Layered coordinate flip coding method, device and system based on constellation joint shaping

Abstract

The present invention discloses a hierarchical coordinate reversal encoding method, device, and system based on constellation joint shaping. The method comprises probabilistically shaping an original pseudo-random binary sequence to generate a binary sequence with a non-uniform probability distribution; performing serial-to-parallel conversion on the non-uniform probability distribution binary sequence and mapping it onto a pre-generated three-dimensional constellation; utilizing a key and a four-dimensional multi-phase hyperchaotic system to generate four different chaotic sequences, two of which are used to encrypt subcarriers and symbols, respectively; combining the remaining two chaotic sequences into a new chaotic sequence; and using the new chaotic sequence to perform coordinate reversal on constellation points on the three-dimensional constellation to complete constellation point encryption. The present invention can ensure the security of the communication system while effectively reducing the damage to transmission performance.

Description

Technical Field

[0001] The present invention belongs to the field of optical communication technology, and in particular relates to a layered coordinate flip coding method, device and system based on constellation joint shaping. Background Art

[0002] Passive Optical Network (PON) technology has evolved from time-division multiplexing (TDM-PON) to wavelength-division multiplexing (WDM-PON) to orthogonal frequency-division multiplexing (OFDM-PON) to improve spectrum utilization and time-frequency resource utilization. OFDM-PON offers high spectrum efficiency and robustness against multipath fading and inter-symbol interference, meeting the requirements of high-capacity, ultra-high-speed optical communications. However, it faces the pressing challenge of addressing the Shannon limit bottleneck caused by nonlinear effects in the fiber channel. This makes it difficult to balance capacity with high-performance transmission requirements, particularly in access scenarios with limited power budgets.

[0003] Among the new coding and modulation technologies, geometric shaping (GS) optimizes the minimum Euclidean distance (MED) by optimizing the position distribution of constellation points in Euclidean space, thereby improving the system's ability to resist nonlinear effects and noise. Probabilistic shaping (PS) reduces the probability of high-energy constellation points and increases the probability of low-energy points through statistical probability distribution control, thereby improving the power efficiency of the communication system, bringing the fiber-optic communication capacity closer to the Shannon limit and achieving high-performance transmission of the system.

[0004] Existing constellation shaping research has mostly been conducted in two dimensions, with limited consideration given to the simultaneous optimization of the geometric position and probability distribution of higher-order constellations in three dimensions and beyond. Compared to two-dimensional constellations, three-dimensional constellations can maximize MED through spatial dimension optimization, improving system robustness under the same power constraints. Combining probabilistic constellation shaping techniques further optimizes the distribution of three-dimensional constellation points, increasing the transmission frequency of points within the constellation and thereby reducing the overall average power of the constellation. This improves the constellation gain index, thereby enhancing overall system transmission performance.

[0005] Furthermore, although joint constellation shaping technology utilizes GS and PS to optimize the spatial structure and probability distribution of signals, achieving simultaneous improvements in the robustness and capacity of communication systems, the downlink of the PON still utilizes a broadcast transmission mechanism. Unauthorized optical network units (ONUs) can exploit shared fiber channels to intercept sensitive data and even interfere with legitimate user communications through signal replay and packet injection. Furthermore, quantum computing's potential to crack existing asymmetric encryption algorithms poses a significant challenge to traditional encryption systems, making it crucial to improve the security of communication systems. Traditional data encryption mechanisms are typically deployed at the upper or physical layer of the optical network. While upper-layer encryption can enhance the system's fundamental protection capabilities, inherent algorithmic limitations make it difficult to achieve end-to-end full-link protection.

[0006] In physical layer encryption, digital signal processing (DSP) techniques are used to dynamically perturb the optical carrier phase or perform chaotic interleaving of subcarriers, mapping the plaintext information into a light field distribution with temporal and spatial randomness, further enhancing the security of communication systems. Digital chaotic encryption, due to its sensitivity to initial conditions, long-term unpredictability, wide-spectrum noise-like properties, and inherent compatibility with optical communication systems, has become a cutting-edge research direction for improving the security of optical networks. Notably, research has shown that the multidimensional space in 3D modulation allows for more flexible constellation encryption transformations and increases the key space. However, existing encryption technologies often introduce phase noise at the transmitter (TX), disrupting the signal constellation. While this makes the signal appear more like random noise, it also degrades performance at the receiver (RX), increasing the bit error rate (BER), and ultimately reducing system transmission performance. Therefore, ensuring the security of communication systems while maintaining minimal degradation of transmission performance is an urgent challenge. Summary of the Invention

[0007] To address the above problems, the present invention proposes a layered coordinate flip coding method, device and system based on constellation joint shaping, which can effectively reduce the damage to transmission performance while ensuring the security of the communication system.

