A processing method and device for encoding and decoding

Abstract

The application discloses a processing method and device for encoding and decoding. A sending end obtains basic parameters of an RM code and a plurality of information bits to be processed, determines a bit index set according to a predefined superposition ratio, a superposition mode and the basic parameters, encodes the plurality of information bits to be processed according to a preset encoding mode and the bit index set, and obtains a coded codeword. The preset encoding mode is determined by a Plotkin recursive structure or a corresponding generating matrix of a preset partial superposition. The coded codeword is modulated, the modulated signal is sent to a receiving end through a channel, so that the receiving end performs channel decoding on demodulated information through a preset decoding algorithm and outputs.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of communication, more particularly, to a processing method and device for encoding and decoding. BACKGROUND

[0002] In a wireless communication system, due to the existence of noise in the channel, errors will occur in the process of signal transmission. Channel coding technology can realize error detection and correction at the receiving end by adding some redundant bits, aiming to improve the reliability and anti-interference ability of the wireless communication system. In the research process of channel coding, many excellent coding methods have appeared.

[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 code. At the same time, RM code has developed several famous decoding algorithms, including Dumer's recursive list decoding algorithm, recursive projection aggregation decoding algorithm, etc.

[0004] However, the classic decoding algorithm of RM code, Dumer's recursive list decoding algorithm, cannot quickly and effectively approach the ML decoding performance in medium and long codes, and a large list is often needed in the decoding process of RM code, and the decoding complexity is high. Thus, it is impossible to obtain greater performance gain for the case of longer code length of RM code.

[0005] Therefore, how to obtain greater performance gain for the case of longer code length of RM code is a problem to be solved by the present application. SUMMARY

[0006] Therefore, the present application discloses a processing method and device for encoding and decoding, aiming to reduce the block error rate curve of the partial superposition RM code, thereby narrowing the gap with the lower bound of the maximum likelihood estimation, and obtaining greater performance gain for the case of longer code length.

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

[0008] The first aspect of the present application discloses a processing method for encoding and decoding, which is applied to a sending end, and the method comprises:

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

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

[0011] encoding the plurality of information bits to be processed according to a preset encoding mode and the bit index set, to obtain a code word after encoding; wherein the preset encoding mode is determined by a preset partially superimposed Plotkin recursive structure or a corresponding generator matrix;

[0012] modulating the code word after encoding, and sending the modulated signal to a receiving end through a channel, so that the receiving end performs channel decoding on demodulated information through a preset decoding algorithm and outputs.

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

[0014] If the superimposed mode is the sequential superimposed mode, the number of code bits to be superimposed is obtained through the predefined superimposition ratio, the bit index set is composed of continuous indexes, and the size of the set is the number of code bits to be superimposed;

[0015] If the superimposed mode is the row weight size superimposed mode, the generator matrix of the RM code and the number of code bits to be superimposed are obtained, and an original set is initialized;

[0016] The row weights of the generator matrix are obtained, and a target row with the minimum row weight is determined from the row weights;

[0017] Each column index of the target row element being 1 is searched, and a set composed of each column index and the original set are taken as a union set as a target set;

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

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

[0020] Under the condition that the size of the target set meets the superimposed bit number requirement, the indexes of the number of bits to be superimposed in the new set are output as the bit index set;

[0021] If the size of the target set is less than the number of bits to be superimposed, all elements of the target row are set to 1, and the step of obtaining the row weights of the generator matrix and determining the target row with the minimum row weight from the row weights is returned to be executed until the size of the target set is greater than or equal to the number of bits to be superimposed, and the indexes of the number of bits to be superimposed in the new set are output as the bit index set.

[0022] Preferably, the encoding of the plurality of information bits according to the preset encoding mode and the bit index set comprises:

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

[0024] in the process of preset partial superposition PS-RM code of the sub-code according to the Plotkin recursive structure, the sub-code u is unchanged, and the positions represented by the elements in the bit index set are superimposed in the code word of the sub-code u+v, and the remaining positions are not superimposed and maintained as the sub-code v;

[0025] The expression of the preset partial superposition PS-RM code of the sub-code according to the Plotkin recursive structure is as follows:

[0026]

[0027] wherein m and r are parameters required for defining the RM code; u is a code word of a sub-code PS-RM(m-1, r); v is a code word of a sub-code PS-RM(m-1, r-1); u' is a Hadamard product of u and s; s is a binary mask vector, and the elements of s at all index positions in the bit index set are 1, and the elements at the remaining positions are 0; F is a representation of a number field in mathematics.

[0028] Preferably, the encoding of the plurality of information bits according to the preset encoding mode and the bit index set comprises:

[0029] obtaining a generator matrix according to a preset generator matrix recursive expression;

[0030] wherein the preset generator matrix recursive expression is as follows:

[0031]

[0032] wherein G PS-RM (m, r) is a generator matrix; G PS-RM (m-1, r) is a sub-matrix; G' PS-RM (m-1, r) is a sub-matrix; G PS-RM (m-1, r-1) is a sub-matrix; S is a binary diagonal matrix, and the elements of S at the diagonal line positions corresponding to all indexes in the bit index set are 1, and the elements at the remaining diagonal line positions are 0;

[0033] obtaining the information vector to be encoded;

[0034] multiplying the generating matrix and the to-be-encoded information vector to obtain a coded code word.

[0035] The second aspect of the application discloses a processing method for encoding and decoding.

[0036] When a signal is received, the received signal is demodulated to obtain demodulated information; wherein the received signal comprises a modulated signal and noise, and the modulated signal is obtained by determining a bit index set according to a pre-defined superposition ratio, a superposition mode and basic parameters, encoding a plurality of to-be-processed information bits according to a preset encoding mode and the bit index set, and modulating a coded code word obtained by the encoding.

[0037] The demodulated information is channel-decoded by a preset decoding algorithm and output.

[0038] Preferably, the demodulated information is channel-decoded by a preset decoding algorithm and output, comprising:

[0039] The log-likelihood ratio of a demodulated position is obtained.

[0040] According to a preset recursive list decoding algorithm, the log-likelihood ratio of the position represented by the element in the bit index set is recursively decomposed, and the log-likelihood ratios of the remaining positions are kept unchanged to obtain a recursive decomposition result.

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

[0042]

[0043] wherein, is the log-likelihood ratio of the i-th bit of the sub-code v; ln is a natural constant-based logarithmic function; LLR i is the log-likelihood ratio of the i-th bit of the current code word; is the log-likelihood ratio of the i+2 m-1 th bit of the current code word; exp is an exponential function with a natural constant as the base; i is a code word bit index; is a bit index set; is the log-likelihood ratio of the i-th bit of the sub-code u; is the decoding result of the i-th bit of the sub-code v;

[0044] The recursion is performed until a repetition code or a full-space code is reached, and channel decoding is performed according to the recursive decomposition result.

[0045] For a repetition code, a code word of all 0s and a code word of all 1s are added to a candidate list.

