A RAID encoding method, device and computer readable storage medium

By calculating and writing the first and second verification codes in RAID encoding, the problem of character line short circuit during RAID encoding is solved, and more efficient data protection and storage is achieved.

CN114546710BActive Publication Date: 2025-05-16SHANDONG DAI MICROELECTRONICS CO LTD
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Patent Information

Application Number
CN202210169889.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-02-23
Publication Date
2025-05-16
Estimated Expiration
2042-02-23

AI Technical Summary

Technical Problem

During the RAID encoding process, maintaining a 31:1 ratio using multiple stripe blocks will cause the problem of character line short circuit.

Method used

By obtaining the information of the stored address, the number of writes, character lines and data, the first and second verification codes are calculated and written, so as to avoid directly dispatching data to obtain the verification code, reduce the number of striped blocks in the RAID block, and obtain the verification code by encoding the character lines.

Benefits of technology

It effectively avoids the problem of character line short circuit during RAID encoding, and improves the reliability and storage efficiency of data protection.

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Abstract

The present application discloses a RAID encoding method, device and computer-readable storage medium, which relates to the field of computers. By obtaining information of a storage address, a write count, a character line and data, wherein the write count is a natural number greater than or equal to 1; writing data into the storage address; obtaining a first check code and a second check code according to the write count, the character line and the data, and writing the first check code and the second check code into the storage address. Therefore, directly allocating data to obtain the check code is avoided, but the number of stripe blocks in the RAID block is reduced by setting the character line, and then the check code is obtained by encoding the character line, thereby avoiding the problem of character line short circuit.
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Description

Technical Field

[0001] The present application relates to the field of computers, and in particular to a RAID encoding method, device, and computer-readable storage medium. Background Art

[0002] In order to protect the data in computer NAND flash memory (NAND), only the error checking and correction (Error Correcting Code, ECC) was designed for each page. However, as the process was miniaturized and the structure changed from plane to three-dimensional, ECC alone was not enough to protect the data. Finally, someone referred to the design of existing hard disks and proposed Redundant Array of Independent Disks (RAID). This is a way to protect data, using multiple storage check codes (Parity) to restore lost data. The general principle of protection is (2 n -1): 1. The common ratio is 15:1 or 31:1. These 16 or 32 blocks are called RAID blocks (RBLK), which may contain several stripe blocks (SBLK).

[0003] As NAND evolves, the space contained in a die is getting larger and larger, and the number of dies required for the same capacity of memory is getting smaller and smaller. In order to avoid wasting too much space, the best situation is to maintain 31:1. However, using multiple SBLKs at the same time to maintain 31:1 will cause word line short circuit problems.

[0004] In view of the above problems, designing a RAID encoding method to avoid word line short circuit during RAID encoding is an urgent problem to be solved by technicians in this field. Summary of the invention

[0005] The purpose of the present application is to provide a RAID encoding method, device and computer-readable storage medium to avoid word line short circuit during RAID encoding.

[0006] In order to solve the above technical problems, the present application provides a RAID encoding method, including:

[0007] Obtain information about storage addresses, write times, word lines, and data;

[0008] Wherein, the number of write times is a natural number greater than or equal to 1;

[0009] Writing the data into the storage address;

[0010] A first check code and a second check code are acquired according to the number of write times, the word line and the data, and the first check code and the second check code are written into the storage address.

[0011] Preferably, writing the data into the storage address comprises:

[0012] The data is written into the storage address using NVML as a unit.

[0013] Preferably, the acquiring the first verification code and the second verification code according to the number of write times, the word line and the data comprises:

[0014] Determining whether the number of write times and the word lines are both odd numbers or both even numbers;

[0015] If yes, obtaining the first check code according to the first half of the data, and obtaining the second check code according to the second half of the data;

[0016] If not, the second verification code is obtained according to the first half of the data in the data, and the first verification code is obtained according to the second half of the data in the data.

