Coding cache construction method based on linear code and placement distribution array

Abstract

The invention relates to the technical field of communication, and discloses a linear code and placement distribution array-based coding cache construction method, which comprises the following steps of: acquiring a linear code reaching a maximum code distance; based on the linear code reaching the maximum code distance, constructing a placement distribution array based on the linear code, wherein rows and columns of the placement distribution array are linearly changed; designing a coding caching scheme in which the number of file subpackages linearly changes along with the number of users according to a placement distribution array in which rows and columns are linearly changed based on linear codes; the method is based on a placement distribution array constructed by linear codes, on one hand, each element of the array has a clear design principle, and on the other hand, rows and columns of the array can present linear changes; according to the arrangement of the distribution array, a coding cache scheme in which the number of sub-packages of files changes linearly along with the number of users can be designed, coding cache is optimized and realized, the number of sub-packages of files in a coding cache system can be reduced, the problem of waste of storage resources of the users can be solved, and the communication load of a link can be remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and particularly to a coding cache construction method based on linear codes and placement delivery arrays. Background Art

[0002] A placement delivery array (PDA) is an effective combinatorial tool for designing coding cache schemes; in the coding cache scenario, compared with the first centralized coding cache scheme (abbreviated as the "MN scheme"), the coding cache scheme constructed based on the placement delivery array can significantly reduce the number of sub-packets of files, but does not achieve linear changes in the rows and columns of the placement delivery array, resulting in the inability to design a coding cache scheme in which the number of file sub-packets changes linearly with the number of users according to the existing placement delivery arrays. In addition, although relevant researchers have also proposed a novel placement delivery array construction method based on the reflection arc coloring method of regular digraphs, which can achieve linear changes in the rows and columns of the placement delivery array, there is no formula that can be relied on for the design of the positions of some elements in this construction method, that is, the positions of these elements are directly designed as "*", resulting in that users in the coding cache system must store the set of sub-files corresponding to these "*", thus causing a problem of resource waste. Summary of the Invention

[0003] In view of the above deficiencies in the prior art, the present invention provides a coding cache construction method based on linear codes and placement delivery arrays, which is used to solve the problems of excessive number of file sub-packets and inability of the number of file sub-packets to change linearly with the number of users existing in the coding cache scheme designed based on the placement delivery array in the prior art, and at the same time solve the problem of unclear design principles of some elements in the construction of the placement delivery array with linearly changing rows and columns.

[0004] In order to achieve the above object of the invention, the technical solution adopted by the present invention is as follows:

[0005] A coding cache construction method based on linear codes and placement delivery arrays includes the following steps:

[0006] S1. Obtain a linear code with the maximum code distance;

[0007] S2. Based on the linear code with the maximum code distance, construct a placement delivery array with linearly changing rows and columns based on the linear code;

[0008] S3. According to the placement delivery array with linearly changing rows and columns based on the linear code, design a coding cache scheme in which the number of file sub-packets changes linearly with the number of users.

[0009] The present invention has the following beneficial effects:

[0010] The encoding cache construction method based on linear codes and placement distribution arrays proposed by the present invention, which constructs a placement distribution array based on linear codes. On the one hand, each element of the array has a clear and distinct design principle, and on the other hand, the rows and columns of the array can exhibit linear changes. Based on this placement distribution array, an encoding cache scheme with the number of file sub-packets varying linearly with the number of users can be designed. While optimizing and implementing encoding cache, it can not only reduce the number of file sub-packets in the encoding cache system and solve the problem of waste of user storage resources, but also significantly reduce the communication load of the link. Description of the Drawings

[0011] Figure 1 It is a schematic flow chart of the encoding cache construction method based on linear codes and placement distribution arrays proposed by the present invention. Detailed Implementation Modes

[0012] The following describes the detailed implementation modes of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation modes. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

[0013] As Figure 1 shown, the encoding cache construction method based on linear codes and placement distribution arrays includes the following steps:

[0014] S1. Obtain a linear code with the maximum code distance.

