the security of the system. The specific process is as follows:

[0144]

[0145] Where s represents the time domain information matrix of 3D-32QAM, S represents the encrypted time domain matrix, and N represents the number of subcarriers of OFDM. i+1 ' represents the key corresponding to the z chaotic sequence.

[0146] Finally, the encrypted data is sent through parallel-to-serial conversion. At the receiving end, the reverse operation is performed to decrypt the data.

[0147] Figure 7 It is a 3D-PS-PDM transmission system based on intensity modulation-direct detection (IMDD). At the transmitting end, the 3D-PS-PDM signal is first generated by an offline DSP. The signal is encrypted multiple times in bits, symbols, and subcarriers, and then the generated signal is distributed to 240 subcarriers. The 512-point IFFT converts the frequency domain signal into a time domain signal. 240 3D32QAM signals are used, 10 of which are used for channel equalization. A CP with a length of 1 / 16 of the OFDM symbol is added to each symbol as a protection band. Then the digital-to-analog conversion is completed through an arbitrary waveform generator, and the generated electrical signal is amplified by an electrical amplifier and injected into a Mach-Zehnder modulator for photoelectric modulation, and then optically amplified by an erbium-doped fiber amplifier. After being transmitted in a 25km single-mode optical fiber, the signal is distributed to the legal receiving end and the illegal receiving end through a power divider. A variable optical attenuator is set in front of each receiving end to adjust the signal attenuation to adapt to different transmission conditions. The received optical signal is converted into an electrical signal by a photodetector and captured using a mixed signal oscilloscope with a sampling rate of 50GSa / s. Finally, it is decrypted with the corresponding key in the offline DSP to complete the demodulation of 3D-PS-PDM.

[0148] Figure 8 The comparison results of the bit error rate of the 3D 32QAM scheme with only probability shaping (PS32QAM), the 3D 32QAM scheme with only geometric shaping (GS 32QAM), and the 3D 32QAM scheme with joint shaping (GS_PS 32QAM) of the present invention under different optical power conditions are shown. The results show that the 3D32QAM scheme with joint shaping performs best in bit error rate performance. When the bit error rate is 3.8×10-3, the 3D 32QAM scheme with joint shaping achieves a gain of about 0.7dB compared with the 3D 32QAM scheme with only geometric shaping, and achieves a gain of about 1dB compared with the 3D 32QAM scheme with only probability shaping. This further verifies that the joint shaping technology combining geometric shaping with probability shaping can significantly improve the performance gain of the system.

[0149] The present invention first designs a high-security probability shaping method based on three-dimensional constellation joint shaping. First, the chaotic system is driven to generate a chaotic sequence, and the sequence is processed accordingly to obtain the required key. A set of keys are selected to scramble and encrypt the bit stream. The encrypted data stream is subjected to bit stream probability adjustment by the BCPU so that the distribution of bits "1" and "0" meets the expected probability shaping requirements. Subsequently, three-dimensional mapping is performed according to the 3D-32QAM constellation diagram after geometric shaping. Next, the shaped signal is symbol encrypted and subcarrier encrypted in turn to further enhance the confidentiality of the data. At the receiving end, by performing the inverse operation corresponding to the transmitting end, the original signal is gradually decrypted and restored to ensure the integrity and secure transmission of the signal.

[0150] Traditional PS schemes often introduce high complexity in terms of computation, hardware requirements, and overall system power consumption during encoding and decoding, especially when expanding two-dimensional space to three dimensions. To address this problem, this patent proposes a three-dimensional space probability shaping scheme based on BCPU, combined with geometric shaping and constellation point encryption technology. This technology breaks through the limitations of data structure and allows flexible combinations of bits. Probabilistic shaping is achieved by modifying the probability distribution of the bits at the transmitting end, and this process does not involve higher-level symbols or signal amplitudes. The final output is a set of bits converted from the input data source, which can be seamlessly integrated into the subsequent bit-level processing flow, thereby avoiding the coding and computational complexity introduced by traditional probability shaping technology.

