A reed-muller code construction method and system for realizing arbitrary integer dimension selection

Abstract

The present disclosure provides a Reed-Muller code construction method and system for realizing arbitrary integer dimension selection, and relates to the technical field of channel coding and error correction coding, which comprises: obtaining a construction parameter, constructing an adjacent standard RM code interval based on the construction parameter; determining a basic information bit set according to the adjacent standard RM code interval, and determining a candidate supplement set based on the basic information bit set; selecting a supplement index from the candidate supplement set according to a set selection rule, and constructing a target information bit index set; after obtaining the target information bit index set, constructing an input vector with a set length, filling information bits corresponding to the code dimension number into positions whose indexes belong to the target information bit index set, and filling the remaining positions with frozen bits 0, and then performing encoding to obtain a corresponding arbitrary dimension RM code codeword. The present disclosure can realize the selection of arbitrary dimension code on the basis of maintaining the RM code structure and realizing convenience, and the code dimension can be selected as required within a given code length range.

Description

Technical Field

[0001] The present disclosure relates to the technical field of channel coding and error correction coding, and specifically relates to a method and system for constructing Reed-Muller codes that can achieve arbitrary integer-dimensional selection. Background Art

[0002] The statements in this part merely provide background technical information related to the present disclosure and do not necessarily constitute prior art.

[0003] Reed-Muller codes are a class of classical linear block codes with a clear algebraic structure and recursive construction form, and have high research and application value in reliable communication, data storage protection, short code design, and coding schemes related to polar coding.

[0004] Both polar codes and RM codes can be regarded as coding methods obtained by selecting different information bit sets from the coding matrix. The main difference between the two lies in the selection criteria for information bits: polar codes usually select information bits based on the reliability of bit channels, while RM codes usually select information bits based on the Hamming weight of the binary representation corresponding to the row index.

[0005] Although the existing standard RM codes have regular structures and are convenient for analysis, their code dimensions can only take a finite number of discrete values. In other words, for a given code length, the standard RM codes can only achieve several specific dimensions and cannot cover all integer dimensions. If the target code dimension k satisfies |A(r,m)| < k < |A(r + 1,m)|, there is no ready-made construction corresponding exactly to the standard RM code. At this time, if the system requires a certain specific code rate, specific redundancy, or specific complexity compromise scheme, traditional RM codes often cannot be directly adapted. Usually, it can only be achieved by changing the code length, splicing other coding methods, or redesigning the coding structure, and there are still the following limitations: (1) The code rate adjustment granularity is relatively coarse, and it is difficult to meet the refined parameter configuration requirements; (2) The existing standard RM code dimensions are discrete and cannot be adapted to some engineering target dimensions; (3) To match the requirements of the target system, it is often necessary to introduce additional coding or code length adjustment mechanisms, resulting in an increase in implementation complexity and system cost; (4) On the premise of maintaining the original structural advantages of RM codes, there is a lack of a simple, unified, and implementable method for arbitrary dimension expansion. Summary of the Invention

[0006] To address the aforementioned issues, this disclosure proposes a Reed-Muller code construction method and system that enables arbitrary integer dimension selection. While maintaining the RM code structure and ease of implementation, it allows the code dimension to be selected arbitrarily within a given code length range, achieving flexible adjustment of the code dimension and thus meeting different requirements for code rate, redundancy, and error correction capabilities.

[0007] According to some embodiments, the present disclosure adopts the following technical solutions: A method for constructing Reed-Muller codes with arbitrary integer dimension selection includes: Obtain the construction parameters, which include set integer parameters and target code dimension; Construct adjacent standard RM code intervals based on construction parameters; A set of basic information bits is determined based on adjacent standard RM code intervals, and a candidate supplementary set is determined based on the set of basic information bits. Supplementary indices are selected from the candidate supplementary set according to the set selection rules, and a target information bit index set is constructed. After obtaining the target information bit index set, an input vector of a set length is constructed. The information bits of the corresponding code dimension are filled into the positions where the index belongs to the target information bit index set, and the remaining positions are filled with frozen bits 0. Then, encoding is performed to obtain the codeword of the corresponding arbitrary dimension RM code.

