Coding and decoding method and system based on cyclic code error correction

Abstract

The invention discloses a coding and decoding method and system based on cyclic code error correction. The method comprises the following steps: selecting a union of a corresponding circle coset based on the code length of a cyclic code; constructing a corresponding generator polynomial according to the coset of the sub-circle cosets; the sending end converts a signal to be transmitted into a code word based on the generator polynomial, and transmits the code word to a receiving end through a satellite channel; receiving data by a receiving end, and obtaining a syndrome according to the generator polynomial; and judging whether the syndrome is zero or not, if not, entering an error correction process, and if yes, directly decoding to obtain a transmission signal. According to the method, the special cyclic code and the BM algorithm are combined, the error correction amount of the signal after transmission interference is improved through the construction of the special cyclic code, the error correction efficiency is improved by adopting the BM algorithm, and high-efficiency and high-quality error correction is performed on the transmission data; and the constructed cyclic code ensures the reliability of the data in a long-distance and high-noise environment through efficient error correction capability.

Description

Technical Field

[0001] The present invention relates to the field of digital communication technologies, and in particular, to an encoding and decoding method and system based on cyclic code error correction. 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] Satellite communication needs to span complex environments such as the atmosphere and outer space. Digital signals are vulnerable to interference during transmission, such as additive interference: thermal noise (noise of receiving-end electronic devices), cosmic rays (high-energy particle interference), etc., and multiplicative interference: multipath effect (waveform distortion caused by signal reflection), rain attenuation (attenuation when the signal passes through the rain area), etc. These interferences can cause random errors (random bit flips) or burst errors (multiple consecutive bit errors).

[0004] During the transmission of digital signals, due to the influence of interference, the waveform of the code element will deteriorate, and incorrect decisions may occur after being received at the receiving end. The inter-symbol interference caused by multiplicative interference can be corrected by means of equalization, while the influence of additive interference needs to be solved by other means. When designing a digital communication system, consideration should first be given to reasonably selecting modulation systems, demodulation methods, transmission power, etc., so that the additive interference is not sufficient to affect the achievement of the required bit error rate. When the requirements are still not met, error control measures need to be considered.

[0005] Error control coding is also called error correction coding. Different coding methods have different error detection or error correction capabilities. Cyclic code is a type of coding method. As an important linear block code, it has the property of cyclic shift and is widely used in fields such as communication and data storage. Due to its high error detection rate, cyclic code is very effective in detecting random or burst errors, and cyclic code is mostly used for data error control in communication. However, existing research can prove that when the dimension of the cyclic code becomes larger, the corresponding minimum distance will become smaller, which limits its error correction ability. For example, when the dimension k of the conventional cyclic code is (n±1) / 2, the minimum distance of the binary cyclic code that can be constructed cannot reach resulting in less error correction and unable to meet the requirements of high-noise environments such as satellite communication. And at present, the construction of the minimum distance of the cyclic code is still a big problem.

[0006] Existing satellite communication systems usually use RS codes as the outer layer coding to correct burst errors, and use general binary cyclic codes as the inner layer coding to correct random errors. However, the insufficient error correction ability of the inner layer cyclic code will lead to a decline in the overall performance of the system. Summary of the Invention

[0007] To overcome the deficiencies of the above-mentioned prior art, the present invention provides an encoding and decoding method and system based on cyclic code error correction, which combines a special cyclic code and the BM algorithm to perform efficient and high-quality error correction on transmitted data, and can meet the requirements of long-distance and low signal-to-noise ratio scenarios.

[0008] To achieve the above object, one or more embodiments of the present invention provide the following technical solutions:

[0009] In the first aspect, the present invention provides an encoding and decoding method based on cyclic code error correction, including:

[0010] Select the union of the corresponding cyclotomic cosets based on the code length of the cyclic code;

[0011] Construct the corresponding generating polynomial according to the union of the cyclotomic cosets;

[0012] The transmitting end converts the signal to be transmitted into a codeword based on the generating polynomial, and transmits the codeword to the receiving end through the satellite channel;

[0013] The receiving end receives the data, obtains the syndrome according to the generating polynomial; determines whether the syndrome is zero, if not, the data has an error and enters the error correction process, if so, directly decodes to obtain the transmitted signal.

