A high-security-probability shaping method based on three-dimensional constellation joint shaping

Abstract

The application discloses a high-security-probability shaping method based on three-dimensional constellation joint shaping, applies a probability shaping (BCPU-PS) scheme based on a bit-level probability updating strategy to a three-dimensional constellation after geometric shaping, realizes probability shaping by modifying the probability distribution of bit positions of a sending end, and avoids coding and calculation complexity introduced by traditional probability shaping technology. The joint shaping technology improves the transmission rate of a signal and improves the bit error rate performance. In addition, in order to prevent the signal from being eavesdropped or tampered with during transmission, the scheme introduces a chaotic encryption technology, uses a key generated by a three-dimensional chaotic system to perform multi-layer encryption on bits, symbols and time domain subcarriers of the sending end, and thus realizes high security, large capacity and high rate signal transmission.

Description

Technical Field

[0001] This invention relates to a high-security probabilistic shaping method based on three-dimensional constellation joint shaping, belonging to the field of optical communication technology. Background Technology

[0002] In recent years, with the rapid digitalization of society, global data traffic has increased dramatically. Technologies such as 6G, blockchain, and the Internet of Things are incorporating more and more devices into data networks, constantly expanding the boundaries of networks. This means that socio-economic development will place higher demands on the bandwidth and coverage of existing communication networks. Orthogonal Frequency Division Multiplexing (OFDM) has been widely studied due to its high spectral efficiency. OFDM can be implemented through Inverse Fast Fourier Transform (IFFT), and 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 most serious 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 are nearly synchronized at a certain moment, the signal power at that moment will be much higher than the average value, resulting in a high PAPR. A 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] To alleviate this problem, numerous scholars have conducted active research, which, from a technical principle perspective, mainly falls into three categories: amplitude limiting techniques, coding techniques, and constellation expansion techniques. Amplitude limiting techniques restrict the amplitude of signal samples to a fixed value to achieve PAPR suppression, but inevitably introduce additional noise, leading to an increased bit error rate. Coding techniques avoid high peak signals by selecting codewords with low PAPR; however, their encoding and decoding complexity increases rapidly as the modulation order increases. Constellation expansion techniques reduce PAPR by changing the positions of constellation points. Compared to the previous two techniques, constellation expansion not only avoids signal distortion but also effectively reduces PAPR while maintaining relatively low complexity.

[0004] While 3D OFDM can effectively improve system transmission performance, further improvements in transmission rates are still needed to address the rapid development of future communication technologies and ever-changing application demands. This is especially true for 6G communication, where increasing transmission rates is of paramount importance.

[0005] Meanwhile, with the increasing speed of optical network transmission, security issues have become more prominent. High-speed data transmission causes large amounts of sensitive information to flow rapidly within the network, increasing the risk of data interception, tampering, and other malicious attacks. Therefore, encrypting optical network signals is particularly important. Currently, the main encryption methods include: Advanced Encryption Standards (AES), RSA encryption, digital authentication, quantum security technology, and physical layer chaotic encryption. However, traditional upper-layer encryption technologies often expose header information during transmission, leading to a decrease in the security of encrypted information.

[0006] Therefore, those skilled in the art urgently need to solve the problem of how to achieve more secure and efficient signal transmission in existing optical communications. Summary of the Invention

[0007] Objective: To overcome the high complexity introduced by traditional PS schemes in the encoding and decoding processes, particularly in terms of computation, hardware requirements, and overall system power consumption, especially when extending two-dimensional space to three dimensions, and to address the vulnerability of signals to eavesdropping or tampering during transmission, this invention provides a high-security probabilistic 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 as follows:

[0009] Firstly, a high-probability shaping method based on three-dimensional constellation joint shaping specifically includes:

[0010] Step 1: Obtain the bit sequence to be transmitted, generate the first key using three-dimensional chaotic mapping, and encrypt the bit sequence to be transmitted using the first key to obtain the encrypted bit sequence to be transmitted.

[0011] Step 2: Convert the encrypted bit sequence to be transmitted from serial to parallel, and obtain the 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 three-dimensional chaotic mapping, and encrypt the constellation points of the 3D-32QAM signal using the second set of keys to obtain the encrypted 3D-32QAM signal.

