Low-complexity LDPC-Hadamard code coding and decoding method under OTFS modulation

Abstract

The embodiment of the invention relates to a low-complexity LDPC (Low Density Parity Check)-Hadamard code encoding and decoding method under OTFS (Over-The-Flight Switching) modulation, which comprises the following steps: a sending end performs LDPC-Hadamard code encoding after performing cyclic redundancy check on an information sequence to add check information, and performs inverse symplectic finite Fourier transform and Hisenberg transform on a complex value symbol after constellation mapping to output a time domain signal; a sending signal is generated after time delay and Doppler frequency shift are generated through a multi-path time-varying channel; a receiving end carries out Wigner transform and ShengFourier transform on the received sending signal to output a symbol matrix; and carrying out LDPC-Hadamard decoding processing on the received bit stream, removing check information through cyclic redundancy check, and outputting the original bit stream. According to the invention, through LDPC-Hadamard coding and decoding and OTFS modulation and demodulation, double selective fading channels in a high-speed mobile scene can be better dealt with; the LDPC-Hadamard code is combined with the OTFS, so that the error correction performance of the system under a low signal-to-noise ratio is improved, and the reliability of the system in a high-speed mobile environment is enhanced; and the bit error rate performance of the OTFS system under a low signal-to-noise ratio is improved.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of communication technology, and in particular to a low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation. Background Art

[0002] With the rapid development of emerging application technologies such as mobile Internet, Internet of Things and 5G / 6G, modern communication systems must face changing channel conditions and complex interference environments. In order to meet these challenges, the demand for communication systems in high-noise and high-dynamic environments is increasing. Information theory shows that channel coding can overcome the interference of channel noise and improve communication capabilities. With the development of channel coding, channel coding can be divided into two categories according to different decoding algorithms: hard decision decoding and soft decision decoding. Channel coding using hard decision decoding mainly includes Hamming code, RM code, BCH code and RS code. The above codes appeared earlier. Although they have the advantages of fixed algebraic structure, simple coding method, easy hardware implementation and low decoding complexity, the coding gain is low and cannot meet the requirements of modern communication systems. Channel coding using soft decision decoding mainly includes Turbo code and Polar code, which are decoded based on soft decision decoding algorithms based on confidence propagation. Because of the use of a variety of mathematical analysis tools, these codes have good mathematical structures and can approach or even reach the Shannon capacity limit. However, the above encoding faces the problem of high encoding and decoding complexity and is not conducive to hardware implementation.

[0003] Existing technical solutions:

[0004] 1. OTFS combined with LDPC code: The original data first passes through the LDPC encoder, and the LDPC code encodes the data to increase redundancy so that errors can be corrected during transmission. The encoded bit stream is converted into symbols through a mapper (such as a QAM modulator). Each symbol represents a specific complex value, and these symbols will be placed in the time-frequency grid. The mapped symbols are arranged on the time-frequency grid and mapped to the delay-Doppler domain through SFFT transformation. The delay-Doppler domain can embed the symbols into the time-varying characteristics of the channel to ensure the stability of the signal in high-speed scenarios. The modulated signal is transmitted through the wireless channel. At the receiving end, the signal is returned to the time-frequency domain through an inverse transform and channel equalization is performed. Finally, the equalized symbols pass through the LDPC decoder and use the belief propagation algorithm to correct the errors generated during transmission.

[0005] 2. OTFS combined with Polar code: The original data first passes through the Polar encoder, and the Polar code encodes the data to increase redundancy so that errors can be corrected during transmission. The encoded bit stream is converted into symbols through a mapper (such as a QAM modulator). Each symbol represents a specific complex value, and these symbols will be placed in the time-frequency grid. The mapped symbols are arranged on the time-frequency grid and mapped to the delay-Doppler domain through SFFT transformation. The delay-Doppler domain can embed symbols into the time-varying characteristics of the channel to ensure the stability of the signal in high-speed scenarios. The modulated signal is transmitted through the wireless channel. At the receiving end, the signal is inversely transformed back to the time-frequency domain and channel equalization is performed. Finally, the equalized symbols pass through the Polar decoder, and the belief propagation algorithm is used to correct the errors generated during transmission.

