Coding and decoding processing method and device

Abstract

The invention discloses a coding and decoding processing method and device, and the method comprises the steps: a transmitting end obtains a basic parameter of an RM code and a plurality of to-be-processed information bits, determines a bit index set according to a predefined superposition proportion, a superposition mode and the basic parameter, carries out the coding of the to-be-processed information bits according to a preset coding mode and the bit index set, and carries out the decoding of the to-be-processed information bits. The preset coding mode is determined by a preset partially superposed Plotkin recursive structure or a corresponding generation matrix, modulating the coded code word, and sending the modulated signal to a receiving end through a channel, so that the receiving end performs channel decoding on the demodulated information through a preset decoding algorithm and outputs the demodulated information.

Description

Technical Field

[0001] The present application relates to the field of communication technology, and more specifically, to a coding and decoding processing method and device. Background Art

[0002] In wireless communication systems, errors may occur during signal transmission due to the presence of noise in the channel. Channel coding technology is to add some redundant bits to achieve error detection and correction at the receiving end, aiming to improve the reliability and anti-interference ability of wireless communication systems. In the process of channel coding research, many excellent coding methods have emerged.

[0003] As a classic algebraic code, Reed-Muller (RM) code can be constructed by Plotkin's (u, u+v) recursive structure, and RM code has good maximum likelihood (ML) decoding performance under short codes. At the same time, RM code has also developed several well-known decoding algorithms, including Dumer's recursive list decoding algorithm, recursive projection aggregation decoding algorithm, etc.

[0004] However, Dumer's recursive list decoding algorithm, a classic decoding algorithm for RM codes, cannot quickly and effectively approach the ML decoding performance for medium-length codes. The decoding process of RM codes often requires a large list and has high decoding complexity, which results in a failure to achieve significant performance gains for RM codes with longer code lengths.

[0005] Therefore, how to obtain a greater performance gain when the code length of the RM code is longer is an urgent problem to be solved in this application. Summary of the invention

[0006] In view of this, the present application discloses a coding and decoding processing method and device, which aims to reduce the block error rate curve of a partially superimposed RM code, thereby narrowing the gap with its maximum likelihood estimate lower bound, and achieving a greater performance gain especially for cases with longer code lengths.

[0007] In order to achieve the above purpose, the disclosed technical solution is as follows:

[0008] In a first aspect, the present application discloses a coding and decoding processing method, which is applied to a transmitting end and includes:

[0009] Obtaining basic parameters of the RM code and a plurality of information bits to be processed;

[0010] Determine a bit index set according to a predefined superposition ratio, superposition mode and the basic parameters;

[0011] Encoding the plurality of information bits to be processed according to a preset encoding method and the bit index set to obtain an encoded codeword; wherein the preset encoding method is determined by a preset partially superimposed Plotkin recursive structure or a corresponding generator matrix;

[0012] The encoded codeword is modulated, and the modulated signal is sent to a receiving end through a channel, so that the receiving end performs channel decoding on the demodulated information through a preset decoding algorithm and outputs it.

[0013] Preferably, the superposition mode includes at least a sequential superposition mode or a row-size superposition mode, and the bit index set is determined according to the predefined superposition ratio, superposition mode and basic parameters, including:

[0014] If the superposition mode is a sequential superposition mode, the number of codeword bits to be superimposed is obtained by a predefined superposition ratio, the bit index set is composed of continuous indexes, and the set size is equal to the number of codeword bits to be superimposed;

[0015] If the superposition mode is the row-weight superposition mode, obtaining the generator matrix of the RM code and the number of codeword bits to be superimposed, and initializing the original set;

[0016] Obtaining each row weight of the generator matrix, and determining a destination row with the smallest row weight from among the row weights;

[0017] Searching for each column index whose target row element is 1, and taking the union of the set formed by each column index and the original set as the target set;

[0018] Determine the size of the target set, and judge whether the size of the target set is greater than or equal to the number of superimposed bits;

[0019] If the size of the target set is greater than or equal to the number of bits to be superimposed, determining that the size of the target set meets the requirement on the number of superimposed bits;

[0020] When the size of the target set meets the requirement of the number of superimposed bits, outputting the index of the number of bits to be superimposed in the new set as the bit index set;

[0021] If the size of the target set is smaller than the number of bits to be superimposed, set all elements of the target row to 1, return to the step of obtaining the row weights of the generating matrix, and determine the target row with the smallest row weight from the row weights, until the size of the target set is greater than or equal to the number of bits to be superimposed, and output the index of the number of bits to be superimposed in the new set as the bit index set.

[0022] Preferably, encoding the plurality of information bits to be processed according to a preset encoding mode and the bit index set to obtain an encoded codeword includes:

[0023] Decomposing the information bits to be encoded according to the Plotkin recursive structure of the RM code until decomposing into a repetition code or a full-space code, obtaining corresponding sub-information bits, and performing RM code encoding on the sub-information bits; wherein the Plotkin recursive structure is determined by the sub-code u and the sub-code u+v;

[0024] In the process of superimposing the PS-RM code on the subcode according to the Plotkin recursive structure, the subcode u is kept unchanged, and in the codeword of the subcode u+v, the positions represented by the elements in the bit index set are superimposed, and the remaining positions are not superimposed and maintained as the subcode v;

[0025] The expression of the PS-RM code for pre-setting the subcode according to the Plotkin recursive structure is as follows:

[0026]

[0027] Among them, m and r are parameters required for the definition of RM code; u is the codeword of subcode PS-RM(m-1, r); v is the codeword of subcode PS-RM(m-1, r-1); u′ is the Hadamard product of u and s; s is a binary mask vector, and the elements of all index positions in the bit index set where s is located are 1, and the elements of the remaining positions are 0; F is the representation of number field in mathematics.

[0028] Preferably, encoding the information bits according to a preset encoding mode and the bit index set to obtain an encoded codeword includes:

[0029] Obtain a generator matrix according to a preset generator matrix recursively;

[0030] Among them, the preset generation matrix recursive expression is as follows:

[0031]

[0032] Among them, G PS-RM (m, r) is the generator matrix; G PS-RM (m-1, r) is a submatrix; G′ PS-RM (m-1, r) is a submatrix; G PS-RM (m-1, r-1) is a submatrix; S is a binary diagonal matrix, and the elements of S at the diagonal positions corresponding to all indices in the bit index set are 1, and the elements at the other diagonal positions are 0;

[0033] Obtaining the information vector to be encoded;

[0034] The generator matrix and the information vector to be encoded are multiplied to obtain an encoded codeword.

[0035] The second aspect of the present application discloses a coding and decoding processing method, which is applied to a receiving end and includes:

[0036] When a signal is received, the received signal is demodulated to obtain demodulated information; wherein the received signal includes a modulated signal and noise, and the modulated signal is determined by the transmitter according to a predefined superposition ratio, superposition mode and basic parameters, a bit index set is determined, a plurality of information bits to be processed are encoded according to a preset encoding mode and the bit index set, and the encoded codeword is modulated to obtain;

[0037] The demodulated information is channel-decoded using a preset decoding algorithm and then outputted.

[0038] Preferably, channel decoding is performed on the demodulated information by a preset decoding algorithm and output, including:

[0039] Get the demodulated log-likelihood ratio;

[0040] According to a preset recursive list decoding algorithm, recursively decompose the log-likelihood ratios of the positions represented by the elements in the bit index set, and keep the log-likelihood ratios of the remaining positions unchanged, to obtain a recursive decomposition result;

[0041] The calculation formula of the preset recursive list decoding algorithm is:

[0042]

[0043] in, is the log-likelihood ratio of the ith bit of the subcode v; ln is a logarithmic function with a natural constant as the base; LLR i is the log-likelihood ratio of the i-th bit of the current codeword; The i+2th of the current codeword m-1 The log-likelihood ratio of bits; exp is an exponential function with a natural constant as the base; i is the codeword bit index; is a bit index set; is the log-likelihood ratio of the i-th bit of subcode u; is the decoding result of the i-th bit of subcode v;

[0044] Recursively until a repetitive code or a full-space code is reached, and channel decoding is performed according to the recursive decomposition result;

[0045] For repetitive codes, add all-0 codewords and all-1 codewords to the candidate list;

[0046] For the full-space code, four code words meeting preset conditions are selected and added to the candidate list; the preset conditions are determined according to the posterior probability value of the code words;

[0047] Calculate the posterior probability values ​​of all codewords in the candidate list, return the first L codewords that meet the preset conditions according to the posterior probability values ​​of all codewords in the candidate list, and obtain the decoding result to complete the process of channel decoding the demodulated information and output it, where L is the set list size.