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

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

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

[0017] Step 1.2: Obtain the chaotic sequence x using a three-dimensional chaotic system. i+1 The expression for the three-dimensional chaotic system is as follows:

[0018]

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

[0020] Step 1.3: Based on the chaotic sequence x... i+1 Calculate the key x corresponding to the chaotic sequence x. i+1 '.

[0021] Wherein, 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] Here, floor(·) represents the integer function downwards, and mod(·) represents the remainder function.

[0024] Step 1.4: Based on 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 formula for calculating the encrypted bit sequence T to be transmitted is as follows:

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

[0027] XOR stands for Exclusive OR logical operation.

[0028] As a preferred embodiment, 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. Among them, the length of G1, G2 and G3 is (3 / 13)M, and the length of G4 and G5 is (2 / 13)M, where M is the length of the encrypted bit sequence to be transmitted.

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

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

[0032] Step 2.4: Combine all EWB(R) in G4 i The effective weighted bit sequence of G4 is formed by adding the effective weighted bit sequence of G4 to the end of G4 to form an integer G4. All EWB(H) in G5 are then processed. i The effective weighted bit sequence of G5 is formed by adding the effective weighted bit sequence of G5 to the end of G5 to form the shaped G5. G1, G2, G3, the shaped G4 and the shaped G5 are then converted from parallel to serial (P / S) to obtain the updated sequence.

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

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

[0035] Step 4.2: Obtain the chaotic sequence y using a three-dimensional chaotic system. i+1 The expression for the three-dimensional chaotic system is as follows:

[0036]

[0037] Where, x i+1 Let x represent the chaotic sequence after the (i+1)th iteration, and y represent the chaotic sequence after the (i+1)th i+1 Let y represent the chaotic sequence after the (i+1)th iteration, and z represent the chaotic sequence of y. i+1 Let x represent the chaotic sequence z after the (i+1)th iteration. i Let x represent the chaotic sequence after the i-th iteration, and y represent the chaotic sequence after the i-th iteration. i Let y represent the chaotic sequence after the i-th iteration, and z represent the chaotic sequence after the i-th iteration. i Let z represent the chaotic sequence after the i-th iteration. a, b, and c represent system parameters.

[0038] Step 4.3: Based on the chaotic sequence y... i+1 Calculate the key y corresponding to the chaotic sequence y. i+1 '.

[0039] Wherein, the key y corresponds to the chaotic sequence y. i+1 The formula for calculating ' is as follows:

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

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

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

[0043] Q = q·y i+1 '

[0044] Where 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 embodiment, step 5 specifically includes:

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

[0047] Step 5.2: Obtain the chaotic sequence z using a three-dimensional chaotic system. i+1 The expression for the three-dimensional chaotic system is as follows:

[0048]

[0049] Where, x i+1 Let x represent the chaotic sequence after the (i+1)th iteration, and y represent the chaotic sequence after the (i+1)th i+1 Let y represent the chaotic sequence after the (i+1)th iteration, and z represent the chaotic sequence of y. i+1 Let x represent the chaotic sequence z after the (i+1)th iteration. i Let x represent the chaotic sequence after the i-th iteration, and y represent the chaotic sequence after the i-th iteration. i Let y represent the chaotic sequence after the i-th iteration, and z represent the chaotic sequence after the i-th iteration. i Let z represent the chaotic sequence after the i-th iteration. a, b, and c represent system parameters.

[0050] Step 5.3: Based on the chaotic sequence z i+1 Calculate the key z corresponding to the chaotic sequence z. i+1 '.

[0051] Wherein, the key z corresponding to the z chaotic sequence i+1 The formula for calculating ' is as follows:

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

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

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

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

[0056] S = s·z i+1 '.

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

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

[0059] Beneficial Effects: This invention provides a high-security probabilistic shaping method based on joint shaping of a three-dimensional constellation. It applies a bit-level probability update strategy-based probabilistic shaping (BCPU-PS) scheme to a geometrically shaped three-dimensional constellation. Probabilistic shaping is achieved by modifying the probability distribution of bits at the transmitting end, avoiding the coding and computational complexity introduced by traditional probabilistic shaping techniques. The joint shaping technique improves both the signal transmission rate and bit error rate performance. Furthermore, to prevent eavesdropping or tampering during transmission, the scheme introduces chaotic encryption technology. Using a key generated by a three-dimensional chaotic system, multiple layers of encryption are applied to the bits, symbols, and time-domain subcarriers at the transmitting end, thereby achieving high-security, high-capacity, and high-speed signal transmission.