[0046] For the full space code, four code words meeting preset conditions are selected to join a candidate list; the preset conditions are determined according to the posterior probability values of the code words;

[0047] The posterior probability values of all code words in the candidate list are calculated, the first L code words meeting the preset conditions are returned according to the posterior probability values of all code words in the candidate list, and a decoding result is obtained, so as to complete the process of channel decoding of the demodulated information and output, wherein L is a set list size.

[0048] Preferably, it further comprises:

[0049] A normalized signal-to-noise ratio is set;

[0050] Different superposition ratios are set according to fixed steps as intervals;

[0051] According to the encoded code words and the channel decoding result, the block error rates under different superposition ratios are counted;

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

[0053] The third aspect of the present application discloses a processing device for encoding and decoding, which is applied to a sending end, and the device comprises:

[0054] An acquisition unit is configured to acquire basic parameters of an RM code and a plurality of information bits to be processed;

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

[0056] An encoding unit is configured to encode the plurality of information bits to be processed according to a preset encoding mode and the bit index set, to obtain encoded code words; wherein the preset encoding mode is determined by a Plotkin recursive structure with a preset partial superposition or a corresponding generator matrix;

[0057] A modulation and sending unit is configured to modulate the encoded code words, and send the modulated signals to a receiving end through a channel, so that the receiving end performs channel decoding on demodulated information through a preset decoding algorithm and outputs.

[0058] Preferably, the superposition mode at least includes a sequential superposition mode or a row weight size superposition mode, and the determination unit comprises:

[0059] A first acquisition module is configured to acquire a generator matrix of an RM code and a number of code word bits to be superposed, and initialize an original set, if the superposition mode is the row weight size superposition mode;

[0060] The second obtaining module is configured to obtain each row weight of the generation matrix, and determine a target row with the minimum row weight from the each row weight;

[0061] The searching module is configured to search each column index with the target row element being 1, and take a union set of the each column index and the original set as a target set;

[0062] The first determining module is configured to determine the size of the target set, and judge whether the size of the target set is greater than or equal to the superimposed bit number;

[0063] The second determining module is configured to determine that the size of the target set meets the superimposed bit number requirement if the size of the target set is greater than or equal to the to-be-superimposed bit number;

[0064] The output module is configured to output the index of the to-be-superimposed bit number in the new set as a bit index set if the size of the target set meets the superimposed bit number requirement.

[0065] The setting module is configured to set all elements of the target row to 1 if the size of the target set is less than the to-be-superimposed bit number, and return to execute the step of obtaining each row weight of the generation matrix and determining a target row with the minimum row weight from the each row weight until the size of the target set is greater than or equal to the to-be-superimposed bit number, and output the index of the to-be-superimposed bit number in the new set as a bit index set.

[0066] The fourth aspect of the present application discloses a processing device for encoding and decoding, which is applied to a receiving end, and the device comprises:

[0067] The demodulation unit is configured to demodulate the received signal to obtain demodulated information when the signal is received; wherein the received signal comprises a modulated signal and noise; the modulated signal is obtained by determining a bit index set according to a predefined superimposed ratio, superimposed mode and basic parameters, encoding a plurality of to-be-processed information bits according to a preset encoding mode and the bit index set, and modulating the encoded code word.

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

[0069] According to the technical solution, the application discloses a processing method and device for encoding and decoding. A sending end obtains basic parameters of an RM code and a plurality of information bits to be processed, determines a bit index set according to a predefined superposition ratio, superposition mode and basic parameters, encodes the plurality of information bits to be processed according to a preset encoding mode and the bit index set, and obtains a coded codeword. The preset encoding mode is determined by a Plotkin recursive structure or a corresponding generating matrix of a preset partial superposition. The coded 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 demodulated information through a preset decoding algorithm and outputs the information. According to the above scheme, in the Plotkin recursive structure (u, u+v) of the RM code, u superposed on v is regarded as interference when v is decoded first, and because the decoding error of the RM code is dominated by v, the accuracy of decoding v can be improved by determining the bit index set according to the predefined superposition ratio, superposition mode and basic parameters on the basis of the preset encoding mode, that is, the preset recursive structure, and then superposing only the bits at positions corresponding to elements in the bit index set of the subcode u on the subcode v instead of superposing the bits at all positions. Therefore, the block error rate can be reduced. When the PS-RM code is constructed, the superposition positions, that is, the row weight size superposition mode, are carefully selected, so that the block error rate can be better reduced, the gap with the lower bound of maximum likelihood decoding can be reduced, and great performance gain can be obtained especially for a long code length. BRIEF DESCRIPTION OF DRAWINGS

[0070] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description only constitute the embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative effort on the basis of the provided drawings.

[0071] Figure 1 A schematic diagram of a communication system disclosed by the embodiments of the present application;

[0072] Figure 2 A flowchart of a processing method for encoding and decoding disclosed by the embodiments of the present application;

[0073] Figure 3 A flowchart of determining a bit index set disclosed by the embodiments of the present application;

[0074] Figure 4 A flowchart of encoding a plurality of information bits to be processed according to a preset encoding mode and a bit index set disclosed by the embodiments of the present application;

[0075] Figure 5Another flowchart for encoding a plurality of information bits to be processed according to a preset encoding mode and a bit index set is disclosed in the embodiments of the present application.

[0076] Figure 6 A schematic diagram of recursive construction of a PS-RM code is disclosed in the embodiments of the present application.

[0077] Figure 7 A schematic diagram of a generator matrix of a PS-RM code is disclosed in the embodiments of the present application.

[0078] Figure 8 A schematic diagram of code redistribution of a PS-RM code is disclosed in the embodiments of the present application.

[0079] Figure 9 Another flowchart of a processing method for encoding and decoding is disclosed in the embodiments of the present application.

[0080] Figure 10 A flowchart of decoding of a PS-RM code is disclosed in the embodiments of the present application.

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

[0082] Figure 12 An example diagram of a curve of a block error rate of a PS-RM (8, 3) with a superposition ratio is disclosed in the embodiments of the present application.

[0083] Figure 13 A curve of a block error rate of a PS-RM (8, 3) with a normalized signal-to-noise ratio Eb / N0 is disclosed in the embodiments of the present application.

[0084] Figure 14 A curve of a block error rate of a PS-RM (9, 3) with a superposition ratio is disclosed in the embodiments of the present application.

[0085] Figure 15 A curve of a block error rate of a PS-RM (9, 3) with a normalized signal-to-noise ratio Eb / N0 is disclosed in the embodiments of the present application.

[0086] Figure 16 A curve of a block error rate of a PS-RM (10, 2) with a superposition ratio is disclosed in the embodiments of the present application.

[0087] Figure 17 A curve of a block error rate of a PS-RM (10, 2) with a normalized signal-to-noise ratio Eb / N0 is disclosed in the embodiments of the present application.

[0088] Figure 18 A schematic diagram of a processing device for encoding and decoding is disclosed in the embodiments of the present application.

[0089] Figure 19 Another structure schematic diagram of a processing device for encoding and decoding disclosed by the embodiment of the present application is shown in the figure.