[0014] In a further technical solution, the specific steps of selecting the union of the corresponding cyclotomic cosets based on the code length of the cyclic code are as follows:

[0015] Find a corresponding set of the code length such that the set is the union of the cyclotomic cosets, and the absolute value of the union of the cyclotomic cosets is the difference between the modulus n and the dimension;

[0016] If there is a certain continuous number that is a subset of the union of the cyclotomic cosets, the minimum distance d of the code > δ, where δ represents an integer greater than 1 and less than n - 1.

[0017] In a further technical solution, based on the cyclic code with code length n = 2 m - 1, determine whether m is odd or even, and obtain the union of the cyclotomic cosets for odd and even numbers respectively.

[0018] In a further technical solution, the minimum distance of the cyclic code when m is odd is The minimum distance of the cyclic code when m is even is

[0019] In a further technical solution, the conversion of the signal to be transmitted into binary data and then into a codeword based on the generating polynomial is expressed as:

[0020] c(x) = d(x)·x n-k mod g(x)

[0021] Among them, c(x) represents the codeword, d(x) represents the binary data, n represents the code length of the cyclic code, k represents the dimension, and g(x) represents the generating polynomial.

[0022] A further technical solution is that the expression of the syndrome is:

[0023] S(x)≡r(x)modg(x)

[0024] Among them, S(x) represents the syndrome, r(x) represents the data received by the receiving end, and g(x) represents the generating polynomial.

[0025] A further technical solution is that the error correction process is to use the Berlekamp-Massey algorithm to correct the data to obtain the correct codeword.

[0026] In a second aspect, the present invention provides an encoding and decoding system based on cyclic code error correction, including:

[0027] A cyclic code construction module, which is configured to: select the union of the corresponding cyclotomic cosets based on the code length of the cyclic code; construct the corresponding generating polynomial according to the union of the cyclotomic cosets;

[0028] An encoding module, which is configured to: at the sending end, based on the generating polynomial, convert the signal to be transmitted into a codeword, and transmit the codeword to the receiving end through a satellite channel;

[0029] A decoding module, which is configured to: at the receiving end, when receiving the data, obtain the syndrome according to the generating polynomial; judge whether the syndrome is zero, if not, the data has an error and enters the error correction process, if so, directly decode to obtain the transmitted signal.

[0030] In a third aspect, the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps in an encoding and decoding method based on cyclic code error correction as described in the first aspect are implemented.

[0031] In a fourth aspect, the present invention provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the program, the steps in an encoding and decoding method based on cyclic code error correction as described in the first aspect are implemented.

[0032] The above one or more technical solutions have the following beneficial effects:

[0033] The present invention combines a special cyclic code and the BM algorithm, improves the error correction amount after the signal is affected by transmission interference through the construction of the special cyclic code, and uses the BM algorithm to improve the error correction efficiency, and performs high-efficiency and high-quality error correction on the transmitted data, which can meet the requirements of long-distance and low signal-to-noise ratio scenarios, such as data error correction in satellite communication.

[0034] The present invention provides several construction methods for cyclic codes with different code lengths, such that the obtained cyclic codes satisfy when the dimension k = (n ± 1) / 2 For the case where the code length n = 2 m - 1, when m is even, the lower bound of the constructed minimum distance is already very close to And when m is odd, the lower bound of the constructed minimum distance has exceeded Greatly improving the error correction ability of cyclic codes in information transmission. In satellite communication, the constructed cyclic codes ensure the reliability of data in a long - distance and high - noise environment through efficient error correction ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The accompanying drawings forming a part of this invention are used to provide a further understanding of the invention. The schematic embodiments and descriptions thereof of the invention are used to explain the invention and do not unduly limit the invention.