[0008] As one embodiment, construction parameters are obtained, including set integer parameters and target code dimension, including: Input integer parameters With target code dimension The code length And satisfying,

[0009] At the same time, select the selection rules for additional information bits.

[0010] As one embodiment, the construction of adjacent standard RM code intervals based on construction parameters includes: Determine the integers that satisfy the following formula :

[0011] like Then, directly set the target information bit index set as follows:

[0012] Then the construction is complete.

[0013] As one embodiment, the step of determining a basic information bit set based on adjacent standard RM code intervals, and determining a candidate supplementary set based on the basic information bit set, includes: when

[0014] First, use the standard RM code. All information bits are used as the basic information bits, that is, let,

[0015] Obviously, ; Construct the candidate supplement set:

[0016] The elements in this set are all from Expand to The number of indexes that need to be added for newly added information bit indexes is: .

[0017] As one embodiment, the selection rule includes two methods: random selection and selection based on channel reliability. The random selection rule is to randomly select from the candidate supplementary set C. t The indexes constitute a supplementary index set D; the selection based on channel reliability first targets an index of length D. The reliability metric of the corresponding bit channel is determined by the position of each bit. Then, the reliability of each candidate index is compared only within the candidate supplementary set C, and the one with the highest reliability is selected. The indexes constitute the supplementary index set D.

[0018] As one embodiment, the encoding method is as follows:

[0019] This yields the corresponding RM codewords of arbitrary dimensions.

[0020] According to some embodiments, the present disclosure adopts the following technical solutions: A Reed-Muller code construction system that enables arbitrary integer dimension selection includes: A parameter construction module is used to obtain construction parameters, which include set integer parameters and target code dimension; The target information bit index set construction module is used to construct adjacent standard RM code intervals based on the construction parameters; A basic information bit set is determined based on adjacent standard RM code intervals, and a candidate supplementary set is determined based on the basic information bit set; a supplementary index is selected from the candidate supplementary set according to the set selection rules, and a target information bit index set is constructed. The encoding module is used to construct an input vector of a set length after obtaining the target information bit index set, fill the information bits of the corresponding code dimension into the positions where the index belongs to the target information bit index set, fill the remaining positions with frozen bits 0, and then encode to obtain the codeword of the corresponding arbitrary dimension RM code.

[0021] According to some embodiments, the present disclosure adopts the following technical solutions: A computer program product includes a computer program that, when executed by a processor, implements the Reed-Muller code construction method for arbitrary integer dimension selection.

[0022] According to some embodiments, the present disclosure adopts the following technical solutions: A non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the aforementioned method for constructing Reed-Muller codes with arbitrary integer dimension selection.

[0023] According to some embodiments, the present disclosure adopts the following technical solutions: An electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute a Reed-Muller code construction method for implementing arbitrary integer dimension selection.

[0024] Compared with the prior art, the beneficial effects of this disclosure are as follows: This disclosure discloses a method for constructing Reed-Muller codes with arbitrary integer dimension selection. It involves a method for constructing RM codes with arbitrary dimensions that allows the code dimension to be selected as needed within a given code length, while maintaining the RM code structure and ease of implementation. Without changing the basic generator matrix and overall coding framework of the RM code, for any given target code dimension k, a corresponding information bit index set is constructed. This ensures that the resulting code inherits the structural characteristics of the standard RM code while achieving flexible adjustment of the code dimension, thereby meeting different requirements for code rate, redundancy, and error correction capabilities. Furthermore, for newly added information bits located between adjacent standard RM codes, this disclosure also allows selection based on channel reliability, ensuring that the construction result maintains the structural characteristics of the RM code while also considering channel adaptability.

[0025] This disclosure presents a method for constructing Reed-Muller codes with arbitrary integer dimension selection, enabling continuous selection of the code dimension. It overcomes the limitation of standard RM codes, which can only take a few discrete dimensions, allowing the code dimension to range from 1 to... Choose as needed.

[0026] This disclosure presents a method for constructing Reed-Muller codes with arbitrary integer dimension selection, while maintaining the structural advantages of the original RM codes. This disclosure is still based on... The unified encoding framework does not change the basic recursive structure of RM codes, making it easy to continue using existing encoding and decoding implementations.