[0060] Compared with existing technologies, the advantages of this invention are as follows:

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

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

[0063] 3. To ensure high security during signal transmission, a chaotic system is used to perform multiple encryption operations on the signal, providing efficient and low-complexity signal transmission while ensuring high security. Attached Figure Description

[0064] Figure 1 This is a flowchart illustrating the method of the present invention.

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

[0066] Figure 3 This is a schematic diagram of the BCPU-PS process in this invention.

[0067] Figure 4 This diagram illustrates the constellation point distribution of 3D 32QAM after bit-level probability shaping and after joint probability shaping. Figure 4 Figure (a) in the middle is a schematic diagram of the constellation point distribution after PS 3D 32QAM bit probability shaping. Figure 4 Figure (b) in the middle 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 each constellation point appearing.

[0068] Figure 5 This is a schematic diagram of a 3-D HICM cascade mapping, where, Figure 5 Figure (a) shows the bifurcation diagram corresponding to system parameter a. Figure 5 Figure (b) shows the bifurcation diagram corresponding to system parameter b. Figure 5 Figure (c) shows the bifurcation diagram corresponding to system parameter c.

[0069] Figure 6 An illustration of the constellation encryption.

[0070] Figure 7 This is a structural diagram of the experimental apparatus corresponding to the method of the present invention.

[0071] Figure 8 Bit error rate curves for different 3D 32QAM schemes after passing through optical fiber. Detailed Implementation

[0072] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0073] The present invention will be further described below with reference to specific embodiments.

[0074] Example 1:

[0075] This embodiment introduces a high-security probability shaping method based on three-dimensional constellation joint shaping, such as... Figure 1As shown, at the transmitting end, a key set is first generated using HICM (Hernon Infinite Concatenation) three-dimensional chaotic mapping. The first key set is selected to encrypt the input bits. The encrypted bits are then processed by BCPU (Bit-Level Probability Update Strategy) to adjust the bit probability, resulting in a bit "1" with a much higher probability of "0" in the adjusted bitstream. The adjusted bitstream is then mapped to a 3D-32QAM signal that meets the probability shaping requirements using three-dimensional mapping. Next, a second key set is selected to perform a second layer of encryption on the probability-shaped constellation. After encryption, the frequency domain signal is converted to a time domain signal using 2D IFFT transformation. Finally, a third key set is selected to scramble the time-domain subcarriers, completing the third layer of encryption.

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

[0077] Specifically, this includes:

[0078] Step 1: Obtain the bit sequence to be transmitted, generate the first key using three-dimensional chaotic mapping, and encrypt the bit sequence to be transmitted using the first key to obtain the encrypted bit sequence to be transmitted.

[0079] Step 2: Convert the encrypted bit sequence to be transmitted from serial to parallel, and obtain the 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 three-dimensional chaotic mapping, and encrypt the constellation points of the 3D-32QAM signal using the second set of keys to obtain the encrypted 3D-32QAM signal.

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

[0083] Furthermore, step 1 specifically includes:

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

[0085] Step 1.2: Obtain the chaotic sequence x using a three-dimensional chaotic system. i+1 The expression for the three-dimensional chaotic system is as follows:

[0086]

[0087] Where, x i+1 Let x represent the chaotic sequence after the (i+1)th iteration, and y represent the chaotic sequence after the (i+1)th i+1 Let y represent the chaotic sequence after the (i+1)th iteration, and z represent the chaotic sequence of y. i+1 Let x represent the chaotic sequence z after the (i+1)th iteration. i Let x represent the chaotic sequence after the i-th iteration, and y represent the chaotic sequence after the i-th iteration. i Let y represent the chaotic sequence after the i-th iteration, and z represent the chaotic sequence after the i-th iteration. i Let z represent the chaotic sequence after the i-th iteration. a, b, and c represent system parameters.

[0088] Step 1.3: Based on the chaotic sequence x... i+1 Calculate the key x corresponding to the chaotic sequence x. i+1 '.

[0089] Wherein, 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] Here, floor(·) represents the integer function downwards, and mod(·) represents the remainder function.

[0092] Step 1.4: Based on 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 formula for calculating the encrypted bit sequence T to be transmitted is as follows:

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

[0095] XOR stands for Exclusive OR logical operation.