[0048] Preferably, it also includes:

[0049] Set the normalized signal-to-noise ratio;

[0050] Set different overlay ratios for intervals based on a fixed step size;

[0051] According to the encoded codewords and the results of channel decoding, the block error rates under different superposition ratios are counted;

[0052] According to the block error rates under different stacking ratios, the stacking ratio with the smallest block error rate is selected as the optimal value under the normalized signal-to-noise ratio.

[0053] In a third aspect, the present application discloses a coding and decoding processing device, which is applied to a transmitting end and includes:

[0054] An acquisition unit, used for acquiring basic parameters of the RM code and a plurality of information bits to be processed;

[0055] A determination unit, configured to determine a bit index set according to a predefined superposition ratio, superposition mode and the basic parameters;

[0056] An encoding unit, used for encoding the plurality of information bits to be processed according to a preset encoding method and the bit index set to obtain an encoded codeword; wherein the preset encoding method is determined by a preset partially superimposed Plotkin recursive structure or a corresponding generator matrix;

[0057] The modulation and transmission unit is used to modulate the encoded codeword and send the modulated signal to the receiving end through the channel, so that the receiving end performs channel decoding on the demodulated information through a preset decoding algorithm and outputs it.

[0058] Preferably, the superposition method includes at least a sequential superposition method or a row-size superposition method, and the determination unit includes:

[0059] A first acquisition module is used to acquire a generator matrix of the RM code and the number of codeword bits to be superimposed, and initialize an original set if the superposition mode is the row-major-size superposition mode;

[0060] A second acquisition module is used to acquire the row weights of the generator matrix and determine the target row with the smallest row weight from the row weights;

[0061] A search module, used for searching for each column index whose target row element is 1, and taking the union of the set formed by each column index and the original set as the target set;

[0062] A first determination module, used to determine the size of a target set, and judge whether the size of the target set is greater than or equal to the number of superimposed bits;

[0063] A second determination module is used to determine that the size of the target set meets the requirement on the number of superimposed bits if the size of the target set is greater than or equal to the number of bits to be superimposed;

[0064] An output module, configured to output an index of the number of bits to be superimposed in a new set as a bit index set when the size of the target set meets the requirement of the number of superimposed bits;

[0065] A setting module is used to set all elements of the destination row to 1 if the size of the destination set is smaller than the number of bits to be superimposed, return to execute the step of obtaining the row weights of the generating matrix and determining the destination row with the smallest row weight from the row weights, until the size of the destination set is greater than or equal to the number of bits to be superimposed, and output the index of the number of bits to be superimposed in the new set as a bit index set.

[0066] In a fourth aspect, the present application discloses a coding and decoding processing device, which is applied to a receiving end and includes:

[0067] A demodulation unit is used to demodulate the received signal when receiving the signal to obtain demodulated information; wherein the received signal includes a modulated signal and noise; the modulated signal is determined by the transmitter according to a predefined superposition ratio, superposition mode and basic parameters, a bit index set is determined, a plurality of information bits to be processed are encoded according to a preset encoding mode and the bit index set, and the encoded codeword is modulated to obtain;

[0068] The decoding output unit is used to perform channel decoding on the demodulated information through a preset decoding algorithm and output it.

[0069] It can be known from the above technical scheme that the present application discloses a coding and decoding processing method and device, wherein the transmitting end obtains the basic parameters of the RM code and multiple information bits to be processed, determines the bit index set according to the predefined superposition ratio, superposition mode and basic parameters, encodes the multiple information bits to be processed according to the preset coding mode and the bit index set, and obtains the encoded codeword, wherein the preset coding mode is determined by the Plotkin recursive structure of the preset partial superposition or the corresponding generating matrix, modulates the encoded codeword, and sends the modulated signal to the receiving end through the channel, so that the receiving end performs channel decoding on the demodulated information through the preset decoding algorithm and outputs it. Through the above scheme, considering the Plotkin recursive structure (u,u+v) of the RM code, when v is first decoded, the u superimposed on it is regarded as a kind of interference, and because the decoding error of the RM code is dominated by v, the bit index set is determined according to the predefined superposition ratio, superposition method and basic parameters based on the preset coding method, that is, the preset recursive structure, and then only the bits at the corresponding positions of the elements in the bit index set of the subcode u are selected to be superimposed on the subcode v, rather than superimposing all positions, which can increase the accuracy of decoding v and reduce the block error rate. When constructing the PS-RM code, the superposition position, that is, the row weight superposition method, will be carefully selected, so as to better reduce the block error rate and narrow the gap with its maximum likelihood decoding lower bound, especially for the case of longer code lengths, a larger performance gain can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0071] Figure 1 A schematic diagram of a communication system disclosed in an embodiment of the present application;

[0072] Figure 2 A schematic diagram of a process flow of a coding and decoding method disclosed in an embodiment of the present application;

[0073] Figure 3 A flowchart of determining a bit index set disclosed in an embodiment of the present application;

[0074] Figure 4 A flowchart of encoding a plurality of information bits to be processed according to a preset encoding method and a bit index set disclosed in an embodiment of the present application;

[0075] Figure 5Another flowchart of encoding multiple information bits to be processed according to a preset encoding method and a bit index set disclosed in an embodiment of the present application;

[0076] Figure 6 A schematic diagram of a recursive construction of a PS-RM code disclosed in an embodiment of the present application;

[0077] Figure 7 A schematic diagram of a generator matrix of a PS-RM code disclosed in an embodiment of the present application;

[0078] Figure 8 A schematic diagram of a PS-RM code redistribution disclosed in an embodiment of the present application;

[0079] Fig. 9 A flowchart of another encoding and decoding processing method disclosed in an embodiment of the present application;

[0080] Fig.10 A decoding flow chart of a PS-RM code disclosed in an embodiment of the present application;

[0081] Fig.11 A flowchart of searching for an optimal superposition ratio of a PS-RM code disclosed in an embodiment of the present application;

[0082] Fig.12 This is an example diagram of a curve showing a change in block error rate versus superposition ratio of PS-RM (8, 3) disclosed in an embodiment of the present application;

[0083] Fig.13 The block error rate of PS-RM (8, 3) disclosed in the embodiment of the present application varies with the normalized signal-to-noise ratio Eb / N0;

[0084] Fig.14 The block error rate of PS-RM (9, 3) disclosed in the embodiment of the present application varies with the superposition ratio;

[0085] Fig.15 The block error rate of PS-RM (9, 3) disclosed in the embodiment of the present application varies with the normalized signal-to-noise ratio Eb / N0;

[0086] Fig.16 The block error rate of PS-RM (10, 2) disclosed in the embodiment of the present application varies with the superposition ratio;

[0087] Fig.17 The block error rate of PS-RM (10, 2) disclosed in the embodiment of the present application varies with the normalized signal-to-noise ratio Eb / N0;

[0088] Fig.18 A schematic diagram of the structure of a coding and decoding processing device disclosed in an embodiment of the present application;

[0089] Fig.19 A schematic diagram of the structure of another encoding and decoding processing device disclosed in an embodiment of the present application;

[0090] Fig. 20 This is a schematic diagram of the structure of an electronic device disclosed in an embodiment of the present application. DETAILED DESCRIPTION

[0091] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0092] In this application, the terms "comprises", "comprising" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or device comprising the element.

[0093] As can be seen from the background technology, the classic decoding algorithm of RM code, Dumer's recursive list decoding algorithm, cannot quickly and effectively approach the ML decoding performance when the code is medium or long. The decoding process of RM code often requires a large list, and the decoding complexity is high. As a result, it is impossible to obtain a large performance gain when the code length of RM code is long. Therefore, how to obtain a large performance gain when the code length of RM code is long is a problem that needs to be solved urgently in this application.