[0027] This disclosure presents a method for constructing Reed-Muller codes with arbitrary integer dimension selection. The method is simple and low-cost to implement. It only requires supplementing the information bit sets of adjacent standard RM codes with a few indices, without redesigning the generator matrix or introducing additional complex encoding modules.

[0028] This disclosure presents a method for constructing Reed-Muller codes with arbitrary integer dimension selection, facilitating engineering parameter matching. The target dimension can be flexibly set to meet the specific requirements of communication or storage systems regarding code rate, redundancy, and performance tradeoffs, thereby increasing the freedom of parameter design.

[0029] This disclosure presents a method for constructing Reed-Muller codes with arbitrary integer dimension selection, exhibiting good scalability. It can employ either a random selection strategy or a channel reliability-based selection strategy, facilitating the selection of a more suitable construction method for different application scenarios.

[0030] This disclosure presents a method for constructing Reed-Muller codes with arbitrary integer dimension selection, balancing structural integrity and performance adaptability. For newly added information bits, filtering can be performed based on bit channel reliability, enabling arbitrary-dimensional RM codes to better adapt to given channel environments and performance requirements while maintaining the basic structure of RM codes.

[0031] This disclosure presents a method for constructing Reed-Muller codes with arbitrary integer dimension selection, achieving both flexible code dimension adjustment and good block error rate (BLER) performance. Under the same code length, code dimension, list size, and SCL decoding conditions, the arbitrary-dimensional Reed-Muller codes constructed in this disclosure are compared with standard polar codes in block error rate (BLER) simulations. The results show that under the indicated binary erasure channel (BEC) and additive white Gaussian noise (AWGN) channel test conditions, the BLER of the codes constructed by this method is generally lower than that of the standard polar codes, especially in the low erasure probability or high signal-to-noise ratio range. Specifically, the arbitrary-dimensional Reed-Muller codes constructed using a random selection method achieve lower BLERs under most simulation parameters, and the arbitrary-dimensional Reed-Muller codes constructed using a reliability-based selection method also exhibit good overall performance. Therefore, this disclosure not only enables arbitrary-dimensional construction but also achieves good block error rate performance and practical decoding performance under specific simulation conditions. Attached Figure Description

[0032] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0033] Figure 1 For the embodiments of this disclosure m =4. Code length N Under condition 16, the diagram shows the information bit index distribution of the standard RM code and the arbitrary dimension RM code of this disclosure. The blue positions represent the information bits of RM(1,4); the blue and green positions together represent the information bits of RM(2,4); when it is necessary to construct an intermediate dimension code, some indices can be further selected from the green positions as additional information bits.

[0034] Figure 2 The following is a simulation result diagram of the block error rate and signal-to-noise ratio under the conditions of n=128, k=38, L=128, SCL decoder and AWGN channel in the embodiment of this disclosure; Figure 3 The following is a simulation result diagram of the block error rate and signal-to-noise ratio under the conditions of n=128, k=70, L=128, SCL decoder and AWGN channel in the embodiment of this disclosure; Figure 4 The following is a simulation result diagram of the block error rate and signal-to-noise ratio under the conditions of n=128, k=80, L=128, SCL decoder and AWGN channel in the embodiment of this disclosure; Figure 5The following is a simulation result diagram of the block error rate and signal-to-noise ratio under the SCL decoder and AWGN channel in the embodiment of this disclosure when n=256, k=168, L=256; Figure 6 The following is a simulation result diagram of the block error rate and erase probability under the SCL decoder and BEC channel in the embodiment of this disclosure when n=128, k=56, L=128; Figure 7 The following is a simulation result diagram of the block error rate and erase probability under the SCL decoder and BEC channel in the embodiment of this disclosure when n=128, k=60, L=128; Figure 8 The following is a simulation result diagram of the block error rate and erase probability under the SCL decoder and BEC channel in the embodiment of this disclosure when n=128, k=70, L=128; Figure 9 The figure shows the simulation results of the block error rate and erase probability under the SCL decoder and BEC channel in the embodiments of this disclosure when n=128, k=80, L=128. Detailed Implementation

[0035] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0036] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0037] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this disclosure. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0038] Terminology Explanation Reed-Muller codes are a class of classic linear block codes with a definite algebraic structure and recursive construction form. They have high research and application value in reliable communication, data storage protection, short code design, and coding schemes related to polar coding.