[0006] 3. OTFS combined with Turbo code: The original data is first passed through the Turbo encoder, and the Tubo code encodes the data to increase redundancy so that errors can be corrected during transmission. The encoded bit stream is converted into symbols through a mapper (such as a QAM modulator). Each symbol represents a specific complex value, and these symbols will be placed in the time-frequency grid. The mapped symbols are arranged on the time-frequency grid and mapped to the delay-Doppler domain through SFFT transformation. The delay-Doppler domain can embed symbols into the time-varying characteristics of the channel to ensure the stability of the signal in high-speed scenarios. The modulated signal is transmitted through the wireless channel. At the receiving end, the signal is inversely transformed back to the time-frequency domain and channel equalization is performed. Finally, the equalized symbols pass through the Turbo decoder and use the belief propagation algorithm to correct the errors generated during transmission.

[0007] Disadvantages of existing technology:

[0008] 1. OTFS combined with LDPC code: LDPC code can provide good error correction performance in a noisy environment, but the error correction performance is reduced in the case of complex Doppler effect. The solution combined with Hadamard code can often further reduce the bit error rate. Hadamard transform reduces the impact of single-point interference on the overall signal by evenly distributing the signal energy in multiple dimensions.

[0009] 2. OTFS combined with Polar code: The core advantage of Polar code is its efficient transmission under ideal channels, but in high-speed motion scenarios, such as vehicle-mounted communications or drone communications, Polar code does not have strong enough error correction capabilities. The LDPC-Hadamard scheme can improve the stability of the signal through Hadamard transform in a high-dynamic environment.

[0010] 3. OTFS combined with Turbo code: Turbo code performs well when the code length is short, but its performance is inferior to LDPC code when the code length is long, and it cannot fully approach the Shannon limit. LDPC code has good error correction performance when the code length is long, while Hadamard code can further improve the reliability and bit error rate performance of the overall system, forming better long-distance communication capabilities.

[0011] Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions.

[0012] It should be noted that this section is intended to provide background or context for the technical solutions of the present invention stated in the claims. The description herein is not admitted to be prior art by inclusion in this section. Summary of the invention

[0013] The object of the present invention is to provide a low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation, thereby solving one or more problems caused by limitations and defects of related technologies at least to a certain extent.

[0014] The present invention provides a low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation, comprising the following steps:

[0015] The transmitting end performs cyclic redundancy check on the information sequence and adds check information, and then performs LDPC-Hadamard code encoding to form coded data;

[0016] Performing constellation mapping on the encoded data, and performing OTFS modulation on the complex-valued symbols after constellation mapping, wherein the OTFS modulation includes performing inverse symplectic finite Fourier transform and Heisenberg transform on the complex-valued symbols to output a time domain signal,

[0017] The time domain signal is subjected to a time delay and Doppler frequency shift through a multipath time-varying channel to generate a transmission signal;

[0018] The receiving end performs OTFS demodulation on the received transmission signal, wherein the OTFS demodulation includes performing Wigner transform and symplectic Fourier transform on the transmission signal to output a symbol matrix.

[0019] Performing constellation inverse mapping on the symbol matrix to restore the received bit stream;

[0020] The received bit stream is subjected to LDPC-Hadamard decoding, and the decoded bit stream is subjected to cyclic redundancy check to remove the check information and output the original bit stream.

[0021] In an exemplary embodiment of the present disclosure, the LDPC-Hadamard code is a concatenated code combining LDPC code and Hadamard code, including:

[0022] The LDPC code is constructed by using a low-complexity quasi-cyclic method and encoded using a shift register;

[0023] The LDPC coded output is Hadamard coded.

[0024] In an exemplary embodiment of the present disclosure, the LDPC code is constructed using a low-complexity quasi-cyclic method and encoded using a shift register, including:

[0025] A check matrix is ​​formed by a plurality of permutation matrices or shift matrices, wherein each submatrix in the check matrix is ​​a cyclic shift matrix, wherein the cyclic shift matrix cyclically shifts the elements of the vector;

[0026] By using the quasi-circular structure of the check matrix, the check matrix is ​​converted into a systematic form through Gaussian elimination method to obtain a generator matrix.

[0027] The generator matrix and the information bit vector are encoded via matrix multiplication.

[0028] In an exemplary embodiment of the present disclosure, the expression formulas of the check matrix and the cyclic shift matrix are respectively:

[0029]

[0030] P i =I i

[0031] Among them, H is the check matrix, P i,j It is a cyclic shift matrix or zero matrix of size z×z, called a permutation matrix or unit shift matrix. The entire matrix consists of m b ×n b sub-matrices, each of which is a z×z cyclic shift matrix or a zero matrix. i It means to shift the columns of the identity matrix cyclically to the right by i positions.

[0032] In an exemplary embodiment of the present disclosure, the expression of the system form is:

[0033] H=[P|I]

[0034] Among them, P is a submatrix and I is the identity matrix.