[0151] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A high-security probability shaping method based on three-dimensional constellation joint shaping, characterized by: Specifically include: Step 1: Obtain a bit sequence to be transmitted, generate a first set of keys using a three-dimensional chaotic map, encrypt the bit sequence to be transmitted using the first set of keys, and obtain an encrypted bit sequence to be transmitted; Step 2: Convert the encrypted bit sequence to be transmitted from serial to parallel and obtain an updated sequence through BCPU operation; Step 3: Perform 3D-QPSK constellation mapping on the updated sequence to obtain the constellation points of the 3D-32QAM signal; Step 4: Generate a second set of keys using a three-dimensional chaotic map, and encrypt the constellation points of the 3D-32QAM signal using the second set of keys to obtain an encrypted 3D-32QAM signal; Step 5: Map the encrypted 3D-32QAM signal to each subcarrier in the OFDM system. After completing the subcarrier mapping, use the inverse frequency domain transform to convert the frequency domain 3D-OFDM signal into a time domain signal. Use the three-dimensional chaotic mapping to generate the third set of keys. Use the third set of keys to encrypt the time domain signal to obtain the encrypted 3D-32QAM signal time domain signal.

2. The high-security probability shaping method based on three-dimensional constellation joint shaping according to claim 1 is characterized in that: The step 1 specifically includes: Step 1.1: Obtain the bit sequence t to be transmitted; Step 1.2: Using the three-dimensional chaotic system, obtain the chaotic sequence x i+1 , where the three-dimensional chaotic system expression is as follows: Among them, x i+1 represents the chaotic sequence x after the i+1th iteration, y i+1 represents the chaotic sequence y after the i+1th iteration, z i+1 represents the chaotic sequence z after the i+1th iteration; x i represents the chaotic sequence x after the i-th iteration, y i represents the chaotic sequence y after the i-th iteration, z i represents the z chaotic sequence after the i-th iteration; a, b, c represent system parameters; Step 1.3: According to the chaotic sequence x i+1 , calculate the key x corresponding to the chaotic sequence x i+1 '; Among them, the key x corresponding to the chaotic sequence x i+1 'The calculation formula is as follows: x i+1 '=floor(mod(x i+1 ·10 5 ,2)) Among them, floor(·) represents the downward integer function, mod(·) represents the remainder function; Step 1.4: According to the key x corresponding to the chaotic sequence x i+1 'Encrypt the bit sequence t to be transmitted to obtain the encrypted bit sequence T to be transmitted; The calculation formula of the encrypted bit sequence T to be transmitted is as follows: T=XOR(t,x i+1 ') Among them, XOR represents an exclusive OR logic operation.

3. The high-security probability shaping method based on three-dimensional constellation joint shaping according to claim 1 is characterized in that: The step 2 specifically includes: Step 2.1: Convert the encrypted bit sequence to be transmitted from serial to parallel to obtain five parallel sequences G1, G2, G3, G4 and G5; wherein the lengths of G1, G2 and G3 are all (3 / 13)M, the lengths of G4 and G5 are both (2 / 13)M, and M is the length of the encrypted bit sequence to be transmitted; Step 2.2: Group the bit streams in groups of k bits each in G4 and add an extra bit EWB (R i ), add an extra bit EWB (H) before each bit group of G5 i ), where EWB(R i ) represents the effective weighted bit of the ith group in G4, EWB(H i ) represents the effective weighted position of the ith group in G5, and k is an integer greater than or equal to 2; Step 2.3: If the number of "1"s in the bit group of G4 or G5 is less than k / 2, the corresponding EWB (R i ) and EWB(H i ) is set to "1", and the data in the bit group of G4 or G5 is bit-reversed; if the number of "1" in the bit group of G4 or G5 is greater than or equal to k / 2, the corresponding EWB (R i ) and EWB(H i ) is set to "0", and the data bits in the bit group of G4 or G5 remain unchanged; Step 2.4: Remove all EWB (R i ) to form the effective weighted bit sequence of G4, and add the effective weighted bit sequence of G4 to the end of G4 to form the shaped G4, and add all EWB (H i ) to form a G5 effective weighted bit sequence, and add the G5 effective weighted bit sequence to the end of G5 to form a shaped G5, and perform parallel to serial (P / S) conversion on G1, G2, G3, the shaped G4 and the shaped G5 to obtain an updated sequence.