[0008] In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

[0009] In a first aspect, the present invention provides a layered coordinate flip coding method based on constellation joint shaping, comprising:

[0010] Probabilistically reshape the original pseudo-random binary sequence to generate a binary sequence with non-uniform probability distribution;

[0011] Performing serial-to-parallel conversion on the binary sequence of the non-uniform probability distribution and mapping the sequence onto a pre-generated three-dimensional constellation;

[0012] Using a key and a four-dimensional multiphase hyperchaotic system, four different chaotic sequences are generated. Two of the chaotic sequences are used to encrypt the subcarriers and symbols respectively, and the other two chaotic sequences are combined into a new chaotic sequence. The new chaotic sequence is then used to flip the coordinates of the constellation points on the three-dimensional constellation to complete the encryption of the constellation points.

[0013] In combination with the first aspect, optionally, the three-dimensional constellation is a regular octagonal rhombus three-dimensional constellation.

[0014] In combination with the first aspect, optionally, the method for generating the regular octagonal rhombus three-dimensional constellation includes:

[0015] Step (1): On the xy plane, construct a square with a side length of 4, with the origin of the coordinate axis as the geometric center; connect the midpoints of the opposite sides of the square, and divide the large square into four small squares with a side length of 2. Use the eight points on the outer circle of the large square as the eight constellation points, and fix MED to 2, so as to determine the positions of the eight constellation points when z = 0;

[0016] Step (2): Select any one of the four small squares in step 1 as a cross section of a regular octagonal rhombus, and expand it in the positive and negative directions of the z-axis to form a regular octagonal rhombus with an edge length of 2;

[0017] Step (3) using the four outer faces of the regular octagonal rhombus as the base of a regular tetrahedron, and extending outward to form four regular tetrahedrons with a side length of 2;

[0018] Step (4): According to steps (2) and (3), the other three small squares in step (1) are respectively expanded toward the z-axis to form three regular octagonal rhombuses, and the outer cross-sections thereof are selected as the bottom surfaces to extend outward to form a regular tetrahedron, thereby obtaining a regular octagonal rhombus three-dimensional constellation.

[0019] In combination with the first aspect, optionally, the constellation point coordinates and mapping rules of the regular octagonal rhombus three-dimensional constellation are:

[0020] .

[0021] In combination with the first aspect, optionally, the four different chaotic sequence generation methods include:

[0022] Get a key, the key includes 、 、 and ;

[0023] The key is introduced into a four-dimensional multiphase hyperchaotic system to generate a first chaotic sequence, a second chaotic sequence, a third chaotic sequence, and a fourth chaotic sequence. The calculation formulas of the first chaotic sequence, the second chaotic sequence, the third chaotic sequence, and the fourth chaotic sequence are:

[0024] ,

[0025] Where, is the first chaotic sequence, is the second chaotic sequence, is the third chaotic sequence, It is the fourth chaos sequence; 、 、 、 are the state variables of the four-dimensional multiphase hyperchaotic system, and their initial values ​​are 、 、 and ; 、 、 All are system parameters of the four-dimensional multiphase hyperchaotic system.

[0026] In combination with the first aspect, optionally, the using two chaotic sequences to encrypt the subcarriers and symbols respectively specifically includes:

[0027] Based on the first chaotic sequence and the second chaotic sequence , generate the first scrambled matrix and the second scrambled matrix ;

[0028] Using the first scrambled matrix and the second scrambled matrix , encrypting the subcarriers and symbols respectively.

[0029] In combination with the first aspect, optionally, the first scrambled matrix The generation formula is:

[0030] ,

[0031] ,

[0032] The second scrambled matrix The generation formula is:

[0033] ,

[0034] ,

[0035] in, is the ascending sorting function, is the remainder function, is the floor function, Indicates the transposition operation of a matrix. 、 is the binary sequence obtained based on the sixth decimal place of the chaotic sequence.

[0036] In combination with the first aspect, optionally, combining the other two chaotic sequences into a new chaotic sequence, and using the new chaotic sequence to perform coordinate flipping on constellation points on the three-dimensional constellation, specifically includes:

[0037] Based on the third chaotic sequence and the fourth chaos sequence , generate a binary sequence and ;in, , , is the remainder function, is the floor function;

[0038] Based on the binary sequence and , generating a new chaotic sequence , , chaotic sequence It only contains the four numbers 00, 01, 10, and 11, and these four numbers are arranged randomly;

[0039] use Indicates the The coordinates of the constellation points are , Represents chaotic sequence The number, through chaotic sequence The number in controls the corresponding constellation point to perform the corresponding polar coordinate flip transformation operation. The mathematical expression of the polar coordinate flip transformation operation is:

[0040] ,

[0041] in, Indicates that after the flip operation The coordinates of the constellation points;

[0042] when When , it means that the constellation point coordinates are flipped symmetrically about the origin;

[0043] when When , it means that the constellation point coordinates are flipped symmetrically about the plane xy=0;

[0044] when When , it means that the constellation point is flipped symmetrically about the plane x+y=0;

[0045] when When , it means that the constellation points are flipped symmetrically about the plane z=0.