[0035] In an exemplary embodiment of the present disclosure, the expression for encoding the generator matrix and the information bit vector by matrix multiplication is:

[0036] c=uG

[0037] Among them, c is the code, u is the information bit vector, and G is the generator matrix.

[0038] In an exemplary embodiment of the present disclosure, the OTFS modulation includes performing an inverse symplectic finite Fourier transform and a Heisenberg transform on the complex-valued symbol to output a time domain signal, including:

[0039] Convert the complex-valued symbol from the Delay-Doppler domain to the time-frequency domain by inverse discrete sigmoid Fourier transform;

[0040] The time-frequency domain signal is converted into the time domain signal through the Heisenberg transform.

[0041] In an exemplary embodiment of the present disclosure, the OTFS demodulation includes performing Wigner transform and symplectic Fourier transform on the transmission signal to output a symbol matrix, including:

[0042] Perform Wigner transform on the transmitted signal to restore the representation of the signal in the Delay Doppler domain;

[0043] Through the symplectic Fourier transform, the signal is remapped from the time-frequency domain to the Delay-Doppler domain and the symbol matrix is ​​output.

[0044] In an exemplary embodiment of the present disclosure, the constellation mapping adopts QAM or PSK.

[0045] In an exemplary embodiment of the present disclosure, the LDPC-Hadamard decoding includes:

[0046] The BP algorithm is used to iteratively decode the LDPC code of the received signal;

[0047] After LDPC decoding is completed, the output soft information is passed to the Hadamard decoding part, and the fast Hadamard transform is used to decode the Hadamard code.

[0048] The present disclosure proposes a low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation, which can include the following beneficial effects: on the one hand, through OTFS pre-processing and OTFS post-processing, it can better cope with the dual-selective fading channel in the high-speed mobile scenario; on the other hand, by combining LDPC-Hadamard code with OTFS, the error correction performance of the system under low signal-to-noise ratio is improved, more information can be transmitted under the same bandwidth conditions, the spectrum efficiency and transmission rate are improved, and the reliability of the system in the high-speed mobile environment is enhanced; on the other hand, through LDPC-Hadamard coding, the low-density characteristics of LDPC code are combined with the strong error correction performance of Hadamard code, and the error performance of the OTFS system under low signal-to-noise ratio is further improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0050] Figure 1 A schematic diagram showing the steps of a low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation in an exemplary embodiment of the present invention;

[0051] Figure 2 A schematic diagram of the basic architecture of OTFS in an exemplary embodiment of the present invention is shown;

[0052] Figure 3 A schematic diagram of an LDPC-Hadamard coding structure in an exemplary embodiment of the present invention is shown;

[0053] Figure 4 A schematic diagram of the LDPC-Hadamard decoding structure in an exemplary embodiment of the present invention is shown;

[0054] Figure 5 A schematic diagram of fast Hadamard transform in an exemplary embodiment of the present invention is shown;

[0055] Figure 6 A schematic diagram showing the comparison of the error performance of LDPC-Hadamard code and LDPC code in an OTFS system in an exemplary simulation experiment of the present invention is shown. DETAILED DESCRIPTION

[0056] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0057] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0058] This exemplary embodiment provides a low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation, such as Figure 1-Figure 2 As shown, the following steps may be included:

[0059] S101: The transmitting end performs cyclic redundancy check on the information sequence and adds check information, and then performs LDPC-Hadamard coding to form coded data.

[0060] S102: Perform constellation mapping on the encoded data, and perform OTFS modulation on the complex-valued symbols after constellation mapping, wherein the OTFS modulation includes performing inverse symplectic finite Fourier transform and Heisenberg transform on the complex-valued symbols to output a time domain signal.

[0061] S103: The time domain signal is subjected to a multipath time-varying channel to generate a time delay and Doppler frequency shift to generate a transmission signal.

[0062] S104: The receiving end performs OTFS demodulation on the received transmission signal, wherein the OTFS demodulation includes performing Wigner transform and symplectic Fourier transform on the transmission signal to output a symbol matrix.

[0063] S105: Perform constellation inverse mapping on the symbol matrix to restore the received bit stream.

[0064] S106: Perform LDPC-Hadamard decoding on the received bit stream, remove the check information from the decoded bit stream through a cyclic redundancy check, and output the original bit stream.