[0017] Preferably, before acquiring the information of the storage address, the number of write times, the word line and the data, the method further includes:

[0018] Initialize the storage address information, the write times, and the word line;

[0019] The first check code and the second check code are cleared.

[0020] Preferably, after writing the first check code and the second check code into the storage address, the method further includes:

[0021] Add 1 to the write count to obtain a new write count;

[0022] Acquire information of a new storage address according to the new number of write times;

[0023] Determine whether the new number of writes is 2 n -1; where n is the number of bare crystals in the die;

[0024] If yes, writing the first verification code and the second verification code into the new storage address;

[0025] If not, return to the step of obtaining the information of the storage address, the number of write times, the word line and the data.

[0026] Preferably, the information for initializing the storage address includes:

[0027] The channel, chip enable and page of the storage address are set to 0, 0, and 0 respectively.

[0028] Preferably, n is a positive integer not less than 4.

[0029] In order to solve the above technical problems, the present application also provides a RAID encoding device, including:

[0030] A first acquisition module is used to acquire information of a storage address, a write count, a word line, and data; wherein the write count is a natural number greater than or equal to 1;

[0031] A first writing module, used for writing the data into the storage address;

[0032] A second acquisition module, used for acquiring a first check code and a second check code according to the number of write times, the word line and the data;

[0033] The second writing module is used to write the first verification code and the second verification code into the storage address.

[0034] In order to solve the above technical problems, the present application also provides another RAID encoding device, including:

[0035] Memory for storing computer programs;

[0036] A processor is used to implement the steps of the above-mentioned RAID encoding method when executing the computer program.

[0037] In order to solve the above technical problem, the present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned RAID encoding method are implemented.

[0038] The RAID encoding method provided by the present application obtains information of a storage address, a write count, a character line, and data, wherein the write count is a natural number greater than or equal to 1; writes data into the storage address; obtains a first check code and a second check code according to the write count, the character line, and the data, and writes the first check code and the second check code into the storage address. It can be seen that the above technical solution avoids directly allocating data to obtain a check code, but reduces the number of stripe blocks in a RAID block by setting a character line, and then obtains a check code by encoding the character line, thereby avoiding the problem of a character line short circuit.

[0039] In addition, the present application also provides a RAID encoding device and a computer-readable storage medium, with the same effects as above. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0041] Figure 1 A flowchart of a RAID encoding method provided in an embodiment of the present application;

[0042] Figure 2 A schematic diagram of the RAID encoding structure provided in an embodiment of the present application;

[0043] Figure 3 A flowchart of another RAID encoding method provided in an embodiment of the present application;

[0044] Figure 4 A schematic diagram of the structure of a RAID encoding device provided in an embodiment of the present application;

[0045] Figure 5 A schematic diagram of the structure of another RAID encoding device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0047] The core of this application is to provide a RAID encoding method, device and computer-readable storage medium.

[0048] In order to enable those skilled in the art to better understand the present application, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0049] RAID is a way to protect data, using multiple storage parity codes to restore lost data. The general protection rule is (2n-1):1. The common ratio is n is 4 or 5, that is, 15:1 or 31:1. The cost of 7:1 is too high, so this ratio is not common. 16 or 32 blocks are called RAID blocks (RBLK), which may contain several stripe blocks (SBLK). To avoid wasting too much space, the best situation is to maintain 31:1.

[0050] With the development of NAND, the space contained in a grain is getting larger and larger, and the number of grains required for the same capacity of memory is getting smaller and smaller. In order to avoid wasting too much space, the best situation is to maintain 31:1. Using multiple SBLKs at the same time to maintain a 31:1 ratio will make it difficult to manage the flash conversion layer of the storage controller and increase the difficulty of garbage collection. There will also be a word line short circuit, which is a physical error phenomenon of the grain and is one of the objects to be protected by the parity check code. In this embodiment, a RAID encoding method is proposed. Figure 1 A flowchart of a RAID encoding method provided in an embodiment of the present application. Figure 1 As shown, including:

[0051] S10: Acquire storage address information, write times, word lines, and data; wherein the write times is a natural number greater than or equal to 1.

