WO2022033566A1

WO2022033566A1 - Coding or decoding method in finite field and related device

Info

Publication number: WO2022033566A1
Application number: PCT/CN2021/112380
Authority: WO
Inventors: 郑若滨; 李宗鹏; 孙奇福; 唐汉琦
Original assignee: 华为技术有限公司
Priority date: 2020-08-14
Filing date: 2021-08-13
Publication date: 2022-02-17
Also published as: CN114079475A

Abstract

Disclosed in embodiments of the present application are a coding or decoding method in a finite field, a receiving end, and an intermediate node. In a scenario where the computing power of a sending end, a receiving end, and an intermediate node is inconsistent, using a finite field having a nested structure for coding effectively reduces the computational complexity during decoding, improves the decoding speed and data throughout, and ensures the accuracy of decoding.

Description

A finite field encoding or decoding method and related device

This application claims the priority of the Chinese patent application filed on August 14, 2020 with the application number 202010820658.2 and the invention titled "A Coding or Decoding Method and Related Apparatus for a Limited Field", the entire contents of which are obtained through Reference is incorporated in this application.

technical field

The present application relates to the field of communication technologies, and in particular, to a finite field encoding or decoding method and related devices.

Background technique

Network Coding (NC), which was born in 2000, proposes how to achieve the network communication capacity determined by the "maximum flow minimum cut theorem" when a single sender or multiple senders multicast or broadcast to multiple receivers in a communication network. An idea of the limit. In a traditional communication network, intermediate nodes (such as base stations or routing switches, etc.) only complete the "store-and-forward" function, and regard information as "goods", so it is considered that information cannot be superimposed. This cognitive limitation makes it difficult for the network to achieve maximum streaming. NC pointed out that if the intermediate nodes are allowed to encode multiple input information streams and then send them, the network communication can achieve the maximum stream transmission.

In order to implement network coding, the sender, receiver, and intermediate nodes must be consistent in the same finite field (such as Galois field (GF)) for encoding and decoding. 2 ⁸ ), then all intermediate nodes participating in network coding are required to perform recoding in the finite field of GF(2 ⁸ ), and all receivers are required to perform recoding in the finite field of GF(2 ⁸ ). domain to decode. Therefore, in the process of data transmission, each network node needs to be configured with coding and decoding parameters consistent with the transceiver end for each stream or each application.

The computing capabilities (also called encoding or decoding capabilities) of the sender, the receiver, and the intermediate nodes are very different, and it is difficult to use a consistent finite field to encode or decode, which affects the popularization and application of network coding.

SUMMARY OF THE INVENTION

Embodiments of the present application provide a finite field encoding or decoding method, specifically including: a finite field encoding and decoding method, a finite field decoding method, and a finite field re-encoding method. In the scenario where the computing power of the terminal, the receiving terminal and the intermediate node is inconsistent, the finite field with the nested structure is used for encoding, which effectively reduces the computational complexity during decoding, improves the decoding speed and data throughput, and ensures the decoding. code accuracy.

In the first aspect, an embodiment of the present application proposes a finite field encoding method, including:

Using the first encoding coefficient matrix to perform encoding processing on the k source data blocks to generate k first encoded data blocks, the first encoded data blocks correspond to a group of encoding coefficients in the first encoding coefficient matrix, and k is a positive integer;

One or more first encoded packets are generated according to the k first encoded data blocks, where the first encoded packet includes one or more first encoded data blocks and first encoded data blocks corresponding to the one or more first encoded data blocks a set of coding coefficients in the coding coefficient matrix;

Wherein, the first coding coefficient matrix includes coding coefficients of the first finite field and coding coefficients of the second finite field, the first finite field and the second finite field are finite fields with a nested structure, and the order of the second finite field The number is higher than the first finite field, and the finite field with nested structure satisfies the following relationship: the order has a multiple relationship, and the characteristic number is consistent;

Send one or more first encoded messages.

Specifically, the transmitting end uses the first encoding coefficient matrix to perform encoding processing on k source data blocks in a group (Generation) to obtain one or more first encoded data blocks (eg, k first encoded data blocks). The first coding coefficient matrix includes coding coefficients of the first finite field and coding coefficients of the second finite field, and k is a positive integer. The first finite field, and the second finite field, are finite fields with nested structures, where the first finite field is GF(E ^d ), and the second finite field is GF(E ^D ), where E is a prime number , d is a positive integer, D is a positive integer, D=q*d, q is a positive integer greater than 1.

The first coded message further includes one or more source data blocks, where the source data blocks correspond to a group of coding coefficients in the unit matrix, and the size of the unit matrix is the same as that of the first coding coefficient matrix. A set of coding coefficients in the identity matrix, also called coding coefficients of the source data block.

A group of coding coefficients in the first coding coefficient matrix corresponding to the first coded data block is also referred to as coding coefficients of the first coding coefficient matrix.

The first finite field and the second finite field may include multiple finite fields, and the first coding coefficient matrix includes two or more finite fields with a nested structure.

In the embodiment of the present application, the sender encodes the source data block in multiple finite fields with nested structures, so that the receiver can receive packets of finite fields with nested structures. Due to the finite field with nested structure, the elements and operations of the higher-order finite field, including the elements and operations of the lower-order finite field, are sent. Therefore, the receiving end can, according to its own computing power and application requirements, first, decode the encoded data of the finite field with a higher order in a finite field with a lower order, and secondly, decode the result of the previous decoding in the order of the finite field. Continue decoding in higher finite fields. The computational complexity is effectively reduced, the decoding speed and data throughput are improved, and the decoding accuracy is guaranteed.

In combination with the first aspect, in a possible implementation manner of the first aspect,

The source data block is: p _j , where j is a positive integer, 1≤j≤k;

The coding coefficients of the first finite field and the coding coefficients of the second finite field are α _n,k , where n is a positive integer;

The one or more first encoded data blocks include: c _n , wherein,

Exemplarily, it is assumed that a group includes k source data blocks, that is, p _j ={p ₁ ˜p _k }, where j is a positive integer, and 1≤j≤k. The transmitting end generates one or more first encoded data blocks c _n ={c 1˜c _n } according to p ₁ _to p _k , where n is a positive integer. Wherein, c ₁ is a first encoded data block obtained by encoding p ₁ to p _k in the finite fields of GF(E ^d ) and GF(E ^D ), that is, the sender uses GF(E ^d ) and GF(E ^D ) ) The coding coefficients α _1,1 ...α _1,k in the finite field encode p ₁ to p _k to obtain c ₁ , where c ₁ can satisfy the following formula:

where α _1,1 . . . α _1,k are coding coefficients in the finite fields of GF(E ^d ) and GF(E ^D ).

cn is the first encoded data block obtained by encoding _p ₁ to p _k in the finite fields of GF(E ^d ) and GF(E ^D ), that is, the sender adopts the finite fields of GF(E ^d ) and GF(E ^D ) The coding coefficients α _n,1 ...α _n,k in , encode p ₁ to p _k to obtain c _n , where c _n can satisfy the following formula:

where α _n,1 . . . α _n,k are coding coefficients in the finite fields of GF(E ^d ) and GF(E ^D ).

With reference to the first aspect, in a possible implementation manner of the first aspect, the one or more first encoded packets further include a finite field order, the finite field order and the first encoded data block, and/or a source Corresponding to the data block, the finite field order is the finite field order of a group of coding coefficients in the first coding coefficient matrix corresponding to the first coded data block, and/or the finite field order of the coding coefficients of the source data block.

In an optional implementation manner, a first encoded packet carries a first encoded data block (or a source data block).

In another optional implementation manner, a first encoded packet carries multiple first encoded data blocks (and/or one or more source data blocks). There is no specific limitation here.

Specifically, the finite field order may be carried after the first encoded data block, and the finite field order may also be carried before the first encoded data block, which is not limited here.

Exemplarily, if the finite field is GF(E ² ), the order of the finite field may be 2. The finite field order is used to indicate the order of the finite field corresponding to the first encoded data block.

In the embodiment of the present application, the finite field order is carried in the first encoded message, so that the intermediate node or the receiving end can identify the data block corresponding to the finite field order and encode the finite field used. Improved decoding speed.

With reference to the first aspect, in a possible implementation manner of the first aspect, the coding coefficients of the first finite field are carried at the network layer or the data link layer of the first coded message;

The coding coefficients of the second finite field are carried in the transport layer of the first coded message;

The coding coefficients of the source data block are carried in the network layer or data link layer of the first coded packet.

Exemplarily, the coding coefficient of the finite field with lower order (for example, d is less than or equal to 2) is carried in the header of an Internet Protocol (Internet Protocol, IP) packet or an Ethernet (Ethernet, ETH) frame header, for example, it can be set by setting The sixth version of the Internet Protocol (Internet Protocol version 6, IPv6) extension header, IP or ETH extension field implementation; the coding coefficient of the finite field with higher order is carried in the Transmission Control Protocol (Transmission Control Protocol, TCP) packet header, for example Can be carried by setting TCP options.

In the embodiment of the present application, the coding coefficients of different finite fields may be carried in different protocol layers in the first coded message, which is convenient for subsequent nodes to re-encode or decode the first coded message.

In the second aspect, an embodiment of the present application proposes a finite field encoding method, including:

Using the second encoding coefficient matrix to perform encoding processing on the k source data blocks to generate k second encoding data blocks, the second encoding data blocks correspond to a group of encoding coefficients in the second encoding coefficient matrix, and k is a positive integer;

The k second encoded data blocks and k source data blocks are encoded using the third encoding coefficient matrix to generate g third encoded data blocks, the third encoded data block and a set of encoding coefficients in the third encoding coefficient matrix Correspondingly, g is a positive integer;

One or more second coded packets are generated according to the k second coded data blocks and the g third coded data blocks. A second coded packet includes: one or more third coded data blocks and one or more coding coefficients of the third coded data block, the second coded message includes one or more third coded data blocks, and coding coefficients corresponding to the third coding coefficient matrix;

Wherein, the second coding coefficient matrix includes the coding coefficients of the third finite field, the third coding coefficient matrix includes the coding coefficients of the fourth finite field, the third finite field and the fourth finite field are finite fields with a nested structure, and, The order of the fourth finite field is higher than that of the third finite field, and the finite field with nested structure satisfies the following relationship: the order has a multiple relationship, and the characteristic numbers are consistent;

One or more second encoded messages are sent.

Specifically, the coding coefficients corresponding to the third coding coefficient matrix are also referred to as coding coefficients of the third coding coefficient matrix.

The third finite field, and the fourth finite field, are finite fields with nested structures, wherein the third finite field is GF(E ^D1 ), the fourth finite field is GF(E ^d1 ), E is a prime number, d1 is a positive integer, D1 is a positive integer, D1=z*d1, and z is a positive integer greater than 1. The source data block is: p _j , where j is a positive integer, 1≤j≤k; the encoding coefficient of the third finite field is α′ _n,k , n is a positive integer; one or more second encoded data blocks ( For example, the k second encoded data blocks) include: c′ _n , wherein,

The coding coefficient of the fourth finite field is β _m,k+n ; one or more third coded data blocks (eg, g third coded data blocks) include: b _m , wherein,

m is a positive integer.

The transmitting end uses the second encoding coefficient matrix to perform encoding processing on k source data blocks in a group (Generation) to obtain one or more second encoded data blocks, wherein the second encoding coefficient matrix at least includes the encoding of the third finite field coefficient, k is a positive integer. The third finite field is GF(E ^D1 ), E is a prime number, and D1 is a positive integer.

It is assumed that a group contains k source data blocks, that is, p _j ={p ₁ -p _k }, where j is a positive integer, and 1≤j≤k. The transmitting end generates one or more second encoded data blocks c' _n ={c' _1～ c' _n } according to p ₁ to p _k , where n is a positive integer. Wherein, c' ₁ is a second encoded data block obtained by encoding p ₁ to p _k in the finite field of GF(E ^D1 ), that is, the transmitting end adopts the encoding coefficient α′ _{1 in} the finite field of GF(E ^D1 ), ₁ ...α′ _1,k encodes p ₁ to p _k to obtain c′ ₁ , where c′ ₁ can satisfy the following formula:

Among them, α′ _1,1 ···α′ _1,k are the coding coefficients in the finite field of GF(E ^D1 ).

c' _n is the second encoded data block obtained by encoding p ₁ ~ p _k in the finite field of GF(E ^D1 ), that is, the transmitting end adopts the coding coefficients α′ _1,1 . . . α in the finite field of GF(E ^D1 ) ′ _1,k encodes p ₁ to p _k to obtain c' _n , where c' _n can satisfy the following formula:

Among them, α′ _n,1 ···α′ _n,k are the coding coefficients in the finite field of GF(E ^D1 ).

After generating one or more second coded data blocks {c' ₁ ～c' _n }, the sending end uses the third coding coefficient matrix to perform one or more second coded data blocks {c' ₁ ～c' _n } and The k source data blocks {p ₁ to p _k } are encoded to generate one or more third encoded data blocks {b ₁ to b _m }, where m is a positive integer.

Wherein, the third coding coefficient matrix includes at least coding coefficients of the fourth finite field. The third finite field, and the fourth finite field, are finite fields with nested structures, wherein the third finite field is GF(E ^D1 ), the fourth finite field is GF(E ^d1 ), E is a prime number, d1 is a positive integer, D1 is a positive integer, D1=z*d1, and z is a positive integer greater than 1.

The third encoded data block is b _m , where,

Wherein, β _m,k+n are the coding coefficients of the fourth finite field, the k source data blocks are p _j ={p ₁ ~p _k }, j is a positive integer, 1≤j≤k.

In an optional implementation manner, the fourth finite field is the lowest-order finite field currently supported by the sender, and the lowest-order finite field and the third finite field have a nested structure.

In this embodiment of the present application, the sender encodes the source data block in multiple finite fields with nested structures, and the receiver can decode the message in the finite fields with nested structures. Due to the finite field with nested structure, the elements and operations of the higher-order finite field, including the elements and operations of the lower-order finite field, are sent. Therefore, first, the receiving end can decode the encoded data of the finite field with a higher order in a finite field with a lower order according to its own computing power and application requirements. Continue decoding in higher finite fields. The computational complexity is effectively reduced, the decoding speed and data throughput are improved, and the decoding accuracy is guaranteed.

In conjunction with the second aspect, in a possible implementation manner of the second aspect, a second encoded message further includes:

one or more second coded data blocks, and a set of coding coefficients in the second coding coefficient matrix corresponding to the one or more second coded data blocks,

And/or, one or more source data blocks, the source data blocks correspond to a set of coding coefficients in an identity matrix, and the size of the identity matrix is determined by the number of second coded data blocks and the number of source data blocks.

In an optional implementation manner, the source data block is carried in one or more second coding coefficient packets generated by the sender. The data blocks carried by the one or more second coding coefficient packets may be expressed as: {p ₁ ···p _k }∪{c′ ₁ ···c′ _n }∪{b ₁ ···b _m }. The second coding coefficient message may also be referred to as a system code message.

In another optional implementation manner, the source data block and the second encoded data block are not carried in one or more second encoding coefficient packets generated by the sending end. The data blocks carried by the one or more second coding coefficient packets may be represented as: {b ₁ . . . b _m }. The second coding coefficient message may also be referred to as a non-systematic code message.

In this embodiment of the present application, the second encoding coefficient message may be a system code message or a non-system code message, which improves the implementation flexibility of the solution.

In combination with the second aspect, in a possible implementation manner of the second aspect,

The coding coefficients of the third finite field are carried in the transport layer of the second coded message;

The coding coefficients of the fourth finite field are carried in the network layer or the data link layer of the second coded message.

Exemplarily, the coding coefficients of the finite field with a lower order are carried in an Internet Protocol (Internet Protocol, IP) packet header or an Ethernet (Ethernet) frame header, for example, by setting an Internet Protocol version 6 (Internet Protocol version 6) , IPv6) extension header, IP or ETH extension field implementation; the coding coefficient of the finite field with higher order is carried in the Transmission Control Protocol (Transmission Control Protocol, TCP) packet header, for example, it can be carried by setting the TCP option.

In the embodiment of the present application, the coding coefficients of different finite fields may be carried in different protocol layers in the second coded message, which is convenient for subsequent nodes to re-encode or decode the second coded message.

With reference to the second aspect, in a possible implementation manner of the second aspect, one or more second encoded packets further include a finite field order, and the finite field order includes a finite field where the encoding coefficients of the second encoded data block are located The order, the order of the finite field where the coding coefficients of the third coded data block are located, and/or the order of the finite field where the coding coefficients of the source data block are located.

In an optional implementation manner, a second encoded packet carries a third encoded data block (or a source data block, or a second encoded data block).

In another optional implementation manner, a second encoded packet carries multiple third encoded data blocks (and/or one or more source data blocks, and/or one or more second encoded data blocks ). There is no specific limitation here.

With reference to the second aspect, in a possible implementation manner of the second aspect, the second coding coefficient matrix further includes: coding coefficients of a fifth finite field, the fifth finite field and the third finite field have a nested structure, and the third finite field has a nested structure. The order of the fifth finite field is different from the order of the third finite field.

In this embodiment of the present application, the coding coefficients in the second coding coefficient matrix may include multiple finite fields with a nested structure. The sender can be applied to a variety of coding scenarios, which improves the diversity of solutions.

In a third aspect, an embodiment of the present application proposes a finite field recoding method, including:

Receive one or more third encoded messages, where the third encoded message includes g' fourth encoded data blocks, and encoding coefficients corresponding to g' fourth encoded data blocks, where g' is a positive integer;

Use the fourth encoding coefficient matrix to carry out encoding processing to g' fourth encoding data blocks, generate one or more fifth encoding data blocks, and the fifth encoding data blocks correspond to a group of encoding coefficients in the fourth encoding coefficient matrix;

One or more re-encoded packets are generated according to the one or more fifth encoded data blocks, where the re-encoded packet includes one or more fifth encoded data blocks, and fourth encoded data blocks corresponding to the one or more fifth encoded data blocks a set of coding coefficients in the coding coefficient matrix;

Wherein, the finite field of the coding coefficients in the fourth coding coefficient matrix and the finite field of coding coefficients included in the third coding message have a nested structure, and the finite field with the nested structure satisfies the following relationship: the order has a multiple relationship, and, The number of features is consistent;

Send one or more recoded packets.

Specifically, for the convenience of description, the coding coefficient corresponding to the fourth coded data block is also referred to as the coding coefficient of the fourth coded data block.

Exemplarily, the intermediate node may receive a third encoded packet sent by another intermediate node, where the other intermediate node serves as a previous hop node of the intermediate node. The intermediate node may also receive the third encoded message sent by the sender. The third encoded message includes the first encoded message, and/or the second encoded message.

The third encoded message includes g' fourth encoded data blocks and encoding coefficients corresponding to the g' fourth encoded data blocks, where g' is a positive integer.

The intermediate node performs encoding processing on the fourth encoded data block by using the fourth encoding coefficient matrix to generate a fifth encoded data block. The fifth encoded data block corresponds to a set of encoded coefficients in the fourth encoded coefficient matrix. For convenience of description, the coding coefficients in the fourth coding coefficient matrix are referred to as fourth coding coefficients. The fourth encoding coefficient matrix includes one or more fourth encoding coefficients.

The finite field of coding coefficients in the fourth coding coefficient matrix and the finite field of coding coefficients included in the third coding message have a nested structure. Specifically, the finite field of the fourth coding coefficients and the coding coefficients corresponding to the fourth coding data block The finite field has a nested structure, wherein the finite field of the fourth coding coefficient and the finite field of coding coefficients corresponding to the fourth coded data block satisfy the following relationship: the order has a multiple relationship, and the feature numbers are consistent. Exemplarily, when the third coded message is the first coded message, the finite field of the fourth coding coefficient has a nested structure with the first finite field and the second finite field; when the third coded message is the second When encoding the message, the finite field of the fourth coding coefficient has a nested structure with the third finite field and the fourth finite field.

After generating one or more fifth encoded data blocks, the intermediate node generates one or more re-encoded packets. A re-encoded message includes: one or more fifth encoded data blocks, one or more fourth encoded coefficients, and/or, one or more fourth encoded data blocks, one or more fourth encoded data blocks coding coefficients;

In an optional implementation manner, when sending the fifth encoded data block, the intermediate node may use a re-encoded message to carry one fifth encoded data block, or use one re-encoded message to carry multiple encoded data blocks. The transmission is performed in the manner of the fifth encoded data block, which is not specifically limited here.

Taking the way that the intermediate node carries a fifth encoded data block in a recoded packet and sends the recoded packet as an example, the intermediate node can add a packet header to each fifth encoded data block to form a packet, and add the packet to the packet. The corresponding fourth coding coefficient is added to the header or the end of the message and then sent with the message.

Optionally, a finite field order may also be carried in the recoding message, where the finite field order is used to indicate the order of the finite field corresponding to the fifth encoded data block carried in the recoding message. Exemplarily, the finite field order may be a value of a power corresponding to the finite field. For example, it is assumed that in the re-encoded message, the fifth encoded data block (the fourth encoding coefficient corresponding to the fifth encoded data block) is If the finite field is GF(E ² ), the order of the finite field can be 2. The finite field order may also be the maximum power order of the finite field in the recoded message.