[0090] Figure 20 A structure schematic diagram of an electronic device disclosed by the embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0091] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0092] In the present application, the term “comprising”, “containing” or any other variant thereof is intended to cover the non-exclusive inclusion, so that the process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or includes elements inherent to such process, method, article or device. Without more limitations, the element defined by the sentence “including a…” does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0093] As known from the background, the recursive list decoding algorithm of Dumer, the classical decoding algorithm of RM code, cannot quickly and effectively approach the ML decoding performance when the code is medium or long. A large list is often needed in the decoding process of RM code, and the decoding complexity is high. Thus, it cannot obtain a large performance gain in the case of a long code length of RM code. Therefore, how to obtain a large performance gain in the case of a long code length of RM code is a problem to be solved by the present application.

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

[0095] Reference Figure 1 Embodiment one of the application discloses a schematic diagram of a communication system, which is composed of a sending end, a channel and a receiving end. The sending end includes channel encoding and modulation, and the receiving end includes demodulation and channel decoding.

[0096] The communication process between the sending end, the channel and the receiving end is as follows:

[0097] The sending end obtains the basic parameters of the Reed-Muller (RM) code and a k-bit information sequence; wherein 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, code rate (R) and 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 the RM code is a kind of error correction coding technology, in which r and m are two important parameters for describing the characteristics and performance of the coding. m determines n, i.e. the total number of bits after coding. In theory, a longer n can provide stronger error correction capability under certain conditions, but it will also increase the overhead of data transmission or storage. When m is fixed, the size of r determines the size of R, which can be understood as the coding efficiency, indicating the ratio between the data part actually used for storing or transmitting information and n in data transmission or storage. A higher code rate means that the information part occupies a larger proportion in the coding, while a lower code rate means that more redundancy is added to improve the error correction capability. In the context of RM code, by adjusting the values of r and m, different coding efficiency and error correction capability can be achieved to meet specific communication or storage requirements. For example, in RM(2,5) coding, the code length n = 25 = 32, 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 sending end determines the bit index set according to the predefined superposition ratio, superposition mode and basic parameters

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

[0102]

[0103] All (u, u'+v) superpositions in the encoding process can use the same or different partial superposition ratios; and a is a predefined superposition ratio. The bit index set; the superposition mode at least includes a sequential superposition mode or a row weight size superposition mode; the sequential superposition mode includes performing partial superposition from front to back, superposing the first p bits of u on v, and performing partial superposition from back to front, superposing the last p bits of u on v; and the row weight size superposition mode refers to selecting the column index set as The column index of the non-zero element in the row with a smaller row weight is preferentially added to the column index set Until the required The size of the set is reached.

[0104] It should be noted that for any superposition mode, the PS-RM code superposition index set of any parameter is fixed when the given partial superposition ratio a is given. It can be calculated offline and stored in the memory. Thus, the calculation complexity of encoding and decoding is not increased.

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

[0106] The Plotkin recursive structure of the preset partial superposition and the corresponding generator matrix are described in S203 in Embodiment 2.

[0107] The sending end modulates the code word of n bits after coding, to obtain a modulated signal, and transmits the modulated signal to the receiving end through a channel.

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

[0109] The log-likelihood ratio of a code bit c is defined as the ratio of the likelihood probability of c being 0 to the likelihood probability of c being 1, and then taking the logarithm, that is, as shown in equation (3).

[0110]

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

[0112] The beneficial effects of the embodiment one of the present application are as follows: considering the Plotkin recursive structure (u, u+v) of the RM code, when decoding v first, u superimposed thereon is regarded as a kind of interference, and since the RM code decoding error is dominated by v, by presetting the encoding mode, i.e., the basis of the preset recursive structure, the bit index set is determined according to the predefined superimposition ratio, superimposition mode and basic parameters, and then only the bits at the positions corresponding to the elements in the bit index set of the subcode u are superimposed on the subcode v, instead of superimposing on all positions, which can increase the accuracy of decoding v, thereby reducing the block error rate. When the PS-RM code is constructed, the superimposed positions, i.e., the row weight size superimposition mode, are carefully selected, so that the block error rate can be better reduced, the gap with the lower bound of the maximum likelihood decoding can be narrowed, and especially for the case of long code length, a large performance gain can be obtained.

[0113] Reference Figure 2 Embodiment two of the present application discloses a processing method for encoding and decoding, which is applied to the sending end of the communication system of the above-mentioned embodiment Figure 1 The processing method for encoding and decoding mainly comprises the following steps:

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

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

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

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

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

[0119] The superposition mode at least includes a sequential superposition mode or a row weight size superposition mode.

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

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

[0122] The predefined superposition ratio is shown as the above formula (2).

[0123] All (u, u'+v) superpositions in the encoding process can adopt the same or different partial superposition ratios.

[0124] The sequential superposition mode includes performing partial superposition from front to back, superposing the first p bits of u on v, and the specific process is shown as formula (4).

[0125]

[0126] Wherein, m is the logarithmic length.

[0127] The sequential superposition mode includes performing partial superposition from front to back, superposing the first p bits of u on v, and the specific process is shown as formula (4).

[0128]

[0129] That is

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

[0131] A2: If the superposition mode is the row weight size superposition mode, the generator matrix of the RM code and the number of code word bits to be superposed α·2 m-1 are obtained, and the original set

[0132] The row weight size superposition mode is the row weight size of the RM code matrix, and the column index set is selected as according to the row weight size of the RM code matrix. The column index of the column in which the non-zero element of the row with smaller row weight is preferentially added to until the required set size is reached.

[0133] Generating matrix: For an (n, k) linear block code, if u = (u1, u2, ..., u3)... k If is the information sequence to be encoded, then the corresponding codeword can be generated by c = u·G = (c1, c1, ..., c1) n Given a matrix G with k rows and n columns, it is called the generating matrix.

[0134] According to the above encoding method, when encoding PS-RM(m, r), the codeword bits to be partially superimposed come from PS-RM(m-1, r). When the number of superimposed codeword bits is constant, i.e. α·2 m-1 Choosing the index of the codeword bit position to be superimposed is crucial to the structure and performance of the code itself. Because unsuperimposed positions will result in the corresponding column of its generator matrix being set to 0, if the row weight of a row that was originally smaller becomes even smaller during this process, it may lead to a performance degradation. Therefore, this embodiment, from the perspective of the row weight of the RM(m-1, r) generator matrix, prioritizes selecting the codeword bits whose column index contains the non-zero element in the row with the smaller superimposed row weight.

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

[0136] A4: Search for the column indices of the target row where each element is 1, and then combine the set of these column indices with the original set to obtain the target set (the new set).

[0137] Calculate the row weight of each row in the generated matrix G, find the row with the smallest row weight, search for the column indices where the element in that row is 1, and combine the sets of all column indices. Take the union as the new set

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

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

[0141] Where, if the target set size The size of the destination set meets the superposition bit number requirement.

[0142] If , A7 is executed. Otherwise, A8 is executed.

[0143] A7: When the size of the destination set meets the superposition bit number requirement, the indexes of the bit number (α·2 m-1 ) to be superposed in the new set are output as the bit index set.

[0144] When the size of the destination set meets the superposition bit number requirement, the first α·2 m-1 indexes in the set are output; otherwise, the row is set to all 1s.