[0065] The present disclosure proposes a low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation, which can include the following beneficial effects: on the one hand, through OTFS pre-processing and OTFS post-processing, it can better cope with the dual-selective fading channel in the high-speed mobile scenario; on the other hand, by combining LDPC-Hadamard code with OTFS, the error correction performance of the system under low signal-to-noise ratio is improved, more information can be transmitted under the same bandwidth conditions, the spectrum efficiency and transmission rate are improved, and the reliability of the system in the high-speed mobile environment is enhanced; on the other hand, through LDPC-Hadamard coding, the low-density characteristics of LDPC code are combined with the strong error correction performance of Hadamard code, and the error performance of the OTFS system under low signal-to-noise ratio is further improved.

[0066] The following is a more detailed description of each step of the above method in this exemplary embodiment.

[0067] Step S101: the transmitting end performs cyclic redundancy check on the information sequence and adds check information, and then performs LDPC-Hadamard code encoding to form coded data.

[0068] Specifically, the input bit stream u first passes through a cyclic redundancy process (CRC) to generate a bit stream c′ with a check code.

[0069] The LDPC-Hadamard code is encoded in the channel coding link.

[0070] First, LDPC encoding is performed. In the Tanner graph of the traditional LDPC code, information bits are assigned to variable nodes, and the variable nodes are connected to the check nodes to form the graph structure. The check nodes represent parity check constraints, and each check node is connected to multiple variable nodes to ensure that the weighted sum of these variable nodes meets certain parity check rules.

[0071] Secondly, Hadamard encoding is performed. LDPC-Hadamard code introduces Hadamard constraints on the basis of standard LDPC code. Its bipartite graph is similar to that of standard LDPC code, but the difference is that the check node becomes a super check node, and the super check node connects multiple variable nodes. However, their check relationship is not a simple parity check, but based on Hadamard code. These nodes introduce Hadamard transformation, making the encoding process more complicated and having stronger error correction capability. The output after Hadamard encoding is x, and its formula is expressed as:

[0072] x=H·c′ (1)

[0073] H is the Hadamard transformation matrix.

[0074] S102: Perform constellation mapping on the encoded data, and perform OTFS modulation on the complex-valued symbols after constellation mapping, wherein the OTFS modulation includes performing inverse symplectic finite Fourier transform and Heisenberg transform on the complex-valued symbols to output a time domain signal.

[0075] Specifically, constellation mapping is performed on the Hadamard-encoded data x to convert it into complex-valued symbols for transmission. A constellation mapping scheme such as QAM (quadrature amplitude modulation) or PSK (phase shift keying) is used. Using QAM, the mapped symbol is x[k,l], where k and l represent the Doppler index and delay index in the Delay-Doppler domain, respectively. The expression is:

[0076] x[k,l]=Modulate(x) (2)

[0077] The symbol x[k,l] will be transformed from the Delay-Doppler domain to the time-frequency domain by the inverse discrete symplectic Fourier transform (ISFFT). The expression of the symbol after ISFT processing is:

[0078] x[n,m]=ISFFT(x[k,l]) (3)

[0079] Where n and m are indices in the time-frequency domain. The time-frequency domain signal is then converted to a time domain signal x(t) through the Heisenberg transform, which is used to prepare the transmission signal:

[0080]

[0081] Among them, g tx (t) is the transmit window function, T is the symbol duration, and Δf is the subcarrier spacing.

[0082] S103: The time domain signal is subjected to a multipath time-varying channel to generate a time delay and Doppler frequency shift to generate a transmission signal.

[0083] Specifically, after the Heisenberg transform, the signal x(t) is transmitted through the multipath time-varying channel h(τ,ν). The channel produces time delay and Doppler frequency shift on the signal, and the received signal r(t) can be expressed by convolution as:

[0084] r(t)=∫∫h(τ,ν)x(t-τ)e j2πν(t-τ) dτdν+w(t) (5)

[0085] Where w(t) is the noise in the channel and h(τ,ν) is the channel response.

[0086] S104: The receiving end performs OTFS demodulation on the received transmission signal, wherein the OTFS demodulation includes performing Wigner transform and symplectic Fourier transform on the transmission signal to output a symbol matrix.

[0087] Specifically, the receiving end first performs a Wigner Transform on the received signal r(t) to restore the representation of the signal in the Delay-Doppler domain. Then, the signal is remapped from the time-frequency domain to the Delay-Doppler domain through SFFT (Sympilix Fourier Transform) and the symbol matrix is ​​output:

[0088] y[n,m]=SFFT(r(t)) (6)

[0089] S105: Perform constellation inverse mapping on the symbol matrix to restore the received bit stream.