In the embodiment of the present application, the intermediate node re-encodes the message output by the transmitting end, so that the transmitting end and the intermediate node can form a distributed encoding, that is, the transmitting end encodes a part, and the intermediate node encodes another part In this way, the sender can perform coding with lower complexity, and further re-encode the message output by the sender through the intermediate node, thereby reducing the network load and improving the transmission efficiency.

With reference to the third aspect, in a possible implementation manner of the third aspect, the order of the finite field of the encoding coefficients (the fourth encoding coefficient) in the fourth encoding coefficient matrix is equal to the lowest order of the finite field in the network where the intermediate node is located ;

Or, the finite field order of the coding coefficients in the fourth coding coefficient matrix is less than or equal to the highest order of the finite field in the network where the intermediate node is located;

Or, the finite field order of the coding coefficients in the fourth coding coefficient matrix is greater than or equal to the lowest order of the finite field in the network where the intermediate node is located.

Specifically, in an optional implementation manner, the order of the finite field of the fourth coding coefficient is equal to the lowest order of the finite field in the network where the intermediate node is located. Exemplarily, when the lowest order of the finite field in the network where the intermediate node is located is d0, the finite field of the lowest order is GF(E ^d0 ), E is a prime number, and d0 is a positive integer. Then the finite field where the fourth coding coefficient is located is GF(E ^d0 ).

In another optional implementation manner, the finite field order of the fourth coding coefficient is less than or equal to the highest order of the finite field in the network where the intermediate node is located, or, the finite field order of the fourth coding coefficient is greater than or equal to The lowest order of the finite field in the network where the intermediate nodes are located. Exemplarily, when the lowest order of the finite field in the network where the intermediate node is located is d0, the finite field of the lowest order is GF(E ^d0 ), E is a prime number, and d0 is a positive integer. The highest order of the finite field in the network where the intermediate node is located is dmax, the finite field of the highest order is GF(E ^dmax ), and dmax is a positive integer. Then the value range of the order of the fourth finite field is: less than or equal to dmax, and greater than or equal to d0.

In the embodiment of the present application, the finite field order of the fourth coding coefficient may have various value schemes. This makes the intermediate node applicable to various network scenarios. Increased the scope of application of intermediate nodes.

In combination with the third aspect, in a possible implementation manner of the third aspect,

The fourth encoded data block is Xi, 1≤i≤u, i is a positive integer, and u is a positive integer;

The fourth coding coefficient is γ _uv , where v is a positive integer greater than 1;

The fifth encoded data block is Y _v , where,

Among them, 1≤j≤v.

Specifically, the third encoded message (including the first encoded message/the second encoded message) is X ₁ to X _i , wherein a third encoded message may include a fourth encoded data block and the fourth encoded message Coding coefficients corresponding to the data block. The intermediate node multiplies X ₁ ˜X _i by the fourth coding coefficient matrix to obtain new messages Y ₁ ˜Y _v . The coding coefficients included in the fourth coding coefficient matrix belong to the re-coded finite field, and the coding coefficients in the first row of the fourth coding coefficient matrix may be {γ _1,1 ...γ _1,v }, X ₁ to X _u and { Multiply γ _1,1 ...γ _1,v } to obtain Y ₁ , and so on, the coding coefficient of the uth row of the fourth coding coefficient matrix can be {γ _u,1 ...γ _u,v }, X ₁ ～X _u Multiply by {γ _u,1 …γ _u,v } to get Y _v .

In a fourth aspect, an embodiment of the present application proposes a finite field decoding method, the method comprising:

Receive one or more fourth encoded messages, wherein, a fourth encoded message includes the encoding coefficients of t' sixth encoded data blocks and t' sixth encoded data blocks, and t' is a positive integer;

The first decoding method is used to perform decoding operations on one or more fourth coded messages in a low-order finite field and a high-order finite field to generate k source data blocks, where k is a positive integer,

The low-order finite field is the finite field with the lowest order in the network where the receiver is located, and the high-order finite field is any higher-order finite field of the coding coefficients corresponding to the sixth encoded data block, and the order of the high-order finite field is higher than the low-order finite field. The order of the second-order finite field, the lower-order finite field and the higher-order finite field have a nested structure, and the finite field with the nested structure satisfies the following relationship: the order has a multiple relationship, and the characteristic number is consistent;

Alternatively, a second decoding method is used to perform a decoding operation on one or more fourth encoded packets in the highest-order finite field of the encoding coefficients corresponding to the sixth encoded data block to generate k' source data blocks, the highest-order finite The domain is the highest-order finite domain of the coding coefficients corresponding to the sixth coded data block, and k' is a positive integer.

Specifically, the receiving end receives one or more fourth encoded packets. The fourth encoded message may be: a second encoded message or a re-encoded message. The second encoded message may be directly sent by the intermediate node to the receiving end, or may be forwarded to the receiving end after being encoded (also called re-encoding) by the intermediate node, which is not limited here.

In the embodiment of the present application, the fourth encoded message received by the receiving end is encoded by using a finite field with a nested structure. From the perspective of decoding speed or throughput, the decoding operation of the high-order finite field in the decoding process is transformed into a low-order finite field (for example, the lowest-order finite field in the current network), which effectively reduces the computational complexity and improves the Decoding speed and data throughput.

With reference to the fourth aspect, in a possible implementation manner of the fourth aspect, the first decoding method is used to perform a decoding operation on one or more fourth encoded packets, and the generation of k source data blocks includes:

performing a first decoding operation on one or more fourth encoded messages in a low-order finite field;

For the result obtained by the first decoding operation, a second decoding operation is performed in a high-order finite field to generate k source data blocks.

In the embodiment of the present application, when decoding is performed at the receiving end, decoding may be performed in a low-order finite field first, and the decoding result of the lower-order finite field may be used to further decode in a higher-order finite field, and finally a or multiple source data blocks. Decoding in a low-order finite field effectively reduces the computing power requirements of the receiver. The decoding reserved in the high-order finite field improves the decoding success rate.

With reference to the fourth aspect, in a possible implementation manner of the fourth aspect, a first decoding operation is performed on one or more fourth encoded packets in a low-order finite field, including:

According to the coding coefficients corresponding to the sixth coded data block in the one or more fourth coded messages, the coding coefficients of the lower-order finite field and the coding coefficients of the higher-order finite field are determined;

The low-order domain coding coefficient matrix is composed of the coding coefficients of the low-order finite field;

According to the low-order domain coding coefficient matrix, the first decoding matrix and the second decoding matrix are composed, wherein,

The coding coefficients corresponding to the high-order finite field in the coding coefficients of the first decoding matrix form the first high-order field coding coefficient group, and the finite field of the first high-order field coding coefficient group is all the coding coefficients corresponding to the sixth coded data block. The finite field with the lowest order among the higher-order finite fields;

Among the coding coefficients of the second decoding matrix, the coding coefficients corresponding to the high-order finite field form the second high-order field coding coefficient group, and the finite field of the second high-order field coding coefficient group is divided by the coding coefficients corresponding to the sixth coded data block. The finite fields of other coding coefficients other than the first high-order finite field coding coefficient group, and the finite field order of the second high-order field coding coefficient group is less than or equal to the highest-order finite field order supported by the receiving end;

Perform a decoding operation on the second decoding matrix to generate a first decoding sub-matrix and a second decoding sub-matrix, wherein the first decoding sub-matrix is a zero matrix, and the second decoding matrix is a diagonal coefficient of 1 the identity matrix of ;

When the second decoding matrix performs a decoding operation, the first decoding matrix is synchronously decoded to generate a third decoding sub-matrix and a fourth decoding sub-matrix;

In an optional implementation manner, the number of rows of the third decoding sub-matrix is the same as the number of rows of the first decoding sub-matrix, and the number of rows of the fourth decoding sub-matrix is the same as the number of rows of the second decoding sub-matrix number the same;

In another optional implementation manner, the number of columns of the third decoding sub-matrix is consistent with the number of columns of the first decoding sub-matrix, and the number of columns of the fourth decoding sub-matrix is the same as the number of columns of the second decoding sub-matrix. The number of columns is the same;

When the first decoding matrix performs a decoding operation, a synchronous decoding operation is performed on the sixth encoded data block corresponding to the first decoding matrix to generate data to be decoded.

With reference to the fourth aspect, in a possible implementation manner of the fourth aspect,

For the result obtained by the first decoding operation, a second decoding operation is performed in a high-order finite field, and generating one or more source data blocks includes:

The result obtained by the first decoding operation includes the third decoding sub-matrix, the fourth decoding sub-matrix, and the data to be decoded,

According to the fourth decoding sub-matrix, the fifth decoding sub-matrix corresponding to the fourth decoding sub-matrix is determined, and the fifth decoding sub-matrix is composed of coding coefficients of high-order finite fields;

A sixth decoding sub-matrix is generated according to the fourth decoding sub-matrix and the fifth decoding sub-matrix, wherein the vectors in the sixth decoding sub-matrix are composed of a set of coding coefficients of the fifth decoding sub-matrix and the fourth decoding sub-matrix. A set of coding coefficients of the code sub-matrix is obtained by addition in the finite field corresponding to the fifth decoding sub-matrix;

According to the third decoding sub-matrix and the sixth decoding sub-matrix, form a fourth decoding matrix;

A decoding operation is performed on the fourth decoding matrix to generate a unit matrix with a diagonal coefficient of 1;

When performing a decoding operation on the fourth decoding matrix, a synchronous decoding operation is performed on the data to be decoded to generate k source data blocks.

With reference to the fourth aspect, in a possible implementation manner of the fourth aspect, the first decoding matrix and the second decoding matrix are formed according to the low-order domain coding coefficient matrix, including:

According to the low-order domain coding coefficient matrix, a first decoding matrix, a second decoding matrix and a third decoding matrix are formed, wherein the coding coefficients corresponding to the high-order finite field in the third decoding matrix form the third high-order domain coding Coefficient group, the finite field of the third higher-order domain coding coefficient group is the coding coefficients corresponding to the sixth coded data block except the first higher-order finite-field coding coefficient group and the second higher-order finite-field coding coefficient group. Other coding coefficients The finite field of , the order of the finite field corresponding to the third high-order field coding coefficient group is higher than the highest-order finite field order supported by the receiver;

A decoding operation is performed on the third decoding matrix to generate a zero matrix.

In this embodiment of the present application, the receiving end may discard packets that exceed its own computing power, so as to save computing resources and improve decoding speed.

With reference to the fourth aspect, in a possible implementation manner of the fourth aspect, for k source data blocks, where k is a positive integer,

When the following conditions are met, the w fourth encoded packets are decoded, including:

in,

for

matrix,

satisfy

The third decoding matrix is

The high-order domain coding coefficient matrix is G, the high-order domain coding coefficient matrix is composed of coding coefficients of the high-order finite domain, and the low-order domain coding coefficient matrix H, w is a positive integer.

In the embodiment of the present application, the receiving end determines the decoding time point of the fourth encoded message by detecting the fourth encoded message. After receiving a sufficient number of fourth coded packets, the receiving end decodes these fourth coded packets to ensure the accuracy of the decoding.

In conjunction with the fourth aspect, in a possible implementation manner of the fourth aspect, a second decoding method is used to perform a decoding operation on one or more fourth encoded packets to generate one or more source data blocks, including:

In the highest-order finite field corresponding to the coding coefficients of the sixth coded data block, the sixth coded data block is decoded, so that the matrix formed by the coding coefficients of the sixth coded data block is decoded to obtain a unit matrix;

When the matrix composed of the coding coefficients of the sixth coded data block is subjected to a decoding operation, a synchronous decoding operation is performed on the sixth coded data block to generate k' source data blocks.

In the embodiment of the present application, the fourth encoded message received by the receiving end is encoded by using a finite field with a nested structure. In a finite field with a nested structure, an equivalent multiplication table (or an equivalent addition table) can be used to perform multiplication (or addition). Therefore, when decoding is performed at the receiving end, the sixth encoded data block can be decoded within the highest-order finite field corresponding to the encoding coefficients of the sixth encoded data block. The computational complexity is effectively reduced, and the decoding speed and data throughput are improved. Moreover, the implementation flexibility of the solution is improved.

In a fifth aspect, the present application provides a network device, comprising:

The processing module is configured to use the first coding coefficient matrix to perform coding processing on the k source data blocks to generate k first coded data blocks, where the first coded data blocks correspond to a set of coding coefficients in the first coding coefficient matrix, and k is a positive integer;

The processing module is further configured to generate one or more first encoded messages according to the k first encoded data blocks, where the first encoded message includes one or more first encoded data blocks and one or more first encoded data blocks a group of coding coefficients in the first coding coefficient matrix corresponding to the data block;

The transceiver module is used for sending one or more first encoded messages.

In some optional embodiments of the present application,

The source data block is: p _j , where j is a positive integer, 1≤j≤k;

The one or more first encoded data blocks include: c _n , wherein,

In some optional embodiments of the present application, the first encoded message further includes one or more source data blocks, the source data blocks correspond to a set of encoding coefficients in the unit matrix, and the size of the unit matrix is the same as that of the first encoding coefficient matrix same.

In some optional embodiments of the present application, the coding coefficients of the first finite field are carried at the network layer or the data link layer of the first coded message;

The coding coefficients of the second finite field are carried in the transport layer of the first coded message.

In a sixth aspect, the present application provides a network device, comprising:

The processing module is configured to use the second encoding coefficient matrix to perform encoding processing on the k source data blocks to generate k second encoded data blocks, where the second encoded data blocks correspond to a set of encoding coefficients in the second encoding coefficient matrix, and k is a positive integer;

The processing module is further configured to perform encoding processing on the k second encoded data blocks and the k source data blocks by using the third encoding coefficient matrix to generate g third encoded data blocks, the third encoded data block and the third encoding coefficient matrix Corresponding to a set of coding coefficients in , g is a positive integer;

The processing module is further configured to generate one or more second encoded packets according to the k second encoded data blocks and the g third encoded data blocks, where a second encoded packet includes: one or more third encoded data blocks encoding coefficients of the block and one or more third encoded data blocks, the second encoded message includes one or more third encoded data blocks, and encoding coefficients corresponding to the third encoding coefficient matrix;

The transceiver module is used for sending one or more second encoded messages.

In some optional embodiments of the present application, the second encoded message further includes:

In some optional embodiments of the present application, the source data block is: p _j , where j is a positive integer, and 1≤j≤k;

The coding coefficient of the third finite field is α′ _n,k , where n is a positive integer;

The one or more second encoded data blocks include: c' _n , wherein,

The coding coefficient of the fourth finite field is β _m,k+n ;

The one or more third encoded data blocks include: b _m , wherein,

m is a positive integer.

In some optional embodiments of the present application, the coding coefficients of the third finite field are carried in the transport layer of the second coded message;

In some optional embodiments of the present application, the one or more second encoded packets further include a finite field order, and the finite field order includes the finite field order where the encoding coefficients of the second encoded data block are located, and the third encoded data The order of the finite field where the coding coefficients of the block are located, and/or the order of the finite field where the coding coefficients of the source data block are located.

In some optional embodiments of the present application, the second coding coefficient matrix further includes: coding coefficients of a fifth finite field, where the fifth finite field and the third finite field have a nested structure, wherein the fifth finite field and the third finite field have a nested structure. The three finite fields satisfy the following relationship: the order has a multiple relationship, and the characteristic numbers are consistent.

In a seventh aspect, the present application provides a network device, comprising:

A transceiver module, configured to receive one or more third encoded packets, where the third encoded packet includes g' fourth encoded data blocks and encoding coefficients corresponding to the g' fourth encoded data blocks, where g' is a positive integer ;

A processing module, configured to perform encoding processing on g' fourth encoded data blocks by using the fourth encoding coefficient matrix to generate one or more fifth encoded data blocks, the fifth encoded data block and a group of the fourth encoded coefficient matrix Corresponding coding coefficients;

The processing module is further configured to generate one or more re-encoded messages according to one or more fifth encoded data blocks, where the re-encoded message includes one or more fifth encoded data blocks and one or more fifth encoded data blocks a group of coding coefficients in the fourth coding coefficient matrix corresponding to the data block;

The transceiver module is also used to send one or more recoded messages.

In some optional embodiments of the present application, the finite field order of the coding coefficients in the fourth coding coefficient matrix is equal to the lowest order of the finite field in the network where the intermediate node is located;

In some optional embodiments of the present application, the fourth encoded data block is Xi, 1≤i≤u, i is a positive integer, and u is a positive integer;

The fourth coding coefficient is γ _u,v , where v is a positive integer greater than 1;

The fifth encoded data block is Y _v , where,

Among them, 1≤j≤v.

In an eighth aspect, the present application provides a network device, comprising:

The transceiver module is used to receive one or more fourth encoded messages, where the fourth encoded message includes t' sixth encoded data blocks and encoding coefficients corresponding to the t' sixth encoded data blocks, where t' is a positive integer ;

a processing module, configured to perform a decoding operation on one or more fourth encoded messages in a low-order finite field and a high-order finite field by using the first decoding method, and generate k source data blocks, where k is a positive integer;

or,

The processing module is further configured to perform a decoding operation on one or more fourth encoded messages in the highest-order finite field of the encoding coefficients corresponding to the sixth encoded data block by using the second decoding method to generate k" source data blocks , the highest-order finite field is the highest-order finite field of the coding coefficients corresponding to the sixth coded data block.

In some optional embodiments of the present application,

a processing module, specifically configured to perform a first decoding operation on one or more fourth encoded packets in a low-order finite field;

The processing module is specifically configured to perform a second decoding operation on the result obtained by the first decoding operation in a high-order finite field to generate k source data blocks.

In some optional embodiments of the present application, the processing module is specifically configured to determine, according to the coding coefficients corresponding to the sixth coded data block in one or more fourth coded packets, the coding coefficients of the lower-order finite field and the coding coefficients of the higher-order finite field the coding coefficients of the domain;

a processing module, which is specifically used to form a low-order domain coding coefficient matrix from coding coefficients of a low-order finite field;

The processing module is specifically configured to form a first decoding matrix and a second decoding matrix according to the low-order domain encoding coefficient matrix, wherein the encoding coefficients corresponding to the high-order finite field in the encoding coefficients of the first decoding matrix form the first high-order finite field. A sub-domain coding coefficient group, the finite field of the first higher-order domain coding coefficient group is the finite field with the lowest order among all the higher-order finite fields of the coding coefficients corresponding to the sixth coded data block;

The processing module is specifically used to perform a decoding operation on the second decoding matrix to generate a first decoding sub-matrix and a second decoding sub-matrix, wherein the first decoding sub-matrix is a zero matrix, and the second decoding matrix is identity matrix;

The processing module is specifically configured to perform a synchronous decoding operation on the first decoding matrix when the second decoding matrix performs a decoding operation to generate a third decoding sub-matrix and a fourth decoding sub-matrix, wherein the third decoding sub-matrix is The number of rows of the sub-matrix is the same as the number of rows of the first decoding sub-matrix, the number of rows of the fourth decoding sub-matrix is the same as the number of rows of the second decoding sub-matrix, or the columns of the third decoding sub-matrix The number is consistent with the column number of the first decoding sub-matrix, and the column number of the fourth decoding sub-matrix is consistent with the column number of the second decoding sub-matrix;

The processing module is specifically configured to perform a synchronous decoding operation on the sixth encoded data block to generate data to be decoded when the first decoding matrix performs a decoding operation.

In some optional embodiments of the present application, the result obtained by the first decoding operation includes the third decoding sub-matrix, the fourth decoding sub-matrix, and the data to be decoded,

The processing module is specifically used for determining the fifth decoding sub-matrix corresponding to the fourth decoding sub-matrix according to the fourth decoding sub-matrix, and the fifth decoding sub-matrix is composed of coding coefficients of high-order finite fields;

The processing module is specifically configured to generate a sixth decoding sub-matrix according to the fourth decoding sub-matrix and the fifth decoding sub-matrix, wherein the vectors in the sixth decoding sub-matrix are composed of a group of the fifth decoding sub-matrix. The coding coefficients and a group of coding coefficients of the fourth decoding sub-matrix are obtained by addition in the finite field corresponding to the fifth decoding sub-matrix;

a processing module, specifically configured to form a fourth decoding matrix according to the third decoding sub-matrix and the sixth decoding sub-matrix;

a processing module, specifically configured to perform a decoding operation on the fourth decoding matrix to generate a unit matrix;

The processing module is specifically configured to perform a synchronous decoding operation on the data to be decoded when performing a decoding operation on the fourth decoding matrix to generate k source data blocks.

In some optional embodiments of the present application,

The processing module is specifically used to form a first decoding matrix, a second decoding matrix and a third decoding matrix according to the low-order domain encoding coefficient matrix, wherein the encoding coefficients corresponding to the high-order finite field in the third decoding matrix are composed of The third high-order domain coding coefficient group, the finite field of the third high-order domain coding coefficient group is the coding coefficients corresponding to the sixth coded data block divided by the first high-order finite field coding coefficient group and the second high-order finite field coding coefficients For the finite fields of other coding coefficients outside the group, the finite field order corresponding to the third high-order field coding coefficient group is higher than the highest-order finite field order supported by the receiver;

The processing module is specifically configured to perform a decoding operation on the third decoding matrix to generate a zero matrix.