[0096] Furthermore, 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. Among them, the length of G1, G2 and G3 is (3 / 13)M, and the length of G4 and G5 is (2 / 13)M, where M is the length of the encrypted bit sequence to be transmitted.

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

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

[0100] Step 2.4: Combine all EWB(R) in G4 i The effective weighted bit sequence of G4 is formed by adding the effective weighted bit sequence of G4 to the end of G4 to form an integer G4. All EWB(H) in G5 are then processed. i The effective weighted bit sequence of G5 is formed by adding the effective weighted bit sequence of G5 to the end of G5 to form the shaped G5. G1, G2, G3, the shaped G4 and the shaped G5 are then converted from parallel to serial (P / S) to obtain the updated sequence.

[0101] Furthermore, step 4 specifically includes:

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

[0103] Step 4.2: Obtain the chaotic sequence y using a three-dimensional chaotic system. i+1 The expression for the three-dimensional chaotic system is as follows:

[0104]

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

[0106] Step 4.3: Based on the chaotic sequence y... i+1 Calculate the key y corresponding to the chaotic sequence y. i+1 '.

[0107] Wherein, the key y corresponds to the chaotic sequence y. i+1 The formula for calculating ' is as follows:

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

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

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

[0111] Q = q·y i+1 '

[0112] Where 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, step 5 specifically includes:

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

[0115] Step 5.2: Obtain the chaotic sequence z using a three-dimensional chaotic system. i+1 The expression for the three-dimensional chaotic system is as follows:

[0116]

[0117] Among them, xi +1 Let yi represent the chaotic sequence x after the (i+1)th iteration. +1 Let y represent the chaotic sequence after the (i+1)th iteration, and z represent the chaotic sequence of y. i+1 Let x represent the chaotic sequence z after the (i+1)th iteration. iLet x represent the chaotic sequence after the i-th iteration, and y represent the chaotic sequence after the i-th iteration. i Let y represent the chaotic sequence after the i-th iteration, and z represent the chaotic sequence after the i-th iteration. i Let z represent the chaotic sequence after the i-th iteration. a, b, and c represent system parameters.

[0118] Step 5.3: Based on the chaotic sequence z i+1 Calculate the key z corresponding to the chaotic sequence z. i+1 '.

[0119] Wherein, the key z corresponding to the z chaotic sequence i+1 The formula for calculating ' is as follows:

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

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

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

[0123] The formula for calculating the time-domain signal S of the encrypted 3D-32QAM signal 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 values ​​of the three-dimensional chaotic system are x1 = y1 = z1 = 0.2.

[0126] Example 2:

[0127] This embodiment introduces a transmitter used to execute a high-security probability shaping method based on three-dimensional constellation joint shaping as described in Embodiment 1.

[0128] Example 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 method significantly improves space utilization and alleviates the problem of reduced Euclidean distance between constellation points under higher-order modulation. However, traditional cubic expansion methods, such as... Figure 2As shown in (a), the constellation points are arranged in two 16QAM structures distributed on both sides of the y-axis. This symmetry limits the full utilization of three-dimensional space. To overcome this limitation and maximize the spatial utilization efficiency of the constellation diagram, this invention proposes a geometrically shaped 3D 32QAM (GS-3D-32QAM) constellation design. This 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 three-dimensional space.

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

[0131] Figure 3 The demonstrated bit-blocking PS process based on BCPU is as follows: First, the M-bit serial data from the transmitting end is divided into five parallel sequences (G1, G2, G3, G4, and G5). G1, G2, and G3 are all (3 / 13)M in length, while G4 and G5 are both (2 / 13)M in length. Next, G4 and G5 are divided into i groups, and each group is assigned an extra weighting bit (EWB). During the bit weighting decision process, if the number of "1"s in a group is less than k / 2, the corresponding EWB(Ri) and EWB(Hi) are defined as "1", triggering a bit inversion for that group. Otherwise, the EWB is set to "0", and the group bits remain unchanged. As a key step in BCPU-PS, the bit inversion operation amplifies the probability of "1" bits in sequences G4 and G5 before 3D-32QAM mapping. After the inversion operation, the data stream of the tag bits is appended to the end of the corresponding sequence, followed by a parallel-to-serial (P / S) conversion to generate the final data stream. Finally, the data stream after BCPU-PS operation is modulated into 32QAM-OFDM.