[0036] Figure 1 is a flowchart of the encoding and decoding method of the embodiment of the present invention;

[0037] Figure 2 is a schematic diagram of the generating polynomial and generating matrix obtained in Example 1 of the embodiment of the present invention;

[0038] Figure 3 is a schematic diagram of the generating polynomial and generating matrix obtained in Example 2 of the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0039] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0040] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, 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.

[0041] In the case of no conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0042] Example 1

[0043] As Figure 1As shown in the figure, this embodiment discloses an encoding and decoding method based on cyclic code error correction, and the method includes the following steps:

[0044] S1: Select the union of the corresponding cyclotomic cosets based on the code length of the cyclic code;

[0045] In this embodiment, based on the cyclic code with code length n = 2 m -1, the present invention mainly constructs a cyclic code with a better minimum distance by selecting the 2-cyclotomic coset modulo n.

[0046] First, the following concepts related to cyclotomic cosets will be introduced:

[0047] Denote as the ring of integers modulo n, that is Then for each The 2-cyclotomic coset is represented as:

[0048]

[0049] where i represents any integer greater than or equal to 0 and less than or equal to n - 1, j represents a certain integer greater than or equal to 0 and less than or equal to m, and e i is the smallest positive integer such that i2 j ≡ i (mod n).

[0050] According to the existing theoretical knowledge, if it is necessary to construct a binary cyclic code with dimension k = (n - 1) / 2, first, a corresponding set needs to be found such that A is the union of some cyclotomic cosets and |A| = n - k. For the calculation of the minimum distance, if there exists a certain continuous number then the minimum distance d of the code C > δ. A represents the union of some cyclotomic cosets, and δ represents a certain integer greater than 1 and less than n - 1.

[0051] Judge whether m is odd or even, and adopt corresponding set A construction methods for odd and even numbers respectively, and make the minimum distance

[0052] (1) If m is odd, the steps are as follows:

[0053] First, select the set:

[0054]

[0055] where T represents the subset that satisfies the above conditions of, and ∪ represents the union of the selected cyclotomic cosets.

[0056] And the set:

[0057]

[0058] For the remaining part, place \(x\) and \(-x\) into the sets and That is, there exists a set \(S\) such that:

[0059]

[0060] Then a cyclic code with the defining set can be constructed. Moreover, it can be known that the minimum distance of the constructed cyclic code

[0061] (2) If \(m\) is even, the steps are as follows:

[0062] First, define a mapping:

[0063]

[0064] satisfying

[0065] Then, define a set with the following characteristics on

[0066]

[0067] For any Let

[0068] Furthermore, define the following special sets:

[0069]

[0070] \(T = \{x\in W t (m) : x' = x''\}\)

[0071] \(G = \{x\in W t (m) : x' = x'' + 1 m / 2 \}\).

[0072] Define a mapping:

[0073]

[0074] For any subset \(A\) of, to ensure that \(\pi -1 (A)\) can form the union of several cyclotomic cosets, it is necessary to ensure that \(\rho(A)=A\). Thus, for the part of the set \(W t (m) \setminus(T\cup G)\), it can be divided into two parts \(P1\) and \(P2\), and satisfy:

[0075]

[0076] Based on this, the following two sets can be obtained:

[0077]

[0078] It can be obtained that

[0079] and both are unions of several cyclotomic cosets. Further, a binary cyclic code with the defining set being \(Z_2\) can be obtained. It can be known that the corresponding minimum distance

[0080] Example 1

[0081] When \(m\) is even, take \(m = 4\). At this time, the corresponding code length \(n = 2^m - 1 = 15\). It can be calculated that: 4 -1 = 15, and the following can be calculated:

[0082]

[0083] \(\pi\) -1 (W t (m) ) = {3, 5, 6, 9, 10, 12}

[0084]

[0085] \(\pi\) -1 (B) = {15}

[0086] \(\pi\) -1 (T) = {5, 10}

[0087] \(\pi\) -1 (G) = {3, 6, 9, 12}

[0088] So, \(Z_2=\{3, 6, 9, 7, 11, 12, 13, 14\}\). The parameters of the corresponding cyclic code are \([15, 7, 5]\).