In some optional embodiments of the present application,

For the k source data blocks, when the following conditions are met, the processing module is further configured to decode the w fourth encoded packets, including:

in,

for

matrix,

satisfy

The third decoding matrix is

In some optional embodiments of the present application,

The processing module is specifically configured to decode the sixth coded data block in the highest-order finite field corresponding to the coding coefficients of the sixth coded data block, so that the matrix composed of the coding coefficients of the sixth coded data block is decoded to obtain a unit matrix;

The processing module is specifically configured to perform a synchronous decoding operation on the sixth encoded data block to generate k" source data blocks when the matrix composed of the encoding coefficients of the sixth encoded data block is subjected to a decoding operation.

In a ninth aspect, an embodiment of the present application provides a network device, where the network device can implement the functions performed by the sending end, the receiving end, and the intermediate node in the methods involved in the first, second, third, or fourth aspects. The network device includes a processor, a memory, a receiver connected to the processor and a transmitter connected to the processor; the memory is used for storing program codes and transmitting the program codes to the processor; the processor is used for Drive the receiver and the transmitter to execute the method according to the first, second, third, or fourth aspects above according to the instructions in the program code; the receiver and the transmitter are respectively connected to the processor to execute the methods of the above-mentioned aspects. Operations of the sender, the receiver and the intermediate node in the method. Specifically, the transmitter can perform the operation of sending, and the receiver can perform the operation of receiving. Optionally, the receiver and the transmitter can be a radio frequency circuit, and the radio frequency circuit can receive and send messages through an antenna; the receiver and the transmitter can also be a communication interface, and the processor and the communication interface are connected through a bus, and the processing The server implements receiving or sending messages through this communication interface.

In a tenth aspect, an embodiment of the present application provides a network device. The network device may include entities such as network equipment, terminal equipment, or chips. The network device includes: a processor and a memory; the memory is used for storing instructions; the processor is used for Execution of the instructions in the memory causes the network device to perform the method of any of the aforementioned first or second or third or fourth aspects.

In an eleventh aspect, embodiments of the present application provide a computer-readable storage medium that stores one or more computer-executable instructions. When the computer-executable instructions are executed by a processor, the processor executes the first aspect or the first aspect described above. Any possible implementation manner of the second aspect, the third aspect or the fourth aspect.

In a twelfth aspect, an embodiment of the present application provides a computer program product (or computer program) that stores one or more computer-executable instructions. When the computer-executable instructions are executed by the processor, the processor executes the aforementioned first Any possible implementation of the aspect or the second aspect or the third aspect or the fourth aspect.

In a thirteenth aspect, the present application provides a chip system, where the chip system includes a processor for supporting a computer device to implement the functions involved in the above aspects. In a possible design, the chip system further includes a memory for storing necessary program instructions and data of the computer device. The chip system may be composed of chips, or may include chips and other discrete devices.

In a fourteenth aspect, the present application provides a communication system, the communication system including the network device in the fifth aspect, sixth aspect, seventh aspect, or eighth aspect.

Description of drawings

FIG. 1a is a schematic diagram of an application scenario involved in an embodiment of the present application;

FIG. 1b is a schematic diagram of another application scenario involved in the embodiment of the present application;

FIG. 1c is a schematic diagram of another application scenario involved in the embodiment of the present application;

FIG. 1d is a schematic diagram of another application scenario involved in the embodiment of the present application;

2 is a schematic diagram of a hardware structure of a network device in an embodiment of the present application;

3a is a schematic structural diagram of a protocol stack proposed by an embodiment of the application;

FIG. 3b is a schematic structural diagram of another protocol stack proposed by an embodiment of the application;

4 is a schematic diagram of an embodiment of a finite field encoding or decoding method proposed by an embodiment of the present application;

FIG. 5 is a schematic diagram of encoding of a transmitting end in an embodiment of the present application;

FIG. 6 is a schematic diagram of encoding of another transmitting end in an embodiment of the present application;

7 is a schematic diagram of an embodiment of another finite field encoding or decoding method proposed by an embodiment of the present application;

FIG. 8 is a schematic diagram of encoding of a transmitting end in an embodiment of the present application;

Fig. 9 is another coding schematic diagram in the embodiment of the application;

Fig. 10 is another coding schematic diagram in the embodiment of the application;

Fig. 11 is another coding schematic diagram in the embodiment of the application;

12 is a schematic diagram of an embodiment of yet another finite field encoding or decoding method proposed by an embodiment of the present application;

13 is a schematic diagram of recoding in an embodiment of the present application;

14 is a schematic diagram of an embodiment of yet another finite field encoding or decoding method proposed by an embodiment of the present application;

15 is a schematic diagram of an embodiment of a decoding operation in an embodiment of the present application;

16 is a schematic diagram of an embodiment of a decoding operation in an embodiment of the present application;

17 is another schematic diagram of decoding in an embodiment of the present application;

18 is another schematic diagram of decoding in an embodiment of the present application;

19 is another schematic diagram of decoding proposed by an embodiment of the present application;

20a is a schematic diagram of an embodiment of yet another finite field encoding or decoding method proposed by an embodiment of the present application;

FIG. 20b is a schematic diagram of decoding in an embodiment of the present application;

20c is another schematic diagram of decoding in the embodiment of the present application;

21 is a schematic diagram of an equivalent multiplication table of a nested field involved in an embodiment of the application;

FIG. 22 is a schematic diagram of an embodiment of a network device in an embodiment of the present application;

FIG. 23 is a schematic diagram of an embodiment of a network device in an embodiment of the present application;

FIG. 24 is a schematic diagram of an embodiment of a network device in an embodiment of the present application;

FIG. 25 is a schematic diagram of an embodiment of a network device in an embodiment of the present application;

FIG. 26 is a schematic diagram of a processing apparatus according to an embodiment of the present application.

detailed description

The embodiment of the present application provides a method for encoding or decoding a finite field. In a scenario where the computing power of the sending end, the receiving end and the intermediate node is inconsistent, the finite field with a nested structure is used for encoding, which effectively reduces the decoding time. The computational complexity is improved, the decoding speed and data throughput are improved, and the decoding accuracy is guaranteed.

The terms "first", "second", etc. in the description and claims of the present application and the above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the terms used in this way Can be interchanged under appropriate circumstances, this is only the way of distinction adopted when describing the objects of the same property in the embodiments of the present application. In addition, the terms "comprising" and "having" and any of their deformations are intended to be Non-exclusive inclusion is covered so that a process, method, system, product or device comprising a series of units is not necessarily limited to those units, but may include other units not expressly listed or inherent to those processes, methods, products or devices .

The technical solutions in the embodiments of the present application will be clearly described below with reference to the accompanying drawings in the embodiments of the present application. In the description of this application, unless otherwise stated, "/" means or means, for example, A/B can mean A or B; "and/or" in this application is only an association relationship that describes an associated object , which means that there can be three kinds of relationships, for example, A and/or B, which can mean that A exists alone, A and B exist at the same time, and B exists alone. In addition, in the description of the present application, "at least one item" refers to one or more items, and "multiple items" refers to two or more items. "At least one item(s) below" or similar expressions thereof refer to any combination of these items, including any combination of single item(s) or plural items(s). For example, at least one item (a) of a, b, or c can represent: a, b, c, ab, ac, bc, or abc, where a, b, c can be single or multiple .

First, some concepts involved in the embodiments of the present application are introduced:

1. Finite field:

A finite field is a field with a finite number of elements. Finite fields can also be called Galois fields (GF). Like other fields, a finite field is a set of operations that are defined for addition, subtraction, multiplication and division and satisfy certain rules. The number of elements of a finite field is called its order, and the order of a finite field is usually a power of a prime number. The characteristic number of a finite field must be a prime number E, so the prime field it contains is isomorphic to Zp. If F is a finite field with characteristic E, then the number of elements in F is E ^d , and d is a positive integer . Finite fields with the same number of elements are isomorphic. Therefore, GF(E ^d ) is usually used to represent the finite field of Ed ^d elements. The multiplicative group of GF(E ^d ) is a cyclic group of order (E ^d -1). The finite field is a well-known technology by those skilled in the art, and the specific description can refer to the prior art, which will not be described here.

In order to make the objectives, technical solutions and advantages of the embodiments of the present application more clear, the embodiments of the present application will be described in further detail below with reference to the accompanying drawings.

A limited-field encoding or decoding method provided by this application can be applied to various communication systems, for example, the Internet of Things (IoT), the narrowband Internet of Things (NB-IoT) ), long term evolution (LTE), it can also be the fifth generation (5G) communication system, it can also be a hybrid architecture of LTE and 5G, it can also be a 5G new radio (NR) system and future communication development new communication systems, etc. The 5G communication system of the present application may include at least one of a non-standalone (NSA) 5G communication system and an independent (standalone, SA) 5G communication system. The communication system may also be a public land mobile network (PLMN) network, a device-to-device (D2D) network, a machine-to-machine (M2M) network, or other networks.

The embodiments of the present application include a variety of application scenarios. For example, please refer to FIGS. 1a-1b. FIG. 1a is a schematic diagram of an application scenario involved in the embodiments of the present application, and FIG. 1b is another application involved in the embodiments of the present application. Schematic diagram of the scene.

In FIG. 1a, the sender supports multiple finite fields with nested structures. In this embodiment of the present application, the finite fields with nested structures may also be referred to as nested fields. Exemplarily, the nested fields supported by the sender include: GF((2 ² ) ^d0 )... GF((2 ² ) ^d )... GF((2 ² ) ^D ), where 0≤d0≤ d≤D, d0 is an integer greater than or equal to zero, d is an integer greater than or equal to zero, and D is an integer greater than or equal to zero. d0, d, and D satisfy that D is divisible by d, and d is divisible by d0. The sender supports encoding in multiple nested fields. The sender may also be referred to as a new-type sender. Optionally, the sender may flexibly select one or more nested fields between GF((2 ² ) ^d0 )˜GF((2 ² ) ^D ) to encode the source data block.

The intermediate node supports one nested field. Exemplarily, the nested fields supported by the intermediate node include: GF((2 ² ) ^d0 ). The intermediate node supports re-encoding of received messages in 1 nested field. The intermediate node may also be referred to as a new type of intermediate node.

The receiving end decodes the message in the nested field (for example: GF((2 ² ) ^d )) supported by itself. Exemplarily, a high-speed lowest-order finite field elimination operation can be performed first to perform partial decoding to reduce the high-order nested field coefficients, and finally the high-order finite field can be used to decode the remaining part of the nested field to improve the decoding calculation. speed. The receiving end may also be referred to as a new type of receiving node.

Based on the application scenario shown in Figure 1a, please refer to Figure 1b. According to the difference in computing power between the intermediate node and the receiving end, the sender can perform nested domain encoding on the source data block in multiple nested domains to generate encoded messages.

The sender sends the coded message to the intermediate node, where the coded message carries the coding coefficients. Intermediate nodes support a single nested domain. The intermediate node with limited computing power re-encodes the encoded message at GF((2 ² ) ^d0 ). The intermediate node sends the recoded message to the receiver.

After the receiving end receives the recoded message, first, in the low-order nested field (eg GF((2 ² ) ^d0 )) supported by the receiving end, the recoded message is decoded in the nested field. Secondly, the receiving end performs further nested field decoding in a supported high-order nested field (eg, GF((2 ² ) ^d )), and decodes to obtain a source data block.

For example, please refer to FIGS. 1c to 1d . FIG. 1c is a schematic diagram of another application scenario involved in the embodiment of the present application, and FIG. 1d is a schematic diagram of another application scenario involved in the embodiment of the present application.

In order to adapt to the existing traditional sender (device), as shown in Figure 1c, the sender supports a single finite field with a nested structure. Exemplarily, the nested fields supported by the sender include GF((2 ² ) ^D ). The sender supports encoding in a single nested field. The sender may also be referred to as a legacy sender.

In order to realize distributed coding, the intermediate node supports multiple nested fields. Exemplarily, the nested fields supported by the intermediate node include: GF((2 ² ) ^d0 )... GF((2 ² ) ^D ). The intermediate node can flexibly select a nested field and re-encode the received message. Optionally, the intermediate node selects GF((2 ² ) ^d0 ) to re-encode the received message. Optionally, the intermediate node may also flexibly select one or more nested fields from GF((2 ² ) ^d0 ) to GF((2 ² ) ^D ) to re-encode the received message.

The intermediate node may also be referred to as a new type of intermediate node. In addition to being compatible with existing traditional sender devices, the advantages of distributed encoding can also reduce the amount of message transmission between the sender and the intermediate node, and the network between the sender and the intermediate node keeps a low transmission load.

Based on the application scenario shown in Figure 1c, please refer to Figure 1d. In Fig. 1d, the sender supports a single nested field, and the sender can encode the source data block in a single nested field to generate an encoded message. The sender sends the coded message to the intermediate node, where the coded message carries the coding coefficients.

The intermediate node supports multiple nested fields. Depending on the computing power of the receiver, the intermediate node can select one or more nested fields to re-encode the encoded message. The intermediate node sends the recoded message to the receiver.

After receiving the re-encoded message, the receiver firstly decodes the re-encoded message in the low-order nested field supported by the receiver. Secondly, the receiving end performs further nested domain decoding in a supported high-order nested domain (eg, GF((2 ² ) ² )), and decodes to obtain a source data block.

It should be noted that FIGS. 1 a to 1 d are only illustrative, and for the specific implementation, please refer to the subsequent embodiments, which will not be repeated here.

The following is a detailed description of the finite field of the nested structure (also referred to as the nested field) proposed by the embodiments of the present application:

Taking the first finite field as GF(E ^d ), and the second finite field as GF(E ^D ) as an example, E is a prime number, d is a positive integer, and D is a positive integer. When the first finite field and the second finite field are finite fields with a nested structure, then d and D satisfy the following relationship: D=q*d, q is a positive integer greater than 1, d is also called a factor of D, Write d|D. The second finite field is a maximum field. It should be noted that, for the convenience of description, in the embodiments of the present application, the finite field of the nested structure is also referred to as a nested field.

A finite field with a nested structure can also be expressed as: the two or more finite fields satisfy the following relationship: the order has a multiple relationship, and the characteristic numbers are consistent.

It should be noted that the first finite field may include one or more finite fields. In this case, the one or more finite fields included in the first finite field and the second finite field also satisfy the above relationship.

Finite fields with nested structures are the mathematical basis for ensuring that coding and decoding across finite fields is feasible. Finite fields GF(E ^D ) and GF(E ^d ) can not only be regarded as D and d extensions based on finite fields GF(E); GF(E ^D ) can also be regarded as q of GF(E ^d ) The second extension, GF(E ^D ) is called the extension field of GF(E ^d ), or GF(E ^D ) is called the q-time extension field of GF(E ^d ).

For example: when E=2, D=4, d=2, for the finite field GF(2 ⁴ ), not only can it be regarded as the fourth-order extension field of GF(2), but also GF(2 ² ) 2-fold extension field of , written as GF(4 ² ) or GF((2 ² ) ² ) or

More generally, GF(2 ⁸ ) can not only be regarded as the 8th expansion field of GF(2), but also can be regarded as GF(4 ⁴ ), GF(16 ² ), and GF( ((2 ² ) ² ) ² ) or

In order to define the algorithm of the q-order extended field of the finite field GF(E ^d ), it is necessary to select a q-order reduced polynomial based on GF(E ^d ). The following describes the definition method between nested fields.

For example: x ⁴ +x+1 is a polynomial of degree 4 of GF(2). Since GF(2 ⁴ ) can also be regarded as GF(4 ² ), the polynomial x ⁴ +x+1 is on GF(2 ² ). Reducible, it can be written as (x ² +x+α)(x ² +x+α ² ), where α∈GF(2 ² ) satisfies α ² +α+1=0, and α is generated by GF(2 ² ) element, GF(2 ² )={0,1,α,α ² }. Therefore, GF(4 ² ) can be further represented by a polynomial x ² +x+α or x ² +x+α ² based on a 2-order approximation polynomial over GF(4). Choose x ² +x+α to be a polynomial based on the 2nd degree reduction on GF(4), let β be the generator of the extended field GF(4 ² ) and satisfy β ² +β+α=0, substitute α ² +α +1=0 After calculation, β ⁴ +β+1=0 can be obtained. After looking up the table in Table 1, we can get α=β ² +β=β ⁵ (from another point of view, α is the generator of GF(4), there must be α ³ =1; β is the generator of GF(4 ² ), There must be β ¹⁵ =1, and α = β ⁵ ). Specifically, Table 1 shows: the polynomial representation and the power representation of the extended field GF(2 ⁴ ) when the approximation polynomial is x ⁴ +x+1, and the binary coefficient of the polynomial in binary representation, and the sum is Correspondence between the binary coefficients (0～15) of the polynomial after decimal.

Table 1

Then the extended field GF(4 ² ) is

The elements of can be written as aβ+b by definition in the form of Table 2, where a,b∈GF(4)={0,1,α, ^α2 }. It can be seen from the above description that all extended field elements can be obtained without repetition and omission in the form of nested fields. Specifically, Table 2 shows: extended domain

Elements are written in the form of aβ+b, where a,b={0,1,α,α ² }, the correspondence between elements.

Table 2

Finite fields with the form of nested fields not only have nested relations in elements (that is, all elements in GF(E ^d ) are contained in GF(E ^D )), but also have nesting in addition and multiplication operations defined by the field. Set of relations, that is, all binary operations in GF(E ^d ) are also included in GF(E ^D ), in other words: the multiplication table of GF(E ^D ) includes the multiplication table of GF(E ^d ), GF The addition table of (E ^D ) includes the addition table of GF(E ^d ).

Exemplary, as shown in Table 3a and Table 3b; Table 4a and Table 4b. Among them, Table 3a represents the addition operation relationship between elements in GF(2 ² ), Table 3b represents the addition operation relationship between elements in GF((2 ² ) ² ); Table 4a represents the multiplication between elements in GF(2 ² ) Operation relationship, Table 4b shows the multiplication operation relationship between elements in GF((2 ² ) ² ). In other words: Table 3a represents the addition operation relationship between elements in GF(4), Table 3b represents the addition operation relationship between elements in GF(4 ² ); Table 4a represents the multiplication operation relationship between elements in GF(4) , and Table 4b shows the multiplication relationship between elements in GF(4 ² ).

It should be noted that, in the embodiments of the present application, for convenience of description, the multiplication table and the addition table are also referred to as binary operation tables.

GF(2 ²) GF(2 ² )	00	11	α alpha		α ² α ²
00	00	11	α alpha		α ² α ²
11	11	00	α ² α ²	αalpha
α alpha	αalpha		α ² α ²	00	11
α ² α ²	α ² α ²	αalpha	11	00

Table 3a

Table 3b

GF(2 ²) GF(2 ² )	11	α alpha		α ² α ²
00	00	00	00
11	11	αalpha	α ² α ²
αalpha	α alpha		α ² α ²	11
α ² α ²	α ² α ²	11	αalpha

Table 4a

Table 4b

Due to the extended domain element

It can be written in the form of aβ+b, where a,b={0,1,α,α ² }, then the 16*16 binary operation table can be divided into 4*4 blocks according to the different values of a and b, Then the block in the upper left corner (the value of a of both elements is 0) is exactly the addition and multiplication relationship of the 4 elements in GF(2 ² ) shown in Table 3a and Table 4a.

For the convenience of description, the embodiment of the present application distinguishes different finite fields according to the order of the finite field. For example, taking the prime number as 2 as an example, the finite field with the number of elements (order) of 2 ¹ can be called GF(2 ¹ ), the finite field with the number of elements (order) 2 ² can be called GF(2 ² ), the finite field with the number of elements (order) 2 ⁿ can be called GF(2 ⁿ ), and so on. It should be understood that the prime number is only 2 for illustration, and the value of the prime number is not specifically limited.

The communication system applied in the embodiments of this application may include one or more sending ends and one or more receiving ends, and the communication system may further include one or more intermediate nodes. Among them, one sender can transmit data to one or more receivers. Multiple senders can also transmit data for one receiver at the same time. A sender can also transmit data for multiple receivers at the same time. The sender can transmit data through one or an intermediate node when transmitting data to the receiver. The embodiments of the present application do not specifically limit the number of sending ends, intermediate nodes, and receiving ends in the communication system and the connection relationship. Exemplarily, the sending end may be a network device, a terminal device, or another device that sends data, or an encoder. The receiving end may be a network device, or a terminal device, or other devices that receive data, or may also be a decoder. The intermediate node may be a network device, for example, a transmission device such as a routing node, a forwarding node, and a relay node, or an encoder, or a terminal device.

The terminal equipment involved in the embodiments of this application is an entity on the user side that is used to receive or transmit signals. The terminal device may be a device that provides voice and data connectivity to the user, for example, a handheld device with a wireless connection function, a vehicle-mounted device, and the like. The terminal device may also be other processing device connected to the wireless modem. Terminal devices can communicate with one or more core networks through a radio access network (RAN). Terminal equipment may also be referred to as wireless terminal, subscriber unit, subscriber station, mobile station, mobile station, remote station, access point , remote terminal, access terminal, user terminal, user agent, user device, or user equipment, etc. Terminal devices may be mobile terminals, such as mobile phones (or "cellular" phones) and computers with mobile terminals, for example, may be portable, pocket-sized, hand-held, computer-built, or vehicle-mounted mobile devices, which are associated with wireless The access network exchanges language and data. For example, the terminal device may also be a personal communication service (PCS) phone, a cordless phone, a session initiation protocol (SIP) phone, a wireless local loop (WLL) station, a personal digital assistant (personal digital assistant, PDA), and other equipment. Common terminal devices include, for example: mobile phones, tablet computers, notebook computers, PDAs, mobile internet devices (MIDs), wearable devices, such as smart watches, smart bracelets, pedometers, etc. The example is not limited to this. The terminal device involved in the embodiment of the present application may also be a terminal device appearing in a public land mobile network (public land mobile network, PLMN) evolved in the future, which is not limited in the embodiment of the present application.