[0052] S11: Write data into the storage address.

[0053] S12: Obtaining a first verification code and a second verification code according to the number of write times, the word line and the data.

[0054] S13: Write the first check code and the second check code into the storage address.

[0055] In a specific implementation, there are many types of storage devices, such as a solid state disk (SSD), a hard disk drive (HDD), etc. The RAID encoding method provided in this embodiment can be applied to any of the above storage devices, and is not limited in this embodiment. At the same time, the data stored in this embodiment is fixed-size data, usually 16K, 32K, etc., and is selected according to user needs and the actual situation of the storage device. Figure 2 This is a schematic diagram of the RAID encoding structure provided in the embodiment of the present application. Figure 2 As shown in the figure, under the condition of reducing the SBLK contained in each RBLK, a group of word lines (WL) is added, and more than one WL or Page is operated in the same SBLK, so that the RAID reaches a better ratio of 31:1. Plane 0 and Plane 1 refer to the specific components of the RAID stripe and are numbered; for the sake of writing performance, the particles can write two blocks at the same time, and at this time, the odd and even blocks will be divided into two groups, namely plane 0 and plane 1.

[0056] Specifically, in RAID encoding, first obtain the information of the storage address in NAND, the number of writes, the set word line and the data written by the host. Store the data in the storage address. Then obtain the first check code and the second check code according to the number of writes, the word line and the data. The first check code and the second check code are both used to retrieve the stored data through the first check code and the second check code once it is lost or erroneous. In this embodiment, there is no restriction on the specific method of obtaining the check code, which depends on the specific implementation situation. The first check code and the second check code are obtained here because the two check codes are not equal, and different Planes calculate different check codes respectively; the two check codes generated at the same time can be either parity consistent or inconsistent, etc., which is not limited in this embodiment, depending on the specific implementation situation. Finally, the first check code and the second check code obtained are stored in the storage address, and the above steps complete a complete RAID encoding process; and the current number of writes is the number of times data is written in this way in a complete RAID encoding process.

[0057] In this embodiment, by obtaining information of the storage address, the number of writes, the word line and the data, wherein the number of writes is a natural number greater than or equal to 1; writing the data into the storage address; obtaining the first check code and the second check code according to the number of writes, the word line and the data, and writing the first check code and the second check code into the storage address. It can be seen that the above technical solution avoids directly allocating data to obtain the check code, but reduces the number of stripe blocks in the RAID block by setting the word line, and then obtains the check code by encoding the word line, avoiding the problem of word line short circuit.

[0058] Based on the above embodiments:

[0059] As a preferred embodiment, writing data into a storage address includes:

[0060] The data is written into the storage address using NVML as a unit.

[0061] It can be understood that, taking the size of the data acquired in the above embodiment as 32K as an example, the non-volatile memory address (NVML) is a plane page, 2plane = 32K. By writing data to the storage address through this unit, it is not necessary for the upper layer to provide a single page for operation, and through a simple general formula, the specific location of the page of which RBLK the current storage should be located can be calculated in each NVML individually.

[0062] Based on the above embodiments:

[0063] As a preferred embodiment, obtaining the first verification code and the second verification code according to the number of write times, the word line and the data includes:

[0064] Determine whether the number of write times and the word lines are both odd numbers or both even numbers;

[0065] If yes, obtain a first check code according to the first half of the data, and obtain a second check code according to the second half of the data;

[0066] If not, the second check code is obtained according to the first half of the data, and the first check code is obtained according to the second half of the data.