[0090] Specifically, the received symbol matrix y[n,m] is restored to the received bit stream y[k,l] through constellation inverse mapping:

[0091] y[k,l]=Demodulate(y[n,m]) (7)

[0092] S106: Perform LDPC-Hadamard decoding on the received bit stream, remove the check information from the decoded bit stream through a cyclic redundancy check, and output the original bit stream.

[0093] Specifically, error correction is performed through LDPC-Hadamard decoding. First, the received bit stream y[k,l] is Hadamard decoded, and its expression is:

[0094] c″=H -1 y[k,l] (8)

[0095] Next, the errors are corrected through LDPC decoding to restore the final bit stream c′:

[0096] c′=LDPC-Decode(c″) (9)

[0097] The decoding process of LDPC-Hadamard codes first performs preliminary error correction through iterative message passing decoding of LDPC codes. In this stage, variable nodes and check nodes exchange confidence information and gradually correct bit errors. Then, at the Hadamard check node, the received bit sequence is processed through the Hadamard transform, and the most likely codeword is selected using maximum likelihood decoding. Hadamard's strong error correction capability helps solve decoding in low signal-to-noise ratio environments.

[0098] The decoded bit stream c′ is then verified by CRC to remove redundant bits and check for bit errors, thus restoring the original bit stream.

[0099]

[0100] Complete the entire transfer process.

[0101] In the disclosed embodiment, the LDPC-Hadamard coding structure can be represented by a Tanner graph for a standard LDPC code, such as Figure 3 As shown on the left. A variable node with degree j is a (j,1) repetition code, where the edge connecting the left and right nodes needs to satisfy both the repetition code constraint at the variable node and the SPC constraint at the check node. It is defined by replacing the SPC code in the LDPC code with any other block code. Consider using Hadamard code at the right check node to obtain LDPC-Hadamard, as Figure 3 As shown in the right part, LDPC-Hadamard codes have good performance under very noisy channel conditions. The present invention only considers the case where all Hadamard code check nodes have the same order.

[0102] First, the construction of QC-LDPC code adopts a low-complexity quasi-cyclic construction method to construct LDPC code, that is, quasi-cyclic LDPC code (Quasi-Cyclic LDPC, referred to as QC-LDPC). QC-LDPC code is a type of structured LDPC code, and its check matrix has a quasi-cyclic structure. This structure can greatly reduce the complexity of hardware implementation, especially in storage and decoding. Its construction process is generally combined with the quasi-cyclic characteristics of the generator matrix or the check matrix, and is generated by cyclic shift. The construction process of QC-LDPC code is as follows:

[0103] 1) Construction of the check matrix

[0104] The check matrix H of a QC-LDPC code is usually composed of several permutation matrices or shift matrices, where each submatrix is ​​a cyclic shift matrix. Therefore, the check matrix of a QC-LDPC code can be expressed as a concatenation of multiple block matrices:

[0105]

[0106] Where P i,j is a cyclic shift matrix or zero matrix of size z×z, called a permutation matrix or unit shift matrix. Therefore, the entire matrix consists of m b ×n b sub-matrices, where each sub-matrix is ​​a z×z cyclic shift matrix or a zero matrix.

[0107] 2) Circular shift matrix

[0108] Circular shift matrix P i is a special matrix that cyclically shifts the elements of a vector. Assuming that represents the z×z identity matrix, the cyclic shift matrix can be expressed as:

[0109] P i =I i (12)

[0110] Among them, I i It means to cyclically shift the columns of the identity matrix to the right by i positions. For example, a simple 4×4 cyclic shift matrix P1 can be expressed as:

[0111]

[0112] 3) Generator Matrix of QC-LDPC Code

[0113] The generator matrix G of the QC-LDPC code can be constructed by the quasi-cyclic property of the check matrix H. The construction method of the generator matrix G is usually based on the following steps: first, the check matrix H is converted into a system form, that is, H = [P|I], where P is a submatrix and I is the identity matrix. Then, using the quasi-cyclic structure of the check matrix, the check matrix can be converted into a system form by Gaussian elimination, thereby obtaining the generator matrix G.

[0114] 4) Coding of QC-LDPC Codes

[0115] The encoding process of QC-LDPC code is relatively simple. Due to its quasi-cyclic structure, it can be encoded using shift registers, which greatly reduces the hardware complexity. Specifically, the encoding of QC-LDPC code can be achieved through matrix multiplication. Given the generator matrix G and the information bit vector u, the codeword c can be generated by matrix multiplication:

[0116] c=uG (14)

[0117] Since the generator matrix G has a quasi-circular structure, the encoding result can be quickly calculated through shift operations.