[0094] In order to solve the above problems, the present application discloses a processing method and device for encoding and decoding, considering the Plotkin recursive structure (u, u+v) of the RM code, when first decoding v, the u superimposed thereon is regarded as a kind of interference, and because the RM code decoding error is dominated by v, the bit index set is determined according to the predefined superposition ratio, superposition method and basic parameters by a preset coding method, that is, on the basis of the preset recursive structure, and then only the bits at the corresponding positions of the elements in the bit index set of the subcode u are selected to be superimposed on the subcode v, rather than superimposing all positions, which can increase the accuracy of the decoding v, thereby reducing the block error rate. When constructing the PS-RM code, the superimposed position, that is, the row weight superposition method, can be carefully selected, so that the block error rate can be better reduced, and the gap with the lower bound of its maximum likelihood decoding can be narrowed, especially for the case of a longer code length, a larger performance gain can be obtained. The specific implementation method is specifically described by the following embodiments.

[0095] refer to Figure 1 The first embodiment of the present invention is a schematic diagram of a communication system disclosed in the present application, and the communication system is composed of a transmitting end, a channel and a receiving end. The transmitting end includes channel coding and modulation, and the receiving end includes demodulation and channel decoding.

[0096] The communication process between the sender, channel and receiver is:

[0097] The transmitter obtains the basic parameters of the Reed-Muller (RM) code and a k-bit information sequence; the basic parameters include the order (r) of the RM code and the logarithmic length (m) of the RM code; the value of k is an integer greater than or equal to 1; the relationship between r, m and the code rate (R) and the code length (n) is n=2 m ; R = k / n. The expression of k is shown in formula (1).

[0098]

[0099] It should be noted that RM code is an error correction coding technology, in which r and m are two important parameters used to describe the characteristics and performance of the code. m determines n, which is the total number of bits after encoding. Theoretically, a longer n can provide stronger error correction capabilities under certain circumstances, but it will also increase the overhead of data transmission or storage. When m is constant, the size of r determines the size of R. R can be understood as the coding efficiency, which indicates the ratio between the data part actually used to store or transmit information and n when transmitting or storing data. A higher code rate means that the information part accounts for a larger proportion in the encoding, while a lower code rate means that more redundancy is added to improve the error correction capability. In the context of RM code, different coding efficiencies and error correction capabilities can be achieved by adjusting the values ​​of r and m to meet specific communication or storage requirements. For example, in RM (2, 5) coding, the code length n = 25 =32, The code rate R = 16 / 32 = 0.5, which means that for each information bit, additional redundant bits are generated to form the code, thereby improving the reliability of the data.

[0100] The transmitter determines the bit index set according to the predefined superposition ratio, superposition mode and basic parameters.

[0101] The predefined stacking ratio is shown in formula (2).

[0102]

[0103] During the encoding process, all (u, u′+v) superpositions can use the same or different partial superposition ratios; α is a predefined superposition ratio; is a bit index set; the superposition method includes at least a sequential superposition method or a row-major superposition method; the sequential superposition method includes partial superposition from front to back, superimposing the first p bits of u onto v, and partial superposition from back to front, superimposing the last p bits of u onto v; the row-major superposition method refers to selecting a column index set as the row-major of the RM code matrix according to its row-major size Prioritize adding the column indices of non-zero elements in rows with smaller row weights Until the required Collection size;

[0104] It should be noted that for any superposition method, when the partial superposition ratio α is given, the PS-RM code superposition index set of any parameter is are fixed. They can be obtained by offline calculation and stored in memory Thus, the computational complexity of encoding and decoding is not increased;

[0105] The transmitter performs channel coding on multiple information bits to be processed according to a preset coding method and a bit index set to obtain an encoded codeword of n bits; wherein the preset coding method is determined by a Plotkin recursive structure with preset partial superposition or a corresponding generator matrix; the value of n is an integer greater than or equal to 1; the codeword refers to an n-dimensional vector obtained by channel coding k information bits to be transmitted at the transmitter, which is called a codeword.

[0106] The description of the preset partially superimposed Plotkin recursive structure and the corresponding generator matrix is ​​embodied in S203 in the second embodiment.

[0107] The transmitting end modulates the encoded codeword of n bits to obtain a modulated signal, and sends the modulated signal to the receiving end through the channel;

[0108] The receiving end receives the signal, demodulates the received signal, then inputs the log-likelihood ratio (LLR) into the decoder and outputs the decoding result; the decoding result is compared bit by bit with the k information bits sent. If all k bits are the same, the decoding is correct, otherwise the decoding is wrong.

[0109] The log-likelihood ratio of a codeword bit c is defined as the logarithm of the likelihood probability of c being 0 to the likelihood probability of c being 1, as shown in formula (3).

[0110]

[0111] Wherein, LLR is log likelihood ratio; y is the received signal; P is the likelihood probability; and c is the codeword bit.

[0112] The beneficial effects of the first embodiment of the present application: Considering the Plotkin recursive structure (u, u+v) of the RM code, when v is first decoded, the u superimposed thereon is regarded as a kind of interference, and because the decoding error of the RM code is dominated by v, the bit index set is determined according to the predefined superposition ratio, superposition method and basic parameters on the basis of the preset coding method, that is, the preset recursive structure, and then only the bits at the corresponding positions of the elements in the bit index set of the subcode u are selected to be superimposed on the subcode v, rather than superimposing all positions, which can increase the accuracy of the translation of v, thereby reducing the block error rate. When constructing the PS-RM code, the superimposed position, that is, the row weight superposition method, will be carefully selected, so that the block error rate can be better reduced, and the gap with its maximum likelihood decoding lower bound can be narrowed, especially for the case of longer code lengths, a larger performance gain can be obtained.

[0113] refer to Figure 2 As shown in the second embodiment of the present application, a coding and decoding processing method is disclosed in the present application, and the coding and decoding processing method is applied to the above embodiment. Figure 1 The transmitting end of the communication system of the present invention mainly comprises the following steps:

[0114] S201: The transmitting end obtains basic parameters of the RM code and a plurality of information bits to be processed.

[0115] It should be noted that the basic parameters include order (r), logarithmic length (m), etc.

[0116] The multiple information bits to be processed are data that a transmitter of the communication system wants to send. The data to be sent is divided into a group every k bits, and is obtained from parameters r and m according to the basic definition of RM code.

[0117] The expression of k is shown in the above formula (1).

[0118] S202: The transmitting end determines a bit index set according to a predefined superposition ratio, superposition mode and basic parameters.

[0119] The superposition method at least includes a sequential superposition method or a row-size superposition method.

[0120] The specific process of the sending end determining the bit index set according to the pre-defined superposition ratio, superposition mode and basic parameters is as follows: Figure 3 As shown in A1-A8.

[0121] A1: If the superposition mode is a sequential superposition mode, the number of codeword bits to be superimposed is obtained by a predefined superposition ratio, and the bit index set is composed of continuous indexes, and the size is the number of codeword bits to be superimposed;

[0122] The predefined stacking ratio is shown in the above formula (2).

[0123] During the encoding process, all (u, u′+v) superpositions may adopt the same or different partial superposition ratios.

[0124] The sequential superposition method includes performing partial superposition from the front to the back, superimposing the first p bits of u onto v, as specifically shown in formula (4).

[0125]

[0126] Where m is the logarithmic length.

[0127] According to the partial superposition from back to front, the p bits after u are superimposed on v, as shown in formula (5).

[0128]

[0129] Right now

[0130] Wherein, u′ is the decoding result; P is the number of bit superposition.

[0131] A2: If the superposition method is row-major superposition, obtain the generator matrix of the RM code and the number of codeword bits to be superimposed α·2 m-1 , and initialize the original collection

[0132] Among them, the row size superposition method is the row size of the RM code matrix, and the column index set is selected according to the row size of the RM code matrix as Prioritize adding the column indices of non-zero elements in rows with smaller row weights Until the required The size of the collection.

[0133] Generator matrix: For (n, k) linear block code, if u = (u1, u1, ..., u k ) is the information sequence to be encoded, then the corresponding codeword can be obtained by c=u·G=(c1, c1, …, c n ) is given, the matrix G with k rows and n columns is called the generating matrix.

[0134] According to the above coding method, when encoding PS-RM(m, r), the codeword bits to be partially superimposed come from PS-RM(m-1, r). m-1 , the selection of the codeword bit position index to be superimposed is particularly important for the structure and performance of the code itself. Because the non-superimposed position will cause the corresponding column of its generator matrix to be set to 0, if the row weight of the row with a smaller row weight becomes smaller during this process, it may cause its performance to degrade. Therefore, the embodiment of the present application starts from the row weight of the RM (m-1, r) generator matrix, and preferentially selects the codeword bit of the column index where the non-zero element in the row with a smaller row weight is located.