In addition, in the embodiments of the present application, the terminal device may also be a terminal device in an Internet of Things (Internet of Things, IoT) system. IoT is an important part of the future development of information technology, and its main technical feature is that items are passed through communication technology. Connect with the network, so as to realize the intelligent network of human-machine interconnection and interconnection of things. In the embodiments of the present application, the IoT technology can achieve massive connections, deep coverage, and power saving of terminals through, for example, a narrow band (narrow band, NB) technology.

In addition, in the embodiment of the present application, the terminal device may also include sensors such as smart printers, train detectors, and gas stations, and the main functions include collecting data (part of terminal devices), receiving control information and downlink data of network devices, and sending electromagnetic waves. , to transmit uplink data to the network device.

The network device involved in the embodiments of this application is an entity on the network side that is used to transmit or receive signals. The network device in this embodiment of the present application may be a device in a wireless network, for example, a RAN node that accesses a terminal to the wireless network. For example, the network device may be an evolved base station (evolutional Node B, eNB or e-NodeB) in LTE, or a new radio controller (NR controller), or a gNode B (gNB) in the 5G system. ), it can be a centralized unit (CU), a new wireless base station, a remote radio module, a micro base station, a relay, or a distributed unit , DU), can be a home base station, can be a transmission reception point (transmission reception point, TRP) or a transmission point (transmission point, TP) or any other wireless access device, but the embodiment of the present application is not limited to this. A network device can cover one or more cells.

The network architecture and service scenarios described in the embodiments of the present application are for the purpose of illustrating the technical solutions of the embodiments of the present application more clearly, and do not constitute a limitation on the technical solutions provided by the embodiments of the present application. The evolution of the architecture and the emergence of new business scenarios, the technical solutions provided in the embodiments of the present application are also applicable to similar technical problems.

Network coding is mainly used in multicast networks, and coding is performed at intermediate nodes to improve the information transmission rate. ^In network coding, the sender, receiver, and intermediate nodes must be consistent in the same finite field (GF) for encoding and decoding. All intermediate nodes participating in network coding are required to re-encode in a finite field of order ²⁸ , and all receivers must decode in a finite field of order ²⁸ ; therefore, all networks participating in network coding The node device needs to support coding and decoding parameters that are configured for each stream or each application to be consistent with the sender and the receiver.

However, the sender, the receiver, and the intermediate node must be consistent in the same finite field to encode and decode, but the intermediate node usually has limited coding computing power, which becomes the bottleneck of data throughput.

Second, the computing capabilities of the terminals are far from each other, which may result in the inability to carry out multicast or unicast applications. For example, low-power IoT devices, TVs and other household devices with limited computing power can only use a finite field with a smaller order, such as a finite field with an order of 2 ¹ , for encoding and decoding to reduce overhead and computing costs; Devices with high computing power, such as servers, computers or smart phones, can handle the encoding and decoding of finite fields above GF(2 ⁸ ). Therefore, when considering multicast applications, if the sender chooses to encode in the finite field of GF(2 ⁸ ), for example, all receivers are required to decode in the finite field of GF(2 ⁸ ). The computing power of receiving devices such as smart phones can meet the decoding requirements and decoding is smooth, but devices such as TVs under the same multicast tree cannot decode due to insufficient computing power, resulting in the failure of multicast applications. When considering unicast applications, intermediate nodes often choose to perform encoding and decoding in a low-order finite field, such as in GF(2 ¹ ), in order to eliminate the data throughput bottleneck caused by limited coding computing power, while the sender and receiver It is also necessary to perform coding and decoding in the same finite field (ie, GF(2 ¹ )), but due to the poor performance of coding and decoding in GF(2 ¹ ), the communication between the sender and the receiver cannot meet the service quality of the upper-layer application. (quality of service, QoS) requirements.

In addition, the embodiments of the present application may also be applicable to other future-oriented communication technologies, such as 6G and the like. The network architecture and service scenarios described in this application are for the purpose of illustrating the technical solutions of this application more clearly, and do not constitute a limitation on the technical solutions provided by this application. appears, the technical solutions provided in this application are also applicable to similar technical problems.

FIG. 2 is a schematic diagram of a hardware structure of a network device in an embodiment of the present application. The network device may be a possible implementation manner of the sending end, the receiving end or the intermediate node in the embodiment of the present application. As shown in FIG. 2 , the network device includes at least a processor 204 , a memory 203 , and a transceiver 202 , and the memory 203 is further configured to store instructions 2031 and data 2032 . Optionally, the network device may further include an antenna 206 , an I/O (input/output, Input/Output) interface 210 and a bus 212 . The transceiver 202 further includes a transmitter 2021 and a receiver 2022. In addition, the processor 204 , the transceiver 202 , the memory 203 and the I/O interface 210 are communicatively connected to each other through the bus 212 , and the antenna 206 is connected to the transceiver 202 .

The processor 204 can be a general-purpose processor, such as, but not limited to, a central processing unit (Central Processing Unit, CPU), or can be a special-purpose processor, such as, but not limited to, a digital signal processor (Digital Signal Processor, DSP), application Application Specific Integrated Circuit (ASIC) and Field Programmable Gate Array (FPGA), etc. Furthermore, the processor 204 may also be a combination of multiple processors. In particular, in the technical solutions provided in the embodiments of the present application, the processor 204 may be configured to execute the relevant steps of the communication method in the subsequent method embodiments. The processor 204 may be a processor specially designed to perform the above steps and/or operations, or may be a processor that performs the above steps and/or operations by reading and executing the instructions 2031 stored in the memory 203, the processor 204 Data 2032 may be required in performing the steps and/or operations described above.

The transceiver 202 includes a transmitter 2021 and a receiver 2022 . In an optional implementation manner, the transmitter 2021 is used to transmit signals through the antenna 206 . The receiver 2022 is used to receive signals through at least one of the antennas 206 . In particular, in the technical solutions provided in the embodiments of the present application, the transmitter 2021 may be specifically configured to be executed by at least one antenna among the antennas 206. For example, the communication method in the When it is an intermediate node, the operation performed by the transceiver module or the sending module in the sender, receiver, or intermediate node.

In this embodiment of the present application, the transceiver 202 is configured to support the network device to perform the aforementioned receiving function and sending function. A processor with processing capabilities is considered processor 204 . The receiver 2022 may also be referred to as a receiver, an input port, a receiving circuit, and the like, and the transmitter 2021 may be referred to as a transmitter, a transmitter, or a transmitting circuit, and the like.

The processor 204 may be configured to execute the instructions stored in the memory 203 to control the packet (or message) received by the transceiver 202 and/or send the message, so as to complete the function of the network device in the method embodiment of the present application. As an implementation manner, the function of the transceiver 202 may be implemented by a transceiver circuit or a dedicated chip for transceiver. In this embodiment of the present application, a packet (or message) received by the transceiver 202 may be understood as an input packet (or message) by the transceiver 202, and a packet (or message) sent by the transceiver 202 may be understood as an output packet by the transceiver 202 (or message).

The memory 203 may be various types of storage media, such as random access memory (Random Access Memory, RAM), read only memory (Read Only Memory, ROM), non-volatile RAM (Non-Volatile RAM, NVRAM), and Programmable ROM (Programmable ROM, PROM), Erasable PROM (Erasable PROM, EPROM), Electrically Erasable PROM (Electrically Erasable PROM, EEPROM), Flash memory, optical memory and registers, etc. The memory 203 is specifically used to store the instructions 2031 and the data 2032, and the processor 204 can perform the steps and/or operations in the method embodiments of the present application by reading and executing the instructions 2031 stored in the memory 203. Data 2032 may be required during the operations and/or steps in the example.

Optionally, the network device may further include an I/O interface 210, and the I/O interface 210 is used for receiving instructions and/or data from peripheral devices, and outputting instructions and/or data to peripheral devices.

The method part of the embodiment of the present application is described below. First, a protocol stack proposed by an embodiment of the present application is introduced. The coding coefficients of the nested fields proposed in the embodiments of the present application may be carried in different layers of the protocol stack in the transmitting end, the intermediate node or the receiving end.

In an optional implementation manner, please refer to FIG. 3a, which is a schematic structural diagram of a protocol stack proposed by an embodiment of the present application. In the applicable system architecture of Figure 3a, the sender supports encoding of higher-order finite fields (high-order nested fields) and lower-order finite fields (low-order nested fields), and intermediate nodes support lower-order encodings Re-encoding of the finite field (low-order nesting field) of , the receiving end supports the decoding of the finite field with higher order (high-order nesting field) and the finite field with lower order (low-order nesting field). The order of a finite field with a higher order (higher-order nested field) is higher than the order of a finite field with a lower order (a lower-order nested field).

In the sender, the coding coefficients of the finite field with higher order are carried in the transport layer, and the sender uses the coding coefficients of the finite field with higher order to encode the data of the transport layer; The coding coefficients of the finite field are carried in the network layer (and/or the data link layer), and the sender uses the coding coefficients of the finite field of lower order to layer) data is encoded. Exemplarily, the network layer includes an Internet protocol (Internet protocol) layer, and the transport layer includes a Transmission Control Protocol (Transmission Control Protocol, TCP) layer.

Intermediate nodes (eg, intermediate node 1 . . . intermediate node n in the figure) re-encode the data of the network layer (and/or the data link layer) using coding coefficients of a finite field with a lower order. The lower-order finite field coding coefficients used by the intermediate nodes are carried in the network layer (and/or the data link layer). Optionally, some or all of the intermediate nodes in the intermediate nodes may re-encode the message from the sender by using the coding coefficients of the finite field with a lower order; or not re-encode the message from the sender, but It is to directly forward the message from the sender to the next-hop intermediate node or the receiver.

The receiving end uses the coding coefficients of the finite field of higher order to decode the data of the transmission layer; the receiving end uses the coding coefficients of the finite field of the lower order to decode the data of the network layer (and/or the data link layer). decoding.

In this embodiment, the above-mentioned protocol stack structure ensures that the TCP reliability from the sender to the receiver is not damaged.

In another optional implementation manner, please refer to FIG. 3b, which is a schematic structural diagram of another protocol stack proposed by an embodiment of the present application. In the applicable system architecture of Figure 3b, the sender supports encoding of a finite field with a higher order (high-order nested field), and the intermediate node supports recoding of a finite field with a lower order (low-order nested field). The terminal supports the decoding of finite fields with higher order (high-order nested fields) and finite fields with lower orders (lower-order nested fields).

In the transmitting end, the coding coefficients of the finite field with higher order are carried in the transport layer, and the transmitting end uses the coding coefficients of the finite field with higher order to encode the data of the transport layer. Exemplarily, the transport layer includes a Transmission Control Protocol (Transmission Control Protocol, TCP) layer.

Intermediate nodes (eg, intermediate node 1 . . . intermediate node n in the figure) re-encode the data of the network layer (and/or the data link layer) using coding coefficients of a finite field with a lower order. The lower-order finite field coding coefficients used by the intermediate nodes are carried in the network layer (and/or the data link layer). Exemplarily, the network layer includes an Internet protocol (Internet protocol) layer. Optionally, some or all of the intermediate nodes in the intermediate nodes may re-encode the message from the sender by using the coding coefficients of the finite field with a lower order; or not re-encode the message from the sender, but It is to directly forward the message from the sender to the next-hop intermediate node or the receiver.

In this embodiment, distributed coding is used on the basis of compatibility with existing network devices (transmitters). The packet transmission volume between the sender and the intermediate node is reduced, and the network transmission load between the sender and the intermediate node is reduced.

Secondly, a method for encoding or decoding a finite field proposed by an embodiment of the present application can be applied to the foregoing Figs. 1a-1d. In this communication system, there may be an intermediate node between the sender and the receiver to re-encode the message sent by the sender, or there may be no intermediate node between the sender and the receiver; There are intermediate nodes between, but the intermediate nodes do not perform recoding, which is not specifically limited in this application. The methods on the sending end side, the intermediate node side, and the receiving end side are respectively described below.

Please refer to FIG. 4 , which is a schematic diagram of an embodiment of a finite field encoding method proposed by an embodiment of the present application. The finite field encoding method is applied to the sender, including:

401. The transmitting end uses the first encoding coefficient matrix to perform encoding processing on the k source data blocks to generate one or more first encoded data blocks.

In this embodiment, the transmitting end uses the first encoding coefficient matrix to perform encoding processing on k source data blocks in a group (Generation) to obtain k first encoded data blocks. The first coding coefficient matrix includes coding coefficients of the first finite field and coding coefficients of the second finite field, and k is a positive integer. The first finite field and the second finite field are finite fields with nested structure, and the order of the second finite field is higher than that of the first finite field, and the finite field with nested structure satisfies the following relationship: the order has a multiple relationship , and the number of features is the same.

Specifically, the first finite field and the second finite field are finite fields with nested structures, wherein the first finite field is GF(E ^d ), and the second finite field is GF(E ^D ), wherein, E is a prime number, d is a positive integer, D is a positive integer, D=q*d, and q is a positive integer greater than 1.

It should be noted that, the coding coefficient matrix (such as the first coding coefficient matrix, the second coding coefficient matrix, etc.) involved in the embodiments of the present application may include multiple sets of coding coefficients, wherein an element of a row of the coding coefficient matrix is a set of coding coefficients , or, a column of elements of the coding coefficient matrix is a set of coding coefficients. When multiplying multiple data blocks with a coding coefficient matrix, you can multiply multiple data blocks with each set of coding coefficients. For example, if one row of the coding coefficient matrix is a set of coding coefficients, the k source data blocks are When performing encoding processing with the first encoding coefficient matrix, each row element of the first encoding coefficient matrix may be multiplied by k source data blocks respectively. If one column of the coding coefficient matrix is a set of coding coefficients, when the k source data blocks are encoded with the first coding coefficient matrix, each column element of the first coding coefficient matrix can be multiplied by the k source data blocks respectively . For the convenience of description, the following description is given by taking an example that one row of the coding coefficient matrix is a set of coding coefficients. It should be understood that when the elements of a column of the coding coefficient matrix are a set of coding coefficients, the logic of the sender encoding the source data block is similar to the logic of the sender coding the source data block when the elements of a row of the coding coefficient matrix are a set of coding coefficients. .

Specifically, as shown in FIG. 5 , FIG. 5 is a schematic diagram of encoding at a transmitting end in an embodiment of the present application. It is assumed that a group contains k source data blocks, that is, p _j ={p ₁ -p _k }, where j is a positive integer, and 1≤j≤k. The transmitting end generates one or more first encoded data blocks c _n ={c 1˜c _n } according to p ₁ _to p _k , where n is a positive integer. Wherein, c ₁ is a first encoded data block obtained by encoding p ₁ to p _k in the finite fields of GF(E ^d ) and GF(E ^D ), that is, the sender uses GF(E ^d ) and GF(E ^D ) ) The coding coefficients α _1,1 ...α _1,k in the finite field encode p ₁ to p _k to obtain c ₁ , where c ₁ can satisfy the following formula:

Exemplarily, as shown in FIG. 6 , FIG. 6 is a schematic diagram of encoding of another transmitting end in an embodiment of the present application. Suppose a group contains k source data blocks p _j , where j = 1,2,...,k. This set of data is represented by a matrix P, written as: P=[p ₁ p ₂ …p _k ] ^T . Define a first encoding coefficient matrix of dimension (k+n)*k: G=[I _k A ₁ . . . A _D ] ^T . Among them, the matrix I _k is a k*k unit matrix, and the unit matrix is a matrix in which the diagonal element is 1, and the other elements are 0. The matrix Ad is an r _d ×k matrix based on the coding coefficients of the first finite field GF(E _d ) and the coding coefficients of the second finite field GF(E _D ₎ , 1≤d≤D, let

By left-multiplying P by G, the sender encodes to obtain a plurality of first encoded data blocks, which are written as c ₁ . . . c _n .

In another optional implementation manner, the first coding coefficient matrix may not include the matrix I _k , that is, the first coding coefficient matrix only includes the matrix A _d . Specifically, the first four rows of coding coefficients in the first coding coefficient matrix shown in FIG. 6 may not be multiplied by p ₁ . . . p ₄ , but carry corresponding coding coefficients when sending p ₁ to p _4. For example, When p ₁ is sent, the coded coefficients of the first row in the first coding coefficient matrix are carried, and when p ₂ is sent, the coded coefficients of the second row of the first coding coefficient matrix are carried, and so on.

As shown in FIG. 6, for example, k=4, n=4, the first coding coefficient matrix includes:

A ₁ ^T =[α _1,1 α _1,2 α _1,3 α _1,4 ];

A ₂ ^T =[α _2,1 α _2,2 α _2,3 α _2,4 ];

A ₃ ^T =[α _3,1 α _3,2 α _3,3 α _3,4 ];

A ₄ ^T =[α _4,1 α _4,2 α _4,3 α _4,4 ].

Let 1≤d≤D, where d is a positive integer. The specific code is as follows:

The 5th row of the first coding coefficient matrix

A set of coding coefficients {α _1,1 . . . α _1,4 } in the finite field, the coding coefficients of the fifth row in the first coding coefficient matrix are multiplied by p ₁ to p ₄ to obtain c ₁ . Therefore, a set of coding coefficients corresponding to c ₁ is {α _1,1 ···α _1,4 }.

The sixth row of the first coding coefficient matrix

A set of coding coefficients {α _2,1 . . . α _2,4 } in the finite field, the coding coefficients of the sixth row in the first coding coefficient matrix are multiplied by p ₁ to p ₄ to obtain c ₂ . Therefore, a set of coding coefficients corresponding to c ₂ is {α _2,1 ···α _2,4 }.

The 7th row of the first coding coefficient matrix

A set of coding coefficients {α _3,1 . . . α _3,4 } in the finite field, the coding coefficients in the seventh row in the first coding coefficient matrix are multiplied by p ₁ to p ₄ to obtain c ₃ . Therefore, a set of coding coefficients corresponding to c ₃ is {α _3,1 ···α _3,4 }.

The 8th row of the first coding coefficient matrix

_A set of coding _coefficients _{ α _4,1 _. Therefore, a set of coding coefficients corresponding to c ₄ is {α _4,1 ···α _4,4 }.

In another optional implementation manner, distributed coding may be used. Specifically, the sending end uses coding coefficients of the first finite field to perform coding processing on k source data blocks to generate one or more coded data blocks. The sending end sends an encoded message carrying the encoded data block to the intermediate node, and the intermediate node performs encoding processing on the encoded message using the encoding coefficients of the second finite field.

Alternatively, the transmitting end uses the coding coefficients of the second finite field to perform coding processing on the k source data blocks to generate one or more coded data blocks. The sending end sends an encoded message carrying the encoded data block to the intermediate node, and the intermediate node performs encoding processing on the encoded message using the encoding coefficients of the first finite field.

402. The sending end generates one or more first encoded packets.

In this embodiment, the transmitting end generates one or more first encoded packets according to the k first encoded data blocks and the first encoded coefficient matrix. The first coded message includes one or more first coded data blocks and a set of coding coefficients in the first coding coefficient matrix corresponding to the one or more first coded data blocks.

In an optional implementation manner, the first encoded message further includes one or more source data blocks, the source data blocks correspond to a set of encoding coefficients in the unit matrix, and the size of the unit matrix is the same as that of the first encoding coefficient matrix .

Exemplarily, as shown in FIG. 6 , the first encoded message sent by the sender includes p ₁ to p ₄ and c ₁ to c ₄ , and when sending p ₁ , it carries the encoding coefficient of the first row in the first encoding coefficient matrix. {1000}, when sending p ₂ , carry the coding coefficient {0100} in the second row of the first coding coefficient matrix, when sending p ₃ , carry the coding coefficient {0010} in the third row in the first coding coefficient matrix, when sending p ₄ When sending c ₁ , it carries the coding coefficient {α _1,1 ... α _1,4 } of the fifth row in the first coding coefficient matrix, and when sending c ₂ When sending c 3, it carries the coding coefficients of the sixth row in the first coding coefficient matrix {α _2,1 ... α _2,4 }, and when sending c ₃ , it carries the coding coefficients of the seventh row of the first coding coefficient matrix {α _3,1 ... α _{3 ,4} }, when sending c ₄ , the encoding coefficients {α _4,1 ···α _4,4 } of the 8th row in the first encoding coefficient matrix are carried.

Optionally, one or more first encoded packets further include a finite field order, the finite field order corresponds to the first encoded data block, and/or the source data block, and the finite field order is the first encoded data block. The order of the finite field where a group of coding coefficients in the corresponding first coding coefficient matrix is located, and/or the order of the finite field where the coding coefficients of the source data block are located. The finite field order can be carried after the first coded data block (as shown in FIG. 6 ), and the finite field order can also be carried before the first coded data block (“header” shown in FIG. 6 ). This There are no restrictions.