[0067] In the above embodiment, there is no limitation on the specific method of obtaining the check code, which is determined according to the specific implementation situation. As a preferred embodiment, in this embodiment, firstly, according to the previously obtained write times, it is determined whether the write times are all even numbers or all odd numbers. If the write times and the word lines are all even numbers or all odd numbers, the first half of the data is used to calculate the first check code, and the second half of the data is used to calculate the second check code; if not, the first half of the data is used to calculate the second check code, and the second half of the data is used to calculate the first check code.

[0068] It should be noted that in this embodiment, the first half of the data and the second half of the data are divided according to the storage address. Specifically, the first half of the data is divided from the starting address of the storage address to half of the data size, and the remaining part of the data is the second half of the data. Taking 32K data as an example, in the specific implementation, it can be first determined whether the number of writes is an even number; if the number of writes is an even number, it is determined whether the character line is an even number; if the character line is an even number, the first check code is obtained based on the first 16K tuples in the data, and the second check code is obtained based on the last 16K tuples in the data. The calculation method is to XOR all the 16K data of the Page in pairs and finally obtain the 16K check code parity; if the character line is an odd number, the second check code is obtained based on the first 16K tuples in the data, and the first check code is obtained based on the last 16K tuples in the data. If the number of write times is odd, determine whether the word line is even; if the word line is even, obtain the second check code according to the first 16K tuples in the data, and obtain the first check code according to the last 16K tuples in the data; if the word line is odd, obtain the first check code according to the first 16K tuples in the data, and obtain the second check code according to the last 16K tuples in the data. It can be understood that in the specific implementation, it is also possible to first determine the parity of the word line and then determine the parity of the number of write times. The implementation in this embodiment is only a preferred embodiment and does not limit the specific implementation scheme.

[0069] In this embodiment, RAID encoding is implemented through an alternating RAID encoding process, wherein the problem of word line short circuit is solved through parity verification of word lines.

[0070] Figure 3 A flowchart of another RAID encoding method provided in an embodiment of the present application. Figure 3 As shown, before obtaining the information of the storage address, the number of write times, the word line and the data material, it also includes:

[0071] S14: Initialize the storage address information, write times, and word lines.

[0072] S15: Clear the first check code and the second check code.

[0073] It is understandable that the address, the number of writes, and the word line are initialized before the RAID encoding is performed so that data can be subsequently written to the storage address. The specific method for initializing the storage address is not limited in this embodiment and depends on the specific implementation situation. At the same time, the first check code and the second check code in the storage address are cleared to enable the first check code and the second check code obtained by calculation to be subsequently written.

[0074] like Figure 3 As shown, after writing the first check code and the second check code into the storage address, the method further includes:

[0075] S16: Add 1 to the number of write times to obtain a new number of write times.

[0076] S17: Obtain information of a new storage address according to the new number of write times.

[0077] S18: Determine whether the new write count is 2 n -1; wherein n is the number of bare dies of the die; if so, proceed to step S19, if not, return to step S10.

[0078] S19: Write the first verification code and the second verification code into a new storage address.

[0079] It can be understood that after obtaining two check codes, the number of writes is increased by 1. Then, the information of the new storage address is obtained according to the new number of writes, so as to know the address of the next write. Then, it is determined whether the number of writes is 2. n -1; where n is the number of bare dies of the die, which is determined by the actual number of bare dies and is not limited in this embodiment. If yes, the first check code and the second check code are written into the address; if no, the step of obtaining the information of the storage address, the number of writes, the number of word lines, and the byte data is returned to execute again and repeat the entire encoding process.

[0080] Based on the above embodiments:

[0081] As a preferred embodiment, the information for initializing the storage address includes:

[0082] Set the channel of the storage address to 0, chip enable to 0, and page to 0 respectively.

[0083] It is understandable that when accessing NAND flash memory, in order to ensure the maximum access bandwidth, the access unit SBLK is often defined as (channel)*(chip enable)*(plane). Under this access unit, as long as this unit is used for access, it is guaranteed that each access using this unit can reach the maximum bandwidth and ensure the access efficiency of the host. Therefore, when initializing the storage address, the channel of the storage address is set to 0, the chip enable is set to 0, and the page is set to 0, so that data can be written to the storage address later.