[0132] Figure 4 Figures (a) and (b) show the constellation point distribution of 3D 32QAM after bit-level probability shaping and after joint probability shaping, respectively. In the bit data stream after BCPU-PS, the probability of "1" appearing is significantly higher than "0". Therefore, the more "1"s in the last two bits of a symbol, the greater its probability of occurrence. During constellation mapping, symbols with the last two bits being "11" are selectively placed closest to the origin, while symbols with the last two bits being "00" are placed on the outermost edge of the constellation. Figure 4(c) shows the probability of each constellation point appearing after the simulation experiment. The average probability of the last two digits of the symbol being "11", "10 / 01", and "00" is 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 constellations.

[0133] The chaotic system employed in this invention is a three-dimensional HICM cascaded mapping, which couples the Henon map and the ICMIC (one-dimensional infinite folding map) map, increasing the address space of the chaotic sequence. Cascading increases the complexity of the mapping structure. The definition of the three-dimensional HICM cascaded mapping is:

[0134]

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

[0136] The system parameters are set to a = 1, b = 0.3, c = 20, and the initial values ​​of the chaotic system are x1 = y1 = z1 = 0.2. The bifurcation diagram of the three-dimensional HICM cascaded chaotic map is shown below. Figure 5 As shown, the characteristics of the chaotic dynamical system were directly observed through the bifurcation diagram of the three-dimensional HICM cascade mapping, revealing that the system exhibits extremely complex chaotic behavior.

[0137] To enhance security, the 3D-32QAM signal is encrypted using a three-layer encryption method. The encryption process proposed in this invention is as follows: Figure 6 As shown. The encryption system consists of three layers: bits, constellation, and time-domain subcarriers. Bit encryption uses MATLAB to randomly generate a bitstream. Then, the bitstream and the key group are encrypted using an XOR operation. The specific process is as follows:

[0138]

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

[0140] After signal mapping using 3D-32QAM, the positional information of the constellation points is interfered with by scrambling the symbol distribution, thus achieving encryption of the constellation points. The specific process is as follows:

[0141]

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

[0143] After bit and constellation encryption, the 3D-32QAM data enters the OFDM module and undergoes 2D-IFFT processing to generate a time-domain signal. Subsequently, a third key is used to scramble the time-domain signal, further enhancing system security. 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 in OFDM. i+1 ' represents the key corresponding to the z-chaotic sequence.

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

[0147] Figure 7 This is a 3D-PS-PDM transmission system based on Intensity Modulation-Direct Detection (IMDD). At the transmitter, the 3D-PS-PDM signal is first generated by an offline DSP. This signal undergoes multiple encryption at the bit, symbol, and subcarrier levels. The generated signal is then distributed to 240 subcarriers, and a 512-point IFFT converts the frequency domain signal to a time domain signal. 240 3D32QAM signals are used, with 10 used for channel equalization. A CP of 1 / 16th the length of an OFDM symbol is added as a guard band to each symbol. Then, an arbitrary waveform generator performs digital-to-analog conversion, and the resulting electrical signal is amplified by an electrical amplifier and injected into a Mach-Zehnder modulator for opto-modulation. It is then optically amplified by an erbium-doped fiber amplifier. After transmission through 25km of single-mode fiber, the signal is distributed to legitimate and illegitimate receivers by a power divider. Each receiver is preceded by a variable optical attenuator to adjust 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 50 GSa / s. Finally, the demodulation of 3D-PS-PDM is completed in an offline DSP using the corresponding key.

[0148] Figure 8 This paper presents a comparison of the bit error rate (BER) as a function of received optical power for three 3D 32QAM schemes: probability-only shaping (PS32QAM), geometry-only shaping (GS32QAM), and the combined shaping 3D 32QAM scheme of this invention (GS_PS 32QAM), under different optical power conditions. The results show that the combined shaping 3D32QAM scheme exhibits the best BER performance. At a BER of 3.8 × 10⁻³, the combined shaping 3D 32QAM scheme achieves a gain of approximately 0.7 dB compared to the geometry-only shaping scheme, and approximately 1 dB compared to the probability-only shaping scheme. This further verifies that the combined shaping technique, integrating geometry and probability shaping, can significantly improve system performance.