[0015] In this embodiment, by obtaining a linear code with the maximum code distance, a practical linear code is obtained for subsequent steps to construct a placement distribution array with linearly changing rows and columns based on the linear code.

[0016] Specifically, the linear code with the maximum code distance in step S1 is C q (λ, d), and its information bits satisfy the following conditions:

[0017]

[0018] where q represents a prime power, that is, the number of elements in the finite field λ represents a general parameter used to connect the code length of the linear code and the maximum code distance, d represents the actually achievable maximum code distance, k q (λ, d) represents the information bits of the linear code C q (λ, d), represents equal to, max represents taking the maximum value, k represents the dimension of the information bits of the linear code, represents the set of positive integers, d′ Denote (λ + d, k, d ′ ) q the minimum code distance of the linear code, denote existence, s.t. denote making it satisfy, and n denote the code length of the linear code.

[0019] S2. Based on the linear code achieving the maximum code distance, construct a placement and distribution array whose rows and columns are linearly variable based on the linear code.

[0020] Specifically, step S2 specifically includes:

[0021] Utilize the finite field on the m-dimensional vectors i and j to respectively identify the rows and columns of the placement and distribution array, and design each element of the placement and distribution array using the size relationship between the weight w(i - j) of the vectors i and j and the vector weight parameter t, generating a placement and distribution array whose rows and columns are linearly variable based on the linear code, specifically as follows:

[0022] Step1: Select a prime power q, set the number of elements on the finite field to be q, and make the vector weight parameter t satisfy the constraint condition 0 < t ≤ m; where,

[0023] Step2: Use the m-dimensional vectors i and j on the finite field to respectively identify the rows and columns of the placement and distribution array A = [a i,j , then the sizes of the rows and columns of the placement and distribution array A are both q m ; where, a i,j represents the element in the i-th row and j-th column of the placement and distribution array A.

[0024] Step3: Obtain the weight w(i - j) of the vectors i and j, that is:

[0025]

[0026] where, u represents the coordinate index of the vector i or j, and i u , j u respectively represent the u-th coordinate of the vectors i and j, and |·| represents counting the quantity of the content between the two vertical lines.

[0027] Step4: When w(i - j) ≥ t, then there is:

[0028] a i,j = *

[0029] where, * represents a special symbol of the placement and distribution array.

[0030] Step5: When w(i - j) < t, then there is:

[0031]

[0032] Among them, represents the index of the coordinate positions where the numerical values of the corresponding coordinates of vector i and vector j, after subtraction, are not 0. represents the numerical value corresponding to the -th coordinate of vector i. represents the numerical value corresponding to the -th coordinate of vector j. Λ represents the quotient space of the linear code C q (λ, d). The element of [m] represents the set from 1 to m, i.e., {1, …, m}. represents the number of coordinates where the numerical values of the corresponding coordinates of vector i and vector j, after subtraction, are not 0. represents the over the finite field -dimensional linear subspace. represents the over the finite field -dimensional linear subspace. represents that when the λ value is m - t, the actually achievable maximum code distance d is for the linear code. represents the vector obtained by removing the numerical value at the -th coordinate position from the m-dimensional vector i over the finite field .

[0033] Step6: Generate a placement and distribution array with linearly varying rows and columns based on the linear code, i.e.:

[0034]

[0035] Specifically, the expression for the number of columns K of the placement and distribution array with linearly varying rows and columns based on the linear code is:

[0036] K = q m .

[0037] Specifically, the expression for the number of rows F of the placement and distribution array with linearly varying rows and columns based on the linear code is:

[0038] F = q m .

[0039] Specifically, the expression for the number Z of the special symbol * elements in each column of the placement and distribution array with linearly varying rows and columns based on the linear code is:

[0040]

[0041] Among them, l represents the vector dimension.