[0046] In a second aspect, the present invention provides a layered coordinate flip encoding device based on constellation joint shaping, comprising:

[0047] The binary sequence generation module is used to perform probability shaping on the original pseudo-random binary sequence to generate a binary sequence with non-uniform probability distribution;

[0048] a mapping module, configured to perform serial-to-parallel conversion on the binary sequence of the non-uniform probability distribution and then map the converted sequence onto a pre-generated three-dimensional constellation;

[0049] The encryption coding module is used to use the key and the four-dimensional multi-phase hyperchaotic system to generate four different chaotic sequences, use two of the chaotic sequences to encrypt the subcarriers and symbols respectively, use the other two chaotic sequences to combine into a new chaotic sequence, and use the new chaotic sequence to flip the coordinates of the constellation points on the three-dimensional constellation to complete the encryption of the constellation points.

[0050] In a third aspect, the present invention provides a hierarchical coordinate flip coding system based on constellation joint shaping, comprising a storage medium and a processor;

[0051] The storage medium is used to store instructions;

[0052] The processor is configured to operate according to the instructions to execute the method according to any one of the first aspects.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] This patent proposes a hierarchical coordinate reversal encoding method, device, and system based on constellation joint shaping. During the signal generation process, probability shaping technology is used to generate a binary sequence with a non-uniform probability distribution, which can reduce the average energy of the constellation diagram. During constellation mapping, the geometric position distribution of the constellation points is optimized based on the designed three-dimensional constellation diagram to maximize the mean energy density (MED). Secondly, using chaotic encryption technology, the subcarriers and symbols of the signal are perturbed and encrypted through a four-dimensional multi-phase hyperchaotic model, and coordinate reversal encryption is used to achieve multi-layer encryption protection. Ultimately, constellation point masking is achieved without introducing additional noise, ensuring efficient and secure information transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive work, among which:

[0056] Figure 1 This is a flow chart of a layered coordinate flip coding method based on constellation joint shaping according to an embodiment of the present invention;

[0057] FIG2( a ) is a flow chart showing one embodiment of the present invention for generating a regular octagonal rhombus 3D constellation diagram;

[0058] FIG2( b ) is a second flow chart of generating a regular octagonal rhombus 3D constellation diagram according to an embodiment of the present invention;

[0059] FIG2( c ) is a third flow chart of generating a regular octagonal rhombus three-dimensional constellation diagram according to an embodiment of the present invention;

[0060] FIG2( d ) is a fourth flow chart of generating a regular octagonal rhombus 3D constellation diagram according to an embodiment of the present invention;

[0061] FIG2( e ) is a fifth flow chart of generating a regular octagonal rhombus three-dimensional constellation diagram according to an embodiment of the present invention;

[0062] Figure 3 A phase diagram of a four-dimensional multiphase hyperchaotic model according to an embodiment of the present invention;

[0063] Figure 4 A schematic diagram of coordinate flip encryption principle according to an embodiment of the present invention;

[0064] Figure 5 (a) is a comparison of the bit error rate curves of the legal receiving end and the illegal receiving end after recovering the original data;

[0065] Figure 5(b) shows the comparison of the bit error rate at the receiving end before and after encryption;

[0066] Figure 6 The figure is a comparison chart of the bit error rate performance between the three-dimensional constellation based on the regular octagonal rhombus and the traditional three-dimensional constellation based on the regular hexahedron. DETAILED DESCRIPTION

[0067] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0068] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features specified as "first" and "second" may explicitly or implicitly include at least one of such features. In addition, the technical solutions between the various embodiments can be combined with each other, but this must be based on the fact that ordinary technicians in this field can implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0069] Example 1

[0070] An embodiment of the present invention provides a layered coordinate flip coding method based on constellation joint shaping, comprising the following steps:

[0071] (1) Probabilistically reshape the original pseudo-random binary sequence to generate a binary sequence with non-uniform probability distribution;

[0072] (2) performing serial-to-parallel conversion on the binary sequence of the non-uniform probability distribution and mapping the sequence onto a pre-generated three-dimensional constellation;

[0073] (3) Using the key and the four-dimensional multiphase hyperchaotic system, four different chaotic sequences are generated. Two of the chaotic sequences are used to encrypt the subcarriers and symbols respectively. The other two chaotic sequences are combined into a new chaotic sequence. The new chaotic sequence is used to flip the coordinates of the constellation points on the three-dimensional constellation to complete the encryption of the constellation points.

[0074] Based on this scheme, during the signal generation process, probability shaping technology is used to generate a binary sequence with a non-uniform probability distribution, which can reduce the average energy of the constellation diagram. During constellation mapping, the geometric distribution of constellation points is optimized based on the designed three-dimensional constellation diagram to maximize the mean energy density (MED). Secondly, chaotic encryption technology is used to perturb and encrypt the signal's subcarriers and symbols using a four-dimensional multi-phase hyperchaotic model, and coordinate flip encryption is used to achieve multi-layer encryption protection. Ultimately, constellation point masking is achieved without introducing additional noise, ensuring efficient and secure information transmission.