4. The high-security probability shaping method based on three-dimensional constellation joint shaping according to claim 1 is characterized in that: The step 4 specifically includes: Step 4.1: Obtain the constellation point q of the 3D-32QAM signal; Step 4.2: Using the three-dimensional chaotic system, obtain the chaotic sequence y i+1 , where the three-dimensional chaotic system expression is as follows: Among them, xi +1 represents the chaotic sequence x after the i+1th iteration, yi +1 represents the chaotic sequence y after the i+1th iteration, z i+1 represents the chaotic sequence z after the i+1th iteration; x i represents the chaotic sequence x after the i-th iteration, y i represents the chaotic sequence y after the i-th iteration, z i represents the z chaotic sequence after the i-th iteration; a, b, c represent system parameters; Step 4.3: According to the chaotic sequence y i+1 , calculate the key y corresponding to the chaotic sequence y i+1 '; Among them, the key y corresponding to the chaotic sequence y i+1 The calculation formula of ' is as follows: y i+1 '=fix(mod(abs(y i+1 ·10 6 ),N))+1 Where, fix(·) represents an integer function, mod(·) represents a remainder function, abs(·) represents an absolute value function, and N represents the number of subcarriers of OFDM. Step 4.4: According to the key y corresponding to the chaotic sequence y i+1 'Encrypt the constellation point q of the 3D-32QAM signal to obtain the encrypted 3D-32QAM signal Q; Q=q·y i+1 ' Wherein, q represents the three-dimensional coordinate matrix of the constellation points of the 3D-32QAM signal, and Q represents the three-dimensional coordinate matrix of the encrypted constellation points.

5. The high-security probability shaping method based on three-dimensional constellation joint shaping according to claim 1 is characterized in that: The step 5 specifically includes: Step 5.1: Map the encrypted 3D-32QAM signal to each subcarrier in the OFDM system. After completing the subcarrier mapping, use the inverse frequency domain transform to convert the frequency domain 3D-OFDM signal into a time domain signal s; Step 5.2: Using the three-dimensional chaotic system, obtain the z chaotic sequence z i+1 , where the three-dimensional chaotic system expression is as follows: Among them, xi +1 represents the chaotic sequence x after the i+1th iteration, yi +1 represents the chaotic sequence y after the i+1th iteration, z i+1 represents the chaotic sequence z after the i+1th iteration; x i represents the chaotic sequence x after the i-th iteration, y i represents the chaotic sequence y after the i-th iteration, z i represents the z chaotic sequence after the i-th iteration; a, b, c represent system parameters; Step 5.3: According to the chaotic sequence z i+1 , calculate the key z corresponding to the z chaotic sequence i+1 '; Among them, the key z corresponding to the z chaotic sequence i+1 The calculation formula of ' is as follows: z i+1 '=fix(mod(abs(z i+1 ·10 6 ),N))+1 Where, fix(·) represents an integer function, mod(·) represents a remainder function, abs(·) represents an absolute value function, and N represents the number of subcarriers of OFDM. Step 5.4: According to the key z corresponding to the z chaotic sequence i+1 'Encrypt the time domain signal s to obtain an encrypted 3D-32QAM signal time domain signal S; The calculation formula of the encrypted 3D-32QAM signal time domain signal S is as follows: S=s·z i+1 '。 6. A high-security probability shaping method based on three-dimensional constellation joint shaping according to any one of claims 2, 4 or 5, characterized in that: The system parameters are a=1, b=0.3, c=20 and the initial value of the three-dimensional chaotic system is x1=y1=z1=0.

2.

7. A transmitting end, characterized in that: The transmitting end is used to execute a high-security probability shaping method based on three-dimensional constellation joint shaping in claims 1 to 6.

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