[0135] A3: Obtain the row weights of the generated matrix and determine the destination row with the smallest row weight from among the row weights.

[0136] A4: Search for the column indexes whose target row element is 1, and take the union of the set formed by the column indexes and the original set as the target set (new set).

[0137] Count the row weights of each row of the generated matrix G, find the row with the smallest row weight, search for the column index whose element in the row is 1, and add the set of all column indices to the set Take the union as a new set

[0138] A5: Determine the size of the target set and determine whether the size of the target set is greater than or equal to the number of superimposed bits (α·2 m-1 ).

[0139] In S305, the current set is determined size With α·2 m-1 The size relationship of the target set is to determine whether the size of the target set is greater than or equal to the number of superimposed bits (α·2 m-1 );

[0140] A6: If the size of the target set is greater than or equal to the number of bits to be superimposed (α·2 m-1 ), determine that the size of the target set meets the requirement for the number of superposition bits.

[0141] Among them, if the target set size Determine whether the size of the destination set meets the requirement on the number of superposition bits.

[0142] like Then execute A7. Otherwise, execute A8.

[0143] A7: When the size of the target set meets the requirement of the number of superimposed bits, output the number of bits to be superimposed in the new set (α·2 m-1 ) as a set of bit indices.

[0144] When the size of the target set meets the requirement of the number of superposition bits, the output set Middle front α·2 m-1 otherwise, set the row to all 1s.

[0145] A8: If the size of the target set is smaller than the number of bits to be superimposed (α·2 m-1 ), set all elements of the destination row to 1, return to the step of obtaining the row weights of the generator matrix, and determine the destination row with the smallest row weight from the row weights, until the size of the destination set is greater than or equal to the number of bits to be superimposed (α·2 m-1 ), output the number of bits to be superimposed in the new set (α·2 m-1 ) as a bit index set. For any superposition method, when the partial superposition ratio α is given, the PS-RM code superposition index set of any parameter is According to the method, these sets can be obtained by offline calculation and stored in memory. This does not increase the computational complexity of encoding and decoding.

[0146] For example, the present application provides the following example: when the stacking is performed according to the row size, when the same stacking ratio α=7 / 8 is used, all index sets involving partial stacking in the PS-RM (7, 2) code are: use Indicates the set of bit position indices of the PS-RM (m-1, r) words to be superimposed when encoding PS-RM (7, 2), including the following:

[0147]

[0148] In the present application, for α·2 m-1 If the number is not an integer, it will be rounded up.

[0149] S203: The transmitter encodes the plurality of information bits to be processed according to a preset encoding method and a bit index set to obtain an encoded codeword; wherein the preset encoding method is determined by a preset partially superimposed Plotkin recursive structure or a corresponding generator matrix. Specifically, the transmitter encodes the plurality of information bits to be processed according to the preset encoding method and a bit index set to obtain an encoded codeword. Figure 4 B1-B2 in, and Figure 5 As shown in C1-C3 in . Among them, B1-B2 is encoded according to the preset partially superimposed Plotkin recursive structure. C1-C3 is encoded according to the preset generated matrix expression.

[0150] B1: According to the Plotkin recursive structure (u, u+v) of the RM code, all the information bits to be encoded are decomposed until they are decomposed into a repetition code or a full-space code, the corresponding sub-information bits are obtained, and the sub-information bits are encoded with the RM code.

[0151] It should be noted that u and v are both subcodes in the Plotkin recursive construction. The Plotkin recursive construction of RM code is shown in formula (6):

[0152] RM(m, r)={(u, u+v): u∈RM(m-1, r), v∈RM(m-1, r-1)} (6)

[0153] Among them, u is the codeword of the subcode RM(m-1, r), and v is the codeword of the subcode RM(m-1, r-1). In other words, the codeword of RM(m, r) consists of two halves, the first half is the codeword u of the corresponding subcode RM(m-1, r), and the second half is the superposition of the codeword u of the subcode RM(m-1, r) and the codeword v of the subcode RM(m-1, r-1): u+v.

[0154] According to formula (6), the k-length information bit sequence is similarly recursively decomposed into two sub-information bit sequence lengths: k1 and k2 are sent to the encoding with parameters (m-1, r) and (m-1, r-1) respectively.

[0155] When recursion reaches m=g, r=0, the information bit length is 1, and the bit is repeatedly encoded for 2 times. g times, the return length is 2 g Repeating code.

[0156] When recursion reaches m = r = h, the length is The information bit sequence and generator matrix Perform modulo 2 multiplication, where the matrix is ​​generated for The h-th Kronecker power, and return the encoded result.

[0157] Among them, the repetition code and the full-space code represent two types of leaf nodes.

[0158] B2: In the process of presetting the partial superposition PS-RM code for subcodes according to the Plotkin recursive structure of the RM code, keep the subcode u unchanged. In the codewords of the latter half subcode u + v, only perform the superposition operation on the positions represented by the elements in the bit index set, and do not perform superposition on the remaining positions and maintain them as the subcode v.

[0159] Specifically, for any given PS-RM code with parameters 0 < r < m, the recursive construction method is as shown in formula (7):

[0160]

[0161] Among them, both m and r are parameters required for the definition of the RM code; u is the codeword of the subcode PS-RM(m - 1, r); v is the codeword of the subcode PS-RM(m - 1, r - 1); u′ is the Hadamard product of u and s; s is a binary mask vector, and the elements at all index positions in the bit index set where s is located are 1, and the elements at the remaining positions are 0; F represents the number field in mathematics.

[0162] After completing the encoding of the two child nodes of any node in the above encoding process, perform the (u, u′ + v) merge on the encoded codewords returned by the two child nodes, where u is the encoded codeword from PS-RM(m - 1, r), v is the encoded codeword from PS-RM(m - 1, r - 1), and u′ is obtained by setting some positions of u to 0, and return (u, u′ + v). Specifically, it can be seen from Figure 6 Continue to explain.

[0163] Exemplarily, assume Figure 6 The vertical bar shaded squares in represent u = [u1, u2, u3, u4, u5, u6, u7, u8], the horizontal bar shaded squares represent v = [v1, v2, v3, v4, v5, v6, v7, v8], and the blank squares represent 0. Then Figure 5 u′ in is [u1, 0, u3, u4, 0, u6, 0, u8]. At this time, the partial superposition encoding is (u, u′ + v) =

[0164] where the addition is all modulo 2 addition, and the result after superposition is represented by the common shading of the horizontal and vertical bars.

[0165] The specific numerical values of the various parameters involved in the above introduction are all examples and do not constitute limitations; in actual application scenarios, the specific numerical values of the relevant parameters can be set according to the actual situation.

[0166] C1: Obtaining a generator matrix according to a preset generator matrix recursive expression (i.e., a generator matrix recursive expression of a PS-RM code);

[0167] The recursive expression of the generator matrix of the PS-RM code is shown in formula (8).

[0168]

[0169] Among them, G PS-RM (m, r) is the generator matrix; G PS-RM (m-1, r) is a submatrix; G′ PS-RM (m-1, r) is a submatrix; G PS-RM (m-1, r-1) is a submatrix; S is a binary diagonal matrix, and the elements of S at the diagonal positions corresponding to all indexes in the bit index set are 1, and the elements at the other diagonal positions are 0.

[0170] Selection Matrix s i ∈F2, i = 1, 2, ..., 2 m-1 , is a binary diagonal matrix, that is, the submatrix G′ PS-RM Some columns of (m-1, r) are selected from the submatrix G PS-RM (m-1, r) corresponding column, the rest of the columns are set to all 0.

[0171] The elements of the mask vector s and the diagonal elements of the selection matrix S

[0172] Each bit of u′ u i is the i-th bit of u;

[0173] Submatrix G′ PS-RM Each column of (m-1, r) g i is the submatrix G PS-RM The i-th column vector of (m-1, r).

[0174] C2: Get the information vector to be encoded.

[0175] C3: Multiply the generation matrix and the information vector to be encoded to obtain the encoded codeword (PS-RM codeword).

[0176] In C3, the information vector to be encoded is multiplied modulo 2 by the generator matrix to obtain the PS-RM codeword.