[0118] Next, Hadamard encoding is performed. The Hadamard matrix is ​​a square matrix defined on a binary alphabet. r )The Hadamard matrix can be constructed as follows:

[0119]

[0120] The Hadamard matrix ±H n The columns of {±h j:j=0,1,...,2 r -1}. It can be proved that ±H n Each column of H forms a linear space, and the dimension of this linear space is r+1. n Replace {+1,-1} in each column with {0,1} to get a parameter of (2 r ,r+1) linear block code, that is, Hadamard code.

[0121] The generator matrix G of the Hadamard code in systematic form H,r+1 It can be obtained by recursion:

[0122]

[0123] Among them, J r It is with G H,r Matrices of the same order have the following form:

[0124]

[0125] The recursive termination condition is:

[0126]

[0127] The codeword c of the systematic Hadamard code with r being an even number has the following properties:

[0128]

[0129] That is, the bits at corresponding positions in the codeword satisfy the parity check relationship. This property plays an important role in LDPC-Hadamard.

[0130] Hadamard code encoding process, the Hadamard code encoding process maps the information bits to the rows of the Hadamard matrix, and generates codewords through this mapping. Assuming there are k bits of information, the Hadamard code encoding process maps the information bits to the rows of the Hadamard matrix. For m bits of information, it can be encoded with a length of n = 2 m Code word.

[0131] Assume that the input information vector is u=[u0,u1,...,u m-1 ], there are m information bits in total. According to the encoding rule of Hadamard code, each information vector corresponds to a row in the Hadamard matrix. Map the information bit u to a row of the Hadamard matrix. Define the Hadamard matrix H n The i-th row of h i , then the encoded codeword c is a row in the matrix, that is:

[0132] c=h u (20)

[0133] Among them, h u represents a row in the Hadamard matrix, and the position of the row is determined by the binary value of the information bit u. The following example illustrates the above encoding process.

[0134] Let m = 2, then n = 2 2 =4, the corresponding Hadamard matrix H4 is:

[0135]

[0136] If the input information bit u=[1,0], its binary value is 2, then the encoded codeword is the third row of H4:

[0137] c=[1,1,-1,-1] (22)

[0138] From the above process, it can be seen that the LDPC-Hadamard coding method is a cascade coding scheme that combines LDPC codes and Hadamard codes. The system first performs LDPC encoding on the input data to generate codewords that are sparse and easy to implement in hardware. The sparsity of LDPC coding makes it have low complexity in large data transmission. Next, the output of the LDPC code is Hadamard encoded to further improve the anti-noise performance. As a maximum distance separable code, Hadamard coding can effectively correct errors in environments with extremely low signal-to-noise ratios. Through this cascade method, LDPC-Hadamard coding not only has the high efficiency of LDPC codes, but also uses Hadamard codes to enhance the robustness of the system in noisy and interfering environments, and is suitable for communication systems with high reliability requirements.

[0139] In the disclosed embodiment, the LDPC-Hadamard decoding structure is as follows: Figure 4 As shown, information is iteratively exchanged between the variable nodes and the Hadamard check nodes. After a certain number of iterations, the decoder outputs the decoding result.

[0140] The BP decoding algorithm of LDPC code is an iterative process that approximates the maximum likelihood estimation through message passing. LDPC code can be represented as a sparse check matrix H, where each row corresponds to a check node and each column corresponds to a variable node. The BP decoding algorithm of LDPC is performed on this factor graph.

[0141] 1) Initially, the received signal y=[y1,y2,...,y n ] is transmitted through the channel. For each variable node i, the initialization message (i.e. the prior probability of each bit) is:

[0142]

[0143] Among them, P(c i =0|y i ) and P(c i =1|y i ) represent the given received signal y i When the code word bit c i is the probability of being 0 or 1. For an AWGN channel, these probabilities can be calculated based on a Gaussian distribution.

[0144] 2) Iterative message transmission: BP decoding of LDPC codes mainly performs message transmission on the factor graph. In each iteration, information is transmitted from the variable node to the check node, which processes it and then transmits it back to the variable node.

[0145] The variable node sends messages to the connected check nodes. These messages are updated based on the signals received by the variable node and the information sent from other check nodes. For each variable node i and its connected check node j, the transmitted message m i→j for:

[0146]

[0147] Among them, L(q i ) is the log-likelihood ratio of the received signal, r k→i It is the information from other check nodes k to variable node i. N(i)\j represents all check nodes connected to variable node i, except j.