[0145] A8: When the size of the destination set is smaller than the bit number (α·2 m-1 ) to be superposed, all elements of the destination row are set to 1, and the step of determining the destination row with the smallest row weight from the row weights of the generated matrix is returned to be executed until the size of the destination set is greater than or equal to the bit number (α·2 m-1 ) to be superposed, and the indexes of the bit number (α·2 m-1 ) to be superposed in the new set are output as the bit index set. For any superposition mode, the PS-RM code superposition index set is fixed when the partial superposition ratio α is given. According to the method, the sets can be calculated offline and stored in memory , so as not to increase the calculation complexity of coding and decoding.

[0146] Exemplarily, the embodiments of the present application give all index sets involved in partial superposition in a PS-RM(7, 2) code when the same superposition ratio α = 7 / 8 is used under the sorting according to the row weight size. is denoted as the PS-RM(m-1, r) bit position index set to be superposed when the PS-RM(7, 2) is coded, which includes the following:

[0147]

[0148] In the embodiments of the present application, for α·2 m-1 that is not an integer, rounding is uniformly taken.

[0149] ​S203: The sending end encodes the plurality of information bits to be processed according to the preset encoding mode and the bit index set, to obtain the encoded code word; wherein the preset encoding mode is determined by the preset partially superimposed Plotkin recursive structure or the corresponding generating matrix. The specific process 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 code word is shown in B1-B2 in Figure 4 , and Figure 5 C1-C3. Among them, B1-B2 is encoded according to the preset partially superimposed Plotkin recursive structure. C1-C3 is encoded according to the preset generating matrix expression.

[0150] B1: Decompose all information bits to be encoded according to the Plotkin recursive structure (u, u+v) of the RM code, until the decomposition is to the repetition code or the full space code, to obtain the corresponding sub-information bits, and encode the sub-information bits by the RM code.

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

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

[0153] Among them, u is the code word of the sub-code RM(m-1, r), and v is the code word of the sub-code RM(m-1, r-1). In other words, the code word of RM(m, r) is composed of the front and back two parts, the front part is the code word u of the corresponding sub-code RM(m-1, r), and the back part is the superposition of the code word u of the sub-code RM(m-1, r) and the code word v of the sub-code RM(m-1, r-1): u+v.

[0154] According to formula (6), the k-long information bit sequence is recursively decomposed into two sub-information bit sequences with lengths of and respectively.

[0155] Among them, when recursion is performed to m=g, r=0, the length of the information bit at this time is 1, the bit is repeated and encoded, and the length of the repetition code is 2 g . g

[0156] When recursion is performed to m=r=h, the information bit sequence with a length of is multiplied by the generating matrix in modulo 2, wherein the generating matrix is the h-th Kronecker power of the identity matrix, and returns the encoding result.

[0157] where the repetition code and the all-space code are denoted as two kinds of leaf nodes.

[0158] B2: In the process of presetting partial superposition PS-RM code to the subcode according to the Plotkin recursive structure of the RM code, the subcode u is kept unchanged, and in the codeword of the second half of the subcode u+v, only the positions represented by the elements in the bit index set are superimposed, and the rest of the positions are not superimposed and maintained as the subcode v.

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

[0160]

[0161] where m and r are parameters required for defining 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 of all index positions in the bit index set of s are 1, and the elements of the rest of the positions are 0; F is the representation of the number field in mathematics.

[0162] When the above encoding process is completed for two subnodes of any one node, the encoded codewords returned by the two subnodes are merged as (u, u'+v), where u is from the PS-RM(m-1, r) encoding codeword, v is from the PS-RM(m-1, r-1) encoding codeword, and u' is to set some positions of u to 0, and (u, u'+v) is returned. For details, please refer to Figure 6 Continue to explain.

[0163] Exemplarily, it is assumed that Figure 6 The vertical shaded block in represents u=[u1, u2, u3, u4, u5, u6, u7, u8], the horizontal shaded block represents v=[v1, v2, v3, v4, v5, v6, v7, v8], and the blank block represents 0, then Figure 5 u'=[u1, 0, u3, u4, 0, u6, 0, u8] in this case, the partial superposition encoding is (u, u'+v) =

[0164] where the addition is all modulo 2 addition, and the superimposed result is represented by the horizontal and vertical shading.

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

[0166] C1: obtaining a generator matrix according to a preset recursive expression of a generator matrix (i.e., a recursive expression of a generator matrix 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] wherein, G PS-RM (m, r) is a 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; and S is a binary diagonal matrix, wherein elements at diagonal line positions corresponding to all index sets in the bit index set are 1, and elements at other diagonal line positions are 0.

[0170] The selection matrix S s i ∈F2, i = 1, 2, …, 2 m-1 is a binary diagonal matrix, that is, part of columns of the submatrix G' PS-RM (m-1, r) are selected from the corresponding columns of the submatrix G PS-RM (m-1, r), and the remaining columns are set to all 0.

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

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

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

[0174] C2: obtaining an information vector to be encoded.

[0175] C3: multiplying the generator matrix and the information vector to be encoded to obtain a code word after encoding (a PS-RM code word).

[0176] In C3, the information vector to be encoded is multiplied with the generator matrix in modulo 2 to output the PS-RM code word.

[0177] Exemplarily, the generator matrix of PS-RM (3, 2) is shown in formula (9). Figure 7 Firstly, G PS-RM (3, 2) is decomposed into G PS-RM (2, 2) and G'PS-RM (2, 2), G PS-RM (2, 1) and zero matrix. Wherein, G PS-RM (2, 2) is That is 2nd Kronecker power, thus G′ PS-RM (2, 2) is to set part of columns of G PS-RM (2, 2) to 0, in this example, to set the last two columns to 0, that is

[0178] Then G PS-RM (2, 1) is further decomposed into G PS-RM (1, 1), G′ PS-RM (1, 1), G PS-RM (1, 0) and zero matrix, wherein G′ PS-RM (1, 1) is to set part of columns of G PS-RM (1, 1) to 0, in this example, to set the last column to 0, that is In addition, G PS-RM (1, 0) = [1 1], so the generating matrix of PS-RM(3, 2) is obtained, and then the input information sequence to be encoded is multiplied by the generating matrix modulo 2 to obtain the code word.

[0179] It should be noted that in this example, the same part superposition ratio is used for all part superpositions in the generating matrix, and the superposition ratio is 1 / 2, that is, for a two-column submatrix, one column is set to 0; for a four-column submatrix, two columns are set to 0. Alternatively, the specific value of the superposition ratio and the position of the superposition are not limited in the present application.

[0180] Figure 8 The row weight size superposition manner provided by the embodiment is shown, when the same superposition ratio a = 7 / 8 is used, the code weight distribution of PS-RM(7, 2) is shown, that is, the code weight of all possible information sequences after encoding is counted, and compared with the code weight distribution of RM(7, 2).

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

[0182] It should be noted that the specific values of the parameters involved in the above introduction are examples and do not constitute a limitation, and the application does not limit the above three superposition modes, and in actual application scenarios, the actual situation can be selected according to the actual situation.