[0089] Example 2

[0090] When \(m\) is odd, take \(m = 5\). At this time, the corresponding code length \(n = 2^m - 1 = 31\), and \((m + 1) / 2 = 3\). It can be calculated that: 5 -1 = 31, \((m + 1) / 2 = 3\), and the following can be calculated:

[0091] \(A_1=\{1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 17, 18, 20, 24\}\)

[0092] \(-A_1=\{7, 11, 13, 14, 15, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30\}\)

[0093] The parameters of the cyclic code corresponding to the defined set A1 are [31, 16, 7].

[0094] S2: Construct a corresponding generating polynomial according to the union of the cyclotomic cosets;

[0095] In this embodiment, for the generating polynomial g(x), the dimension of g(x) is denoted as k, which is the length of the information bits.

[0096] For example, when m is even and m = 4, the corresponding generating polynomial is g(x) = x 4 + x 3 + 1.

[0097] S3: The transmitting end converts the signal to be transmitted into a codeword based on the generating polynomial, and transmits the codeword to the receiving end through the satellite channel;

[0098] In this embodiment, the transmitting end first converts the signal to be transmitted to obtain binary data d(x), and converts it into a transmitted codeword c(x) = d(x) · x n-k mod g(x). That is, filling the shift register realizes fast encoding. Example: The original data is 1010 (corresponding polynomial is g(x) = x 3 + x), and the encoded codeword is 101000001000.

[0099] By introducing redundancy through the generating polynomial, errors caused by noise or attenuation in the satellite channel can be corrected.

[0100] S4: The receiving end receives the data, obtains the syndrome according to the generating polynomial; judges whether the syndrome is zero. If not, the data has an error, and the data is corrected through the Berlekamp-Massey algorithm (BM algorithm) to obtain the correct codeword c(x), and then the codeword c(x) is decoded to obtain the transmitted signal. If so, the transmitted signal is directly decoded.

[0101] In this embodiment, the calculation expression of the syndrome is:

[0102] S(x) ≡ r(x) mod g(x)

[0103] where S(x) represents the syndrome, r(x) represents the data received by the receiving end, and g(x) represents the generating polynomial.

[0104] After receiving the signal, demodulation is performed to restore the radio frequency signal to binary data, which may contain error bits. For the received codeword r(x), the corresponding syndrome S(x) needs to be calculated. If S(x) ≠ 0, there is an error, and the error can be corrected through the Berlekamp-Massey algorithm to improve the error correction efficiency.

[0105] Generally speaking, for a cyclic code with a minimum distance of d, (d - 1) / 2 errors can be corrected. For example, the constructed binary cyclic code [15, 7, 5] can correct 2 errors. Therefore, when the dimension remains constant, the larger the minimum distance of the constructed cyclic code, the more errors can be corrected. The minimum distances of the binary cyclic code constructions given in the present invention all exceed which improves the error correction ability during communication. In satellite communication, cyclic codes ensure the reliability of data in long-distance and high-noise environments through their efficient error correction ability.

[0106] Embodiment 2

[0107] This embodiment discloses an encoding and decoding system based on cyclic code error correction, including:

[0108] A cyclic code construction module configured to: select the union of corresponding cyclotomic cosets based on the code length of the cyclic code; construct a corresponding generator polynomial according to the union of the cyclotomic cosets;

[0109] An encoding module configured to: at the sending end, convert a signal to be transmitted into a codeword based on the generator polynomial, and transmit the codeword to the receiving end through a satellite channel;

[0110] A decoding module configured to: at the receiving end, receive data, obtain a syndrome according to the generator polynomial; determine whether the syndrome is zero. If not, the data has errors and enters the error correction process. If so, directly decode to obtain the transmitted signal.

[0111] Embodiment 3

[0112] The purpose of this embodiment is to provide a computing device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the method in Embodiment 1 are implemented.

[0113] Embodiment 4

[0114] The purpose of this embodiment is to provide a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, the steps of the method in Embodiment 1 are executed.