[0039] set up

[0040] in, Representation matrix The Kronecker exponentiation. For parameters of... The encoding matrix has a code length of .

[0041] The encoding process based on this matrix can be written as follows:

[0042] in, For length is The bit vector has positions belonging to the information bit index set that carry information bits, while the remaining positions are frozen bits, which are usually set to 0.

[0043] Both polar codes and RM codes can be viewed as derived from matrices. The two encoding methods are derived by selecting different sets of information bits. The main difference between the two lies in the selection criteria of the information bits: polar codes usually select information bits based on the reliability of the bit channel, while RM codes usually select information bits based on the Hamming weight of the binary representation corresponding to the row index.

[0044] For standard Reed-Muller codes Its code length is The dimension is,

[0045] In the standard definition, if natural sequential numbering is used, that is, the relevant indexes are arranged according to... Number them, and denote the natural order index as... The information bits of a standard RM code are typically selected from those that satisfy the following conditions:

[0046] Those positions, among them, Indicates index of Hamming weight in binary representation; The order parameter of the Reed-Muller code is used to determine the standard. The range of information bit indexes in the code; given hour, The larger the value, the more information bits that meet the conditions are indexed, and the larger the corresponding code dimension.

[0047] It should be noted that the entire text of this specification and its figures are numbered in reverse order, that is, the relevant bit positions or the corresponding rows of the generator matrix are numbered according to... arrive The sequential numbering. Let the reverse numbering index be... Then there is,

[0048] Therefore, under the reverse numbering method adopted in this specification, the information bit index set of the standard RM code can be represented as follows:

[0049] because and exist The bitwise binary representation is the bitwise inversion of each other. The above expression can also be equivalently written as:

[0050] The above definitions are consistent with the index set in the subsequent embodiments of this specification.

[0051] For example, when At that time, for Under natural ordinal numbering, satisfy The index is After mapping to reverse numbering, the corresponding index set is:

[0052] Similarly, for In the reverse numbering method of this specification, its information bit index set is as follows:

[0053] While existing standard RM codes are structurally regular and easy to analyze, their code dimension can only take a finite number of discrete values, i.e.,

[0054] In other words, for a given code length Standard RM codes can only implement certain specific dimensions and cannot cover dimensions from 1 to 1. All integer dimensions between.

[0055] Specifically, when the target code dimension satisfy,

[0056] At that time, there was no ready-made construction that completely corresponded to the standard RM code. and Representing sets respectively and The number of elements in the code, that is, the number of information bits in the standard RM(r,m) code and the standard RM(r+1,m) code.

[0057] Example 1 One embodiment of this disclosure provides a method for constructing Reed-Muller codes that can achieve arbitrary integer dimension selection, the method steps of which include: Step 1: Obtain the construction parameters, which include the set integer parameters and the target code dimension; Step 2: Construct adjacent standard RM code intervals based on the construction parameters; Step 3: Determine the basic information bit set based on adjacent standard RM code intervals, and determine the candidate supplementary set based on the basic information bit set; Step 4: Select supplementary indices from the candidate supplementary set according to the set selection rules, and construct the target information bit index set; Step 5: After obtaining the target information bit index set, construct an input vector of a set length, fill the information bits of the corresponding code dimension into the positions where the index belongs to the target information bit index set, fill the remaining positions with frozen bits 0, and then encode to obtain the codeword of the corresponding arbitrary dimension RM code.

[0058] As one embodiment, the basic idea of ​​the Reed-Muller code construction method for arbitrary integer dimension selection disclosed herein is as follows: For a given integer parameter and target code dimension If the target code dimension Exactly equal to a certain standard RM code dimensionality

[0059] Then the information bit index set of the standard RM code is directly adopted. .

[0060] If the target code dimension If the dimension is not equal to the dimension of any standard RM code, then there always exists some integer. So that,

[0061] remember,

[0062]

[0063] At this point, the goal is to construct a new set of information bit indexes. To satisfy it

[0064] and

[0065] In other words, this disclosure performs interpolation-based expansion between the information bit index sets of two adjacent standard RM codes: first, all information bits in the lower-order standard RM code are retained, and then several indices are supplemented from the newly added information bits in the higher-order standard RM code, until the target code dimension is reached. . and Representing sets respectively and The number of elements in the code, that is, the number of information bits in the standard RM(r,m) code and the standard RM(r+1,m) code.