[0075] In a specific implementation of the embodiment of the present invention, the three-dimensional constellation is a regular octagonal rhombus three-dimensional constellation. Specifically, the method for generating the regular octagonal rhombus three-dimensional constellation includes:

[0076] Step (1): On the xy plane, construct a square with a side length of 4, with the origin of the coordinate axis as the geometric center; connect the midpoints of the opposite sides of the square to divide the large square into four small squares with a side length of 2, and use the eight points on the outer circle of the large square as the eight constellation points; fix MED to 2 to determine the positions of the eight constellation points when z = 0;

[0077] Step (2): Select any one of the four small squares in step 1 as a cross section of a regular octagonal rhombus, and expand it in the positive and negative directions of the z-axis to form a regular octagonal rhombus with an edge length of 2;

[0078] Step (3) using the four outer faces of the regular octagonal rhombus as the base of a regular tetrahedron, and extending outward to form four regular tetrahedrons with a side length of 2;

[0079] Step (4): According to steps (2) and (3), the other three small squares in step (1) are respectively expanded toward the z-axis to form three regular octagonal rhombuses, and the outer cross-sections thereof are selected as the bottom surfaces to extend outward to form a regular tetrahedron, thereby obtaining a regular octagonal rhombus three-dimensional constellation.

[0080] The CFM value of the regular octagonal rhombus three-dimensional constellation in the above solution is 0.7059.

[0081] In a specific implementation of the embodiment of the present invention, the constellation point coordinates and mapping rules of the regular octagonal rhombus three-dimensional constellation are:

[0082] .

[0083] In a specific implementation of the embodiment of the present invention, the four different chaotic sequence generation methods include:

[0084] Get a key, the key includes 、 、 and ;

[0085] The key is introduced into a four-dimensional multiphase hyperchaotic system to generate a first chaotic sequence, a second chaotic sequence, a third chaotic sequence, and a fourth chaotic sequence. The calculation formulas of the first chaotic sequence, the second chaotic sequence, the third chaotic sequence, and the fourth chaotic sequence are:

[0086] ,

[0087] Where, is the first chaotic sequence, is the second chaotic sequence, is the third chaotic sequence, It is the fourth chaos sequence; 、 、 、 are the state variables of the four-dimensional multiphase hyperchaotic system, and their initial values ​​are 、 、 and ; 、 、 All are system parameters of the four-dimensional multiphase hyperchaotic system.

[0088] In a specific implementation of the embodiment of the present invention, the encrypting of the subcarriers and symbols respectively by using two chaotic sequences specifically includes:

[0089] Based on the first chaotic sequence and the second chaotic sequence , generate the first scrambled matrix and the second scrambled matrix ;

[0090] The subcarriers and symbols are encrypted respectively using the first scrambling matrix and the second scrambling matrix.

[0091] In a specific implementation of the embodiment of the present invention, the first scrambled matrix The generation formula is:

[0092] ,

[0093] ,

[0094] The second scrambled matrix The generation formula is:

[0095] ,

[0096] ,

[0097] in, is the ascending sorting function, is the remainder function, is the floor function, Indicates the transposition operation of a matrix. 、 is the binary sequence obtained based on the sixth decimal place of the chaotic sequence.

[0098] In a specific implementation of the embodiment of the present invention, combining the other two chaotic sequences into a new chaotic sequence, and using the new chaotic sequence to perform coordinate flipping on constellation points on a three-dimensional constellation, specifically includes:

[0099] Based on the third chaotic sequence and the fourth chaos sequence , generate a binary sequence and ;in, , , is the remainder function, is the floor function;

[0100] Based on the binary sequence and , generating a new chaotic sequence , , chaotic sequence There are only four numbers: 00, 01, 10, and 11, and these four numbers are arranged randomly;

[0101] use Indicates the The coordinates of the constellation points are , Represents chaotic sequence The number, through chaotic sequence The number in controls the corresponding constellation point to perform the corresponding polar coordinate flip transformation operation. The mathematical expression of the polar coordinate flip transformation operation is:

[0102] ,

[0103] in, Indicates that after the flip operation The coordinates of the constellation points;

[0104] when When , it means that the constellation point coordinates are flipped symmetrically about the origin;

[0105] when When , it means that the constellation point coordinates are flipped symmetrically about the plane xy=0;

[0106] when When , it means that the constellation point is flipped symmetrically about the plane x+y=0;

[0107] when When , it means that the constellation points are flipped symmetrically about the plane z=0.

[0108] The layered coordinate flip coding method based on constellation joint shaping in the embodiment of the present invention is described in detail below with reference to a specific implementation manner.

[0109] The optical transmission system can be divided into two parts: a transmitter and a receiver. The layered coordinate reversal coding method based on constellation joint shaping in the embodiment of the present invention is applied to the transmitter.