[0177] For example, the generator matrix of PS-RM (3, 2) is Figure 7 First, G PS-RM (3, 2) is decomposed into G PS-RM (2, 2), G′PS-RM (2, 2), G PS-RM (2, 1) and zero matrix. Among them, G PS-RM (2, 2) is Right now The second Kronecker power of G′ PS-RM (2, 2) is to convert G PS-RM Some columns of (2, 2) are set to 0. In this example, the last two columns are set to 0, that is,

[0178] Then G PS-RM (2, 1) continues to decompose into G PS-RM (1, 1), G′ PS-RM (1,1),G PS-RM (1,0) and zero matrix, where G′ PS-RM (1, 1) is G PS-RM Some columns of (1, 1) are set to 0. In this example, the last column is set to 0, that is, In addition, G PS-RM (1, 0) = [1 1], thus the generator matrix of PS-RM (3, 2) is obtained, and then the codeword can be obtained by multiplying the input information sequence to be encoded modulo 2 by the generator matrix.

[0179] It should be noted that in this example, all partial superpositions in the generated matrix adopt the same partial superposition ratio, and the superposition ratio is 1 / 2, that is, for a sub-matrix with two columns, one of the columns is set to 0; for a sub-matrix with four columns, two of the columns are set to 0. Optionally, the present application does not limit the specific value of the superposition ratio and the position of the selected superposition.

[0180] Figure 8 The row weight superposition method provided in this embodiment is demonstrated. When the same superposition ratio α=7 / 8 is adopted, the code weight distribution of PS-RM(7,2), that is, the code weight after encoding all possible information sequences is counted and compared with the code weight distribution of RM(7,2).

[0181] Figure 8 In the figure, the horizontal axis is the code weight; the vertical axis is the number of code words; the orange bar graph represents the code weight distribution of RM(7,2), and the blue bar graph represents the code weight distribution of PS-RM(7,2). It can be seen that the code weight of RM(7,2) code is only distributed in 1, 32, 48, 56, 64, 72, 80, 96, 128, while that of PS-RM(7,2) code is distributed in most code weights from 14 to 108, and the minimum non-zero code weight of PS-RM(7,2) is 14, which is smaller than the minimum non-zero code weight of RM(7,2) 32.

[0182] It should be noted that the specific values ​​of the parameters involved in the above introduction are for example only and do not constitute a limitation. In addition, this application does not limit the above three superposition methods. In actual application scenarios, you can choose according to the actual situation.

[0183] S204: modulate the encoded codeword, and send the modulated signal to the receiving end through the channel, so that the receiving end performs channel decoding on the demodulated information through a preset decoding algorithm and outputs it.

[0184] The beneficial effects of the second embodiment of the present application: Considering the Plotkin recursive structure (u, u+v) of the RM code, when v is first decoded, the u superimposed thereon is regarded as a kind of interference, and because the decoding error of the RM code is dominated by v, the bit index set is determined according to the predefined superposition ratio, superposition method and basic parameters on the basis of the preset coding method, that is, the preset recursive structure, and then only the bits at the corresponding positions of the elements in the bit index set of the subcode u are selected to be superimposed on the subcode v, rather than superimposing all positions, which can increase the accuracy of the translation of v, thereby reducing the block error rate. When constructing the PS-RM code, the superimposed position, that is, the row weight superposition method, will be carefully selected, so that the block error rate can be better reduced, and the gap with its maximum likelihood decoding lower bound can be narrowed, especially for the case of longer code lengths, a larger performance gain can be obtained.

[0185] refer to Fig. 9 Embodiment 3 is another encoding and decoding processing method disclosed in this application, and the encoding and decoding processing method is applied to the above embodiment. Figure 1 The receiving end of the disclosed communication system, the encoding and decoding processing method mainly includes the following steps:

[0186] S901: When the receiving end receives a signal, it demodulates the received signal to obtain demodulated information; wherein the received signal includes a modulated signal and noise; the modulated signal is determined by the transmitting end according to a predefined superposition ratio, superposition method and basic parameters, a bit index set is determined, a plurality of information bits to be processed are encoded according to a preset encoding method and a bit index set, and the encoded codeword is modulated to obtain.

[0187] S902: The receiving end performs channel decoding on the modulated signal using a preset recursive list decoding algorithm and outputs the signal.

[0188] Specifically, the received signal is demodulated to obtain demodulated information, and the demodulated information is channel decoded and outputted using a preset decoding algorithm. Fig.10 As shown in D1-D6:

[0189] D1: The receiving end obtains the demodulated log-likelihood ratio.

[0190] In the present application embodiment, if Figure 1 The modulation of the transmitter adopts binary phase shift keying (BPSK) modulation, and the binary code word bit 0 is mapped to the signal +1, and the bit 1 is mapped to the signal -1. Then the channel is assumed to adopt the additive white Gaussian noise (AWGN) channel, and the Gaussian white noise is superimposed on the transmitted signal. Then the calculation formula of the demodulated logarithmic likelihood ratio of the receiving end is shown in formula (9):

[0191]

[0192] Where y is the received signal; σ 2 is the variance of Gaussian white noise.

[0193] It should be noted that the above only takes BPSK modulation and AWGN channel as an example, and the log-likelihood ratio can also be obtained in other scenarios.

[0194] D2: The receiving end recursively decomposes the log-likelihood ratio of the position represented by the element in the bit index set according to the preset recursive list decoding algorithm, and keeps the log-likelihood ratio of the remaining positions unchanged, and obtains the recursive decomposition result (first translation Retranslation ).

[0195] The calculation formula of the preset recursive list decoding algorithm is shown in formula (10) and formula (11):

[0196]

[0197] Will Input into PS-RM(m-1, r-1) decoder, output decoding result

[0198] Will Input into PS-RM(m-1, r) decoder, output decoding result

[0199] in, is the log-likelihood ratio of the ith bit of the subcode v; ln is a logarithmic function with a natural constant as the base; LLR i is the log-likelihood ratio of the i-th bit of the current codeword; The i+2th of the current codeword m-1 The log-likelihood ratio of bits; exp is an exponential function with a natural constant as the base; i is the codeword bit index; is a bit index set; is the log-likelihood ratio of the i-th bit of the subcode u; is the decoding result of the i-th bit of subcode v;

[0200] Among them, if That is, the i-th bit u of u i Superimposed on the i-th bit v of v i At this time, there is no difference between decoding RM code using Dumer's recursive list and decoding RM code using Dumer's recursive list. The calculation formula is: It is directly equivalent to Because at this time u i Not superimposed on v i So v i The log-likelihood ratio of can be obtained directly. After that, if Same as RM code, u i It is equivalent to repeating it twice. LLR i and to merge; if u i Only sent once, its log-likelihood ratio is equal to LLR i .

[0201] and Indicates the subcode in the corresponding decoding process. (Conventionally, the superscript \hat{} is usually used to indicate the estimated result. Because the decoding is not necessarily correct, there may be decoding errors due to noise, that is, is not necessarily equal to the true value u, It is not necessarily equal to the true value v, so as to distinguish it).

[0202] D3: The receiving end recursively reaches the repetitive code or the full-space code, and performs channel decoding based on the recursive decomposition result;

[0203] D4: For repetitive codes, the receiver adds all-0 codewords and all-1 codewords to the candidate list;

[0204] D5: For the full-space code, the receiver selects 4 code words that meet the preset conditions and adds them to the candidate list; the preset conditions are determined according to the posterior probability value of the code words;

[0205] D6: Calculate the posterior probability values ​​of all codewords in the candidate list, return the first L codewords that meet the preset conditions based on the posterior probability values ​​of all codewords in the candidate list, and obtain the decoding result to complete the channel decoding process of the demodulated information and output it, where L is the set list size.

[0206] Specifically, the calculation formula for the posterior probability of the codewords in the candidate list is shown in formula (12):

[0207]

[0208] Where c is the codeword translated from the leaf node; y is the corresponding signal. According to the Bayesian formula, that is, formula (13):

[0209]

[0210] Similarly, we can get formula (14):

[0211]

[0212] When all partial superpositions in the encoding process use the same superposition ratio, the method for searching the optimal superposition ratio of the PS-RM code is as follows: Fig.11 As shown in F1-F4 in.

[0213] F1: Set the normalized signal-to-noise ratio.

[0214] Among them, normalized signal-to-noise ratio: The signal-to-noise ratio is generally defined as the ratio of the average signal power to the average noise power, while the normalized signal-to-noise ratio refers to the ratio of each binary bit energy (Eb) to the noise power spectral density (N0), recorded as Eb / N0;

[0215] For example, when BPSK modulation and AWGN channel are used, the variance σ of the normalized signal-to-noise ratio and Gaussian white noise is 2 The relationship is: Where R is the bit rate.