[0066] Based on the above ideas, the specific implementation process of the Reed-Muller code construction method for arbitrary integer dimension selection disclosed in this paper is as follows: Step 1: Obtain the construction parameters, which include the set integer parameters and the target code dimension; Specifically, input integer parameters With target code dimension The code length And satisfying,

[0067] in, The code length is used to select the selection rule for additional information bits, which is either a subsequent random selection rule or a selection rule based on channel reliability.

[0068] Step 2: Construct adjacent standard RM code intervals; Determine the integers that satisfy the following formula :

[0069] Note: If Then directly set,

[0070] The construction is then complete, where, For the new information bit index set. For the information bit index set of standard RM code, For indexing.

[0071] Step 3: Determine the set of basic information bits; when

[0072] First, use the standard RM code. All information bits are used as the basic information bits, that is, let,

[0073] Obviously, .in, The set of basic information bits, This indicates the number of information bit indices it contains.

[0074] Step 4: Determine the candidate supplement set; Construct the candidate supplement set:

[0075] The symbol " " represents the set difference operation, that is, belonging to But not belonging to The set of indices.

[0076] The elements in this set are all from Expand to The newly added information bit index. The number of indexes that need to be supplemented is,

[0077] in, RM ( r +1, m ) indicates that the order is r +1, the number of variables is m The standard Reed-Muller code contains information bits. RM ( r , m The set of information bits.

[0078] Step 5: Select supplementary indices from the candidate supplementary set; Select from candidate supplement set C t Let D be an index that satisfies:

[0079] Further, selecting supplementary indices from the candidate supplementary set according to the set selection rules specifically includes: (a) Method 1: Random selection.

[0080] From the candidate supplement set Random selection The indexes constitute the supplementary index set. This method is simple to implement and is suitable for scenarios with low requirements for construction complexity and where random selection of candidate positions is allowed.

[0081] (ii) Method 2: Selection based on channel reliability.

[0082] Referring to the information bit selection idea of ​​polar codes, first for lengths of The reliability metric of the corresponding bit channel is determined by the position of each bit, and then only in the candidate supplementary set... The reliability of each candidate index is compared, and the one with the highest reliability is selected. The indexes constitute the supplementary index set. .

[0083] The reliability metric can be a reliability order obtained from theoretical analysis, density evolution results, Gaussian approximation results, Bhattacharyya parameters, bit error probability estimates, or other metrics that can reflect the quality of the corresponding bit channel. When using this method, the basic information bit set... The code remains unchanged, and only the newly added positions are subjected to reliability screening, so that while achieving arbitrary code dimension construction, the newly added information bits are more adapted to the target channel conditions.

[0084] As one embodiment, for example, for a binary erase channel, let the channel erase probability be... The initial Bhattacharyya parameter is During the polarization recursion process, the Bhattacharyya parameter for each bit channel is calculated according to the following formula:

[0085]

[0086] The smaller the Z value, the higher the reliability of the corresponding bit channel. For additive white Gaussian noise (AWGN) channels, a Gaussian approximation method can be used to obtain the average reliability of each bit channel based on the initial signal-to-noise ratio. , A larger value indicates a more reliable corresponding bit channel. After obtaining the reliability ranking, only the t most reliable indices are selected from the candidate supplementary set C as the supplementary index set D.

[0087] Step 6: Form the target information bit index set; definition

[0088] but satisfy,

[0089] Thus, the dimension of the target code is obtained. RM codes of any dimension.

[0090] Step 7: Encode; Obtain the information bit index set After that, the construction length is input vector .Will Each information bit is filled into the index. The positions are filled with frozen bits 0, and then encoded using the following formula:

[0091] This allows us to obtain the corresponding RM codewords of any dimension.

[0092] Example 2 One embodiment of this disclosure provides a method for constructing Reed-Muller codes with arbitrary integer dimension selection. Taking the construction of a code with a code length of 16 and a target code dimension of 8 as an example, the specific process is as follows: Pick The code length is

[0093] In this embodiment, the index uses a reverse numbering method, that is, the relevant positions are numbered according to... The sequential numbering.