[0149] This invention first designs a high-security probabilistic shaping method based on three-dimensional constellation joint shaping. First, a chaotic system is driven to generate a chaotic sequence, which is then processed to obtain the required key. A set of keys is selected to scramble and encrypt the bitstream. The encrypted data stream undergoes bitstream probability adjustment via a BCPU, ensuring the distribution of bits "1" and "0" conforms to the expected probabilistic shaping requirements. Subsequently, a three-dimensional mapping is performed based on the geometrically shaped 3D-32QAM constellation diagram. Next, the shaped signal undergoes symbol encryption and subcarrier encryption sequentially to further enhance data confidentiality. At the receiving end, the original signal is decrypted and recovered step by step by performing the inverse operation corresponding to the transmitting end, ensuring signal integrity and secure transmission.

[0150] Traditional PS (Probabilistic Signal Shaping) schemes often introduce significant complexity in terms of computation, hardware requirements, and overall system power consumption during encoding and decoding, especially when extending two-dimensional space to three dimensions, where this complexity increases further. To address this issue, this patent proposes a three-dimensional spatial probabilistic shaping scheme based on a BCPU, combined with geometric shaping and constellation point encryption techniques. This technology overcomes the limitations of data structures, allowing for flexible bit combinations. Probabilistic shaping is achieved by modifying the probability distribution of bits at the transmitting end, a process that does not involve higher-level symbol or signal amplitude. The final output is a set of bits converted from the input data source, which can be seamlessly integrated into subsequent bit-level processing flows, thus avoiding the encoding and computational complexity introduced by traditional probabilistic shaping techniques.

[0151] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A high security probability shaping method based on three-dimensional constellation joint shaping, characterized in that: Specifically comprising: Step 1: obtaining a bit sequence to be transmitted, generating a first group of keys by using a three-dimensional chaotic mapping, encrypting the bit sequence to be transmitted by using the first group of keys, and obtaining an encrypted bit sequence to be transmitted; Step 2: performing serial-to-parallel conversion on the encrypted bit sequence to be transmitted, and obtaining an updated sequence by using a BCPU operation; Step 3: performing 3D-QPSK constellation mapping on the updated sequence, and obtaining a 3D-32QAM signal constellation point; Step 4: generating a second group of keys by using a three-dimensional chaotic mapping, encrypting the 3D-32QAM signal constellation point by using the second group of keys, and obtaining an encrypted 3D-32QAM signal; Step 5: mapping the encrypted 3D-32QAM signal to each subcarrier in an OFDM system, converting the frequency domain 3D-OFDM signal into a time domain signal after completing subcarrier mapping, generating a third group of keys by using a three-dimensional chaotic mapping, encrypting the time domain signal by using the third group of keys, and obtaining an 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, characterized in that: The step 1 specifically comprises: Step 1.1: obtaining a bit sequence to be transmitted t; Step 1.2: Obtain x chaotic sequence x by using a three-dimensional chaotic system i+1 wherein the three-dimensional chaotic system is expressed as follows: wherein x i+1 represents the x chaotic sequence after the i+1th iteration, y i+1 represents the y chaotic sequence after the i+1th iteration, z i+1 represents the z chaotic sequence after the i+1th iteration; x i represents the x chaotic sequence after the ith iteration, y i represents the y chaotic sequence after the ith iteration, z i represents the z chaotic sequence after the ith iteration; a, b, c represent system parameters; Step 1.3: Calculate the key x corresponding to the x chaotic sequence according to x chaotic sequence x i+1 i+1 ';​ wherein the x chaotic sequence corresponds to a key x i+1 The calculation formula is as follows: x i+1 ' = floor(mod(x i+1 · 10 5 , 2)) Wherein, floor(·) represents a down integer function, and mod(·) represents a remainder function; Step 1.4: encrypt the bit sequence t to be transmitted according to the key x corresponding to the x chaotic sequence i+1 encrypt the bit sequence t to be transmitted to obtain the encrypted bit sequence T to be transmitted; Wherein, the encrypted bit sequence to be transmitted T is calculated according to the following formula: T = XOR(t, x i+1 ') Wherein, XOR represents an exclusive or logical operation.