[0148] The check node updates information based on the messages of the variable nodes it is connected to. For each check node j and its connected variable node i, the message r transmitted j→i for:

[0149]

[0150] Among them, tanh -1 is the inverse hyperbolic tangent function, and N(j)\i represents all variable nodes connected to the check node j, except i.

[0151] 3) Decisions and hard judgments

[0152] At the end of each iteration, each variable node updates its estimate based on the initial received information and the message received from the check node. For each variable node j, we calculate its posterior log-likelihood ratio:

[0153]

[0154] Then for each qi Making a hard judgment:

[0155]

[0156] After each iteration, the current estimated codeword Check whether all validation conditions are met, i.e. If it is satisfied, the decoding is successful; if it is not satisfied, the next round of iteration is performed.

[0157] Fast APP decoding of Hadamard codes,In the iterative steps of the posterior probability (APP) decoding algorithm of Hadamard codes, the product of the Hadamard matrix and the current vector is used to update the probability information in each step. However, the complexity of directly calculating these products is high. The introduction of the fast Hadamard transform (FHT) can significantly reduce this computational complexity. FHT uses the structural characteristics of the Hadamard matrix to speed up the operation through recursive decomposition, making the iterative decoding of Hadamard codes more efficient.

[0158] The n-order Hadamard matrix, general method to calculate y = H n x requires n(n-1) addition operations, that is, 2 r (2 r -1) times, but the complexity can be significantly reduced by using the properties of the Hadamard matrix.

[0159]

[0160] In this way, it can be converted into H n / 2 x′ and H n / 2 x″. This process is repeated recursively until it reaches H1. It can be proved that this method only requires r2 r The computational complexity is greatly reduced by adding times. The above calculation y = H n The method of x is called FHT.

[0161] The fast Hadamard transform is very similar to the fast Fourier transform. Figure 5 The steps of the fast APP decoding algorithm of Hadamard code are as follows:

[0162] Let x = (X0, X1, ..., X n-1 ) is the sending sequence (x i ∈{+1,-1}), y=(y1,y2,...,y n-1 ) is the received sequence, then the posterior probability log-likelihood ratio is:

[0163]

[0164] in, In order to calculate γ(±h j ) Need to calculate the inner product The latter is Notice that The fast Hadamard transform can be used to calculate γ(±h j ) can be easily obtained.

[0165] In the decoding process of LDPC-Hadamard code, the LLR-BP (Log-Likelihood Ratio Belief Propagation) algorithm is first used to iteratively decode the LDPC code of the received signal. The algorithm continuously updates the LLR values ​​of the variable nodes and the check nodes by message passing on the bipartite graph corresponding to the check matrix of the LDPC code, and gradually approaches the optimal decoding result. After completing the LDPC decoding, the output soft information will be passed to the Hadamard decoding part. For the decoding of Hadamard code, the fast Hadamard transform (FHT) is used for processing. The FHT algorithm can quickly and efficiently perform Hadamard transforms, significantly reducing the computational complexity, thereby restoring the original information data. The entire LDPC-Hadamard decoding process achieves efficient and low-complexity decoding performance by combining two algorithms, which is suitable for communication systems in high-noise environments.

[0166] In order to verify the method of this application, the following simulation experiments were conducted: Comparison of error performance between LDPC-Hadamard code and LDPC code in OTFS system.

[0167] In the OTFS system, the signal is severely affected by delay spread and Doppler frequency shift after passing through the multipath time-varying channel. The LDPC-Hadamard code has better error correction performance in complex environments than using LDPC code alone because it combines the anti-interference characteristics of Hadamard coding.

[0168] like Figure 6 As shown in the figure, the experimental parameters are set as the number of information bits K = 1024, the code rate R = 1 / 9, and simulations are performed under different signal-to-noise ratio conditions (Eb / N0). The bit error rate (BER) comparison curve shows the bit error performance of the two coding methods under the same conditions. The experimental results show that as the signal-to-noise ratio increases, the bit error rate of the LDPC-Hadamard code is significantly lower than that of the traditional LDPC code, especially in the low signal-to-noise ratio area (such as Eb / N0 is lower than 0dB), its performance advantage is particularly obvious. In the signal-to-noise ratio range of -0.8 to 0.6dB, the bit error rate of the LDPC-Hadamard code remains at a low level, showing higher stability and anti-interference ability.