[0216] F2: Set different overlay ratios for intervals based on a fixed step size.

[0217] F3: According to the encoded codewords and the results of channel decoding, the block error rates under different superposition ratios are counted.

[0218] Different superposition ratios are set from 0 to 1 with fixed step lengths, the encoding and decoding methods of the PS-RM code are repeatedly executed, and the block error rates under different superposition ratios are counted.

[0219] Specifically, according to Figure 1 The communication process of the Monte Carlo simulation is performed at each superposition ratio. First, the transmitter generates random bits as the information bits to be encoded, then performs PS-RM code encoding, adds Gaussian white noise with variance after BPSK modulation, and decodes after calculating LLR at the receiver. Finally, it is determined whether the decoding is correct and stops after reaching a certain number of simulations. Calculate the block error rate.

[0220] The block error rate is the ratio of the number of codewords decoded incorrectly by the receiving end to the total number of codewords sent by the sending end.

[0221] F4: According to the block error rates under different stacking ratios, the stacking ratio with the minimum block error rate is selected as the optimal value.

[0222] Fig.12 and Fig.13 The block error rate curve of PS-RM(8,3) is shown. Fig.12 The block error rate of PS-RM (8, 3) varies with the stacking ratio, where the normalized signal-to-noise ratio is set to E. b / N0=3dB, the superposition mode selection is based on the row weight and the superposition mode selects the bit index set as During the encoding process, all partial superpositions use the same superposition ratio, the superposition ratio is searched with a step size of 1 / 64, the decoding list size is 4, and for each superposition ratio, when 200 codewords are decoded incorrectly, the decoding stops and the block error rate is calculated.

[0223] from Fig.12 It can be seen that the stacking ratio with the smallest block error rate is 15 / 16.

[0224] Fig.13 Is adopted Fig.12 The block error rate curve of the optimal stacking ratio 15 / 16 obtained by searching varies with the normalized signal-to-noise ratio. The stacking method is the row-size stacking method, and the decoding list sizes are 4, 16, and 64 respectively. When 200 codewords are decoded incorrectly at each normalized signal-to-noise ratio, the block error rate is stopped and calculated. The red line is the block error rate curve of the RM code, and the blue line is the block error rate curve of the PS-RM code.

[0225] from Fig.13 It can be seen that as the normalized signal-to-noise ratio increases, the block error rate gradually decreases; as the decoding list size increases, the block error rate curve also gradually decreases. More importantly, it can be clearly seen that when the above stacking method is used and the stacking ratio is 15 / 16, the performance of PS-RM (8, 3) is significantly better than RM (8, 3). For example, when the block error rate is 10 -4 When the decoding list size is 16, the normalized signal-to-noise ratio required for PS-RM is about 3.55dB; while the normalized signal-to-noise ratio required for RM is about 3.8dB, which is improved by about 0.25dB.

[0226] It should be noted that ML decoding refers to comparing all codewords in the codebook with the received signal to find the codeword with the largest likelihood probability P(y|c). In practice, the ML lower bound is usually used to determine whether the performance of the decoding algorithm is close to ML decoding.

[0227] Specifically, when a codeword is decoded And decoding error When c is compared with The likelihood probability size is, if The likelihood probability of is larger, which means that even if ML decoding is used, it cannot be decoded correctly, and the error in this case is counted; on the contrary, if the likelihood probability of c is larger, ML decoding may be able to decode correctly. Fig.13 The ML lower bound in is obtained by adding the above judgment conditions, and setting the decoding list size to 1024. The above situation stops when 100 codewords are wrong. It can be seen that the ML lower bounds of RM (8, 3) and PS-RM (8, 3) are basically the same, which also shows that PS-RM (8, 3) can effectively narrow the gap between the actual performance and the ML lower bound.

[0228] Fig.14 and Fig.15 The block error rate curve of PS-RM (9, 3) is shown. Fig.14 The block error rate of PS-RM (9, 3) varies with the stacking ratio, where the normalized signal-to-noise ratio is set to E. b / N0=3.5dB, the stacking mode selects the row weight stacking mode. During the encoding process, all partial stacking uses the same stacking ratio. The stacking ratio is searched in steps of 1 / 64. The decoding list size is 4. For each stacking ratio, when 200 codewords are decoded incorrectly, stop and calculate the block error rate. Fig.14 It can be seen that the stacking ratio with the smallest block error rate is 15 / 16. Fig.15 Is adopted Fig.14 The block error rate curve of the optimal stacking ratio 15 / 16 obtained by searching varies with the normalized signal-to-noise ratio. The stacking method is the same as above, and the decoding list sizes are 16, 64, and 256 respectively. When 200 codewords are decoded incorrectly at each normalized signal-to-noise ratio, the block error rate is stopped and calculated. The red line is the block error rate curve of the RM code, and the blue line is the block error rate curve of the PS-RM code. Fig.14 It can be seen that when the block error rate is 10 -4 When the decoding list size is 64, the normalized signal-to-noise ratio required by PS-RM is about 3.3dB, while the normalized signal-to-noise ratio required by RM is about 3.85dB, which is improved by about 0.55dB; for the ML lower bound, the decoding list size is set to 1024, and the method stops when 100 codewords are wrong under ML judgment. The ML lower bound of PS-RM(9,3) is about 0.2dB rightward than that of RM(9,3).

[0229] Fig.16 and Fig.17 The block error rate curve of PS-RM(10,2) is shown. Fig.13The block error rate of PS-RM (10, 2) varies with the stacking ratio, where the normalized signal-to-noise ratio is set to E. b / N0=3.5dB, the stacking mode selects the row weight stacking mode. During the encoding process, all partial stacking uses the same stacking ratio. The stacking ratio is searched in steps of 1 / 128. The decoding list size is 4. For each stacking ratio, when 200 codewords are decoded incorrectly, stop and calculate the block error rate. Fig.16 It can be seen that the superposition ratio with the smallest block error rate is about 7 / 8. Fig.17 Is adopted Fig.16 The block error rate curve of the optimal stacking ratio 7 / 8 obtained by searching varies with the normalized signal-to-noise ratio. The stacking method is the same as above, and the decoding list sizes are 4, 16, and 64 respectively. When the decoding error reaches 200 codewords at each normalized signal-to-noise ratio, the block error rate is stopped and calculated. The red line is the block error rate curve of the RM code, and the blue line is the block error rate curve of the PS-RM code. Fig.17 It can be seen that when the block error rate is 10 -4 , when the decoding list size is 16, the normalized signal-to-noise ratio required for PS-RM is about 3.95dB, while the normalized signal-to-noise ratio required for RM is about 4.95dB, which is improved by about 1.00dB; and for the ML lower bound, the decoding list size is set to 1024, and it stops when 100 codewords are wrong under ML judgment, and the ML lower bound of PS-RM (10, 2) is about 0.4dB right-shifted than that of RM (10, 2). Finally, based on the above embodiments, it can be seen that the longer the code length, the greater the performance improvement of PS-RM code compared with RM code.

[0230] The beneficial effects of the third embodiment of the present application: Considering the Plotkin recursive structure (u, u+v) of the RM code, when v is first decoded, the u superimposed thereon is regarded as a kind of interference, and because the decoding error of the RM code is dominated by v, the bit index set is determined according to the predefined superposition ratio, superposition method and basic parameters on the basis of the preset coding method, that is, the preset recursive structure, and then only the bits at the corresponding positions of the elements in the bit index set of the subcode u are selected to be superimposed on the subcode v, rather than superimposing all positions, which can increase the accuracy of the translation of v and reduce the block error rate. When constructing the PS-RM code, the superimposed position, that is, the row weight superposition method, will be carefully selected, so as to better reduce the block error rate and narrow the gap with its maximum likelihood decoding lower bound, especially for the case of longer code lengths, a larger performance gain can be obtained.