[0183] S204: The encoded code word is modulated, and the modulated signal is sent 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.

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

[0185] Reference Figure 9 Embodiment three shown in the application discloses another encoding and decoding processing method, which is applied to the receiving end of the communication system disclosed in the above embodiment Figure 1 The encoding and decoding processing method mainly includes the following steps:

[0186] S901: When the receiving end receives the signal, the received signal is demodulated to obtain demodulated information; wherein the received signal includes a modulated signal and noise; the modulated signal is obtained by the sending end according to the predefined superposition ratio, superposition mode and basic parameters, determining the bit index set, encoding the multiple to-be-processed information bits according to the preset encoding method and the bit index set, and modulating the encoded code word.

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

[0188] The specific process of demodulating the received signal to obtain demodulated information, and performing channel decoding on the demodulated information through a preset decoding algorithm and outputting is shown as D1-D6 in Figure 10

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

[0190] In the embodiments of the present application, if Figure 1 The modulation of the sending end in the middle adopts binary phase shift keying (BPSK) modulation, maps binary code bit 0 as signal +1 and bit 1 as signal -1, then the channel hypothesis adopts an additive white Gaussian noise (AWGN) channel, superimposes Gaussian white noise on the sending signal, and the calculation formula of the log likelihood ratio of the demodulation of the receiving end is shown in formula (9):

[0191]

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

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

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

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

[0196]

[0197] The is input into the PS-RM(m-1, r-1) decoder, and the decoding result

[0198] The is input into the PS-RM(m-1, r) decoder, and the decoding result

[0199] wherein is the log likelihood ratio of the i-th bit of the subcode v; ln is the natural constant base logarithm function; LLR i is the log likelihood ratio of the i-th bit of the current code word; is the log likelihood ratio of the i+2 m-1 bit of the current code word; exp is the natural constant base exponential function; i is the code bit index; is the bit index set; is the log-likelihood ratio of the i-th bit of the sub-code u; is the decoding result of the i-th bit of the sub-code v;

[0200] where if i.e. the i-th bit of u i is superimposed on the i-th bit of v i , there is no difference between decoding with Dumer's recursive list for RM codes, and the calculation of can be easily obtained; if is directly equal to because at this time u i is not superimposed on v i , and thus the log-likelihood ratio of v i can be directly obtained. Similarly, after decoding , if is the same as the RM code, u i is equivalent to being transmitted twice, and according to the LLRs i and are combined; if u i is transmitted only once, its log-likelihood ratio is equal to the LLR i .

[0201] and denote the sub-codes in the corresponding decoding process. (Conventionally, the superscript \hat{} is usually used to represent the estimated result. Because decoding is not necessarily correct, decoding errors can occur due to noise, that is, does not necessarily equal the true value u, nor does

[0202] D3: The receiving end recursively reaches the repetition code or the full space code, and performs channel decoding according to the recursive decomposition result;

[0203] D4: For the repetition code, the receiving end adds the all-0 code word and the all-1 code word to the candidate list;

[0204] D5: For the full space code, the receiving end selects four code words that meet the preset condition to add to the candidate list; the preset condition is determined according to the a posteriori probability value of the code word;

[0205] D6: The a posteriori probability values of all code words in the candidate list are calculated, the first L code words that meet the preset condition are returned according to the a posteriori probability values of all code words in the candidate list, to obtain the decoding result, so as to complete the process of channel decoding of the demodulated information and output, wherein L is the set list size.

[0206] Specifically, the code word posterior probability calculation formula in the candidate list is shown as formula (12):

[0207]

[0208] Wherein, c is the code word translated by the leaf node; y is the corresponding signal, according to the Bayes formula, that is, formula (13):

[0209]

[0210] Similarly, formula (14) can be obtained:

[0211]

[0212] When all the superimposed parts in the encoding process adopt the same superimposed ratio, the way to obtain the optimal superimposed ratio of the PS-RM code search is shown as F1-F4 in the following. Figure 11

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

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

[0215] Exemplarily, when BPSK modulation and AWGN channel are adopted, the relationship between the normalized signal-to-noise ratio and the variance σ 2 of the Gaussian white noise is: Wherein, R is the code rate.

[0216] F2: Set different superimposed ratios according to the fixed step interval.

[0217] F3: According to the encoded code word and the result of the channel decoding, the block error rate under different superimposed ratios is counted.

[0218] Set different superimposed ratios at fixed step intervals from 0 to 1, repeat the encoding and decoding method of the PS-RM code, and count the block error rate under different superimposed ratios.

[0219] Specifically, the Monte Carlo simulation is carried out under each superimposed ratio according to the communication process of Figure 1 First, the sending end generates random bits as the to-be-encoded information bits, then, the PS-RM code is encoded, the BPSK modulation is carried out after the Gaussian white noise with variance is added, the receiving end calculates the LLR and then decodes, finally, it is judged whether the decoding is correct, and the simulation is stopped after a certain number of simulations, and the block error rate is calculated by ​​

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

[0221] F4: Select the stacking ratio with the lowest block error rate as the optimal value based on the block error rate under different stacking ratios.

[0222] Figure 12 and Figure 13 The block error rate curves for PS-RM(8,3) are shown. Figure 12 This is a curve showing the block error rate of PS-RM(8,3) as a function of the stacking ratio, where the normalized signal-to-noise ratio is set to a specific value of E. b / N0 = 3dB, the stacking method is selected based on the row weight, and the bit index set is used as the stacking method. During the encoding process, all parts are superimposed using the same superposition ratio, and the superposition ratio is searched in steps of 1 / 64. The decoding list size is 4. For each superposition ratio, the decoding stops when 200 codewords are decoded and the block error rate is calculated.

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

[0224] Figure 13 Is adopted Figure 12 The optimal stacking ratio of 15 / 16 obtained from the search is shown as the block error rate (BRR) versus normalized signal-to-noise ratio (SNR). The stacking method is the same as the row weight stacking method, with decoding list sizes of 4, 16, and 64. At each normalized SNR, decoding stops and the BRR is calculated when 200 codewords are decoded incorrectly. The red line represents the BRR curve for RM codes, and the blue line represents the BRR curve for PS-RM codes.

[0225] from Figure 13 It can be seen that the block error rate (BRR) gradually decreases as the normalized signal-to-noise ratio (SNR) increases; the BRR curve also gradually decreases as the decoder list size increases. More importantly, it is evident that PS-RM(8,3) significantly outperforms RM(8,3) when using the above stacking method and a stacking ratio of 15 / 16, for example, when the BRR is 10... -4 When the decode list size is 16, the normalized signal-to-noise ratio required by PS-RM is about 3.55dB; while the normalized signal-to-noise ratio required by RM is about 3.8dB, an improvement of about 0.25dB.

[0226] It should be noted that ML decoding refers to comparing all codewords in the codebook with the received signal and finding the codeword with the highest likelihood probability P(y|c). In practice, the performance of the decoding algorithm is usually judged to be close to that of ML decoding based on the lower bound of ML.