[0169] The simulation results show that by introducing the anti-noise characteristics of Hadamard codes, LDPC-Hadamard codes significantly improve the system's bit error performance under low signal-to-noise ratio conditions, making it more suitable for communication needs in high-speed mobile environments.

[0170] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification.

[0171] Those skilled in the art will readily appreciate other embodiments of the present invention after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses or adaptations of the present invention, which follow the general principles of the present invention and include common knowledge or customary techniques in the art that are not disclosed by the present invention. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present invention are indicated by the appended claims.

Claims

1. A low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation, characterized in that: The following steps are involved: The transmitting end performs cyclic redundancy check on the information sequence and adds check information, and then performs LDPC-Hadamard code encoding to form coded data; Performing constellation mapping on the encoded data, and performing OTFS modulation on the complex-valued symbols after constellation mapping, wherein the OTFS modulation includes performing inverse symplectic finite Fourier transform and Heisenberg transform on the complex-valued symbols to output a time domain signal; The time domain signal is subjected to a time delay and Doppler frequency shift through a multipath time-varying channel to generate a transmission signal; The receiving end performs OTFS demodulation on the received transmission signal, wherein the OTFS demodulation includes performing Wigner transform and symplectic Fourier transform on the transmission signal to output a symbol matrix; Performing constellation inverse mapping on the symbol matrix to restore the received bit stream; The received bit stream is subjected to LDPC-Hadamard decoding, and the decoded bit stream is subjected to cyclic redundancy check to remove the check information and output the original bit stream.

2. The low-complexity LDPC-Hadamard code encoding method under OTFS modulation according to claim 1, characterized in that: The LDPC-Hadamard code is a concatenated code combining LDPC code and Hadamard code, including: The LDPC code is constructed by using a low-complexity quasi-cyclic method and encoded using a shift register; The LDPC coded output is Hadamard coded.

3. The low-complexity LDPC-Hadamard code encoding method under OTFS modulation according to claim 2, characterized in that: The method of constructing LDPC code by using a low-complexity quasi-cyclic method and encoding by using a shift register comprises: A check matrix is ​​formed by a plurality of permutation matrices or shift matrices, wherein each submatrix in the check matrix is ​​a cyclic shift matrix, wherein the cyclic shift matrix cyclically shifts the elements of the vector; Using the quasi-circular structure of the check matrix, the check matrix is ​​converted into a system form through Gaussian elimination method to obtain a generator matrix. The generator matrix and the information bit vector are encoded via matrix multiplication.

4. The low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation according to claim 3, characterized in that: The expressions of the check matrix and the cyclic shift matrix are respectively: P i =I i Among them, H is the check matrix, P i,j It is a cyclic shift matrix or zero matrix of size z×z, called a permutation matrix or unit shift matrix. The entire matrix consists of m b ×n b sub-matrices, each of which is a z×z cyclic shift matrix or a zero matrix. i It means to shift the columns of the identity matrix cyclically to the right by i positions.

5. The low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation according to claim 4, characterized in that: The expression of the system form is: H=[P|I] Among them, P is a submatrix and I is the identity matrix.

6. The low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation according to claim 5, characterized in that: The expression for encoding the generator matrix and the information bit vector by matrix multiplication is: c=uG Among them, c is the code, u is the information bit vector, and G is the generator matrix.

7. The low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation according to claim 1, characterized in that: The OTFS modulation includes performing an inverse symplectic finite Fourier transform and a Heisenberg transform on the complex-valued symbol to output a time domain signal, including: Convert the complex-valued symbol from the Delay-Doppler domain to the time-frequency domain by inverse discrete sigmoid Fourier transform; The time-frequency domain signal is converted into the time domain signal through the Heisenberg transform.

8. The low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation according to claim 1, characterized in that: The OTFS demodulation includes performing Wigner transform and sigma Fourier transform on the transmission signal to output a symbol matrix, including: Perform Wigner transform on the transmitted signal to restore the representation of the signal in the Delay Doppler domain; Through the symplectic Fourier transform, the signal is remapped from the time-frequency domain to the Delay-Doppler domain and the symbol matrix is ​​output.

9. The low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation according to claim 1, characterized in that: The constellation mapping adopts QAM or PSK.

10. The low-complexity LDPC-Hadamard code encoding and decoding method under OTFS modulation according to claim 1, characterized in that: The LDPC-Hadamard decoding includes: The BP algorithm is used to iteratively decode the LDPC code of the received signal; After LDPC decoding is completed, the output soft information is passed to the Hadamard decoding part, and the Hadamard code is decoded using fast Hadamard transform.

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