[0110] The layered coordinate flip coding method based on constellation joint shaping specifically includes the following steps:

[0111] Step (1) uses DSP to generate a pseudo-random binary sequence as the original data, performs probability shaping on the pseudo-random binary sequence, and generates a binary sequence with non-uniform probability distribution (i.e. Figure 1 Distribution matching in );

[0112] In the probability distribution design phase, the core of probability shaping is to adjust the probability of occurrence of constellation points without changing their geometric positions in the constellation diagram. This method is implemented by increasing the probability of occurrence of inner ring constellation points and reducing the probability of occurrence of outer ring constellation points, effectively improving the performance index of the constellation diagram, thereby enhancing the system's robustness against noise interference and helping to reduce the bit error rate. In an additive white Gaussian noise environment, the Maxwell-Boltzmann distribution is considered to be an ideal choice for optimizing the average power of the constellation diagram. Each signal point The probability distribution of can be defined by the following expression:

[0113]

[0114] in, is the probability distribution of discrete constellation points, Represents the energy of the constellation point, is a non-negative proportional factor used to determine the distribution pattern of the constellation and the information entropy of the modulation format. When , the constellation points are evenly distributed and the information entropy is maximized. In the embodiment of the present invention, a constant component distribution matching scheme is used as a distribution matcher to optimize the probability distribution of the constellation.

[0115] Step (2) converts the binary sequence of the non-uniform probability distribution into serial-to-parallel and maps it to a pre-generated three-dimensional constellation (i.e. Figure 1 constellation mapping in );

[0116] The three-dimensional constellation is a regular octagonal rhombus three-dimensional constellation, and its generation method specifically includes:

[0117] Constellation performance is determined by both MED and average power. Increasing MED helps combat noise, but it also increases average power, which in turn increases BER. A key metric for measuring constellation system performance is the constellation gain factor (CFM). Maximizing CFM significantly reduces BER. The CFM calculation formula is:

[0118] ,

[0119] ,

[0120] in, Used to indicate The corresponding value when the average power of the dimensional constellation is converted to two-dimensional space, Indicates a specific constellation point configuration, which includes the location information of all constellation points and is used to distinguish different constellations; represent The total number of constellation points in the dimensional constellation diagram, Indicates the constellation point Coordinate vector in dimensional space, The norm is used to quantify the Euclidean distance between constellation points. Therefore, the minimum Euclidean distance between constellation points is Under the condition of being fixed at 2, through geometric structure design, as long as all points are brought as close to the origin as possible, the average power can be reduced and the constellation performance index can be improved.

[0121] Figure 2(a) shows the structure of the regular octagonal rhombus-shaped three-dimensional constellation geometric shaping proposed in this embodiment. Using the aforementioned CFM calculation formula, its CFM value can be calculated to be 0.7059. The construction principle is as follows: First, a square with a side length of 4 is constructed on the xy plane with the coordinate axis origin as the geometric center. The midpoints of the opposite sides of the square are connected and represented by dotted lines. The large square is now divided into four smaller squares with a side length of 2. The eight points on the outer circle of the large square serve as the eight constellation points. To make constellation construction more intuitive and simple, the center origin is temporarily retained, as shown in Figure 2(b). The MED is fixed at 2, thus determining the positions of the eight constellation points at z = 0. As is well known, each face of a regular octagonal rhombus is an equilateral triangle of the same size and side length. The second step is to use any of the four smaller squares in Figure 2(b) as a cross-section of the regular octagonal rhombus. This is then expanded in the positive and negative z-axis directions to form a regular octagonal rhombus with a side length of 2, as shown in Figure 2(c). The third step, as shown in Figure 2(d), select the four outer faces of the regular octagonal rhombus from the second step as the bases of regular tetrahedra, and extend them outward to form four regular tetrahedra with a side length of 2. The fourth step, as shown in Figure 2(e), is similar to the second and third steps. The other three small squares from the first step are extended along the z-axis to form three regular octagonal rhombuses, and their outer cross-sections are selected as the bases to extend outward to form regular tetrahedra. It should be emphasized that there are 33 constellation points in the figure at this time. To ensure the high symmetry of the designed constellation points, there should originally be 9 constellation points in the middle layer, but only the outer 8 constellation points are retained, and the center point, i.e. the origin, is deleted. The designed 32-point constellation is now highly symmetrical.

[0122] The probability and mapping rules of each constellation point are shown in Table 1:

[0123] Table 1 Constellation point coordinates and mapping rules

[0124] .

[0125] Step (3) uses the key and the four-dimensional multiphase hyperchaotic system to generate four different chaotic sequences, uses two of the chaotic sequences to encrypt the subcarriers and symbols respectively, uses the other two chaotic sequences to combine into a new chaotic sequence, and uses the new chaotic sequence to flip the coordinates of the constellation points on the three-dimensional constellation to complete the encryption of the constellation points. Specifically, it includes the following steps:

[0126] In the embodiment of the present invention, a four-dimensional multiphase hyperchaotic system is used to generate a chaotic sequence. The four-dimensional multiphase hyperchaotic system can be expressed as:

[0127] ,

[0128] Where, is the first chaotic sequence, is the second chaotic sequence, is the third chaotic sequence, It is the fourth chaos sequence; 、 、 、 are the state variables of the four-dimensional multiphase hyperchaotic system, and their initial values ​​are 、 、 and ; 、 、 are all system parameters of the four-dimensional multiphase hyperchaotic system. =0.5, =2, =0.8, the four-dimensional multiphase hyperchaotic system has two positive Lyapunov exponents, proving that the four-dimensional multiphase hyperchaotic system is a hyperchaotic system. 、 、 and The four-dimensional multiphase hyperchaotic system is solved by the fourth-order Runge-Kutta method. The four chaotic sequences of the four-dimensional multiphase hyperchaotic model have the value ranges of (-12.9, 12.1), (-48.4, 53.9), (-4.8, 27.1), and (-5.4, 5.2). Figure 3 .