Exemplarily, the coding coefficients of the finite field with lower order (for example, d is less than or equal to 2) are carried in the Internet Protocol (Internet Protocol, IP) packet header or Ethernet (Ethernet) frame header, for example, by setting the sixth Internet Protocol version 6 (IPv6) extension header, IP or ETH extension field implementation; the coding coefficients of the finite field with higher order (for example, d is greater than 2) are carried in the TCP packet header, for example, by setting the TCP option to carry.

In an optional implementation manner, the source data block is carried in one or more first coding coefficient packets generated by the sender. The data blocks carried by the one or more first coding coefficient packets may be represented as: {p ₁ ···p _k }∪{c ₁ ···c _n }. The first coding coefficient message may also be referred to as a system code message.

In another optional implementation manner, the source data block is not carried in one or more first coding coefficient packets generated by the sending end. The data blocks carried by the one or more first coding coefficient packets may be represented as: {c ₁ . . . c _n }. The first coding coefficient message may also be referred to as a non-systematic code message.

403. The sending end sends one or more first encoded packets.

The above-mentioned finite field encoding method can also be used as a decoding method in reverse, that is, the encoding end and the decoding end are implemented by opposite ends.

The sender encodes the source data block, and there are many different implementations. Please refer to FIG. 7 , which is a schematic diagram of an embodiment of yet another finite field encoding method proposed by an embodiment of the present application. The finite field encoding method is applied to the sender, including:

701. The transmitting end uses the second encoding coefficient matrix to perform encoding processing on the k source data blocks to generate one or more second encoded data blocks.

In this embodiment, the transmitting end uses the second encoding coefficient matrix to perform encoding processing on k source data blocks in a group (Generation) to obtain k second encoded data blocks. The second encoded data block and the second encoding coefficient matrix A set of coding coefficients corresponding to , wherein the second coding coefficient matrix includes at least coding coefficients of the third finite field, and k is a positive integer. The third finite field is GF(E ^D1 ), E is a prime number, and D1 is a positive integer.

Specifically, as shown in FIG. 8 , FIG. 8 is a schematic diagram of encoding at a transmitting end in an embodiment of the present application. It is assumed that a group contains k source data blocks, that is, p _j ={p ₁ -p _k }, where j is a positive integer, and 1≤j≤k. The transmitting end generates one or more second encoded data blocks c' _n ={c' _1˜c ' _n } according to the second encoding matrix G and the source data P{p ₁ ˜p _k }, where n is a positive integer. Among them, c' ₁ is a second encoded data block obtained by encoding p ₁ to p _k in the finite field of GF(E ^D1 ), that is, the transmitting end adopts the encoding coefficients α′ ₁₁ . . . in the finite field of GF(E ^D1 ). α′ _1k encodes p ₁ to p _k to obtain c′ ₁ , where c′ ₁ can satisfy the following formula:

Let 1≤d1≤D1, and d1 is a positive integer. The specific code is as follows:

The 5th row of the second coding coefficient matrix

A set of coding coefficients {α' _1,1 ... α' _1,4 } in the finite field, and the coding coefficients in the 5th row in the second coding coefficient matrix are multiplied by p ₁ -p ₄ to obtain c' ₁ . Therefore, a set of coding coefficients corresponding to c′ ₁ is α′ _1,1 ···α′ _1,4 .

The 6th row of the second coding coefficient matrix

A set of coding coefficients {α' _2,1 ... α' _2,4 } in the finite field, the coding coefficients in the sixth row in the second coding coefficient matrix are multiplied by p ₁ -p ₄ to obtain c' ₂ . Therefore, a set of coding coefficients corresponding to c′ ₂ is {α′ _2,1 …α′ _2,4 }.

The 7th row of the second coding coefficient matrix

A set of coding coefficients {α' _3,1 ... α' _3,4 } in the finite field, the coding coefficients in the 7th row in the second coding coefficient matrix are multiplied by p ₁ -p ₄ to obtain c' ₃ . Therefore, a set of coding coefficients corresponding to c′ ₃ is {α′ _3,1 …α′ _3,4 }.

The 8th row of the second coding coefficient matrix

A set of coding coefficients {α' _4,1 ... α' _4,4 } in the finite field, the coding coefficients in the 8th row in the second coding coefficient matrix are multiplied by p ₁ -p ₄ to obtain c' ₄ . Therefore, a set of coding coefficients corresponding to c′ ₄ is {α′ _4,1 …α′ _4,4 }.

In another optional implementation manner, the second coding coefficient matrix further includes: coding coefficients of a fifth finite field, where the fifth finite field and the third finite field have a nested structure, wherein the fifth finite field and the third finite field have a nested structure. The three finite fields satisfy the following relationship: the order has a multiple relationship, and the characteristic numbers are consistent.

702. Use the third encoding coefficient matrix to perform encoding processing on one or more second encoded data blocks and k source data blocks to generate one or more third encoded data blocks.

In this embodiment, the transmitting end uses the third encoding coefficient matrix to perform encoding processing on k second encoded data blocks and k source data blocks to generate g third encoded data blocks, the third encoded data block and the third encoded coefficients A set of coding coefficients in the matrix corresponds, and g is a positive integer.

Please refer to FIG. 9. FIG. 9 is a schematic diagram of another encoding according to an embodiment of the present application. After the transmitting end generates one or more second encoded data blocks {c′ ₁ ～c′ _n }, the third encoding coefficient matrix G” is used to generate one or more second encoded data blocks {c′ ₁ ～c′ _n } and k source data blocks {p ₁ to p _k } are encoded to generate one or more third encoded data blocks {b ₁ to b _m }, where m is a positive integer.

Wherein, the third coding coefficient matrix includes at least coding coefficients of the fourth finite field. The third finite field, and the fourth finite field, are finite fields with a nested structure, wherein the third finite field is GF(E ^D1 ), the fourth finite field is GF(E ^d1 ), E is a prime number, d1 is a positive integer, D1 is a positive integer, D1=z*d1, and z is a positive integer greater than 1.

The third encoded data block is b _m , where,

In an optional implementation manner, for example, please refer to FIG. 10 , which is another schematic diagram of encoding in an embodiment of the present application. {p ₁ …p _k }∪{c′ ₁ …c′ _n }∪{b ₁ …b _m }, is composed of k source data blocks and n second encoded data blocks {p ₁ …p _k }∪{ c′ ₁ ... c′ _n }, obtained by left-multiplying the second encoding coefficient matrix and the source data block through the third encoding coefficient matrix of (k+n+m)*(k+n) dimension. The encoding method shown in FIG. 10 is also referred to as a systematic code encoding method. The size of the identity matrix in the third encoding coefficient matrix is determined by the number (n) of the second encoded data blocks and the number (k) of the source data blocks. The coding coefficients of the source data block are corresponding elements in the unit matrix, and the coding coefficients of the source data block belong to the fourth finite field.

Taking k=4, n=4, m=1 as an example, the third coding coefficient matrix is a 9*8 matrix, wherein the diagonal elements of the 1st to 8th rows are 1, and the elements other than the diagonal elements are 1. 8*8 matrix whose other elements are 0.

The coding coefficients of the first row in the third coding coefficient matrix are multiplied by p ₁ to p ₄ and c' ₁ to c' ₄ to obtain p ₁ .

The coding coefficients of the second row in the third coding coefficient matrix are multiplied by p ₁ -p ₄ and c' ₁ -c' ₄ to obtain p ₂ .

The coding coefficients of the third row in the third coding coefficient matrix are multiplied by p ₁ to p ₄ and c' ₁ to c' ₄ to obtain p ₃ .

The coding coefficients of the fourth row in the third coding coefficient matrix are multiplied by p ₁ to p ₄ and c' ₁ to c' ₄ to obtain p ₄ .

In the third coding coefficient matrix, the coding coefficients in the fifth row are multiplied by p ₁ -p ₄ and c' ₁ -c' ₄ to obtain c' ₁ .

The coding coefficients of the sixth row in the third coding coefficient matrix are multiplied by p ₁ -p ₄ and c' ₁ -c' ₄ to obtain c' ₂ .

In the third coding coefficient matrix, the coding coefficients in the seventh row are multiplied by p ₁ -p ₄ and c' ₁ -c' ₄ to obtain c' ₃ .

In the third coding coefficient matrix, the coding coefficients in the 8th row are multiplied by p ₁ -p ₄ and c' ₁ -c' ₄ to obtain c' ₄ .

It should be noted that, the coding coefficients of the first 8 rows in the third coding coefficient matrix shown in FIG. 10 may not be multiplied by p ₁ ˜p ₄ and c′ ₁ ˜c’ ₄ , but are sent when p ₁ ˜p ₄ and c' ₁ to c' ₄ carry the corresponding coding coefficients, for example, when sending p ₁ , carry the coding coefficient of the first row in the third coding coefficient matrix, and when sending p ₂ , carry the second coding coefficient in the third coding coefficient matrix Row coding coefficients, etc.

The ninth row of the third coding coefficient matrix is a set of coding coefficients {β _m,1 . . . β _m,4 } for the finite field of GF(2 ¹ ). In the third coding coefficient matrix, the coding coefficients of the ninth row are multiplied by p ₁ to p ₄ and c' ₁ to c' ₄ to obtain b ₁ . Therefore, a set of coding coefficients corresponding to b ₁ is {β _m,1 ···β _m,8 }.

In another optional implementation manner, for example, please refer to FIG. 11 , which is another schematic diagram of encoding in this embodiment of the present application. The difference between the encoding method shown in FIG. 11 and the encoding method shown in FIG. 10 is that the third encoding coefficient matrix does not include a unit matrix, and the unit matrix refers to a matrix whose diagonal element is 1 and other elements are 0. Specifically, taking k=4, n=4, m=8, and the fourth finite field is GF(2 ¹ ) as an example, the details are as follows:

The coding coefficients of the first row in the third coding coefficient matrix are a set of coding coefficients {β _1,1 . . . β _1,8 } in the finite field of GF(2 ¹ ). _In the third coding coefficient matrix, the _coding _coefficients _{ _β _1,1 _. Therefore, a set of coding coefficients corresponding to b ₁ is {β _1,1 ... β _1,8 }.

The coding coefficients of the second row in the third coding coefficient matrix are a set of coding coefficients {β _2,1 . . . β _2,8 } of the finite field of GF(2 ¹ ). _In the third coding coefficient matrix, the _coding _coefficients _{ _β _2,1 _. Therefore, a set of coding coefficients corresponding to b ₂ is {β _2,1 . . . β _2,8 }.

The coding coefficients of the third row in the third coding coefficient matrix are a set of coding coefficients {β _3,1 . . . β _3,8 } of the finite field of GF(2 ¹ ). _In the _third coding coefficient matrix, the coding _coefficients _{ _β _3,1 _. Therefore, a set of coding coefficients corresponding to b ₃ is {β _3,1 ... β _3,8 }.

The coding coefficients of the fourth row in the third coding coefficient matrix are a set of coding coefficients {β _4,1 . . . β _4,8 } of the finite field of GF(2 ¹ ). _In the third coding coefficient matrix, the _coding _coefficients _{ _β _4,1 _. Therefore, a set of coding coefficients corresponding to b ₄ is {β _4,1 ... β _4,8 }.

The coding coefficients of the fifth row in the third coding coefficient matrix are a set of coding coefficients {β _5,1 . . . β _5,8 } of the finite field of GF(2 ¹ ). _In the third coding coefficient matrix, the _coding _coefficients _{ _β _5,1 _. Therefore, a set of coding coefficients corresponding to b ₅ is {β _5,1 ···β _5,8 }.

The coding coefficients of the sixth row in the third coding coefficient matrix are a set of coding coefficients {β _6,1 . . . β _6,8 } of the finite field of GF(2 ¹ ). _In the third coding coefficient matrix, the _coding _coefficients _{ _β _6,1 _. Therefore, a set of coding coefficients corresponding to b ₆ is {β _6,1 ... β _6,8 }.

In the third coding coefficient matrix, the coding coefficients of the seventh row are a set of coding coefficients {β _7,1 . . . β _7,8 } of the finite field of GF(2 ¹ ). _In the third coding coefficient matrix, the _coding _coefficients _{ _β _7,1 _. Therefore, a set of coding coefficients corresponding to b ₇ is {β _7,1 ... β _7,8 }.

In the third coding coefficient matrix, the coding coefficients of the 8th row are a set of coding coefficients {β _8,1 . . . β _8,8 } of the finite field of GF(2 ¹ ). _In the third coding coefficient matrix, the _coding _coefficients _{ _β _8,1 _. Therefore, a set of coding coefficients corresponding to b ₈ is {β _8,1 ... β _8,8 }.

703. The sending end generates one or more second encoded packets.

In this embodiment, the sending end generates one or more second encoded packets according to the k second encoded data blocks and the g third encoded data blocks, and a second encoded packet includes: one or more third encoded data blocks The coding coefficients of the data block and one or more third coded data blocks, the second coded message includes one or more third coded data blocks, and coding coefficients corresponding to the third coding coefficient matrix.

The one or more second encoded messages further include a finite field order, and the finite field order includes the finite field order where the encoding coefficients of the second encoded data block are located, the finite field order where the encoding coefficients of the third encoded data block are located, and /or, the order of the finite field where the coding coefficients of the source data block are located.

Optionally, the one or more second encoded packets further include a finite field order, the finite field order, and the finite field order includes the finite field order where the encoding coefficients of the second encoded data block are located, and the order of the third encoded data block. The order of the finite field where the coding coefficients are located, and/or the order of the finite field where the coding coefficients of the source data block are located. The finite field order may be carried after the second encoded data block/third encoded data block, and the finite field order may also be carried before the second encoded data block/third encoded data block, which is not limited here.

Exemplarily, if the finite field is GF(E ² ), the order of the finite field may be 2. The finite field order is used to indicate the order of the finite field corresponding to the second encoded data block/third encoded data block.

Exemplarily, the coding coefficients of the finite field with a lower order are carried in an Internet Protocol (Internet Protocol, IP) packet header or an Ethernet (Ethernet) frame header, for example, by setting an Internet Protocol version 6 (Internet Protocol version 6) , IPv6) extension header, IP or ETH extension field implementation; the coding coefficient of the finite field with higher order is carried in the TCP packet header, for example, it can be carried by setting the TCP option.

Exemplarily, taking FIG. 10 as an example, in this implementation manner, the second encoded packet sent by the sender includes p ₁ ˜p ₄ , c′ ₁ ˜c′ ₄ , and b ₁ , and is carried when sending p ₁ The set of coding coefficients is the coding coefficient {10000000} of the first row in the third coding coefficient matrix, and the set of coding coefficients carried when sending p ₂ is the coding coefficient {01000000} of the second row in the third coding coefficient matrix. The set of coding coefficients carried when p ₃ is the coding coefficient of the third row in the third coding coefficient matrix {00100000}, and the set of coding coefficients carried when sending p ₄ is the coding coefficient of the fourth row of the third coding coefficient matrix {00010000 }. A set of coding coefficients carried when sending c' ₁ are the coding _coefficients {α' _1,1 . 00001000}, a set of coding coefficients carried when sending c' ₂ are the coding coefficients {α' _2,1 ... α' _2,4 } in the 6th row in the second coding coefficient matrix and the 6th row in the third coding coefficient matrix Coding coefficients {00000100}, a group of coding coefficients carried when sending c' ₃ is the coding coefficients {α' _3,1 ... α' _3,4 } in the 7th row in the second coding coefficient matrix and in the third coding coefficient matrix The 7th line of coding coefficients {00000010}, a set of coding coefficients carried when sending c' ₄ is the 8th line of coding coefficients {α' _4,1 ... α' _4,4 } in the second coding coefficient matrix and the third coding The 8th row in the coefficient matrix encodes the coefficients {00000001}, and a group of encoding coefficients carried when sending b ₁ is the 9th row encoding coefficients {β _{m, 1} . . . β _{m, 8} } in the third encoding coefficient matrix.

Exemplarily, taking FIG. 11 as an example, in this implementation manner, the second encoded packet sent by the sending end includes b ₁ to b ₈ , and a set of encoding coefficients carried when sending b ₁ is a third encoding coefficient matrix. The coding coefficients in the first row of the encoding coefficient {β _1,1 ...β _1,8 }, a set of encoding coefficients carried when sending b ₂ are the encoding coefficients in the second row in the third encoding coefficient matrix {β _2,1 ...β _{2, 8} }, a set of coding coefficients carried when sending b ₃ is the coding coefficients {β _3,1 ... β 3, ₈ } in the third row in the third coding coefficient matrix, and a set of coding coefficients carried when sending b ₄ is The fourth row in the third encoding coefficient matrix encodes the coefficients {β _4,1 . . . β _4,8 }. A set of coding coefficients carried when sending b ₅ are the coding _coefficients {α′ _1,1 . _5,1 ... β _5,8 }, a set of coding coefficients carried when sending b ₆ are the coding coefficients {α' _2,1 ... α' _2,4 } of the sixth row in the second coding coefficient matrix and the third coding _The _6th row of the coefficient matrix encodes the coefficients { _β _6,1 . α′ _3,4 } and the _7th row coding coefficients { _β _7,1 . Row coding coefficients {α' _4,1 ···α' _4,4 } and the 8th row coding coefficients {β _8,1 ··· β _8,8 } in the third coded coefficient matrix.

704. The sending end sends one or more second encoded packets.

Please refer to FIG. 12. FIG. 12 is a schematic diagram of an embodiment of another finite field recoding method proposed by an embodiment of the present application. This finite field recoding method can be applied to intermediate nodes, including:

1201. The intermediate node receives one or more third encoded packets.

In this embodiment, the intermediate node receives one or more third encoded packets, where the third encoded packets include g' fourth encoded data blocks and encoding coefficients corresponding to g' fourth encoded data blocks, g' is a positive integer. The coding coefficient corresponding to the fourth coded data block is also referred to as the coding coefficient included in the third coded packet.

1202. The intermediate node uses the fourth encoding coefficient matrix to perform encoding processing on the fourth encoded data block to generate a fifth encoded data block.

In this embodiment, the intermediate node uses the fourth encoding coefficient matrix to perform encoding processing on g' fourth encoded data blocks to generate one or more fifth encoded data blocks, the fifth encoded data block and the fourth encoding coefficient matrix A set of coding coefficients corresponds to. For convenience of description, the coding coefficients in the fourth coding coefficient matrix are also referred to as fourth coding coefficients.

The fourth coding coefficient matrix includes one or more fourth coding coefficients, and the finite field of the fourth coding coefficients and the finite field of coding coefficients corresponding to the fourth coded data block have a nested structure, wherein the finite field of the fourth coding coefficients, The finite field of the coding coefficients corresponding to the fourth coded data block satisfies the following relationship: the order has a multiple relationship, and the feature numbers are consistent. Exemplarily, when the third coded message is the first coded message, the finite field of the fourth coding coefficient has a nested structure with the first finite field and the second finite field; when the third coded message is the second When encoding the message, the finite field of the fourth coding coefficient has a nested structure with the third finite field and the fourth finite field.

Specifically, the fourth encoded data block is Xi, 1≤i≤u, i is a positive integer, and u is a positive integer;

The fifth encoded data block is Y _v , where,

Among them, 1≤j≤v.

A specific encoding method in step 1202 is shown in FIG. 13 , which is a schematic diagram of re-encoding in an embodiment of the present application. The third encoded packets (including the first encoded packet/second encoded packet) are X ₁ to X _i , wherein a third encoded packet may include a fourth encoded data block corresponding to the fourth encoded data block The coding coefficients corresponding to the fourth coded data block of . The intermediate node multiplies X ₁ ˜X _i by the fourth coding coefficient matrix to obtain new messages Y ₁ ˜Y _v . The coding coefficients included in the fourth coding coefficient matrix belong to the re-coded finite field, and the coding coefficients in the first row of the fourth coding coefficient matrix may be {γ _1,1 ...γ _1,v }, X ₁ to X _u and { Multiply γ _1,1 ...γ _1,v } to obtain Y ₁ , and so on, the coding coefficient of the uth row of the fourth coding coefficient matrix can be {γ _u,1 ...γ _u,v }, X ₁ ～X _u Multiply by {γ _u,1 …γ _u,v } to get Y _v .

In an optional implementation manner, the order of the finite field of the fourth coding coefficient is equal to the lowest order of the finite field in the network where the intermediate node is located. Exemplarily, when the lowest order of the finite field in the network where the intermediate node is located is d0, the finite field of the lowest order is GF(E ^d0 ), E is a prime number, and d0 is a positive integer. Then the finite field where the fourth coding coefficient is located is GF(E ^d0 ).

1203. The intermediate node generates one or more recoded packets.

In this embodiment, after generating one or more fifth encoded data blocks, the intermediate node generates one or more re-encoded packets. A re-encoded message includes: one or more fifth encoded data blocks, one or more fourth encoded coefficients, and/or, one or more fourth encoded data blocks, one or more fourth encoded data blocks coding coefficients;

Optionally, a finite field order may also be carried in the recoding message, where the finite field order is used to indicate the order of the finite field corresponding to the fifth encoded data block. Exemplarily, the finite field order may be a value of a power corresponding to the finite field. For example, assuming that in the re-encoded message, the finite field of the fifth encoded data block is GF(E ² ), then the finite field order Can be 2. The finite field order may also be the maximum power order of the finite field in the recoded message.