[0042] In this embodiment, when using a finite field m-dimensional vectors are used to identify the rows and columns of the placement and distribution array A = [a i,j . When the weight w(i - j) of vector i and vector j is greater than or equal to t, the element a i,j of the placement and distribution array A is *, that is, when l ≥ t, l dimensions need to be selected from the m-dimensional vector i - j, and it is required that the coordinate components of these l-dimensional vectors are not 0, so that the element a i,j of the placement and distribution array A is *, and there are ways of selection; for one selected way, the coordinate components of these l-dimensional vectors can be represented by the numbers 1, …, (q - 1), and there are (q - 1) l cases. Therefore, the number of special symbol "*" elements in each column of the placement and distribution array is

[0043] Specifically, for the different ordinary symbol element quantity S of the placement and distribution array whose rows and columns change linearly based on a linear code, the expression is:

[0044]

[0045] where k q (m - t, t - l) represents the information bits of a linear code with λ value of m - t and the actual maximum code distance d of t - l, and k q (m - t, d) represents the information bits of a linear code with λ value of m - t and the actual maximum code distance d.

[0046] In this embodiment, according to the satisfied constraint condition (that is: ), it can be known that for there are q l (q - 1) l different pairs, such that Since there are cosets in the quotient space and when w(i - j) < t, then there are Therefore, the number of different ordinary symbol elements in the placement and distribution array is:

[0047] S3. Design an encoding cache scheme in which the number of file packets changes linearly with the number of users based on the placement and distribution array whose rows and columns change linearly based on a linear code.

[0048] In this embodiment, a connection between the placement and distribution array and the cache system is established. A linear coding cache scheme is designed using a placement and distribution array with linearly varying rows and columns constructed based on linear codes. The parameters in the placement and distribution array are used to characterize the performance of the linear coding cache scheme. The implementation principle is as follows: In the (K, F, Z, S) placement and distribution array with linearly varying rows and columns based on linear codes, each row identified by an m-dimensional vector i over a finite field is associated with a sub-file of a file of size F bits in the cache system. At the same time, in the (K, F, Z, S) placement and distribution array with linearly varying rows and columns based on linear codes, each column identified by an m-dimensional vector j over a finite field is associated with a user in the cache system. At the same time, the cache ratio of the users in the cache system is set to obtain a linearly coded cache scheme with an F-partition. The specific operation process is as follows:

[0049] Specifically, step S3 specifically includes S31 - S33:

[0050] S31. Associate the columns of the placement and distribution array with linearly varying rows and columns based on linear codes with the number of users in the (K, M, N) cache system, that is, set the number of columns K of the placement and distribution array with linearly varying rows and columns based on linear codes to be equal to the number of users K in the (K, M, N) cache system; where M represents that each user in the cache system has an independent cache space of size MF bits, and N represents the number of files in the cache system.

[0051] S32. Associate the rows of the placement and distribution array with linearly varying rows and columns based on linear codes with the sub-files of the files in the (K, M, N) cache system, that is, set the number of rows F of the placement and distribution array with linearly varying rows and columns based on linear codes to be equal to the number of sub-files of the files in the cache system.

[0052] S33. Set the cache ratio of the users in the cache system, and based on the cache ratio of the users in the cache system, obtain a linearly coded cache scheme divided by the number of rows of the placement and distribution array with linearly varying rows and columns based on linear codes.

[0053] Specifically, the cache ratio of the users in the cache system in step S33 is:

[0054]

[0055] Specifically, the linearly coded cache scheme divided by the number of rows of the placement and distribution array with linearly varying rows and columns based on linear codes in step S33 includes a placement phase and a distribution phase, specifically:

[0056] In the placement phase, each file W in the cache system e is divided into F = q mSub-files and obtain the sub-files cached by the user, that is:

[0057]

[0058] where W e,i represents the i-th sub-file of the e-th file in the cache system, and U j represents the sub-file cached by user j in the cache system. [0:N) represents the integers from 0 to N - 1, that is, {0, 1, …, N - 1}.

[0059] In this embodiment, in the placement phase, when each user caches N·Z sub-files and the size of each sub-file is 1 / F bits, the size of the sub-files cached by each user is M = N·Z·1 / F, satisfying the user 's cache constraint.