[0129] Set the initial value 、 、 and Importing a four-dimensional multiphase hyperchaotic system will generate a unique set of chaotic sequences 、 、 、 , and then use the obtained chaotic sequences X1, Y1, Z1 and W1 to complete the perturbation of the subcarrier and symbol of the original data and the layered polar coordinate flip encryption. The specific operations are as follows.

[0130]

[0131]

[0132] in, is the ascending sorting function, is the remainder function, is the floor function, Indicates the transposition operation of a matrix. 、 、 、 The chaotic sequence is the binary sequence obtained by the sixth decimal place (i.e. chaotic sequence). 、 Sort in ascending order and take the reciprocal, then transpose and 、 Multiply to generate a first scrambled matrix and the second scrambled matrix , the first scrambled matrix and the second scrambled matrix The orders are the number of subcarriers and the number of symbols, respectively, using the first scrambling matrix and the second scrambled matrix , encrypt the subcarriers and symbols respectively (i.e. Figure 1 This completes the first layer of encryption in the encryption scheme.

[0133] The second layer of encryption uses a layered polar coordinate flip encryption scheme, a chaotic sequence Depend on 、 The purpose of this is to improve the randomness of the layered polar coordinate flipping, and the sequence length corresponds to the product of the number of subcarriers and symbols. is and After performing the remainder operation on 4, we get the chaotic sequence There are only four numbers (00, 01, 10, 11) in the system, and these four numbers are randomly arranged, which just corresponds to the four polar coordinate flipping schemes of layered polar coordinate flipping. The original data, In the constellation mapping stage, these data will be mapped to 32 constellation points according to the mapping rules in Table 1, so The original data will generate constellation points. Indicates the The coordinates of the constellation points are , Represents chaotic sequence The number, through chaotic sequence The number in the control corresponds to the constellation point to perform the corresponding polar coordinate flip transformation operation (i.e. Figure 1 The hierarchical coordinates in the .

[0134] ,

[0135] when When , it means that the constellation point coordinates are flipped symmetrically about the origin;

[0136] when When , it means that the constellation point coordinates are flipped symmetrically about the plane xy=0;

[0137] when When , it means that the constellation point is flipped symmetrically about the plane x+y=0;

[0138] when When , it means that the constellation points are flipped symmetrically about the plane z=0.

[0139] When the above operations are performed on all constellation points, the layered polar coordinate flip encryption is completed, and the constellation points are scrambled, thereby realizing the encryption of the original data. Figure 4 As shown, the chaotic sequence is intercepted One part of it is to demonstrate the use of chaotic sequences to implement the layered polar coordinate flip encryption scheme. It is worth noting that in order to express it more vividly and intuitively, a regular hexahedron constellation diagram is used to demonstrate the layered polar coordinate flip encryption.

[0140] (4) OFDM transmission

[0141] First, an inverse Fourier transform is performed on the constellation points to convert the frequency domain signal into a time domain signal. Next, a cyclic prefix and suffix are added before and after the time domain signal to reduce crosstalk between symbol points. After transmission over the optical fiber channel, the cyclic prefix and suffix are removed and the signal is converted back to the frequency domain using a Fourier transform to recover the valid data matrix.

[0142] (5) Signal reception and demodulation

[0143] Substitute the correct key into the four-dimensional multiphase hyperchaotic system, and use the generated chaotic sequence to recover the subcarrier and symbol of the received data and perform layered polar coordinate flip recovery to obtain the original binary data stream. Then demap the received binary data stream (i.e. Figure 1 Constellation demapping + parallel-to-serial conversion in the system) is performed to restore the original data. Figure 5 (a) shows a comparison of the bit error rate curves of the legal and illegal receivers after the original data is restored. The blue dotted line in the figure represents the hard decision forward error correction threshold (FEC). It can be seen that when the optical power at the receiving end is less than -14.6dBm, the bit error rate of the legal receiver is lower than the decision threshold. At the same time, as the optical power at the receiving end increases, the bit error rate gradually decreases, achieving a better transmission effect. However, the illegal receiver cannot correctly decrypt the encrypted signal because it cannot obtain the correct encryption method. Figure 5 (b) shows a comparison of the bit error rates before and after system encryption. It can be seen from the figure that the bit error rate performance of the encrypted signal is almost the same as that of the normal signal. At a BER of 3.8×10 -3 When compared with the normal signal, the encrypted signal has only less than 0.1dB of receiving sensitivity loss.