[0094] For a standard RM code of this length, its typical dimension is:

[0095] Therefore, when it is necessary to construct a code with a dimension of 8, there is no direct corresponding construction for the standard RM code, and the method disclosed in this paper must be used.

[0096] First of all, there are

[0097]

[0098] because,

[0099] Therefore, the objective dimension Located in standard RM code and Between corresponding dimensions.

[0100] According to the method disclosed herein, the basic information bit set is first obtained.

[0101] Then take the information bit set of the next higher-order standard RM code.

[0102] Therefore, the candidate supplement set is

[0103] Since the target dimension is 8 and the basic set already contains 5 information bits, it is necessary to supplement them. One information bit.

[0104] As one embodiment, a random selection method is selected, specifically as follows: In the candidate supplement set Three indices are randomly selected from the list. For example, if three indices are selected...

[0105] Then the target information bit index set is obtained.

[0106] Subsequently, the 8 information bits are filled into the positions corresponding to the above indices, and the remaining positions are filled with the freeze bit 0.

[0107] Encoding complete.

[0108] Another implementation method, if based on channel reliability selection, involves the following process: For the candidate set For each candidate position in the set, the reliability order of the corresponding bit channel is pre-calculated based on the target channel model or obtained by looking up a table. Then, the reliability of each candidate position is compared only within this candidate set, and the three indices with the highest reliability are selected as the new information bits.

[0109] For example, under a given channel condition, if the three most reliable indices in the candidate set are...

[0110] Then the target information bit index set is obtained.

[0111] It should be noted that the above These are merely illustrative results. The three selected indices may differ depending on the channel model, signal-to-noise ratio, or reliability calculation method, but they all share the commonality of being within the candidate supplementary set. The system prioritizes selecting locations with higher reliability as supplementary information bits.

[0112] As one example, for any integer and arbitrary target dimension Among them, satisfying

[0113] All of these can be constructed using the steps described above: (1) When When the dimension is equal to that of a certain standard RM code, the corresponding standard RM code is used directly; (2) When When located between two adjacent standard RM code dimensions, the required number of indices are supplemented from the newly added information bit set of the higher-order RM code, based on the information bit set of the lower-order RM code. (3) The supplementary position is determined by random rules or rules based on channel reliability, thereby constructing a code dimension that is exactly... RM codes of any dimension.

[0114] Therefore, this disclosure can achieve fine-grained adjustment of the RM code dimension without changing the main framework of standard RM encoding.

[0115] exist Figures 2-9 Under the simulation conditions shown, the BLER simulation of the arbitrary-dimensional RM code constructed in this disclosure is compared with that of the standard polar code. The results show that under the BEC and AWGN channel test conditions shown, the BLER of the code constructed by the method of this disclosure is generally lower than that of the standard polar code, especially in the range of low erasure probability or high signal-to-noise ratio. Among them, the arbitrary-dimensional RM code constructed by random selection achieves a lower BLER under most simulation parameters, and the arbitrary-dimensional RM code constructed by reliability-based selection also shows good overall performance. It can be seen that this disclosure can not only realize arbitrary-dimensional construction, but also achieve good block error performance and actual decoding performance under specific simulation conditions.

[0116] Example 3 One embodiment of this disclosure provides a Reed-Muller code construction system for implementing arbitrary integer dimension selection, comprising: A parameter construction module is used to obtain construction parameters, which include set integer parameters and target code dimension; The target information bit index set construction module is used to construct adjacent standard RM code intervals based on the construction parameters; A basic information bit set is determined based on adjacent standard RM code intervals, and a candidate supplementary set is determined based on the basic information bit set; a supplementary index is selected from the candidate supplementary set according to the set selection rules, and a target information bit index set is constructed. The encoding module is used to construct an input vector of a set length after obtaining the target information bit index set, fill the information bits of the corresponding code dimension into the positions where the index belongs to the target information bit index set, fill the remaining positions with frozen bits 0, and then encode to obtain the codeword of the corresponding arbitrary dimension RM code.

[0117] Example 4 One embodiment of this disclosure provides a computer program product, including a computer program that, when executed by a processor, implements the Reed-Muller code construction method for arbitrary integer dimension selection.

[0118] Example 5 One embodiment of this disclosure provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the Reed-Muller code construction method for arbitrary integer dimension selection.