1204. The intermediate node sends one or more recoded packets.

After receiving the fourth coded message, the receiving end may use multiple decoding methods: the first decoding method, or the second decoding method, which will be described below respectively. The first decoding manner may be directed to the encoding manner of the embodiment shown in FIG. 7 , and the second decoding manner may be directed to the encoding manner of the embodiment shown in FIG. 4 . First, the first decoding method is introduced. Please refer to FIG. 14. FIG. 14 is a schematic diagram of an embodiment of yet another finite field encoding or decoding method proposed by an embodiment of the present application. The finite field decoding method is applied to the receiving end, including:

1401. The receiving end receives one or more fourth encoded packets.

In this embodiment, the receiving end receives one or more fourth encoded packets. Specifically, the fourth encoded message includes: a second encoded message, a re-encoded message, or a message carrying the source data block. The second encoded message may be directly sent by the intermediate node to the receiving end, or may be forwarded to the receiving end by the intermediate node after being encoded (also called: re-encoding), which is not limited here. Specifically, for the detailed introduction of the second encoded message and the re-encoded message, please refer to the foregoing embodiment, and details are not repeated here.

The fourth encoded message includes t' sixth encoded data blocks and encoding coefficients corresponding to the t' sixth encoded data blocks, where t' is a positive integer. Exemplarily, when the fourth encoded packet includes the second encoded packet, the sixth encoded data block includes the second encoded data block, and/or the third encoded data block. When the fourth encoded message includes the re-encoded message, the sixth encoded data block includes the fifth encoded data block.

1402. Perform a first decoding operation on one or more fourth encoded packets in a low-order finite field.

In this embodiment, the receiving end decodes one or more fourth encoded packets in a low-order finite field and a high-order finite field, where the low-order finite field is the finite field with the lowest order in the network where the receiving end is located. The low-order finite field is the finite field with the lowest order in the network where the receiver is located, and the high-order finite field is any higher-order finite field of the coding coefficients corresponding to the sixth encoded data block, and the order of the high-order finite field is higher than the low-order finite field. The order of the second finite field, the lower order finite field and the higher order finite field have a nested structure, wherein, the finite field with the nested structure satisfies the following relationship: the order has a multiple relationship, and the characteristic number is consistent. For ease of understanding, please refer to FIGS. 15-16 . FIG. 15 is a schematic diagram of an embodiment of a decoding operation in an embodiment of the present application, and FIG. 16 is a schematic diagram of an embodiment of a decoding operation in an embodiment of the present application. The first decoding operation is as follows:

According to the coding coefficients of the sixth coded data block in the one or more fourth coded messages, the coding coefficients of the lower-order finite field and the coding coefficients of the higher-order finite field are determined; the coding coefficients of the lower-order finite field are composed of the coding coefficients of the lower-order finite field. Encoding coefficient matrix.

First, a first decoding matrix and a second decoding matrix are formed according to the low-order domain coding coefficient matrix, wherein the coding coefficients corresponding to the high-order finite field in the coding coefficients of the first decoding matrix form the first high-order domain coding coefficients group, the finite field of the first higher-order domain coding coefficient group is the finite field with the lowest order among all the higher-order finite fields of the coding coefficients corresponding to the sixth coded data block; the coding coefficients of the second decoding matrix correspond to the higher-order finite fields. The coding coefficients of the domain form the second high-order domain coding coefficient group, and the finite field of the second high-order domain coding coefficient group is the coding coefficients corresponding to the sixth coded data block except the first high-order finite domain coding coefficient group. The finite field of coefficients, the finite field order of the second high-order field coding coefficient group is less than or equal to the highest-order finite field order supported by the receiving end.

Optionally, a first decoding matrix, a second decoding matrix and a third decoding matrix are formed according to the low-order domain coding coefficient matrix, wherein the coding coefficients corresponding to the high-order finite field in the third decoding matrix form the third decoding matrix. High-order domain coding coefficient group, the finite field of the third high-order domain coding coefficient group is the coding coefficient corresponding to the sixth coded data block, except for the first high-order finite field coding coefficient group and the second high-order finite field coding coefficient group. The finite field of other coding coefficients corresponding to the third high-order domain coding coefficient group is higher than the highest-order finite field order supported by the receiving end; the third decoding matrix is decoded to generate a zero matrix.

Exemplarily, k=4, n=4, r1=1, r2=1, r3=2, D1=3, d0=0, dt=2. The lower-order finite field is GF(2), and the highest-order finite field supported by the receiver is

Also known as: The computing power of the receiver is constrained in the nested domain

, dt=2 is taken as an example for description. Figure 15 shows the low-order domain coding coefficient matrix, where,

The first decoding matrix:

The second decoding matrix:

The third decoding matrix:

Next, perform a decoding operation on the second decoding matrix to generate a first decoding sub-matrix and a second decoding sub-matrix, wherein the first decoding sub-matrix is a zero matrix, and the second decoding matrix is a diagonal coefficient is an identity matrix of 1.

When the second decoding matrix performs the decoding operation, the first decoding matrix is synchronously decoded to generate the third decoding sub-matrix and the fourth decoding sub-matrix.

When the first decoding matrix performs a decoding operation, a synchronous decoding operation is performed on the sixth encoded data block to generate data to be decoded.

In an optional implementation manner, the number of rows of the third decoding sub-matrix is the same as the number of rows of the first decoding sub-matrix, and the number of rows of the fourth decoding sub-matrix is the same as the number of rows of the second decoding sub-matrix The numbers are the same.

In another optional implementation manner, the number of columns of the third decoding sub-matrix is consistent with the number of columns of the first decoding sub-matrix, and the number of columns of the fourth decoding sub-matrix is the same as the number of columns of the second decoding sub-matrix. The number of columns is the same.

Exemplarily, FIG. 15 shows a low-order domain coding coefficient matrix as an example. After the decoding operation, please refer to FIG. 16 , which is a schematic diagram of another decoding operation in an embodiment of the present application.

For the second decoding matrix:

Perform decoding operations such as Gaussian elimination. Get the first decoding sub-matrix:

and the second decoding submatrix:

The rank of the second decoding sub-matrix is also referred to as the rank of the second decoding matrix.

When the second decoding matrix performs a decoding operation, the first decoding matrix synchronizes the decoding operation, such as Gaussian elimination. Obtain the third decoding sub-matrix:

and the fourth decoding submatrix:

In an optional implementation manner, before the receiving end performs the first decoding operation. After the receiving end receives w fourth encoded packets, w is a positive integer. The receiving end judges the w fourth encoded packets for the k source data blocks in a group, and determines whether to perform a decoding operation.

in,

for

matrix,

satisfy

The third decoding matrix is

The high-order domain coding coefficient matrix is G, the high-order domain coding coefficient matrix is composed of the coding coefficients of the high-order finite domain, and the low-order domain coding coefficient matrix H.

Exemplarily, the fourth coded packet includes the second coded packet as an example for description. The second encoding coefficient matrix G=[I _k A ₁ . . . A _D ] ^T , where. The matrix _{Ad is an r d} _× k matrix based on the coded coefficients of the third finite field GF(E ^d1 ) and the coded coefficients of the second finite field GF(E _D1 ). For the convenience of description, let d1=d, D1=D, where 1≤d≤D, let

Assume that the computing power of the receiver is constrained in the nested domain

, d ₀ ≤d _t ≤D, and at a certain moment the receiving end receives w fourth encoded packets (or one or more fourth encoded packets, the number of w fourth encoded packets carried Encoded data blocks) b' ₁ , b' ₂ , ..., b' _w .

The receiving end juxtaposes the coding coefficients of the low-order finite field carried in the header of each fourth coded packet in rows, and obtains a result based on

The low-order domain coding coefficient matrix H of dimension w×(k+n), which satisfies:

[b′ ₁ ^T ,b′ ₂ ^T ,…,b′ _w ^T ] ^T =HG[p ₁ ^T ,p ₂ ^T ,…,p _k ^T ] ^T .

Note that in the low-order domain coding coefficient matrix, finally

elements correspond to the source (the source is the sender or the intermediate node) using more than

The encoded data block obtained by the finite field encoding of higher order. This part of the encoded data block cannot be directly decoded by the receiving end of the current computing power. need to be based on

Gaussian elimination of

Only after the finite field coding coefficients of higher order are obtained, the coded data block that can be used for decoding can be obtained.

Based on the above analysis, the current computing power is

The sufficient and necessary conditions for the decodable judgment of the receiving end are:

in

Is an

matrix, which satisfies:

The third decoding matrix is

pass through

The product can get a (w-rank(H _d ))×(k+n) dimension

- matrix, where last

The column coefficients are all 0. So if you choose the matrix

middle

Row vectors that are linearly independent of each other form a matrix H', then the above judgment conditions are equivalent to the following conditions:

rank(H'G)=k.

The following describes the matrix

and the iterative algorithm for H':

h ^w represents what the receiver receives, and the wth is based on

, a row vector consisting of coding coefficients of a (k+n) dimensional low-order finite field. Suppose there is at least one non-zero element in h ^w . make

means the last in h ^w

A row vector of elements.

1. Initialization: Let the matrix

H', M,

are empty matrices with columns w, (k+n), (k+n) and

List.

2. The receiving end has just received the wth fourth encoded message, and the previous w–1 fourth encoded message has been processed, then for

Do one of the two options below.

A: When

is a zero vector, first use the new matrix

renew

Second, in the current matrix M and

Add an all-zero line below the . Finally determine whether h ^w is linearly independent of all rows in the current H'.

If not, keep H'unchanged; if so, use the new matrix

Update H' (add h ^w as a new row to the linearly independent group), ending the loop.

B: when

is not a zero vector, then determine whether it satisfies the current

All rows in are linearly independent.

If yes, respectively

M.

To update:

If not, perform the following steps: first calculate the (w–1) dimensional row vector k such that

Second, use the new matrix

renew

Further calculate the new vector S=kM+h ^w , respectively in the current matrix M and

Add an all-zero line below the ;

Again, determine whether the vector S is linearly independent of all rows in the current H'; if not, keep H'unchanged; if so, use the new matrix

Update H', ending the loop.

The above iterative process has the following properties:

the non-zero row with

The sum of the number of rows is equal to w;

The non-zero row of the loop remains constant as

A set of basis for row vector spaces.

The row vectors of form a set of basis for the null space of the H _d row vector space. The row vector of H' always remains

a set of basis for row vector spaces where

That is, H is the w×(k+n) low-order domain coding coefficient matrix of w messages.

Exemplarily, for ease of understanding, a specific example is given in the embodiment of the present application to illustrate the above judgment execution process:

Assume parameters k=3, n=2, where r ₁ =r ₂ =1, D=2, d ₀ =0. The second coding coefficient matrix G is defined as

where α _and β are the primitives of GF(2 ₂ ) and GF(2 ₄ ) respectively and satisfy α=β ⁵ .

For a receiver t, GF(2 ² ) is the largest finite field that it can calculate, that is, d _t = 1 (only the addition and multiplication between the primitive element α and its power can be calculated), and it has received Four fourth coded messages, the coding coefficients of which are juxtaposed row by row to obtain the low-order domain coding coefficient matrix H, which is expressed as:

Because at this time

According to the iterative method mentioned earlier, the following can be formed

and H':

The row vector of H' consists of

A set of basis for row vector spaces. according to

The equivalent condition of rank(H'G)=k, calculate

Since 1+α+α ² =0 and rank(H'G)=2<3 in GF(2 ² ), more fourth encoded packets need to be received to complete decoding.

Let h ⁵ =[1 0 0 1 1] be the 5th encoding coefficient vector received by the receiving end, here it is updated and updated according to the iterative algorithm

M.

for:

However, the obtained new vector S=[0 0 0 1 0] does not satisfy the linear relationship with all the rows in the current H', so keep H' unchanged, at this time rank(H'G) also does not change, the original k The fourth encoded message is still undecipherable.

Let h ⁶ =[0 0 1 0 0] be the sixth coding coefficient vector received by the receiver, since the element of the last bit is 0, update it directly

M.

for:

Then it is determined that h ⁶ =[0 0 1 0 0] is linearly independent of all row vectors in H', and H' is updated to:

calculate

It satisfies rank(H'G)=3, indicating that the receiving end has received enough information to implement decoding at this time.

In two special cases, the decision condition

can be further simplified. When the receiver t has the highest computing power in the current network, that is, d _t =D, the above condition is equivalent to rank(HG)=k; when d ₀ =0 and the receiver t has the lowest computing power in the network, that is When d _t =d ₀ =0, the above conditions are equivalent to

In another implementation, when the sender is in the finite field

The second encoded message is generated in the intermediate node and the finite field

In a finite field with a nested structure, the second encoded message is re-encoded. The above decoding judgment conditions can be simplified as:

The second coding coefficient matrix G is expressed as G=[I _k A _D ] ^T , where the matrix A _D is a nested field based

The n×k matrix of . Suppose the computing power is

The packets received by the receiver t are b′ ₁ , b′ ₂ ,…,b′ _w , which can be expressed as:

[b′ ₁ ^T ,b′ ₂ ^T ,…,b′ _w ^T ] ^T =HG[p ₁ ^T ,p ₂ ^T ,…,p _k ^T ] ^T =H[p ₁ ^T ,…,p _k ^T , c ₁ ^T ,…,c _n ^T ],

That is, the _jth row of H corresponds to a set of coding coefficients of the message b'j. If a set of coding coefficients of b' _j includes coding coefficients that exceed the computing power of t at the receiving end, because t cannot be decoded, the message b' _j is directly discarded.

Therefore, it is assumed that the coding coefficients in H belong to

That is, within the computing power of the receiving end t. Since G exists only GF(2) and

There are two kinds of finite field coefficients, so there are only two cases for the decoding decision criterion:

When d _t ≥ D, all the high-order domain decoding coefficients in HG are within the computing power of the receiving end t, that is, the order of the finite field of all high-order domain decoding coefficients in HG is less than or equal to the receiving end. Maximum order of finite fields supported by the terminal. Therefore, the above decoding conditions can be simplified as rank(HG)=k;

When d _t <D, since the second encoded message c _1T ,...,c _nT is based on finite fields

generated, after the receiving end t decodes these second encoded packets, the source data blocks p ₁ , . . . , p _k cannot be obtained by further decoding. Therefore, the receiving end t needs to encode the coefficient matrix H in the low-order domain on the basis of

The linear operation of decoding obtains the source data blocks p ₁ ,...,p _k . The above decoding conditions can be simplified as rank(H)−rank(H _n )=k, where H _n is a submatrix whose matrix H only takes the last n columns.

1403. Perform a second decoding operation on the result obtained by the first decoding operation in a high-order finite field to generate one or more source data blocks.

In this embodiment, after step 1402, the receiving end performs a second decoding operation on the result obtained by the first decoding operation in a high-order finite field to generate one or more source data blocks.

For ease of understanding, on the basis of FIGS. 15-16 , please refer to FIGS. 17-19 , and FIG. 17 is another schematic diagram of decoding in an embodiment of the present application. FIG. 18 is another schematic diagram of decoding according to an embodiment of the present application. Taking the fourth coded message including the second coded message as an example: the second coding coefficient matrix of the second coded message includes coding coefficients of higher-order finite fields in the fourth coded message.

First, a fifth decoding sub-matrix is determined according to the fourth decoding sub-matrix, and the fifth decoding sub-matrix is composed of coding coefficients of a high-order finite field. Exemplarily, the fifth decoding sub-matrix includes: GF(2 ² ) matrix A ₁ =[3 1 2 2],

Matrix A ₂ =[14 3 2 7].

Secondly, according to the fourth decoding sub-matrix and the fifth decoding sub-matrix, generate a sixth decoding sub-matrix, and the vector in the sixth decoding sub-matrix is: a set of coding coefficients of the fifth decoding sub-matrix and the first decoding sub-matrix A set of coding coefficients of the four decoding sub-matrixes are obtained by addition in the finite field corresponding to the fifth decoding sub-matrix.

Exemplarily, a set of coding coefficients of the fifth decoding sub-matrix is: [14 3 2 7], and a set of coding coefficients of the fourth decoding sub-matrix is: [1 0 0 0], both of which are in the fifth decoding The finite field corresponding to the code submatrix

Do addition in , to obtain a set of vectors of the sixth decoding sub-matrix: [15 3 2 7].

After step 1402, the obtained data to be decoded is expressed as: [h1'h2'h3'h4'], where:

1·p ₁ +0·p ₂ +0·p ₃ +1·p ₄ =h′ ₁ (1);

0·p ₁ +1·p ₂ +0·p ₃ +1·p ₄ =h′ ₂ (2);

0·p ₁ +0·p ₂ +1·p ₃ +0·p ₄ +1·c ₁ =h′ ₃ (3);

1·p ₁ +0·p ₂ +0·p ₃ +0·p ₄ +1·c ₂ =h′ ₄ (4)

According to the fourth decoding sub-matrix:

Fifth decoding sub-matrix:

Based on the GF(2 ² ) matrix A ₁ =[3 1 2 2], substituting c ₁ =3·p ₁ +1·p ₂ +2·p ₃ +2·p ₄ into formula (3), we get:

3·p ₁ +1·p ₂ +3·p ₃ +2·p ₄ =h′ ₃ (5);

based on,

Matrix A ₂ =[14 3 2 7], substituting c ₂ =14·p ₁ +3·p ₂ +2·p ₃ +7·p ₄ into formula (4), we get:

15·p ₁ +3·p ₂ +2·p ₃ +7·p ₄ =h′ ₄ (6).

Through the above calculation, the sixth decoding sub-matrix is obtained:

Thirdly, a fourth decoding matrix is obtained according to the third decoding sub-matrix and the sixth decoding sub-matrix. Wherein, the vectors in the sixth decoding sub-matrix are: a set of coding coefficients of the fifth decoding sub-matrix and a set of coding coefficients of the fourth decoding sub-matrix, which are calculated in the finite field corresponding to the fifth decoding sub-matrix. Addition to get.

Exemplarily, please refer to FIG. 18. In FIG. 18, according to the third decoding sub-matrix:

and the sixth decoding submatrix:

Generate the fourth decoding matrix:

Again, the receiving end performs a decoding operation on the fourth decoding matrix to generate a unit matrix with a diagonal coefficient of 1;

When the fourth decoding matrix performs a decoding operation, the data to be decoded is subjected to a synchronous decoding operation to generate one or more source data blocks.

Exemplarily, please refer to FIG. 19 , which is another schematic diagram of decoding proposed by an embodiment of the present application. A decoding process is performed on the fourth decoding matrix. The details are as follows: in the finite field of the third decoding sub-matrix, Gaussian elimination is performed on the fourth decoding matrix. get the matrix

The specific Gaussian elimination steps are as follows:

h' ₃ +3 h' ₁ +h' ₂ ,

h' ₄ +15·h' ₁ +3·h' ₂ ,

Because of the submatrix in it

No further elimination can be done in the finite field of the third decoding sub-matrix, therefore, the matrix

Perform the inverse operation. First, put

The elements in are converted into corresponding elements in the highest-order finite field where the corresponding fifth decoding sub-matrix is located. For example: the low-order finite field of the element "3" in the sub-matrix is GF(2 ² ), and the element "3" is in the corresponding fifth decoding sub-matrix, and the highest-order finite field is

Since element "3" represents "α ² " in GF(2 ² ), while in GF(2 2 )

"α ² " corresponds to "7". Therefore, for the submatrix

convert to get

for the matrix

Inverse:

When the above-mentioned fourth decoding matrix performs a decoding operation, the data to be decoded is subjected to a synchronous decoding operation to generate one or more source data blocks.

In the embodiment of the present application, the fourth encoded message received by the receiving end is encoded by using a finite field with a nested structure. Therefore, when decoding is performed at the receiving end, the decoding can be performed in the low-order finite field first, and the decoding result of the low-order finite field can be used to further decode in the high-order finite field, and finally one or more source data block.

Decoding in a low-order finite field effectively reduces the computing power requirements of the receiver. The decoding reserved in the high-order finite field improves the decoding success rate. From the perspective of decoding speed or throughput, the decoding operation of the high-order finite field in the decoding process is transformed into a low-order finite field (for example, the lowest-order finite field in the current network), which effectively reduces the computational complexity and improves the Decoding speed and data throughput.

Next, the second decoding method is introduced. Please refer to FIG. 20a. FIG. 20a is a schematic diagram of an embodiment of another finite field encoding or decoding method proposed by an embodiment of the present application. This method is applied to the receiving end, including:

2001. The receiving end receives one or more fourth encoded packets.

In this embodiment, it is the same as the foregoing step 1401, and details are not repeated here.

2002. Use the second decoding mode to perform a decoding operation on one or more fourth encoded packets to generate one or more source data blocks.

In this embodiment, the receiving end uses the second decoding method to perform a decoding operation on one or more fourth encoded packets in the highest-order finite field of the encoding coefficients corresponding to the sixth encoded data block to generate k' pieces of source data block, the highest-order finite field is the highest-order finite field of the coding coefficients corresponding to the sixth coded data block, and k' is a positive integer.

Specifically, in the highest-order finite field corresponding to the coding coefficients of the sixth coded data block, the sixth coded data block is decoded, so that the matrix composed of the coding coefficients of the sixth coded data block is decoded to obtain a diagonal line A matrix whose elements are 1 and whose elements are 0 except for the diagonal elements;

When the matrix composed of the coding coefficients of the sixth coded data block is subjected to a decoding operation, the sixth coded data block is subjected to a synchronous decoding operation to generate one or more source data blocks.