[0144] At the same time, the bit error rate performance of the three-dimensional constellation based on the regular octagonal rhombus and the traditional three-dimensional constellation based on the regular hexahedron is also compared. Figure 6 As shown, 3D-C1 represents a three-dimensional constellation based on a regular octagonal rhombus, and 3D-C2 represents a traditional three-dimensional constellation based on a regular hexahedron. When FEC is achieved, as indicated by the light red solid line in the figure, the three-dimensional constellation based on the regular octagonal rhombus designed in this patent achieves approximately 0.3dB of receiver sensitivity gain compared to the traditional three-dimensional constellation based on a regular hexahedron. This demonstrates that the proposed method achieves high-performance communication system transmission while ensuring secure information transmission.

[0145] Example 2

[0146] Based on the same inventive concept as that of Example 1, an embodiment of the present invention provides a layered coordinate flip encoding device based on constellation joint shaping, including:

[0147] The binary sequence generation module is used to perform probability shaping on the original pseudo-random binary sequence to generate a binary sequence with non-uniform probability distribution;

[0148] a mapping module, configured to perform serial-to-parallel conversion on the binary sequence of the non-uniform probability distribution and then map the converted sequence onto a pre-generated three-dimensional constellation;

[0149] The encryption coding module is used to use the key and the four-dimensional multi-phase hyperchaotic system to generate four different chaotic sequences, use two of the chaotic sequences to encrypt the subcarriers and symbols respectively, use the other two chaotic sequences to combine into a new chaotic sequence, and use the new chaotic sequence to flip the coordinates of the constellation points on the three-dimensional constellation to complete the encryption of the constellation points.

[0150] Example 3

[0151] Based on the same inventive concept as that of Example 1, an embodiment of the present invention provides a layered coordinate flip coding system based on constellation joint shaping, including a storage medium and a processor;

[0152] The storage medium is used to store instructions;

[0153] The processor is configured to operate according to the instructions to perform the method according to any one of the embodiments 1.

[0154] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0155] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0156] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0157] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0158] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which are all protected by the present invention.

[0159] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A layered coordinate flip coding method based on constellation joint shaping, characterized in that: include: Probabilistically reshape the original pseudo-random binary sequence to generate a binary sequence with non-uniform probability distribution; After performing serial-to-parallel conversion on the binary sequence of the non-uniform probability distribution, the sequence is mapped onto a pre-generated three-dimensional constellation; four different chaotic sequences are generated using a key and a four-dimensional multi-phase hyperchaotic system; two of the chaotic sequences are used to encrypt subcarriers and symbols, respectively; the other two chaotic sequences are combined into a new chaotic sequence; and the new chaotic sequence is used to flip the coordinates of constellation points on the three-dimensional constellation to complete the encryption of the constellation points; The three-dimensional constellation is a regular octagonal rhombus three-dimensional constellation; The method for generating the regular octagonal rhombus three-dimensional constellation comprises: Step (1): On the xy plane, a square with a side length of 4 is constructed with the origin of the coordinate axis as the geometric center; the midpoints of the opposite sides of the square are connected to each other, and the large square is divided into four small squares with a side length of 2. The eight points on the outer circle of the large square are used as the eight constellation points, and the MED is fixed to 2, thereby determining the positions of the eight constellation points when z = 0; Step (2): Select any one of the four small squares in step 1 as a cross section of a regular octagonal rhombus, and expand it in the positive and negative directions of the z-axis to form a regular octagonal rhombus with an edge length of 2; Step (3) using the four outer faces of the regular octagonal rhombus as the base of a regular tetrahedron, and extending outward to form four regular tetrahedrons with a side length of 2; Step (4), according to steps (2) and (3), the other three small squares in step (1) are respectively expanded toward the z-axis to form three regular octagonal rhombuses, and the outer cross-sections thereof are selected as the bottom surfaces to extend outward to form regular tetrahedrons, thereby obtaining a regular octagonal rhombus three-dimensional constellation; The four different chaotic sequence generation methods include: Obtain a key, wherein the key includes X0, Y0, Z0, and W0; The key is introduced into a four-dimensional multiphase hyperchaotic system to generate a first chaotic sequence, a second chaotic sequence, a third chaotic sequence, and a fourth chaotic sequence. The calculation formulas of the first chaotic sequence, the second chaotic sequence, the third chaotic sequence, and the fourth chaotic sequence are: Where, is the first chaotic sequence, is the second chaotic sequence, is the third chaotic sequence, is the fourth chaotic sequence; X, Y, Z, and W are all state variables of the four-dimensional multiphase hyperchaotic system, and their initial values ​​are X0, Y0, Z0, and W0, respectively; a, b, and c are all system parameters of the four-dimensional multiphase hyperchaotic system.

2. The layered coordinate reversal coding method based on constellation joint shaping according to claim 1, characterized in that: The constellation point coordinates and mapping rules of the regular octagonal rhombus three-dimensional constellation are:

3. The layered coordinate reversal coding method based on constellation joint shaping according to claim 1, characterized in that: The method of using two chaotic sequences to encrypt subcarriers and symbols respectively includes: Based on the first chaotic sequence and the second chaotic sequence Generate the first scrambled matrix X and the second scrambled matrix Using the first scrambled matrix and the second scrambled matrix The subcarriers and symbols are encrypted separately.