[0119] Example 6 One embodiment of this disclosure provides an electronic device, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute a Reed-Muller code construction method for implementing arbitrary integer dimension selection.

[0120] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0121] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0122] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A method for constructing Reed-Muller codes with arbitrary integer dimension selection, characterized in that, include: Obtain the construction parameters, which include set integer parameters and target code dimension; Construct adjacent standard RM code intervals based on construction parameters; A set of basic information bits is determined based on adjacent standard RM code intervals, and a candidate supplementary set is determined based on the set of basic information bits. Supplementary indices are selected from the candidate supplementary set according to the set selection rules, and a target information bit index set is constructed. After obtaining the target information bit index set, an input vector of a set length is constructed. The information bits of the corresponding code dimension are filled into the positions where the index belongs to the target information bit index set, and the remaining positions are filled with frozen bits 0. Then, encoding is performed to obtain the codeword of the corresponding arbitrary dimension RM code.

2. The method for constructing Reed-Muller codes with arbitrary integer dimension selection as described in claim 1, characterized in that, Obtain the construction parameters, which include set integer parameters and target code dimension, including: Input integer parameters With target code dimension The code length And satisfying, in, N For code length, m Integer parameter, For target code dimension.

3. The method for constructing Reed-Muller codes with arbitrary integer dimension selection as described in claim 1, characterized in that, The construction of adjacent standard RM code intervals based on construction parameters includes: Determine the integers that satisfy the following formula : like Then, directly set the target information bit index set as follows: Then the construction is complete; in, For indexing, For the order parameter of the Reed-Muller code, For the target code dimension, m Integer parameter, This indicates a new set of information bit indexes. This represents the information bit index set.

4. The method for constructing Reed-Muller codes with arbitrary integer dimension selection as described in claim 1, characterized in that, The step of determining a basic information bit set based on adjacent standard RM code intervals, and determining a candidate supplementary set based on the basic information bit set, includes: when First, use the standard RM code. All information bits are used as the basic information bits In other words, Obviously, ; Construct the candidate supplement set: The elements in this set are all from Expand to The number of indexes that need to be added for newly added information bit indexes is: in, and Representing sets and The number of elements in the code, that is, the number of information bits in the standard RM(r,m) code and the standard RM(r+1,m) code.

5. The method for constructing Reed-Muller codes with arbitrary integer dimension selection as described in claim 1, characterized in that, The step of selecting supplementary indices from the candidate supplementary set according to the set selection rules includes: The selection rules include two methods: random selection and selection based on channel reliability. The random selection rule is to randomly select from the candidate supplementary set C. t The indexes constitute a supplementary index set D; the selection based on channel reliability first targets an index of length D. The reliability metric of the corresponding bit channel is determined by the position of each bit. Then, the reliability of each candidate index is compared only within the candidate supplementary set C, and the one with the highest reliability is selected. The indexes constitute the supplementary index set D.

6. The method for constructing Reed-Muller codes with arbitrary integer dimension selection as described in claim 1, characterized in that, The encoding method is as follows: This yields the corresponding RM codeword of any dimension. in, For length is bit vector, Represents a matrix.

7. A Reed-Muller code construction system for implementing arbitrary integer dimension selection, comprising: A parameter construction module is used to obtain construction parameters, which include set integer parameters and target code dimension; The target information bit index set construction module is used to construct adjacent standard RM code intervals based on the construction parameters; A basic information bit set is determined based on adjacent standard RM code intervals, and a candidate supplementary set is determined based on the basic information bit set; a supplementary index is selected from the candidate supplementary set according to the set selection rules, and a target information bit index set is constructed. The encoding module is used to construct an input vector of a set length after obtaining the target information bit index set, fill the information bits of the corresponding code dimension into the positions where the index belongs to the target information bit index set, fill the remaining positions with frozen bits 0, and then encode to obtain the codeword of the corresponding arbitrary dimension RM code.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements a Reed-Muller code construction method for arbitrary integer dimension selection as described in any one of claims 1-6.

9. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement a Reed-Muller code construction method for arbitrary integer dimension selection as described in any one of claims 1-6.

10. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to perform a Reed-Muller code construction method for arbitrary integer dimension selection as described in any one of claims 1-6.

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