[0227] Specifically, when a codeword is decoded... and decoding error then compare the likelihood probability of c with If the likelihood probability of c is larger, it means that even if ML decoding is used, the decoding is not correct, and the error is counted; on the contrary, if the likelihood probability of c is larger, it means that ML decoding can be used to decode correctly. The ML lower bound in the above table is obtained by adding the above judgment condition, and the size of the decoding list is set to 1024, and the decoding is stopped when 100 codewords are decoded incorrectly. It can be seen that the ML lower bound of PS-RM(8,3) is basically the same as that of RM(8,3), which also shows that PS-RM(8,3) can effectively reduce the gap between the actual performance and the ML lower bound. Figure 13

[0228] Figure 14 and Figure 15 The block error rate curve of PS-RM(9,3) is shown. Figure 14 The block error rate curve of PS-RM(9,3) is shown. b The block error rate curve of PS-RM(9,3) is shown. Figure 14 It can be seen that the minimum block error rate is 15 / 16. Figure 15 The block error rate curve of PS-RM(9,3) is shown. Figure 14 The block error rate curve of PS-RM(9,3) is shown. Figure 14 It can be seen that when the block error rate is 10 -4 When the decoding list size is 64, the normalized SNR required by PS-RM is about 3.3dB, while the normalized SNR required by RM is about 3.85dB, which is improved by about 0.55dB; and for the ML lower bound, the decoding list size is set to 1024, and the decoding is stopped when 100 codewords are decoded incorrectly under ML judgment, and the ML lower bound of PS-RM(9,3) is right-shifted by about 0.2dB compared with that of RM(9,3).

[0229] Figure 16 and Figure 17 The block error rate curve of PS-RM(9,3) is shown. Figure 13 ​is the curve of the block error rate of PS-RM(10, 2) with the change of the superposition ratio, wherein the specific value of the normalized signal-to-noise ratio is set as E b / No = 3.5 dB, the superposition mode is selected as the row weight size superposition mode, the same superposition ratio is used for all parts of the superposition in the encoding process, the superposition ratio is searched with a step of 1 / 128, the decoding list size is 4, and for each superposition ratio, the decoding is stopped when 200 codewords are decoded incorrectly, and the block error rate is calculated. From Figure 16 It can be seen that the superposition ratio with the minimum block error rate is about 7 / 8. Figure 17 is the curve of the block error rate of PS-RM(10, 2) with the change of the superposition ratio, wherein the specific value of the normalized signal-to-noise ratio is set as E Figure 16 The search is obtained. The block error rate of the optimal superposition ratio 7 / 8 with the change of the normalized signal-to-noise ratio. The superposition mode is the same as above, the decoding list size is 4, 16, and 64 respectively, and the decoding is stopped when 200 codewords are decoded incorrectly at each normalized signal-to-noise ratio, and the block error rate is 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. From Figure 17 It can be seen that when the block error rate is 10 -4 , the normalized signal-to-noise ratio required by the PS-RM is about 3.95 dB when the decoding list size is 16, and the normalized signal-to-noise ratio required by the RM is about 4.95 dB, which is increased by about 1.00 dB; and for the ML lower bound, the decoding list size is set to 1024, and the decoding is stopped every time 100 codewords are decoded incorrectly under the ML judgment, and the ML lower bound of the PS-RM(10, 2) is right shifted by about 0.4 dB than the RM(10, 2). Finally, based on the above embodiment, it can be seen that the longer the code length is, the greater the performance improvement of the PS-RM code compared with the 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 decoded first, u superimposed on it is regarded as a kind of interference, and since the decoding error of the RM code is dominated by v, by presetting the encoding mode, that is, the basic recursive structure, the bit index set is determined according to the predefined superposition ratio, superposition mode and basic parameters, and then only the bits at the positions corresponding to the elements in the bit index set of the subcode u are superimposed on the subcode v, instead of superimposing on all positions, which can increase the accuracy of decoding v, thereby reducing the block error rate. When the PS-RM code is constructed, the superposition position is carefully selected, that is, the row weight size superposition mode, so that the block error rate can be better reduced, and the gap with the maximum likelihood decoding lower bound can be narrowed, especially for the case of long code length, a greater performance gain can be obtained.

[0231] Based on the above embodiment Figure 2 A kind of processing method for encoding and decoding disclosed in the present application embodiment four also discloses a kind of processing device for encoding and decoding, as Figure 18 shown, the processing device for encoding and decoding includes:

[0232] The acquisition unit 1801 is configured to acquire basic parameters of the RM code and a plurality of to-be-processed information bits.

[0233] The determination unit 1802 is configured to determine a bit index set according to a predefined superposition ratio, a superposition manner and the basic parameters.

[0234] The encoding unit 1803 is configured to encode the plurality of to-be-processed information bits according to a preset encoding manner and the bit index set to obtain a coded codeword; wherein the preset encoding manner is determined by a Plotkin recursive structure of a preset partial superposition or a corresponding generation matrix.

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

[0236] Further, the superposition manner at least includes a sequential superposition manner or a row weight size superposition manner, and the determination unit 1802 includes:

[0237] The first determination module is configured to, if the superposition manner is the sequential superposition manner, obtain a number of codeword bits to be superposed through the predefined superposition ratio, and the bit index set is composed of continuous indexes, and the size of the set is the number of the codeword bits to be superposed.

[0238] The first acquisition module is configured to, if the superposition manner is the row weight size superposition manner, acquire a generation matrix of the RM code and the number of the codeword bits to be superposed, and initialize an original set.

[0239] The second acquisition module is configured to acquire each row weight of the generation matrix, and determine a target row with the smallest row weight from the each row weight.

[0240] The search module is configured to search for each column index with an element of the target row being 1, and take a union set of the each column index and the original set as a target set.

[0241] The second determination module is configured 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 the superposed bits.

[0242] The third determination module is configured to, if the size of the target set is greater than or equal to the number of the to-be-superposed bits, determine that the size of the target set meets the superposition bit number requirement.

[0243] The output module is configured to, under the condition that the size of the target set meets the superposition bit number requirement, output indexes of the number of the bits to be superposed in the new set as the bit index set.

[0244] The setting output module is configured to set all elements of the target row to 1 if the size of the target set is smaller than the number of bits to be superimposed, return to the step of obtaining the row weight of each row of the generator matrix, and determine the target row with the minimum 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 indexes of the number of bits to be superimposed in the new set as the bit index set.

[0245] Further, the encoding unit 1803 comprises:

[0246] The decomposition module is configured to decompose the information bits to be encoded according to a Plotkin recursive structure of the RM code until the repetition code or the full space code is obtained, to obtain corresponding sub-information bits, and to encode the sub-information bits by using the RM code; wherein the Plotkin recursive structure is determined by a sub-code u and a sub-code u+v.

[0247] The superimposition module is configured to, in the process of performing a preset partial superimposition PS-RM code on the sub-codes according to the Plotkin recursive structure, keep the sub-code u unchanged, perform a superimposition operation on positions represented by elements in the bit index set in the code word of the sub-code u+v, and keep other positions unchanged and maintain the sub-code v; and an expression for encoding the sub-information bits according to the Plotkin recursive structure is as follows:

[0248]

[0249] wherein m and r are parameters required for defining the RM code; u is a code word of a sub-code PS-RM(m-1, r); v is a code word of a sub-code PS-RM(m-1, r-1); u' is a Hadamard product of u and s; s is a binary mask vector, elements of all index positions in the bit index set are 1, and elements of other positions are 0; and F is a representation of a number field in mathematics.