4. The layered coordinate reversal coding method based on constellation joint shaping according to claim 3, characterized in that: The first scrambled matrix The generation formula is: The second scrambled matrix The generation formula is: Among them, sort() is the ascending sorting function, mod() is the remainder function, floor() is the floor function, T represents the transpose operation of a matrix, and X1 and Y1 are the binary sequences obtained based on the sixth decimal place of the chaotic sequence.

5. The layered coordinate reversal coding method based on constellation joint shaping according to claim 2, characterized in that: The method of combining the other two chaotic sequences into a new chaotic sequence and using the new chaotic sequence to perform coordinate flipping on the constellation points on the three-dimensional constellation specifically includes: Based on the third chaotic sequence and the fourth chaos sequence Generate binary sequences Z1 and W1; where, mod() is the remainder function, floor() is the floor function; Based on the binary sequences Z1 and W1, a new chaotic sequence F is generated, F = [Z1, W1]. The chaotic sequence F contains only four numbers: 00, 01, 10, and 11, and these four numbers are randomly arranged. Use (x m ,y m ,z m ) represents the coordinates of the mth constellation point, and the corresponding one is F(1,m), which represents the mth number in the chaotic sequence F. The corresponding constellation point is controlled by the number in the chaotic sequence F to perform the corresponding polar coordinate flip transformation operation. The mathematical expression of the polar coordinate flip transformation operation is: Among them, (x m ',y m ',z m ') represents the coordinates of the mth constellation point after the flip operation is performed; When F(1,m)=00, it means that the constellation point coordinates are flipped symmetrically about the origin; When F(1,m)=01, it means that the constellation point coordinates are symmetrically flipped about the plane xy=0; When F(1,m)=10, it means that the constellation points are symmetrically flipped about the plane x+y=0; When F(1,m)=11, it indicates that a symmetric flip operation is performed on the constellation points about the plane z=0.

6. A hierarchical coordinate reversal coding device based on constellation joint shaping, characterized in that: include: The binary sequence generation module is used to perform probability shaping on the original pseudo-random binary sequence to generate a binary sequence with non-uniform probability distribution; a mapping module, configured to perform serial-to-parallel conversion on the binary sequence of the non-uniform probability distribution and then map the converted sequence onto a pre-generated three-dimensional constellation; The encryption coding module is used to generate four different chaotic sequences using a key and a four-dimensional multiphase hyperchaotic system. Two of these chaotic sequences are used to encrypt the subcarriers and symbols respectively. The other two chaotic sequences are combined into a new chaotic sequence. The new chaotic sequence is then used to flip the coordinates of the constellation points on the three-dimensional constellation to complete the encryption of the constellation points. The three-dimensional constellation is a regular octagonal rhombus three-dimensional constellation; The method for generating the regular octagonal rhombus three-dimensional constellation comprises: Step (1): On the xy plane, a square with a side length of 4 is constructed with the origin of the coordinate axis as the geometric center; the midpoints of the opposite sides of the square are connected to each other, and the large square is divided into four small squares with a side length of 2. The eight points on the outer circle of the large square are used as the eight constellation points, and the MED is fixed to 2, thereby determining the positions of the eight constellation points when z = 0; Step (2): Select any one of the four small squares in step 1 as a cross section of a regular octagonal rhombus, and expand it in the positive and negative directions of the z-axis to form a regular octagonal rhombus with an edge length of 2; Step (3) using the four outer faces of the regular octagonal rhombus as the base of a regular tetrahedron, and extending outward to form four regular tetrahedrons with a side length of 2; Step (4), according to steps (2) and (3), the other three small squares in step (1) are respectively expanded toward the z-axis to form three regular octagonal rhombuses, and the outer cross-sections thereof are selected as the bottom surfaces to extend outward to form regular tetrahedrons, thereby obtaining a regular octagonal rhombus three-dimensional constellation; The four different chaotic sequence generation methods include: Obtain a key, wherein the key includes X0, Y0, Z0, and W0; The key is introduced into a four-dimensional multiphase hyperchaotic system to generate a first chaotic sequence, a second chaotic sequence, a third chaotic sequence, and a fourth chaotic sequence. The calculation formulas of the first chaotic sequence, the second chaotic sequence, the third chaotic sequence, and the fourth chaotic sequence are: Where, is the first chaotic sequence, is the second chaotic sequence, is the third chaotic sequence, is the fourth chaotic sequence; X, Y, Z, and W are all state variables of the four-dimensional multiphase hyperchaotic system, and their initial values ​​are X0, Y0, Z0, and W0, respectively; a, b, and c are all system parameters of the four-dimensional multiphase hyperchaotic system.

7. A hierarchical coordinate reversal coding system based on constellation joint shaping, characterized in that: including storage media and processors; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the method according to any one of claims 1-5.

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