Exemplarily, as shown in FIG. 20b, FIG. 20b is a schematic diagram of decoding in an embodiment of the present application.

The coding coefficients of the sixth coded data block include: {α″ _1,1 …α″ _1,4 }, {α″ _2,1 …α″ _2,4 }, {α″ _3,1 …α″ _{3, 4} } and {α″ _4,1 …α″ _4,4 }; the sixth encoded data block carried in the fourth encoded message includes: data block X” ₁ , data block X” ₂ , data block X” ₃ and the data block X"_k=4; wherein the coding coefficients carried by the data block X" ₁ are {α" _1,1 ...α" _1,4 }, and the coding coefficients carried by the data block X" ₂ are {α" _2,1 …α″ _2,4 }, the coding coefficients carried by the data block X” ₃ are {α″ _3,1 …α″ _3,4 }, and the coding coefficients carried by the data block X” _k=4 are {α″ _4,1 ...α″ _4,4 }. According to the coding coefficients of the sixth coded data block, a matrix is formed:

Exemplarily, the specific value of the matrix can be:

Among them, the finite field corresponding to the coding coefficient groups [1 0 00] and [0 1 0 0] is GF(2), also known as the first-order field; the finite field corresponding to the coding coefficient group [3 1 2 2] is GF( 2 ² ), also known as the second-order field; the finite field corresponding to the coding coefficient group [15 3 2 26] is

Also known as the 4th domain.

due to

GF(2 ² ) and GF(2) are finite fields with nested structures. The addition, and, and multiplication operations in these three finite fields can be associated using the equivalent addition table and the equivalent multiplication table.

The equivalent multiplication table of GF(2 ² ) and GF(2) is shown in FIG. 21 , and FIG. 21 is a schematic diagram of an equivalent multiplication table of a nested field involved in the embodiment of the present application. The highest-order finite field corresponding to the coded coefficients in the sixth coded data block

Inside, the sixth encoded data block is decoded.

details as follows:

Please refer to FIG. 20c. FIG. 20c is another schematic diagram of decoding according to an embodiment of the present application. Using this equivalent multiplication table, for the above matrix

in a finite field

Gaussian elimination is performed in .

First, as shown in matrix (1) in Figure 20b, using [1 0 0 0] and [0 1 0 0], perform elimination processing on [15 3 2 26] to obtain matrix (2).

Second, in order to perform further elimination of matrix (2). According to the equivalent multiplication table shown in Figure 21, after [0 0 2 6]*9 in matrix (2), matrix (3) can be obtained.

Again, the matrix (3) is further eliminated. According to the equivalent multiplication table shown in Figure 21, after [0 0 1 3]*2 in the matrix (3), the elimination can obtain the matrix (4).

Again, by further elimination of matrix (4), the identity matrix (5) can be obtained,

Optionally, the receiving end discards the fourth encoded message that exceeds its own computing power. For example, when the receiving end supports decoding, the highest-order finite field is

Then when the finite field of the fourth encoded message is

The receiving end discards the fourth encoded message.

In the embodiment of the present application, the fourth encoded message received by the receiving end is encoded by using a finite field with a nested structure. In a finite field with a nested structure, an equivalent multiplication table (or an equivalent addition table) can be used to perform multiplication (or addition). Therefore, when decoding is performed at the receiving end, the sixth encoded data block can be decoded within the highest-order finite field corresponding to the encoding coefficients of the sixth encoded data block. It effectively reduces the computational complexity and improves the decoding speed and data throughput. Moreover, the implementation flexibility of the solution is improved.

The finite field coding method shown in FIG. 4 , the finite field coding method shown in FIG. 7 and the finite field recoding method shown in FIG. 12 are usually applied to the transmitting end (or intermediate node) of the network device with the coding module. In a possible application scenario, the network device with the encoding module also has a decoding module, and the network device can also perform the finite field decoding method shown in FIG. 14 and the finite field decoding method shown in FIG. 20a. The application does not limit the network device that executes the encoding method or the decoding method, and only distinguishes the network device that executes the encoding method or the decoding method. The finite field coding method shown in FIG. 4 , the finite field coding method shown in FIG. 7 and the finite field recoding method shown in FIG. 12 are only disclosed as coding methods in this application to avoid redundancy. It should be understood that the above-mentioned encoding method can also be interpreted as a decoding method, that is, the decoding side performs the reverse execution according to the method of the encoding side, and its technical means is similar to that of the encoding side, and the decoding method performed corresponding to the encoding method also belongs to this application. scope of protection. Similarly, the finite field decoding method shown in FIG. 14 and the finite field decoding method shown in FIG. 20a can also be parsed as encoding methods, that is, the encoding side is executed in reverse according to the method on the decoding side. Similarly, the encoding method performed corresponding to the above-mentioned decoding method also belongs to the protection scope of the present application.

The solutions provided by the embodiments of the present application are described above mainly from the perspective of methods. It can be understood that, in order to implement the above-mentioned functions, the network device includes corresponding hardware structures and/or software modules for executing each function. Those skilled in the art should easily realize that the present application can be implemented in hardware or a combination of hardware and computer software with reference to the modules and algorithm steps of each example described in the embodiments disclosed herein. Whether a function is performed by hardware or computer software driving hardware depends on the specific application and design constraints of the technical solution. Skilled artisans may implement the described functionality using different methods for each particular application, but such implementations should not be considered beyond the scope of this application.

In this embodiment of the present application, the network device (including the transmitting end, the receiving end, and the intermediate node) may be divided into functional modules according to the foregoing method examples. For example, each functional module may be divided into each function, or two or more The functions are integrated in a processing module. The above-mentioned integrated modules can be implemented in the form of hardware, and can also be implemented in the form of software function modules. It should be noted that, the division of modules in the embodiments of the present application is schematic, and is only a logical function division, and there may be other division manners in actual implementation.

The following describes the network device in the present application in detail, please refer to FIG. 22 , which is a schematic diagram of an embodiment of the network device in the embodiment of the present application. The network device can be deployed in network equipment or terminal equipment, and the network device includes:

The processing module 2201 is configured to perform encoding processing on k source data blocks using the first encoding coefficient matrix to generate k first encoded data blocks, where the first encoded data blocks correspond to a set of encoding coefficients in the first encoding coefficient matrix, k is a positive integer;

The processing module 2201 is further configured to generate one or more first encoded packets according to the k first encoded data blocks, where the first encoded packet includes one or more first encoded data blocks, and one or more first encoded data blocks a group of encoding coefficients in the first encoding coefficient matrix corresponding to the encoded data block;

The transceiver module 2202 is configured to send one or more first encoded messages.

In some optional embodiments of the present application,

The source data block is: p _j , where j is a positive integer, 1≤j≤k;

The one or more first encoded data blocks include: c _n , wherein,

In some optional embodiments of the present application, the one or more second encoded packets further include a finite field order, and the finite field order corresponds to the first encoded data block, and/or, the source data block corresponds to a finite field order. The number is the finite field order of a group of coding coefficients in the first coding coefficient matrix corresponding to the first coded data block, and/or the finite field order of the coding coefficients of the source data block.

In a possible implementation manner, the processing module 2201 is configured to perform step 401 and step 402 in the embodiment corresponding to FIG. 4 .

In a possible implementation manner, the transceiver module 2202 is configured to perform step 403 in the embodiment corresponding to FIG. 4 .

Please refer to FIG. 23. FIG. 23 is a schematic diagram of an embodiment of a network device in an embodiment of the present application. Network devices, including:

The processing module 2301 is configured to perform encoding processing on k source data blocks using the second encoding coefficient matrix to generate k second encoded data blocks, where the second encoded data blocks correspond to a set of encoding coefficients in the second encoding coefficient matrix, k is a positive integer;

The processing module 2301 is further configured to use the third encoding coefficient matrix to perform encoding processing on the k second encoded data blocks and the k source data blocks to generate g third encoded data blocks, the third encoded data block and the third encoded coefficients A set of coding coefficients in the matrix corresponds, and g is a positive integer;

The processing module 2301 is further configured to generate one or more second encoded packets according to the k second encoded data blocks and the g third encoded data blocks, where a second encoded packet includes: one or more third encoded data blocks coding coefficients of the data block and one or more third coded data blocks, the second coded message includes one or more third coded data blocks, and coding coefficients corresponding to the third coding coefficient matrix;

The transceiver module 2302 is configured to send one or more second encoded messages.

The one or more second encoded data blocks include: c' _n , wherein,

The coding coefficient of the fourth finite field is β _m,k+n ;

The one or more third encoded data blocks include: b _m , wherein,

m is a positive integer.

In a possible implementation manner, the processing module 2301 is configured to execute step 701 , step 702 and step 703 in the embodiment corresponding to FIG. 7 .

In a possible implementation manner, the transceiver module 2302 is configured to perform step 704 in the embodiment corresponding to FIG. 7 .

Please refer to FIG. 24. FIG. 24 is a schematic diagram of an embodiment of a network device according to an embodiment of the present application. Network devices, including:

The transceiver module 2401 is configured to receive one or more third encoded packets, where the third encoded packets include g' fourth encoded data blocks and encoding coefficients corresponding to the g' fourth encoded data blocks, where g' is positive integer;

The processing module 2402 is configured to use the fourth encoding coefficient matrix to perform encoding processing on g' fourth encoded data blocks, and generate one or more fifth encoded data blocks, one of the fifth encoded data block and the fourth encoded coefficient matrix. Group coding coefficient correspondence;

The processing module 2402 is further configured to generate one or more re-encoded messages according to one or more fifth encoded data blocks, where the re-encoded message includes one or more fifth encoded data blocks, and one or more fifth encoded data blocks a group of encoding coefficients in the fourth encoding coefficient matrix corresponding to the encoded data block;

The transceiver module 2401 is configured to send one or more recoded packets.

In some optional embodiments of the present application, the finite field order of the coding coefficients (fourth coding coefficients) in the fourth coding coefficient matrix is equal to the lowest order of the finite field in the network where the intermediate node is located;

The fifth encoded data block is Y _v , where,

Among them, 1≤j≤v.

In a possible implementation manner, the processing module 2402 is configured to perform step 1202 and step 1203 in the embodiment corresponding to FIG. 12 .

In a possible implementation manner, the transceiver module 2401 is configured to perform step 1201 and step 1204 in the embodiment corresponding to FIG. 12 .

Please refer to FIG. 25. FIG. 25 is a schematic diagram of an embodiment of a network device according to an embodiment of the present application. Network devices, including:

The transceiver module 2501 is configured to receive one or more fourth encoded packets, where the fourth encoded packet includes t' sixth encoded data blocks and encoding coefficients corresponding to the t' sixth encoded data blocks, where t' is positive integer;

The processing module 2502 is configured to perform a decoding operation on one or more fourth encoded messages in a low-order finite field and a high-order finite field by using the first decoding method, and generate k source data blocks, where k is a positive integer;

The processing module 2502 is further configured to perform a decoding operation on one or more fourth encoded packets in the highest-order finite field of the encoding coefficients corresponding to the sixth encoded data block by using the second decoding method to generate k' source data block, the highest-order finite field is the highest-order finite field of the coding coefficients corresponding to the sixth coded data block.

In some optional embodiments of the present application,

The processing module 2502 is specifically configured to perform a first decoding operation on one or more fourth encoded packets in a low-order finite field;

The processing module 2502 is specifically configured to perform a second decoding operation on the result obtained by the first decoding operation in a high-order finite field to generate k source data blocks.

In some optional embodiments of the present application, the processing module 2502 is specifically configured to determine, according to the coding coefficients corresponding to the sixth coded data block in one or more fourth coded packets, the coding coefficients of the lower-order finite field and the coding coefficients of the higher-order finite fields. the coding coefficients of the finite field;

The processing module 2502 is specifically used to form a low-order domain coding coefficient matrix from the coding coefficients of the low-order finite field;

The processing module 2502 is specifically configured to form a first decoding matrix and a second decoding matrix according to the low-order domain encoding coefficient matrix, wherein the encoding coefficients corresponding to the high-order finite field in the encoding coefficients of the first decoding matrix form the first decoding matrix. High-order domain coding coefficient group, the finite field of the first high-order domain coding coefficient group is the finite field with the lowest order among all the high-order finite fields of the coding coefficients corresponding to the sixth coded data block;

The processing module 2502 is specifically configured to perform a decoding operation on the second decoding matrix to generate a first decoding sub-matrix and a second decoding sub-matrix, wherein the first decoding sub-matrix is a zero matrix and the second decoding matrix is the unit matrix;

The processing module 2502 is specifically configured to perform a synchronous decoding operation on the first decoding matrix when the second decoding matrix performs a decoding operation to generate a third decoding sub-matrix and a fourth decoding sub-matrix, wherein the third decoding sub-matrix The number of rows of the code sub-matrix is the same as the number of rows of the first decoding sub-matrix, the number of rows of the fourth decoding sub-matrix is the same as the number of rows of the second decoding sub-matrix, or the number of rows of the third decoding sub-matrix is the same. The number of columns is consistent with the number of columns of the first decoding sub-matrix, and the number of columns of the fourth decoding sub-matrix is consistent with the number of columns of the second decoding sub-matrix;

The processing module 2502 is specifically configured to perform a synchronous decoding operation on the sixth encoded data block to generate data to be decoded when the first decoding matrix performs a decoding operation.

The processing module 2502 is specifically configured to determine a fifth decoding sub-matrix corresponding to the fourth decoding sub-matrix according to the fourth decoding sub-matrix, and the fifth decoding sub-matrix is composed of coding coefficients of high-order finite fields;

The processing module 2502 is specifically configured to generate a sixth decoding sub-matrix according to the fourth decoding sub-matrix and the fifth decoding sub-matrix, wherein the vectors in the sixth decoding sub-matrix are determined by one of the fifth decoding sub-matrix. The set of coding coefficients and the set of coding coefficients of the fourth decoding sub-matrix are obtained by addition in the finite field corresponding to the fifth decoding sub-matrix;

The processing module 2502 is specifically configured to form a fourth decoding matrix according to the third decoding sub-matrix and the sixth decoding sub-matrix;

The processing module 2502 is specifically configured to perform a decoding operation on the fourth decoding matrix to generate a unit matrix;

The processing module 2502 is specifically configured to perform a synchronous decoding operation on the data to be decoded when performing a decoding operation on the fourth decoding matrix, and generate k source data blocks.

In some optional embodiments of the present application,

The processing module 2502 is specifically configured to form a first decoding matrix, a second decoding matrix and a third decoding matrix according to the low-order domain encoding coefficient matrix, wherein the encoding coefficient corresponding to the high-order finite field in the third decoding matrix A third high-order domain coding coefficient group is formed, and the finite field of the third high-order domain coding coefficient group is the coding coefficients corresponding to the sixth coded data block except the first high-order finite field coding coefficient group and the second high-order finite field coding. For the finite fields of other coding coefficients outside the coefficient group, the finite field order corresponding to the third higher-order field coding coefficient group is higher than the highest-order finite field order supported by the receiver;

The processing module 2502 is specifically configured to perform a decoding operation on the third decoding matrix to generate a zero matrix.

In some optional embodiments of the present application,

For k source data blocks, where k is a positive integer, when the following conditions are met,

The processing module 2502 is further configured to decode the w fourth encoded packets, including:

in,

for

matrix,

satisfy

The third decoding matrix is

In some optional embodiments of the present application,

The processing module 2502 is specifically configured to decode the sixth encoded data block in the highest-order finite field corresponding to the encoding coefficients of the sixth encoded data block, so that the matrix composed of the encoding coefficients of the sixth encoded data block is decoded to obtain identity matrix;

The processing module 2502 is specifically configured to perform a synchronous decoding operation on the sixth encoded data block when the matrix composed of the encoding coefficients of the sixth encoded data block is subjected to a decoding operation to generate k' source data blocks.

In a possible implementation manner, the processing module 2502 is configured to perform

steps

1402 and 1403 in the embodiment corresponding to FIG. 14 , and/or step 2002 in the embodiment corresponding to FIG. 20a .

In a possible implementation manner, the transceiver module 2501 is configured to perform step 1401 in the embodiment corresponding to FIG. 14 and/or step 2001 in the embodiment corresponding to FIG. 20a.

The network device in the foregoing embodiment may be a network device, or may be a chip applied in the network device or other combined devices, components, etc. that can implement the functions of the foregoing network device. When the network device is a network device, the transceiver module and the sending module may be transceivers, and the transceiver may include an antenna and a radio frequency circuit, and the processing module may be a processor, such as a baseband chip. When the network device is a component having the functions of the above network equipment, the transceiver module and the sending module may be radio frequency units, and the processing module may be a processor. When the network device is a system-on-chip, the transceiver module may be an input port of the system-on-chip, the sending module may be an output interface of the system-on-chip, and the processing module may be a processor of the system-on-chip, such as a central processing unit (CPU) .

In this embodiment of the present application, the memory included in the network device is mainly used to store software programs and data, for example, to store the first coding coefficient matrix or the second coding coefficient matrix described in the foregoing embodiments. The network device also has the following functions:

A network device, comprising:

a processor, configured to perform encoding processing on k source data blocks by using the first encoding coefficient matrix to generate k first encoded data blocks, where the first encoded data blocks correspond to a set of encoding coefficients in the first encoding coefficient matrix, k is a positive integer;

The processor is further configured to generate one or more first encoded messages according to the k first encoded data blocks, where the first encoded message includes one or more first encoded data blocks and one or more first encoded data blocks a group of coding coefficients in the first coding coefficient matrix corresponding to the data block;

A transceiver, configured to send one or more first encoded messages.

In some optional embodiments of the present application,

The source data block is: p _j , where j is a positive integer, 1≤j≤k;

The one or more first encoded data blocks include: c _n , wherein,

In some optional embodiments of the present application, the one or more second encoded packets further include a finite field order, and the finite field order corresponds to the first encoded data block, and/or, the source data block corresponds to a finite field order. The number is the order of the finite field where the coding coefficients of the first coded data block are located, and/or the order of the finite field where the coding coefficients of the source data block are located.

In a possible implementation manner, the processor is configured to execute step 401 and step 402 in the embodiment corresponding to FIG. 4 .

In a possible implementation manner, the transceiver is configured to perform step 403 in the embodiment corresponding to FIG. 4 .

A network device, comprising:

a processor, configured to use the second encoding coefficient matrix to perform encoding processing on the k source data blocks to generate k second encoded data blocks, where the second encoded data blocks correspond to a set of encoding coefficients in the second encoding coefficient matrix, k is a positive integer;

The processor is further configured to perform encoding processing on the k second encoded data blocks and the k source data blocks by using the third encoding coefficient matrix to generate g third encoded data blocks, the third encoded data block and the third encoded coefficient matrix Corresponding to a set of coding coefficients in , g is a positive integer;

The processor is further configured to generate one or more second encoded packets according to the k second encoded data blocks and the g third encoded data blocks, where a second encoded packet includes: one or more third encoded data blocks encoding coefficients of the block and one or more third encoded data blocks, the second encoded message includes one or more third encoded data blocks, and encoding coefficients corresponding to the third encoding coefficient matrix;

A transceiver for sending one or more second encoded messages.

The one or more second encoded data blocks include: c' _n , wherein,

The coding coefficient of the fourth finite field is β _m,k+n ;

The one or more third encoded data blocks include: b _m , wherein,

m is a positive integer.

In some optional embodiments of the present application, the second coding coefficient matrix further includes: coding coefficients of a fifth finite field, where the fifth finite field and the third finite field have a nested structure, wherein the fifth finite field and the third finite field have a nested structure. The three finite fields satisfy the following relations: the order has a multiple relationship, and the characteristic numbers are consistent.

In a possible implementation manner, the processor is configured to execute step 701 , step 702 and step 703 in the embodiment corresponding to FIG. 7 .

In a possible implementation manner, the transceiver is configured to perform step 704 in the embodiment corresponding to FIG. 7 .

A network device, comprising:

A transceiver, configured to receive one or more third encoded packets, where the third encoded packets include g' fourth encoded data blocks and encoding coefficients corresponding to the g' fourth encoded data blocks, where g' is a positive integer ;

a processor, configured to perform encoding processing on g' fourth encoded data blocks by using the fourth encoding coefficient matrix to generate one or more fifth encoded data blocks, the fifth encoded data block and a group of the fourth encoded coefficient matrix Corresponding coding coefficients;

The processor is further configured to generate one or more re-encoded messages according to the one or more fifth encoded data blocks, where the re-encoded message includes one or more fifth encoded data blocks and one or more fifth encoded data blocks a group of coding coefficients in the fourth coding coefficient matrix corresponding to the data block;

Transceiver for sending one or more recoded messages.

The fifth encoded data block is Y _v , where,

Among them, 1≤j≤v.

In a possible implementation manner, the processor is configured to execute step 1202 and step 1203 in the embodiment corresponding to FIG. 12 .

In a possible implementation manner, the transceiver is configured to perform step 1201 and step 1204 in the embodiment corresponding to FIG. 12 .

A network device, comprising:

a transceiver, configured to receive one or more fourth encoded packets, where the fourth encoded packet includes t' sixth encoded data blocks and encoding coefficients corresponding to the t' sixth encoded data blocks, where t' is a positive integer ;

The processor is used for adopting the first decoding mode to carry out a decoding operation to one or more fourth encoded messages in a low-order finite field and a high-order finite field, and generates k source data blocks, and k is a positive integer;

The processor is further configured to perform a decoding operation on one or more fourth encoded packets in the highest-order finite field of the encoding coefficients corresponding to the sixth encoded data block by using the second decoding method to generate k' source data blocks , the highest-order finite field is the highest-order finite field of the coding coefficients corresponding to the sixth coded data block.