[0115] The steps involved in the devices in the above Embodiments 3 and 4 correspond to those in Method Embodiment 1. For specific implementation manners, reference may be made to the relevant description part of Embodiment 1. The term "computer-readable storage medium" should be understood to include a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0116] Those skilled in the art should understand that the above-mentioned modules or steps of the present invention can be implemented by a general-purpose computer device. Optionally, they can be implemented by program codes executable by a computing device. Thus, they can be stored in a storage device and executed by the computing device, or they can be separately fabricated into individual integrated circuit modules, or multiple modules or steps among them can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0117] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0118] Although the specific implementation manners of the present invention have been described above in conjunction with the accompanying drawings, it is not a limitation to the protection scope of the present invention. Those skilled in the art should understand that, based on the technical solution of the present invention, various modifications or deformations that can be made without creative efforts by those skilled in the art are still within the protection scope of the present invention.

Claims

1. A coding and decoding method based on cyclic code error correction, characterized in that: include: Based on the code length of the cyclic code, the corresponding cyclotomic coset is selected; Constructing a corresponding generating polynomial according to the union of the cyclotomic cosets; The transmitting end converts the signal to be transmitted into a codeword based on the generating polynomial, and transmits the codeword to the receiving end through the satellite channel; The receiving end receives the data, obtains the syndrome according to the generating polynomial, and determines whether the syndrome is zero. If not, the data has errors and enters the error correction process. If so, the data is directly decoded to obtain the transmission signal.

2. A coding and decoding method based on cyclic code error correction as claimed in claim 1, characterized in that: The specific steps of selecting the corresponding cyclotomic coset based on the code length of the cyclic code are: Find a corresponding set of code lengths, so that the set is the union of cyclotomic cosets, and the absolute value of the union of the cyclotomic cosets is the difference between the modulus n and the dimension; If there exists a continuous number that is a subset of the union of the cyclotomic cosets, then the minimum distance of the code d>δ, where δ represents an integer greater than 1 and less than n-1.

3. A coding and decoding method based on cyclic code error correction as claimed in claim 1, characterized in that: Based on code length n=2 m -1 cyclic code, determine whether m is odd or even, and get the union of the circular cosets for odd and even numbers respectively.

4. A coding and decoding method based on cyclic code error correction as claimed in claim 3, characterized in that: When m is an odd number, the minimum distance of the cyclic code is When m is an even number, the minimum distance of the cyclic code is 5. A coding and decoding method based on cyclic code error correction as claimed in claim 1, characterized in that: The signal to be transmitted is converted into binary data, and then converted into a codeword based on a generating polynomial, which is expressed as: c(x)=d(x)·x n-k modg(x) Among them, c(x) represents the code word, d(x) represents binary data, n represents the code length of the cyclic code, k represents the dimension, and g(x) represents the generating polynomial.

6. A coding and decoding method based on cyclic code error correction as claimed in claim 1, characterized in that: The syndrome expression is: S(x)≡r(x)modg(x) Among them, S(x) represents the syndrome, r(x) represents the data received by the receiving end, and g(x) represents the generating polynomial.

7. A coding and decoding method based on cyclic code error correction as claimed in claim 1, characterized in that: The error correction process uses the Berlekamp-Massey algorithm to correct the data to obtain the correct codeword.

8. A coding and decoding system based on cyclic code error correction, characterized in that: include: A cyclic code construction module is configured to: select a corresponding circle-partite coset and a corresponding circle-partite coset based on the code length of the cyclic code; Constructing a corresponding generating polynomial according to the union of the cyclotomic cosets; The encoding module is configured to: the transmitting end converts the signal to be transmitted into a codeword based on the generating polynomial, and transmits the codeword to the receiving end through the satellite channel; The decoding module is configured as follows: when a receiving end receives data, a syndrome is obtained according to the generating polynomial; and whether the syndrome is zero is determined. If not, the data has errors and enters an error correction process. If so, the data is directly decoded to obtain a transmission signal.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in a coding and decoding method based on cyclic code error correction as described in any one of claims 1 to 7 are implemented.

10. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps in the encoding and decoding method based on cyclic code error correction as described in any one of claims 1 to 7 are implemented.

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