[0231] Based on the above embodiments Figure 2 A coding and decoding processing method is disclosed, and the fourth embodiment of the present application also discloses a coding and decoding processing device, such as Fig.18 As shown, the encoding and decoding processing device includes:

[0232] An acquiring unit 1801 is used to acquire basic parameters of the RM code and a plurality of information bits to be processed;

[0233] A determination unit 1802, configured to determine a bit index set according to a predefined superposition ratio, superposition mode and basic parameters;

[0234] The encoding unit 1803 is used to encode the multiple information bits to be processed according to a preset encoding method and a bit index set to obtain an encoded codeword; wherein the preset encoding method is determined by a preset partially superimposed Plotkin recursive structure or a corresponding generator matrix;

[0235] The modulation and transmission unit 1804 is used to modulate the encoded codeword and send the modulated signal to the receiving end through the channel, so that the receiving end performs channel decoding on the demodulated information through a preset decoding algorithm and outputs it.

[0236] Furthermore, the superposition method at least includes a sequential superposition method or a row-size superposition method, and the determination unit 1802 includes:

[0237] A first determination module is used for obtaining the number of codeword bits to be superimposed by a predefined superposition ratio if the superposition mode is a sequential superposition mode, wherein the bit index set is composed of continuous indexes and the set size is equal to the number of codeword bits to be superimposed;

[0238] A first acquisition module is used to acquire a generator matrix of the RM code and the number of codeword bits to be superimposed if the superposition mode is a row-major-size superposition mode, and initialize an original set;

[0239] The second acquisition module is used to acquire the weights of each row of the generated matrix and determine the target row with the smallest row weight from among the row weights;

[0240] A search module is used to search for each column index whose target row element is 1, and take the union of the set formed by each column index and the original set as the target set;

[0241] A second determination module is used to determine the size of the target set and judge whether the size of the target set is greater than or equal to the number of superimposed bits;

[0242] A third determination module is used to determine that the size of the target set meets the requirement on the number of superimposed bits if the size of the target set is greater than or equal to the number of bits to be superimposed;

[0243] An output module, used for outputting an index of the number of bits to be superimposed in a new set as a bit index set when the size of the target set meets the requirement of the number of superimposed bits;

[0244] An output module is set to set all elements of the destination row to 1 if the size of the destination set is smaller than the number of bits to be superimposed, and return to execute the step of obtaining the row weights of the generating matrix and determining the destination row with the smallest row weight from the row weights until the size of the destination set is greater than or equal to the number of bits to be superimposed, and output the index of the number of bits to be superimposed in the new set as a bit index set.

[0245] Furthermore, the encoding unit 1803 includes:

[0246] A decomposition module is used to decompose the information bits to be encoded according to the Plotkin recursive structure of the RM code until they are decomposed into a repetition code or a full-space code, obtain corresponding sub-information bits, and perform RM code encoding on the sub-information bits; wherein the Plotkin recursive structure is determined by the sub-code u and the sub-code u+v;

[0247] The superposition module is used to keep the subcode u unchanged in the process of superimposing the PS-RM code on the subcode according to the Plotkin recursive structure. In the codeword of the subcode u+v, the positions represented by the elements in the bit index set are superimposed, and the remaining positions are not superimposed and maintained as the subcode v. The expression for RM encoding the sub-information bit according to the Plotkin recursive structure is as follows:

[0248]

[0249] Among them, m and r are parameters required for the definition of RM code; u is the codeword of subcode PS-RM(m-1, r); v is the codeword of subcode PS-RM(m-1, r-1); u′ is the Hadamard product of u and s; s is a binary mask vector, and the elements of all index positions in the bit index set where s is located are 1, and the elements of the remaining positions are 0; F is the representation of number field in mathematics.

[0250] Furthermore, the encoding unit 1803 includes:

[0251] The generation module is used to obtain a generation matrix according to a preset generation matrix recursive expression; wherein the preset generation matrix recursive expression is as follows:

[0252]

[0253] Among them, G PS-RM (m, r) is the generator matrix; G PS-RM (m-1, r) is a submatrix; G′ PS-RM (m-1, r) is a submatrix; G PS-RM (m-1, r-1) is a submatrix; S is a binary diagonal matrix, and the elements of S at the diagonal positions corresponding to all indices in the bit index set are 1, and the elements at the other diagonal positions are 0;

[0254] A third acquisition module is used to obtain the information vector to be encoded;

[0255] The product module is used to multiply the generator matrix and the information vector to be encoded to obtain the encoded codeword.

[0256] The beneficial effects of the fourth embodiment of the present application: Considering the Plotkin recursive structure (u, u+v) of the RM code, when v is first decoded, the u superimposed thereon is regarded as a kind of interference, and because the decoding error of the RM code is dominated by v, the bit index set is determined according to the predefined superposition ratio, superposition method and basic parameters on the basis of the preset coding method, that is, the preset recursive structure, and then only the bits at the corresponding positions of the elements in the bit index set of the subcode u are selected to be superimposed on the subcode v, rather than superimposing all positions, which can increase the accuracy of the translation of v and reduce the block error rate. When constructing the PS-RM code, the superimposed position, that is, the row weight superposition method, will be carefully selected, so as to better reduce the block error rate and narrow the gap with its maximum likelihood decoding lower bound, especially for the case of longer code lengths, a larger performance gain can be obtained.

[0257] Based on the above embodiments Fig. 9 Another encoding and decoding processing method disclosed in the present application is also disclosed in the fifth embodiment of the present application. Another encoding and decoding processing device is disclosed, such as Fig.19 As shown, the other encoding and decoding processing device includes:

[0258] The demodulation unit 1901 is used to demodulate the received signal when receiving the signal to obtain demodulated information; wherein the received signal includes the modulated signal and noise; the modulated signal is determined by the transmitter according to the predefined superposition ratio, superposition mode and basic parameters, and a bit index set is determined, and a plurality of information bits to be processed are encoded according to the preset encoding mode and the bit index set, and the encoded codeword is modulated to obtain;

[0259] The decoding output unit 1902 is used to perform channel decoding on the demodulated information through a preset decoding algorithm and output it.

[0260] The beneficial effects of the fifth embodiment of the present application: Considering the Plotkin recursive structure (u, u+v) of the RM code, when v is first decoded, the u superimposed thereon is regarded as a kind of interference, and because the decoding error of the RM code is dominated by v, the bit index set is determined according to the predefined superposition ratio, superposition method and basic parameters on the basis of the preset coding method, that is, the preset recursive structure, and then only the bits at the corresponding positions of the elements in the bit index set of the subcode u are selected to be superimposed on the subcode v, rather than superimposing all positions, which can increase the accuracy of the translation of v and reduce the block error rate. When constructing the PS-RM code, the superimposed position, that is, the row weight superposition method, will be carefully selected, so as to better reduce the block error rate and narrow the gap with its maximum likelihood decoding lower bound, especially for the case of longer code lengths, a larger performance gain can be obtained.

[0261] An embodiment of the present application further provides a storage medium, which includes stored instructions, wherein when the instructions are executed, the device where the storage medium is located is controlled to execute the above-mentioned encoding and decoding processing method.

[0262] The present application also provides an electronic device, whose structural diagram is as follows: Fig. 20 As shown, it specifically includes a memory 2001 and one or more instructions 2002, wherein the one or more instructions 2002 are stored in the memory 2001 and are configured to be executed by one or more processors 2003 to execute the one or more instructions 2002 to perform the above-mentioned encoding and decoding processing method.

[0263] The above is only a preferred specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

[0264] For the aforementioned method embodiments, for the sake of simplicity, they are all described as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the order of the actions described, because according to the present application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0265] It should be noted that each embodiment in this specification is described in a progressive manner, and each embodiment focuses on the differences from other embodiments, and the same or similar parts between the embodiments can be referred to each other. For system embodiments, since they are basically similar to method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0266] The steps in the methods of the embodiments of the present application can be adjusted in order, combined, and deleted according to actual needs.

[0267] Finally, it should be noted that, in this article, relational terms such as first and second, etc. are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations.

[0268] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

[0269] The above is only a preferred implementation of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A coding and decoding processing method, characterized in that: The method is applied to a transmitting end, and the method comprises: Obtaining basic parameters of the RM code and a plurality of information bits to be processed; Determine a bit index set according to a predefined superposition ratio, superposition mode and the basic parameters; Encoding the plurality of information bits to be processed according to a preset encoding method and the bit index set to obtain an encoded codeword; wherein the preset encoding method is determined by a preset partially superimposed Plotkin recursive structure or a corresponding generator matrix; The encoded codeword is modulated, and the modulated signal is sent to a receiving end through a channel, so that the receiving end performs channel decoding on the demodulated information through a preset decoding algorithm and outputs it.