[0084] Based on the above embodiments:

[0085] As a preferred embodiment, n is a positive integer not less than 4. In the above embodiment, it can be seen that n is the number of bare crystals of the grain, which is determined according to the actual number of bare crystal dies. Since the general rule of protection is (2n-1):1, where n is a positive integer. However, in the specific implementation, n is 3, that is, the ratio of 7:1 is too costly. As a preferred embodiment, n is set to a positive integer not less than 4, that is, the ratio is at least 16:1, which is more economical.

[0086] In the above embodiment, a RAID encoding method is described in detail, and the present application also provides an embodiment corresponding to a RAID encoding device. It should be noted that the present application describes the embodiment of the device part from two perspectives, one is based on the perspective of functional modules, and the other is based on the perspective of hardware structure.

[0087] Figure 4 This is a schematic diagram of the structure of a RAID encoding device provided in an embodiment of the present application. Figure 4 As shown, the RAID encoding device includes:

[0088] The first acquisition module 10 is used to acquire information of a storage address, a write count, a word line, and data, wherein the write count is a natural number greater than or equal to 1.

[0089] The first writing module 11 is used to write data into a storage address.

[0090] The second acquisition module 12 is used to acquire the first verification code and the second verification code according to the number of write times, the word line and the data.

[0091] The second writing module 13 is used to write the first verification code and the second verification code into the storage address.

[0092] Since the embodiments of the apparatus part correspond to the embodiments of the method part, please refer to the description of the embodiments of the method part for the embodiments of the apparatus part, which will not be repeated here.

[0093] Figure 5 This is a schematic diagram of the structure of another RAID encoding device provided in an embodiment of the present application. Figure 5 As shown, the RAID encoding device includes:

[0094] The memory 20 is used to store computer programs.

[0095] The processor 21 is used to implement the steps of the RAID encoding method mentioned in the above embodiment when executing the computer program.

[0096] The RAID encoding device provided in this embodiment may include but is not limited to a smart phone, a tablet computer, a laptop computer, or a desktop computer.

[0097] Among them, the processor 21 may include one or more processing cores, such as a 4-core processor, an 8-core processor, etc. The processor 21 can be implemented in at least one hardware form of DSP (Digital Signal Processor), FPGA (Field-Programmable Gate Array), and PLA (Programmable Logic Array). The processor 21 may also include a main processor and a coprocessor. The main processor is a processor for processing data in the awake state, also known as CPU (Central Processing Unit); the coprocessor is a low-power processor for processing data in the standby state. In some embodiments, the processor 21 may be integrated with a GPU (Graphics Processing Unit), which is responsible for rendering and drawing the content to be displayed on the display screen. In some embodiments, the processor 21 may also include an AI (Artificial Intelligence) processor, which is used to process computing operations related to machine learning.

[0098] The memory 20 may include one or more computer-readable storage media, which may be non-transitory. The memory 20 may also include a high-speed random access memory, and a non-volatile memory, such as one or more disk storage devices, flash memory storage devices. In this embodiment, the memory 20 is at least used to store the following computer program 201, wherein, after the computer program is loaded and executed by the processor 21, it can implement the relevant steps of the RAID encoding method disclosed in any of the aforementioned embodiments. In addition, the resources stored in the memory 20 may also include an operating system 202 and data 203, etc., and the storage method may be temporary storage or permanent storage. Among them, the operating system 202 may include Windows, Unix, Linux, etc. Data 203 may include but is not limited to data related to the RAID encoding method.

[0099] In some embodiments, the RAID encoding device may further include a display screen 22 , an input / output interface 23 , a communication interface 24 , a power supply 25 , and a communication bus 26 .