[0060] In the distribution phase, the server receives the request h j from user j, and after receiving the request h j from user j, within the time slot transmits the coded signal to the user; at the same time, the user decodes based on the cached sub-file U j and the received coded signal X to obtain the required sub-files and reconstruct the requested file; where ⊕ represents the exclusive OR operation, represents that the request of user j is the i-th sub-file of the h j -th file.

[0061] In this embodiment, when the server sends a total of S coded signals, since the size of each coded signal is 1 / F bits, the communication load of the link is:

[0062]

[0063] It can be seen from the calculated communication load of the link that the communication load of the link is reduced.

[0064] In summary, the coding cache construction method based on linear codes and placement distribution arrays proposed by the present invention, based on the placement distribution array constructed by linear codes, on the one hand, makes each element of the array have a clear and definite design principle, and on the other hand, the rows and columns of the array can show linear changes; and based on this placement distribution array, a coding cache scheme with the number of file sub-packages varying linearly with the number of users can be designed. While realizing coding cache, it can not only reduce the number of file sub-packages in the coding cache system and solve the problem of waste of user storage resources, but also significantly reduce the communication load of the link.

[0065] In the present invention, specific embodiments are used to elaborate on the principles and implementation manners of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present invention.

[0066] Those of ordinary skill in the art will realize that the embodiments described herein are for helping the reader understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations that do not depart from the essence of the present invention based on these technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A coding cache construction method based on linear codes and placement distribution arrays, characterized in that: It includes the following steps: S1. Obtain a linear code with the maximum code distance; S2. Based on the linear code with the maximum code distance, construct a placement and distribution array whose rows and columns based on the linear code change linearly; S3. According to the placement and distribution array whose rows and columns based on the linear code change linearly, design an encoded caching scheme in which the number of file sub - packets changes linearly with the number of users.

2. The method for constructing a coding cache based on a linear code and a placement distribution array according to claim 1, characterized in that: The linear code that reaches the maximum code distance in step S1 is C q (λ,d), and its information bits satisfy the following conditions: Among them, q represents a prime power, that is, a finite field The number of elements in the above, λ represents the general parameter used to connect the code length and the maximum code distance of the linear code, d represents the maximum code distance that can be achieved, and k q (λ, d) represents the linear code C that achieves the maximum code distance q The information bits of (λ, d), represents equal to, max represents the maximum value, and k represents the dimension of the linear code information bit. represents a set of positive integers, and d′ represents (λ+d,k,d′) q The minimum code distance of a linear code, indicates existence, st indicates that it satisfies, and n indicates the code length of the linear code.

3. The method for constructing a coding cache based on a linear code and a placement distribution array according to claim 2, characterized in that: Step S2 specifically includes: Using finite fields The m-dimensional vector i and vector j on the y-axis respectively identify the rows and columns of the placement distribution array, and use the relationship between the weight w(ij) of the vector i and the vector j and the vector weight parameter t to design each element of the placement distribution array, and generate a placement distribution array whose rows and columns vary linearly based on the linear code, specifically: Step1: Select a prime power q, and set the number of elements in the finite field to be q, and make the vector weight parameter t satisfy the constraint 0 < t ≤ m; where Step 2: Using finite fields The m-dimensional vector i and vector j respectively identify the placement distribution array as A = [a i,j ], the size of the rows and columns of the distribution array A is q m ; Among them, a i,j Indicates placing the element in the i-th row and j-th column of the distribution array A; Step3: Obtain the weight w(i - j) of vector i and vector j, that is: Among them, u represents the coordinate index of vector i or vector j, i u 、j u denote the u-th coordinate of vector i and vector j respectively, and |·| denotes the number of contents in the two vertical lines; Step4: When w(i - j) ≥ t, then there is: a i,j ＝* where * represents a special symbol of the placement and distribution array; Step5: When w(i - j) < t, then there is: in, It represents the index of the coordinate position that is not 0 after subtracting the values ​​of the corresponding coordinates of vector i and vector j. represents the first The value corresponding to the coordinates is represents the first The value corresponding to the coordinates, Λ represents the linear code C that reaches the maximum code distance q The quotient space of (λ,d) elements, [m] represents the set from 1 to m, that is, {1,…,m}, It represents the number of coordinates that are not 0 after subtracting the corresponding coordinate values ​​of vector i and vector j. Representing a finite field on dimensional linear subspace, Representing a finite field on dimensional linear subspace, It means that when the λ value is mt, the maximum code distance d that can be achieved is The linear code of Representing a finite field Remove the first m-dimensional vector i from the A vector containing the values ​​of the coordinate positions; Step6: Generate a placement and distribution array whose rows and columns based on the linear code change linearly, that is:

4. The method for constructing a coding cache based on a linear code and a placement distribution array according to claim 3, characterized in that: The expression for the number of columns K of the placement and distribution array whose rows and columns based on the linear code change linearly is: K=q m 。 5. The method for constructing a coding cache based on a linear code and a placement distribution array according to claim 4, characterized in that: The expression for the number of rows F of the placement and distribution array whose rows and columns based on the linear code change linearly is: F=q m 。 6. The method for constructing a coding cache based on a linear code and a placement distribution array according to claim 5, characterized in that: The expression for the number of special symbol * elements Z in each column of the placement and distribution array whose rows and columns based on the linear code change linearly is: where l represents the vector dimension.

7. The method for constructing a coding cache based on a linear code and a placement distribution array according to claim 6, characterized in that: Different common symbols of the array are distributed based on the linear variation of rows and columns of the linear code The expression for the number of elements S is: Among them, k q (mt,tl) represents the information bits of the linear code whose λ value is mt and the maximum code distance d that can be achieved is tl, k q (mt,d) represents the information bits of a linear code with a λ value of mt and a maximum code distance d that can be achieved.

8. The method for constructing a coding cache based on linear codes and placement distribution arrays according to claim 7, characterized in that: Step S3 specifically includes: S31. Associate the columns of the placement and distribution array whose rows and columns based on the linear code change linearly with the number of users in the (K, M, N) caching system, that is, set the number of columns K of the placement and distribution array whose rows and columns based on the linear code change linearly to be equal to the number of users K in the (K, M, N) caching system; where M represents that each user in the caching system has an independent cache space of size MF bits, and N represents the number of files in the caching system; S32. Associate the rows of the placement and distribution array whose rows and columns based on the linear code change linearly with the sub - files of the files in the (K, M, N) caching system, that is, set the number of rows F of the placement and distribution array whose rows and columns based on the linear code change linearly to be equal to the number of sub - files of the files in the caching system; S33. Set the cache ratio of the users in the caching system, and based on the cache ratio of the users in the caching system, obtain a linear encoded caching scheme divided by the number of rows of the placement and distribution array whose rows and columns based on the linear code change linearly.

9. The method for constructing a coding cache based on linear codes and placement distribution arrays according to claim 8, characterized in that: The cache ratio of the users in the caching system in Step S33 is:

10. The method for constructing a coding cache based on a linear code and a placement distribution array according to claim 9, characterized in that: The linear encoded caching scheme divided by the number of rows of the placement and distribution array whose rows and columns based on the linear code change linearly in Step S33 includes a placement phase and a distribution phase, specifically: In the placement phase, each file W in the cache system is e Divided into F = q m sub-files, and obtain the user's cached sub-files, namely: Among them, W e,i represents the i-th subfile of the e-th file in the cache system, U j represents the subfile cached by user j of the cache system, [0:N) represents an integer from 0 to N-1, i.e., {0,1,…,N-1}; In the distribution phase, the server receives a request h from user j. j , and upon receiving user j's request h j After that, in the time gap Internal transmission coded signal To users; At the same time, the user can j Decode the received coded signal X to obtain the required sub-file and reconstruct the requested file; in, represents the XOR operation, Indicates that user j’s request is the hth j The i-th subfile of a file.

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