[0250] Further, the encoding unit 1803 comprises:

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

[0252]

[0253] wherein G PS-RM (m, r) is a generator matrix; G PS-RM (m-1, r) is a sub-matrix; G' PS-RM (m-1, r) is a sub-matrix; G PS-RM (m-1, r-1) is a sub-matrix; and S is a binary diagonal matrix, elements of diagonal line positions corresponding to all indexes in the bit index set are 1, and elements of other diagonal line positions are 0.

[0254] The third acquisition module is used to acquire the information vector to be encoded.

[0255] The multiplication 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 Embodiment 4 of this application are as follows: Considering the Plotkin recursive structure (u, u+v) of the RM code, when v is decoded first, the u superimposed on it is regarded as interference. Since the decoding error of the RM code is dominated by v, by using a preset encoding method, i.e., a preset recursive structure, and determining the bit index set according to a predefined superposition ratio, superposition method, and basic parameters, and then only selecting the bits at the corresponding positions of the elements in the bit index set of the subcode u to be superimposed on the subcode v, instead of superimposing at all positions, the accuracy of decoding v can be increased, thereby reducing the block error rate. When constructing the PS-RM code, the superposition positions are carefully selected, i.e., a large and small superposition method is adopted, which can better reduce the block error rate and narrow the gap with its maximum likelihood decoding lower bound, especially for the case of a long code length, which can obtain a large performance gain.

[0257] Based on the above embodiments Figure 9 In addition to the disclosed encoding and decoding processing method, Embodiment 5 of this application also discloses another encoding and decoding processing apparatus, such as... Figure 19 As shown, this alternative encoding / decoding processing device includes:

[0258] The demodulation unit 1901 is used to demodulate the received signal when it is received to obtain demodulated information. The received signal includes the modulated signal and noise. The modulated signal is obtained by the transmitting end determining the bit index set according to the predefined superposition ratio, superposition method and basic parameters, encoding multiple information bits to be processed according to the preset encoding method and the bit index set, and modulating the encoded codeword.

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

[0260] The beneficial effect of the fifth embodiment of the present application: considering the Plotkin recursive structure (u, u+v) of the RM code, when decoding v first, the u superimposed on it is regarded as a kind of interference, and since the RM code decoding error is dominated by v, therefore, by presetting the encoding mode, i.e. the basis of the preset recursive structure, determining the bit index set according to the predefined superposition ratio, superposition mode and basic parameters, and then only selecting the bits at the positions corresponding to the elements in the bit index set of the subcode u to superimpose on the subcode v instead of superimposing on all positions, the accuracy of decoding v can be increased, thereby reducing the block error rate. When constructing the PS-RM code, the superposition position, i.e. the row weight size superposition mode, is carefully selected, so that the block error rate can be better reduced, the gap with the lower bound of maximum likelihood decoding is narrowed, and especially for the case of longer code length, greater performance gain can be obtained.

[0261] The embodiment of the present application also provides a storage medium, which comprises stored instructions, wherein the instructions control a device where the storage medium is located to perform the processing method of encoding and decoding as described above when the instructions are executed.

[0262] The embodiment of the present application also provides an electronic device, a structure diagram of which is shown in the figure Figure 20 The embodiment of the present application also provides an electronic device, a structure diagram of which is shown in the figure

[0263] The above is only the preferred specific embodiment of the present application, but the protection scope of the present application is not limited to this, any person skilled in the art can easily think of the transformation or replacement within the technical range disclosed by the present application, which should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be limited by the protection scope of the claims.

[0264] For the foregoing method embodiments, in order to simply describe, they are all expressed as a series of action combinations, but those skilled in the art should know that the present application is not limited to the action sequence described, because according to the present application, certain steps can be performed in other sequences or simultaneously. Secondly, those skilled in the art should know that the embodiments described in the specification all belong to preferred embodiments, and the actions and modules involved are not necessarily necessary for the present application.

[0265] It should be noted that each of the embodiments in the specification is described in progressive mode, and each embodiment focuses on the difference from other embodiments. The same and similar parts between 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 part of the method embodiment.

[0266] The steps in the method of each embodiment of the present application can be adjusted, combined and reduced in sequence according to actual needs.

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

[0268] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can 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 the preferred embodiment of the present application. It should be noted that for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, which should be considered as the protection scope of the present application.

Claims

1. A processing method of coding and decoding, characterized by, The method is applied to a sending end, and the method comprises: acquiring basic parameters of an RM code and a plurality of to-be-processed information bits; determining a bit index set according to a predefined superposition ratio, a superposition mode and the basic parameters; encoding the plurality of to-be-processed information bits according to a preset encoding mode and the bit index set to obtain an encoded code word; wherein the preset encoding mode is determined by a Plotkin recursive structure of a preset partial superposition or a corresponding generating matrix; the preset encoding mode is an encoding mode in which, on the basis of the preset recursive structure, only bits at positions corresponding to elements in a bit index set of a subcode u are selected and superposed onto a subcode v, instead of superposing bits at all positions; modulating the encoded code word, and sending the modulated signal to a receiving end through a channel, so that the receiving end performs channel decoding on demodulated information through a preset decoding algorithm and outputs the information.

2. The method of claim 1, wherein, The superposition mode at least comprises a sequential superposition mode or a row weight size superposition mode, and the determining of the bit index set according to the predefined superposition ratio, the superposition mode and the basic parameters comprises: if the superposition mode is the sequential superposition mode, obtaining the number of to-be-superposed code word bits through the predefined superposition ratio, and the bit index set is composed of continuous indexes, and the size of the set is the number of to-be-superposed code word bits; if the superposition mode is the row weight size superposition mode, acquiring a generating matrix of the RM code and the number of to-be-superposed code word bits, and initializing an original set; acquiring the row weights of the generating matrix, and determining a target row with the smallest row weight from the row weights; searching for each column index of the target row element being 1, and taking the union of a set composed of each column index and the original set as a target set; determining the size of the target set, and judging whether the size of the target set is greater than or equal to the number of to-be-superposed code word bits; if the size of the target set is greater than or equal to the number of to-be-superposed code word bits, it is determined that the size of the target set meets the superposition bit number requirement; under the condition that the size of the target set meets the superposition bit number requirement, outputting indexes of the number of to-be-superposed bits in a new set as the bit index set; if the size of the target set is less than the number of to-be-superposed code word bits, setting all elements of the target row to 1, and returning to execute the step of acquiring the row weights of the generating matrix and determining 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 to-be-superposed code word bits, and outputting indexes of the number of to-be-superposed bits in a new set as the bit index set.