[0100] Those skilled in the art will understand that Figure 5 The structure shown in the figure does not constitute a limitation on the RAID encoding device, and may include more or fewer components than those shown in the figure.

[0101] Finally, the present application also provides an embodiment corresponding to a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps recorded in the above method embodiment are implemented.

[0102] It is understandable that if the method in the above embodiment is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk and other media that can store program code.

[0103] The above is a detailed introduction to a RAID encoding method, device and computer-readable storage medium provided by the present application. The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same and similar parts between the various embodiments can refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can refer to the method part description. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present application, several improvements and modifications can be made to the present application, and these improvements and modifications also fall within the scope of protection of the claims of the present application.

[0104] It should also be noted that, in this specification, relational terms such as first and second, etc. 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 these entities or operations. Moreover, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the statement "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element.

Claims

1. A RAID encoding method, characterized in that: include: Obtain information about storage addresses, write times, word lines, and data; Wherein, the number of write times is a natural number greater than or equal to 1; Writing the data into the storage address; Acquire a first check code and a second check code according to the write count, the word line and the data, and write the first check code and the second check code into the storage address, wherein the current write count is the number of times data is written in this manner in a complete RAID encoding process; Wherein, obtaining a first check code and a second check code according to the number of write times, the word line and the data includes: Performing parity verification on the number of writes and the word line to obtain a verification result; The first check code and the second check code are obtained from the data according to the verification result to implement alternating RAID encoding.

2. The RAID encoding method according to claim 1, characterized in that: Writing the data into the storage address comprises: The data is written into the storage address using NVML as a unit.

3. The RAID encoding method according to claim 1, characterized in that: The obtaining of the first check code and the second check code according to the number of write times, the word line and the data comprises: Determining whether the number of write times and the word lines are both odd numbers or both even numbers; If yes, obtaining the first check code according to the first half of the data, and obtaining the second check code according to the second half of the data; If not, the second verification code is obtained according to the first half of the data in the data, and the first verification code is obtained according to the second half of the data in the data.

4. The RAID encoding method according to claim 1, characterized in that: Before acquiring the information of the storage address, the number of write times, the word line and the data, the method further includes: Initialize the storage address information, the write times, and the word line; The first check code and the second check code are cleared.

5. The RAID encoding method according to claim 1, characterized in that: After writing the first check code and the second check code into the storage address, the method further includes: Add 1 to the write count to obtain a new write count; Acquire information of a new storage address according to the new number of write times; Determine whether the new number of writes is 2 n -1; where n is the number of bare crystals in the die; If yes, writing the first verification code and the second verification code into the new storage address; If not, return to the step of obtaining the information of the storage address, the number of write times, the word line and the data.

6. The RAID encoding method according to claim 4, characterized in that: The information for initializing the storage address includes: The channel, chip enable and page of the storage address are set to 0, 0, and 0 respectively.

7. The RAID encoding method according to claim 5, characterized in that: n is a positive integer not less than 4.

8. A RAID encoding device, characterized in that: include: A first acquisition module is used to acquire information of a storage address, a write count, a word line, and data; wherein the write count is a natural number greater than or equal to 1; A first writing module, used for writing the data into the storage address; A second acquisition module, used for acquiring a first check code and a second check code according to the number of write times, the word line and the data; A second writing module, used for writing the first check code and the second check code into the storage address, and the current number of writes is the number of times data is written in this way in a complete RAID encoding process; Wherein, obtaining a first check code and a second check code according to the number of write times, the word line and the data includes: Performing parity verification on the number of writes and the word line to obtain a verification result; The first check code and the second check code are obtained from the data according to the verification result to implement alternating RAID encoding.

9. A RAID encoding device, characterized in that: include: Memory for storing computer programs; A processor, configured to implement the steps of the RAID encoding method according to any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the RAID encoding method according to any one of claims 1 to 7 are implemented.

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