3. The high security probability shaping method based on three-dimensional constellation joint shaping according to claim 1, characterized in that: The step 2 specifically comprises: Step 2.1: performing serial-to-parallel conversion on the encrypted bit sequence to be transmitted, and obtaining 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: Grouping the bit stream in the way of k bits per group, adding an extra bit EWB(R i ) before each bit group of G4, adding an extra bit EWB(H i ) before each bit group of G5, where EWB(R i ) represents the effective weighting bit of the i-th group in G4, EWB(H i ) represents the effective weighting bit of the i-th 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 ) are set to "1", and the data in the bit group of G4 or G5 is bit-inverted; if the number of "1"s 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 ) are set to "0", and the data bits in the bit group of G4 or G5 are kept unchanged; Step 2.4: form a G4 effective weighted bit sequence with all EWB(R i ) in G4, and append the G4 effective weighted bit sequence to the end of G4 to form a reshaped G4, form a G5 effective weighted bit sequence with all EWB(H i ) in G5, and append the G5 effective weighted bit sequence to the end of G5 to form a reshaped G5, perform parallel-to-serial (P / S) conversion on G1, G2, G3, the reshaped G4, and the reshaped G5 to obtain an updated sequence.

4. The high security probability shaping method based on three-dimensional constellation joint shaping according to claim 1, characterized in that: The step 4 specifically comprises: Step 4.1: obtaining a 3D-32QAM signal constellation point q; Step 4.2: Obtain y chaotic sequence y by using three-dimensional chaotic system i+1 wherein the three-dimensional chaotic system expression is as follows: where xi +1 represents the x chaotic sequence after the i+1 iteration, yi +1 represents the y chaotic sequence after the i+1 iteration, z i+1 represents the z chaotic sequence after the i+1 iteration; x i represents the x chaotic sequence after the i iteration, y i represents the y chaotic sequence after the i iteration, z i represents the z chaotic sequence after the i iteration; a, b, c represent system parameters; Step 4.3: Calculate the key y corresponding to the y chaotic sequence according to y i+1 chaotic sequence i+1 '; wherein the y chaotic sequence corresponds to a key y i+1 The calculation formula is as follows: y i+1 ' = fix(mod(abs(y i+1 ·10 6 ), N) ) + 1 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; Step 4.4: encrypting the constellation point q of the 3D-32QAM signal according to the key y corresponding to the y chaotic sequence i+1 encrypting the constellation point q of the 3D-32QAM signal, to obtain an encrypted 3D-32QAM signal Q; Q = q y i+1 ' Wherein, q represents a three-dimensional coordinate matrix of the 3D-32QAM signal constellation point, and Q represents a three-dimensional coordinate matrix of the encrypted constellation point.

5. The high security probability shaping method based on three-dimensional constellation joint shaping according to claim 1, characterized in that: The step 5 specifically comprises: Step 5.1: mapping the encrypted 3D-32QAM signal to each subcarrier in an OFDM system, converting the frequency domain 3D-OFDM signal into a time domain signal s after completing subcarrier mapping; Step 5.2: Obtain z chaotic sequence z by using three-dimensional chaotic system i+1 wherein the three-dimensional chaotic system expression is as follows: where xi +1 represents the x chaotic sequence after the i+1 iteration, yi +1 represents the y chaotic sequence after the i+1 iteration, z i+1 represents the z chaotic sequence after the i+1 iteration; xi i represents the x chaotic sequence after the i iteration, yi i represents the y chaotic sequence after the i iteration, z i represents the z chaotic sequence after the i iteration; a, b, c represent system parameters; Step 5.3: Calculate the key z corresponding to the z chaotic sequence i+1 Step 5.4: Calculate the key z corresponding to the z chaotic sequence i+1 ' wherein the z chaotic sequence corresponds to a key z i+1 The calculation formula is as follows: z i+1 ' = fix(mod(abs(z i+1 ·10 6 ), N) ) + 1 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; Step 5.4: According to the key z corresponding to the z chaotic sequence i+1 The time domain signal s is encrypted to obtain an encrypted 3D-32QAM time domain signal S. Wherein, the encrypted 3D-32QAM signal time domain signal S is calculated according to the following formula: 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 or 4 or 5, characterized in that: The system parameters are a=1, b=0.3, c=20, and the initial values of the three-dimensional chaotic system are x1=y1=z1=0.

2.

7. A transmitting end, characterized by: The transmitting end is used to execute one of the high-security probability shaping methods based on three-dimensional constellation joint shaping in claims 1 to 6. The transmitting end is used to execute one of the high-security probability shaping methods based on three-dimensional constellation joint shaping in claims 1 to 6.

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