3. The method of claim 1, wherein, The encoding of the plurality of to-be-processed information bits according to the preset encoding mode and the bit index set to obtain the encoded code word comprises: decomposing to-be-encoded information bits according to a Plotkin recursive structure of an RM code until the to-be-encoded information bits are decomposed 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 a subcode u and a subcode u+v. In the process of presetting partial superposition PS-RM code to the subcode according to the Plotkin recursive structure, the subcode u is kept unchanged, and the positions represented by the elements in the bit index set are superimposed in the code word of the subcode u+v, and the remaining positions are not superimposed and maintained as the subcode v; The expression of presetting partial superposition PS-RM code to the subcode according to the Plotkin recursive structure is as follows: ， where m and r are parameters required by the definition of the RM code; u is the code word of the sub-code ; v is the code word of the sub-code ; is the Hadamard product of u and s; s is a binary mask vector, the elements of which in all index positions in the set of bit indexes are 1, and the elements of which in the remaining positions are 0; F is the representation of a number field in mathematics.

4. The method of claim 1, wherein, According to the preset encoding mode and the bit index set, the information bits are encoded to obtain the encoded code word, comprising: According to the preset generator matrix recursive expression, the generator matrix is obtained. The preset generator matrix recursive expression is as follows: ， wherein is a generator matrix; is a sub-matrix; is a sub-matrix; is a sub-matrix; S is a binary diagonal matrix, the elements of S in the diagonal positions corresponding to all index pairs in the set of bit indexes are 1, and the elements of S in the other diagonal positions are 0; An information vector to be encoded is obtained. The generator matrix and the information vector to be encoded are multiplied to obtain the encoded code word.

5. A processing method of coding and decoding, characterized by, 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 comprises a modulated signal and noise; the modulated signal is obtained by a sending end according to a predefined superposition ratio, a superposition mode and basic parameters, determining a bit index set, encoding a plurality of information bits to be processed according to a preset encoding mode and the bit index set, and modulating the encoded code word to obtain the modulated signal; the preset encoding mode is an encoding mode in which the sending end, on the basis of a preset recursive structure, only selects bits at positions corresponding to elements in a bit index set of a subcode u to superimpose on a subcode v, instead of superimposing on all positions; The demodulated information is channel decoded by a preset decoding algorithm and outputted.

6. The method of claim 5, wherein, The demodulated information is channel decoded by a preset decoding algorithm and outputted, comprising: A log-likelihood ratio of the demodulated information is obtained; According to a preset recursive list decoding algorithm, log-likelihood ratios of positions represented by elements in the bit index set are recursively decomposed, and log-likelihood ratios of the remaining positions are kept unchanged to obtain a recursive decomposition result; The calculation formula of the preset recursive list decoding algorithm is as follows: ， ， wherein is the log-likelihood ratio of the i-th bit of the sub-code v; ln is the natural logarithm function; is the log-likelihood ratio of the i-th bit of the current code word; is the log-likelihood ratio of the i-th bit of the current code word; is the log-likelihood ratio of the i-th bit of the current code word; exp is the exponential function with base of the natural number; i is the code word bit index; is the set of bit indices; is the log-likelihood ratio of the i-th bit of the sub-code u; is the decoding result of the i-th bit of the sub-code v; The recursion is performed until a repetition code or a full space code is reached, and the recursive decomposition result is used for channel decoding; For the repetition code, all-0 code words and all-1 code words are added to a candidate list; For the full space code, four code words meeting a preset condition are selected and added to the candidate list; the preset condition is determined according to a posterior probability value of the code word; The posterior probability values of all code words in the candidate list are calculated, the first L code words meeting the preset condition are returned according to the posterior probability values of all code words in the candidate list, a decoding result is obtained, and the process of channel decoding the demodulated information is completed and outputted, wherein L is a set list size.

7. The method of claim 5, wherein, Further comprising: A normalized signal-to-noise ratio is set; Different superposition ratios are set at intervals according to a fixed step size; According to the encoded code word and the result of channel decoding, the block error rate under different superposition ratios is counted; The superposition ratio with the minimum block error rate is selected as the optimal value under the normalized signal-to-noise ratio according to the block error rates under different superposition ratios.

8. A processing device for coding and decoding, characterized by The device is applied to a sending end, and the device comprises: The acquisition unit is configured to acquire basic parameters of an RM code and a plurality of to-be-processed information bits. The determination unit is configured to determine a bit index set according to a predefined superposition ratio, a superposition manner and the basic parameters. The encoding unit is configured to encode the plurality of to-be-processed information bits according to a preset encoding manner and the bit index set to obtain an encoded code word; wherein the preset encoding manner is determined by a Plotkin recursive structure of preset partial superposition or a corresponding generation matrix; the preset encoding manner is an encoding manner of superimposing only bits at positions corresponding to elements in a bit index set of a subcode u on a subcode v according to the bit index set on the basis of a preset recursive structure, instead of superimposing bits at all positions. The modulation and transmission unit is configured to modulate the encoded code word, and transmit the modulated signal to a receiving end through a channel, so that the receiving end performs channel decoding on demodulated information through a preset decoding algorithm and outputs the information.

9. The apparatus of claim 8, wherein, The superposition manner at least includes a sequential superposition manner or a row weight size superposition manner, and the determination unit includes: The first acquisition module is configured to acquire a generation matrix of the RM code and a quantity of to-be-superimposed code word bits if the superposition manner is the row weight size superposition manner, and initialize an original set. The second acquisition module is configured to acquire each row weight of the generation matrix, and determine a target row with a minimum row weight from the each row weight. The search module is configured to search each column index with an element of 1 in the target row, and take a union set of each column index and the original set as a target set. The first determination module is configured to determine a size of the target set, and judge whether the size of the target set is greater than or equal to the quantity of to-be-superimposed code word bits. The second determination module is configured to determine that the size of the target set meets a superposition bit quantity requirement if the size of the target set is greater than or equal to the quantity of to-be-superimposed code word bits. The output module is configured to output an index of a quantity of to-be-superimposed bits in a new set as the bit index set if the size of the target set meets the superposition bit quantity requirement. The setting module is configured to set all elements of the target row to 1 if the size of the target set is less than the quantity of to-be-superimposed code word bits, return to execute the step of acquiring each row weight of the generation matrix and determining the target row with the minimum row weight from the each row weight, and output the index of the quantity of to-be-superimposed bits in the new set as the bit index set until the size of the target set is greater than or equal to the quantity of to-be-superimposed code word bits.

10. A processing device for coding and decoding, characterized by The device is applied to a receiving end, and the device includes: The demodulation unit is configured to demodulate the received signal to obtain demodulated information when the signal is received, wherein the received signal comprises a modulated signal and noise; the modulated signal is obtained by determining a bit index set according to a predefined superposition ratio, a superposition mode and basic parameters, encoding a plurality of information bits to be processed according to a preset encoding mode and the bit index set, and modulating the encoded code word; the preset encoding mode is an encoding mode in which the transmitting end only selects bits at positions corresponding to elements in the bit index set of the sub-code u to superimpose on the sub-code v according to the bit index set on the basis of a preset recursive structure, instead of superimposing bits at all positions. The decoding output unit is configured to perform channel decoding on the demodulated information by using a preset decoding algorithm and output the decoded information.

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