2. The method according to claim 1, characterized in that The superposition mode at least includes a sequential superposition mode or a row-size superposition mode, and the bit index set is determined according to a predefined superposition ratio, superposition mode and basic parameters, including: If the superposition mode is a sequential superposition mode, the number of codeword bits to be superimposed is obtained by a predefined superposition ratio, the bit index set is composed of continuous indexes, and the set size is equal to the number of codeword bits to be superimposed; If the superposition mode is the row-weight superposition mode, obtaining the generator matrix of the RM code and the number of codeword bits to be superimposed, and initializing the original set; Obtaining each row weight of the generator matrix, and determining a destination row with the smallest row weight from among the row weights; Searching for each column index whose target row element is 1, and taking the union of the set formed by each column index and the original set as the target set; Determine the size of the target set, and judge whether the size of the target set is greater than or equal to the number of superimposed bits; If the size of the target set is greater than or equal to the number of bits to be superimposed, determining that the size of the target set meets the requirement on the number of superimposed bits; When the size of the target set meets the requirement of the number of superimposed bits, outputting the index of the number of bits to be superimposed in the new set as the bit index set; If the size of the target set is smaller than the number of bits to be superimposed, set all elements of the target row to 1, return to the step of obtaining the row weights of the generating matrix, and determine the target row with the smallest row weight from the row weights, until the size of the target set is greater than or equal to the number of bits to be superimposed, and output the index of the number of bits to be superimposed in the new set as the bit index set.

3. The method according to claim 1, characterized in that The step of encoding the plurality of information bits to be processed according to the preset encoding mode and the bit index set to obtain the encoded codeword includes: Decomposing the information bits to be encoded according to the Plotkin recursive structure of the RM code until decomposing into a repetition code or a full-space code, obtaining corresponding sub-information bits, and performing RM code encoding on the sub-information bits; wherein the Plotkin recursive structure is determined by the sub-code u and the sub-code u+v; In the process of superimposing the PS-RM code on the subcode according to the Plotkin recursive structure, the subcode u is kept unchanged, and in the codeword of the subcode u+v, the positions represented by the elements in the bit index set are superimposed, and the remaining positions are not superimposed and maintained as the subcode v; The expression of the PS-RM code for pre-setting the subcode according to the Plotkin recursive structure is as follows: Among them, m and r are parameters required for the definition of RM code; u is the codeword of subcode PS-RM(m-1, r); v is the codeword of subcode PS-RM(m-1, r-1); u′ is the Hadamard product of u and s; s is a binary mask vector, and the elements of all index positions in the bit index set where s is located are 1, and the elements of the remaining positions are 0; F is the representation of number field in mathematics.

4. The method according to claim 1, characterized in that: Encoding the information bits according to a preset encoding mode and the bit index set to obtain an encoded codeword includes: Obtain a generator matrix according to a preset generator matrix recursively; Among them, the preset generation matrix recursive expression is as follows: Among them, G PS-RM (m, r) is the generator matrix; G PS-RM (m-1, r) is a submatrix; G′ PS-RM (m-1, r) is a submatrix; G PS-RM (m-1, r-1) is a submatrix; S is a binary diagonal matrix, and the elements of S at the diagonal positions corresponding to all indices in the bit index set are 1, and the elements at the other diagonal positions are 0; Obtaining the information vector to be encoded; The generator matrix and the information vector to be encoded are multiplied to obtain an encoded codeword.

5. A coding and decoding processing method, characterized in that: The method is applied to a receiving end, and the method comprises: When a signal is received, the received signal is demodulated to obtain demodulated information; wherein the received signal includes a modulated signal and noise; the modulated signal is determined by the transmitter according to a predefined superposition ratio, superposition mode and basic parameters, a bit index set is determined, a plurality of information bits to be processed are encoded according to a preset encoding mode and the bit index set, and the encoded codeword is modulated to obtain; The demodulated information is channel-decoded using a preset decoding algorithm and then outputted.

6. The method according to claim 5, characterized in that Channel decoding is performed on the demodulated information by a preset decoding algorithm and the information is output, including: Get the demodulated log-likelihood ratio; According to a preset recursive list decoding algorithm, recursively decompose the log-likelihood ratios of the positions represented by the elements in the bit index set, and keep the log-likelihood ratios of the remaining positions unchanged, to obtain a recursive decomposition result; The calculation formula of the preset recursive list decoding algorithm is: in, is the log-likelihood ratio of the ith bit of the subcode v; ln is a logarithmic function with a natural constant as the base; LLR i is the log-likelihood ratio of the i-th bit of the current codeword; The i+2th of the current codeword m-1 The log-likelihood ratio of bits; exp is an exponential function with a natural constant as the base; i is the codeword bit index; is a bit index set; is the log-likelihood ratio of the i-th bit of subcode u; is the decoding result of the i-th bit of subcode v; Recursively until a repetitive code or a full-space code is reached, and channel decoding is performed according to the recursive decomposition result; For repetitive codes, add all-0 codewords and all-1 codewords to the candidate list; For the full-space code, four code words meeting preset conditions are selected and added to the candidate list; the preset conditions are determined according to the posterior probability value of the code words; Calculate the posterior probability values ​​of all codewords in the candidate list, return the first L codewords that meet the preset conditions according to the posterior probability values ​​of all codewords in the candidate list, and obtain the decoding result to complete the process of channel decoding the demodulated information and output it, where L is the set list size.

7. The method according to claim 5, characterized in that Also includes: Set the normalized signal-to-noise ratio; Set different overlay ratios for intervals based on a fixed step size; According to the encoded codewords and the results of channel decoding, the block error rates under different superposition ratios are counted; According to the block error rates under different stacking ratios, the stacking ratio with the smallest block error rate is selected as the optimal value under the normalized signal-to-noise ratio.

8. A coding and decoding processing device, characterized in that: The device is applied to a transmitting end, and the device includes: An acquisition unit, used for acquiring basic parameters of the RM code and a plurality of information bits to be processed; A determination unit, configured to determine a bit index set according to a predefined superposition ratio, superposition mode and the basic parameters; An encoding unit, used for encoding the plurality of information bits to be processed according to a preset encoding method and the bit index set to obtain an encoded codeword; wherein the preset encoding method is determined by a preset partially superimposed Plotkin recursive structure or a corresponding generator matrix; The modulation and transmission unit is used to modulate the encoded codeword and send the modulated signal to the receiving end through the channel, so that the receiving end performs channel decoding on the demodulated information through a preset decoding algorithm and outputs it.

9. The device according to claim 8, characterized in that The superposition method at least includes a sequential superposition method or a row-size superposition method, and the determination unit includes: A first acquisition module is used to acquire a generator matrix of the RM code and the number of codeword bits to be superimposed, and initialize an original set if the superposition mode is the row-major-size superposition mode; A second acquisition module is used to acquire the row weights of the generator matrix and determine the target row with the smallest row weight from the row weights; A search module, used for searching for each column index whose target row element is 1, and taking the union of the set formed by each column index and the original set as the target set; A first determination module, used to determine the size of a target set, and judge whether the size of the target set is greater than or equal to the number of superimposed bits; A second determination module is used to determine that the size of the target set meets the requirement on the number of superimposed bits if the size of the target set is greater than or equal to the number of bits to be superimposed; An output module, configured to output an index of the number of bits to be superimposed in a new set as a bit index set when the size of the target set meets the requirement of the number of superimposed bits; A setting module is used to set all elements of the destination row to 1 if the size of the destination set is smaller than the number of bits to be superimposed, return to execute the step of obtaining the row weights of the generating matrix and determining the destination row with the smallest row weight from the row weights, until the size of the destination set is greater than or equal to the number of bits to be superimposed, and output the index of the number of bits to be superimposed in the new set as a bit index set.

10. A coding and decoding processing device, characterized in that: The device is applied to a receiving end, and the device includes: A demodulation unit is used to demodulate the received signal when receiving the signal to obtain demodulated information; wherein the received signal includes a modulated signal and noise; the modulated signal is determined by the transmitter according to a predefined superposition ratio, superposition mode and basic parameters, a bit index set is determined, a plurality of information bits to be processed are encoded according to a preset encoding mode and the bit index set, and the encoded codeword is modulated to obtain; The decoding output unit is used to perform channel decoding on the demodulated information through a preset decoding algorithm and output it.

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