In some optional embodiments of the present application,

a processor, specifically configured to perform a first decoding operation on one or more fourth encoded messages in a low-order finite field;

The processor is specifically configured to perform a second decoding operation on the result obtained by the first decoding operation in a high-order finite field to generate k source data blocks.

In some optional embodiments of the present application, the processor is specifically configured to determine, according to the coding coefficients corresponding to the sixth coded data block in one or more fourth coded packets, the coding coefficients of the lower-order finite field and the coding coefficients of the higher-order finite field the coding coefficients of the domain;

a processor, which is specifically used to form a low-order domain coding coefficient matrix from coding coefficients of a low-order finite field;

The processor is specifically configured to form a first decoding matrix and a second decoding matrix according to the low-order domain encoding coefficient matrix, wherein the encoding coefficients corresponding to the high-order finite field in the encoding coefficients of the first decoding matrix form the first high-order finite field. A sub-domain coding coefficient group, the finite field of the first higher-order domain coding coefficient group is the finite field with the lowest order among all the higher-order finite fields of the coding coefficients corresponding to the sixth coded data block;

The processor is specifically configured to perform a decoding operation on the second decoding matrix to generate a first decoding sub-matrix and a second decoding sub-matrix, wherein the first decoding sub-matrix is a zero matrix, and the second decoding matrix is identity matrix;

The processor is specifically configured to perform a synchronous decoding operation on the first decoding matrix when the second decoding matrix performs a decoding operation, and generate a third decoding sub-matrix and a fourth decoding sub-matrix, wherein the third decoding sub-matrix is The number of rows of the sub-matrix is the same as the number of rows of the first decoding sub-matrix, the number of rows of the fourth decoding sub-matrix is the same as the number of rows of the second decoding sub-matrix, or the columns of the third decoding sub-matrix The number is consistent with the column number of the first decoding sub-matrix, and the column number of the fourth decoding sub-matrix is consistent with the column number of the second decoding sub-matrix;

The processor is specifically configured to perform a synchronous decoding operation on the sixth encoded data block to generate data to be decoded when the first decoding matrix performs a decoding operation.

The processor is specifically configured to determine a fifth decoding sub-matrix corresponding to the fourth decoding sub-matrix according to the fourth decoding sub-matrix, and the fifth decoding sub-matrix is composed of coding coefficients of a high-order finite field;

The processor is specifically configured to generate a sixth decoding sub-matrix according to the fourth decoding sub-matrix and the fifth decoding sub-matrix, wherein the vectors in the sixth decoding sub-matrix are determined by a group of the fifth decoding sub-matrix The coding coefficients and a group of coding coefficients of the fourth decoding sub-matrix are obtained by addition in the finite field corresponding to the fifth decoding sub-matrix;

a processor, specifically configured to form a fourth decoding matrix according to the third decoding sub-matrix and the sixth decoding sub-matrix;

a processor, specifically configured to perform a decoding operation on the fourth decoding matrix to generate a unit matrix;

The processor is specifically configured to perform a synchronous decoding operation on the data to be decoded when performing a decoding operation on the fourth decoding matrix to generate k source data blocks.

In some optional embodiments of the present application,

The processor is specifically configured to form a first decoding matrix, a second decoding matrix and a third decoding matrix according to the low-order domain encoding coefficient matrix, wherein the encoding coefficients corresponding to the high-order finite field in the third decoding matrix are composed of The third high-order domain coding coefficient group, the finite field of the third high-order domain coding coefficient group is the coding coefficients corresponding to the sixth coded data block divided by the first high-order finite field coding coefficient group and the second high-order finite field coding coefficients For the finite fields of other coding coefficients outside the group, the finite field order corresponding to the third high-order field coding coefficient group is higher than the highest-order finite field order supported by the receiver;

The processor is specifically configured to perform a decoding operation on the third decoding matrix to generate a zero matrix.

In some optional embodiments of the present application,

The processor is further configured to decode the w fourth encoded packets, including:

in,

for

matrix,

satisfy

The third decoding matrix is

In some optional embodiments of the present application,

The processor is specifically configured to decode the sixth encoded data block in the highest-order finite field corresponding to the encoding coefficients of the sixth encoded data block, so that the matrix composed of the encoding coefficients of the sixth encoded data block is decoded to obtain a unit matrix;

The processor is specifically configured to perform a synchronous decoding operation on the sixth encoded data block to generate k' source data blocks when the matrix composed of the encoding coefficients of the sixth encoded data block is subjected to a decoding operation.

In a possible implementation manner, the processor is configured to execute step 1402 and step 1403 in the embodiment corresponding to FIG. 14 , and/or step 2002 in the embodiment corresponding to FIG. 20a .

In a possible implementation manner, the transceiver is configured to perform step 1401 in the embodiment corresponding to FIG. 14 and/or step 2001 in the embodiment corresponding to FIG. 20a.

It should be noted that the information exchange, execution process and other contents among the modules/or components of the network device are based on the same concept as the method embodiments corresponding to FIGS. 4 to 20a in this application. The descriptions in the method embodiments shown are not repeated here.

It should be noted that, for the specific implementation manner of the network device and the beneficial effects brought about, reference may be made to the descriptions in the respective method embodiments corresponding to FIG. 4-FIG. 20a, and details are not repeated here.

An embodiment of the present application also provides a processing device, please refer to FIG. 26, which is a schematic diagram of a processing device proposed by an embodiment of the present application. The processing device includes a processor 2601 and an interface 2602; the processor 2601 is configured to execute the finite field encoding or decoding method in any of the above method embodiments.

It should be understood that the above-mentioned processing device may be a chip, and the processor 2601 may be implemented by hardware or software. When implemented by hardware, the processor 2601 may be a logic circuit, an integrated circuit, etc.; when implemented by software At this time, the processor 2601 may be a general-purpose processor, which is implemented by reading software codes stored in a memory, and the memory may be integrated in the processor 2601 or located outside the processor 2601 and exist independently.

Wherein, "implemented by hardware" means that the functions of the above-mentioned modules or units are realized by a hardware processing circuit that does not have the function of processing program instructions. The hardware processing circuit can be composed of discrete hardware components or an integrated circuit. In order to reduce power consumption and reduce size, it is usually implemented in the form of integrated circuits. The hardware processing circuit may include ASIC (application-specific integrated circuit, application-specific integrated circuit), or PLD (programmable logic device, programmable logic device); wherein, PLD may include FPGA (field programmable gate array, field programmable gate array) , CPLD (complex programmable logic device, complex programmable logic device) and so on. These hardware processing circuits can be a single semiconductor chip packaged separately (such as packaged into an ASIC); they can also be integrated with other circuits (such as CPU, DSP) and packaged into a semiconductor chip, for example, can be formed on a silicon substrate A variety of hardware circuits and CPUs are individually packaged into a chip, which is also called SoC, or circuits and CPUs for implementing FPGA functions can also be formed on a silicon substrate and individually enclosed into a single chip. Also known as SoPC (system on a programmable chip, programmable system on a chip).

The present application also provides a communication system, which includes at least one or more of a sender, a receiver, and an intermediate node.

An embodiment of the present application further provides a computer-readable storage medium, including instructions, which, when executed on a computer, cause the computer to control a network device to execute any one of the implementations shown in the foregoing method embodiments.

An embodiment of the present application also provides a computer program product, the computer program product includes computer program code, and when the computer program code runs on a computer, the computer can execute any one of the implementations shown in the foregoing method embodiments.

An embodiment of the present application further provides a chip system, including a memory and a processor, the memory is used to store a computer program, and the processor is used to call and run the computer program from the memory, so that the chip executes any one of the implementations shown in the foregoing method embodiments. Way.

Embodiments of the present application further provide a chip system, including a processor, where the processor is configured to call and run a computer program, so that the chip executes any one of the implementations shown in the foregoing method embodiments.

In addition, it should be noted that the device embodiments described above are only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units , that is, it can be located in one place, or it can be distributed to multiple network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution in this embodiment. In addition, in the drawings of the device embodiments provided in the present application, the connection relationship between the modules indicates that there is a communication connection between them, which may be specifically implemented as one or more communication buses or signal lines.

From the description of the above embodiments, those skilled in the art can clearly understand that the present application can be implemented by means of software plus necessary general-purpose hardware. Special components, etc. to achieve. Under normal circumstances, all functions completed by a computer program can be easily implemented by corresponding hardware, and the specific hardware structures used to implement the same function can also be various, such as analog circuits, digital circuits or special circuit, etc. However, a software program implementation is a better implementation in many cases for this application. Based on this understanding, the technical solutions of the present application can be embodied in the form of software products in essence, or the parts that make contributions to the prior art. The computer software products are stored in a readable storage medium, such as a floppy disk of a computer. , U disk, mobile hard disk, ROM, RAM, magnetic disk or optical disk, etc., including several instructions to make a computer device execute the methods described in the various embodiments of the present application.

In the above-mentioned embodiments, it may be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented in software, it can be implemented in whole or in part in the form of a computer program product.

The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present application are generated. The computer may be a general purpose computer, special purpose computer, computer network, or other programmable device. The computer instructions may be stored in or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be downloaded from a website, computer, network device, computing equipment or data center to another website site, computer, network appliance, computing device, or data center by wire (eg, coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (eg, infrared, wireless, microwave, etc.) transmission. The computer-readable storage medium may be any available medium that can be stored by a computer, or a data storage device such as a network device, a data center, or the like that includes one or more available media integrated. The usable media may be magnetic media (eg, floppy disks, hard disks, magnetic tapes), optical media (eg, DVD), or semiconductor media (eg, Solid State Disk (SSD)), and the like.

It is to be understood that reference throughout the specification to "one embodiment" or "an embodiment" means that a particular feature, structure or characteristic associated with the embodiment is included in one or more embodiments of the present application. Thus, appearances of "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily necessarily referring to the same embodiment. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner in one or more embodiments. It should be understood that, in various embodiments of the present application, the size of the sequence numbers of the above-mentioned processes does not mean the sequence of execution, and the execution sequence of each process should be determined by its functions and internal logic, and should not be dealt with in the embodiments of the present application. implementation constitutes any limitation.

Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. Interchangeability, the above description has generally described the components and steps of each example in terms of function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Skilled artisans may implement the described functionality using different methods for each particular application, but such implementations should not be considered beyond the scope of this application.

Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system, device and unit described above may refer to the corresponding process in the foregoing method embodiments, which will not be repeated here.

In the several embodiments provided in this application, it should be understood that the disclosed system, apparatus and method may be implemented in other manners. For example, the apparatus embodiments described above are only illustrative. For example, the division of units is only a logical function division. In actual implementation, there may be other division methods, for example, multiple units or components may be combined or integrated. to another system, or some features can be ignored, or not implemented. On the other hand, the shown or discussed mutual coupling or direct coupling or communication connection may be through some interfaces, indirect coupling or communication connection of devices or units, which may be electrical, mechanical or other forms.

Units described as separate components may or may not be physically separated, and components shown as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution in this embodiment.

In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically alone, or two or more units may be integrated into one unit. The above-mentioned integrated units may be implemented in the form of hardware, or may be implemented in the form of software functional units.

The integrated unit, if implemented as a software functional unit and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the present application can be embodied in the form of software products in essence, or the parts that contribute to the prior art, or all or part of the technical solutions, and the computer software products are stored in a storage medium , including several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods in the various embodiments of the present application.

In a word, the above descriptions are only preferred embodiments of the technical solutions of the present application, and are not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of this application shall be included within the protection scope of this application.

Claims

A finite field encoding method, characterized in that the method comprises:

encoding the k source data blocks using the first encoding coefficient matrix to generate one or more first encoding data blocks, the first encoding data blocks corresponding to a set of encoding coefficients in the first encoding coefficient matrix, k is a positive integer;

One or more first encoded messages are generated according to the one or more first encoded data blocks, where the first encoded message includes one or more of the first encoded data blocks, and one or more of the first encoded data blocks. a group of coding coefficients in the first coding coefficient matrix corresponding to the first coded data block;

The first coding coefficient matrix includes coding coefficients of a first finite field and coding coefficients of a second finite field, and the first finite field and the second finite field are finite fields with a nested structure, and the The order of the second finite field is higher than that of the first finite field, and the finite field with the nested structure satisfies the following relationship: the order has a multiple relationship, and the characteristic numbers are consistent;

The one or more first encoded messages are sent.
The method of claim 1, wherein:

The source data block is: p j , where j is a positive integer, 1≤j≤k;

The coding coefficients of the first finite field and the coding coefficients of the second finite field are α n,k , where n is a positive integer;

One or more of the first encoded data blocks include: c n , wherein,
The method according to claim 1 or 2, characterized in that,

The coding coefficients of the first finite field are carried in the network layer or the data link layer of the first coded message;

The coding coefficients of the second finite field are carried in the transport layer of the first coded message.
A finite field encoding method, characterized in that the method comprises:

encoding the k source data blocks using the second encoding coefficient matrix to generate one or more second encoding data blocks, the second encoding data blocks corresponding to a set of encoding coefficients in the second encoding coefficient matrix, k is a positive integer;

The one or more second encoded data blocks and the k source data blocks are encoded using the third encoding coefficient matrix to generate g third encoded data blocks, the third encoded data blocks and the Corresponding to a group of coding coefficients in the matrix of three coding coefficients, g is a positive integer;

One or more second encoded packets are generated according to the one or more second encoded data blocks and the g third encoded data blocks, and one of the second encoded packets includes: at least one or more of the said third encoded data block and one or more encoding coefficients of said third encoded data block;

Wherein, the second encoding coefficient matrix includes encoding coefficients of a third finite field, the third encoding coefficient matrix includes encoding coefficients of a fourth finite field, and the third finite field and the fourth finite field have embedded The finite field of the nested structure, the order of the fourth finite field is higher than the third finite field, and the finite field with the nested structure satisfies the following relationship: the order has a multiple relationship, and the characteristic number is consistent;

Sending one or more of the second encoded messages.
The method according to claim 4, wherein the second encoded message further comprises:

at least one said second encoded data block, and, at least one encoded coefficient of said second encoded data block,

And/or, at least one of the source data blocks, and, the coding coefficients of at least one of the source data blocks, the coding coefficients of at least one of the source data blocks are corresponding elements in the unit matrix, and the size of the unit matrix is determined by The number of the second encoded data blocks and the number of the source data blocks are determined, and the encoding coefficients of the source data blocks belong to the fourth finite field.
The method according to claim 4 or 5, wherein,

The coding coefficients of the third finite field are carried in the transport layer of the second coded message;

The coding coefficients of the fourth finite field are carried in the network layer or the data link layer of the second coded message.
The method according to any one of claims 4-6, wherein the second coding coefficient matrix further comprises coding coefficients of a fifth finite field, and the fifth finite field and the third finite field have In a nested structure, the order of the fifth finite field is different from the order of the third finite field.
A method for recoding a finite field, wherein the method comprises:

Receive one or more third encoded packets, where the third encoded packets include g' fourth encoded data blocks and encoding coefficients corresponding to the g' fourth encoded data blocks, where g' is positive integer;

Using the fourth encoding coefficient matrix to perform encoding processing on the g' fourth encoded data blocks to generate one or more fifth encoded data blocks, the fifth encoded data block and one of the fourth encoded coefficient matrices Group coding coefficient correspondence;

One or more re-encoded messages are generated according to the one or more fifth encoded data blocks, where the re-encoded message includes one or more of the fifth encoded data blocks, and one or more of the first encoded data blocks. A group of encoding coefficients in the fourth encoding coefficient matrix corresponding to five encoded data blocks;

Wherein, the finite field of the coding coefficients in the fourth coding coefficient matrix and the finite field of the coding coefficients included in the third coding message have a nested structure, and the finite field with the nested structure satisfies the following relationship: The order has a multiple relationship, and the number of features is consistent;

Send one or more of the recoded messages.
The method of claim 8, wherein:

The finite field order of the coding coefficients in the fourth coding coefficient matrix is equal to the lowest order of the finite field in the network where the intermediate node is located;

Or, the finite field order of the coding coefficients in the fourth coding coefficient matrix is less than or equal to the highest order of the finite field in the network where the intermediate node is located;

Or, the finite field order of the coding coefficients in the fourth coding coefficient matrix is greater than or equal to the lowest order of the finite field in the network where the intermediate node is located.
The method according to any one of claims 8-9, wherein,

The fourth encoded data block is Xi, 1≤i≤u, i is a positive integer, and u is a positive integer;

The fourth coding coefficient is γ u,v , where v is a positive integer greater than 1;

The fifth encoded data block is Y v , wherein,
Among them, 1≤j≤v.
A decoding method for a finite field, characterized in that the method comprises:

Receive one or more fourth encoded messages, where the fourth encoded message includes t' sixth encoded data blocks, and encoding coefficients corresponding to the t' sixth encoded data blocks, where t' is a positive integer;

The one or more fourth encoded messages are decoded in a low-order finite field and a high-order finite field by adopting the first decoding method to generate k source data blocks, where k is a positive integer;

The low-order finite field is the finite field with the lowest order in the network where the receiving end is located, the high-order finite field is any high-order finite field of the coding coefficients corresponding to the sixth encoded data block, and the high-order finite field is The order of the finite field is higher than the order of the lower-order finite field, and the lower-order finite field and the higher-order finite field have a nested structure, wherein the finite field with the nested structure satisfies the following relationship: The order has a multiple relationship, and the number of features is consistent;

Alternatively, a second decoding method is used to perform a decoding operation on the one or more fourth encoded packets in the highest-order finite field of the encoding coefficients corresponding to the sixth encoded data block to generate k' source data blocks , the highest-order finite field is the highest-order finite field of the coding coefficients corresponding to the sixth coded data block, and k' is a positive integer.
The method according to claim 11, wherein the first decoding mode is used to decode the one or more fourth encoded packets in the lower-order finite field and the higher-order finite field operation to generate the k source data blocks, including:

performing a first decoding operation on the one or more fourth encoded messages in the low-order finite field;

For the result obtained by the first decoding operation, a second decoding operation is performed in the high-order finite field to generate the k source data blocks.
The method according to claim 12, wherein performing the first decoding operation on the one or more fourth encoded packets in the low-order finite field comprises:

According to the coding coefficients corresponding to the sixth coded data block in the one or more fourth coded messages, determine the coding coefficients of the lower-order finite field and the coding coefficients of the higher-order finite field;

A low-order domain coding coefficient matrix is formed from the coding coefficients of the low-order finite field;

According to the low-order domain coding coefficient matrix, a first decoding matrix and a second decoding matrix are formed, wherein,

The coding coefficients corresponding to the high-order finite field in the coding coefficients of the first decoding matrix form a first high-order field coding coefficient group, and the finite field of the first high-order field coding coefficient group is the sixth coding The finite field with the lowest order among all the higher-order finite fields of the coding coefficients corresponding to the data block;

The coding coefficients corresponding to the high-order finite field in the coding coefficients of the second decoding matrix form a second high-order field coding coefficient group, and the finite field of the second high-order field coding coefficient group is the sixth coding The finite field of other coding coefficients except the first high-order finite field coding coefficient group in the coding coefficients corresponding to the data block, and the finite field order of the second high-order field coding coefficient group is less than or equal to the receiving end the highest order finite field order supported;

Perform a decoding operation on the second decoding matrix to generate a first decoding sub-matrix and a second decoding sub-matrix, wherein the first decoding sub-matrix is a zero matrix, and the second decoding matrix is identity matrix;

When a decoding operation is performed on the second decoding matrix, a decoding operation is performed on the first decoding matrix to generate a third decoding sub-matrix and a fourth decoding sub-matrix, wherein the third decoding sub-matrix is The number of rows of the sub-matrix is the same as the number of rows of the first decoding sub-matrix, the number of rows of the fourth decoding sub-matrix is the same as the number of rows of the second decoding sub-matrix, or, the The number of columns of the third decoding sub-matrix is consistent with the number of columns of the first decoding sub-matrix, and the number of columns of the fourth decoding sub-matrix is consistent with the number of columns of the second decoding sub-matrix;

When a decoding operation is performed on the first decoding matrix, a synchronous decoding operation is performed on the sixth encoded data block to generate data to be decoded.
The method according to claim 13, wherein the second decoding operation is performed on the result obtained by the first decoding operation in the high-order finite field to generate the k source data blocks ,include:

The result obtained by the first decoding operation includes the third decoding sub-matrix, the fourth decoding sub-matrix, and the data to be decoded,

determining, according to the fourth decoding sub-matrix, a fifth decoding sub-matrix corresponding to the fourth decoding sub-matrix, where the fifth decoding sub-matrix is composed of coding coefficients of the higher-order finite field;

A sixth decoding sub-matrix is generated according to the fourth decoding sub-matrix and the fifth decoding sub-matrix, wherein the vectors in the sixth decoding sub-matrix are determined by the values of the fifth decoding sub-matrix. A set of coding coefficients and a set of coding coefficients of the fourth decoding sub-matrix are obtained by addition in the finite field corresponding to the fifth decoding sub-matrix;

forming a fourth decoding matrix according to the third decoding sub-matrix and the sixth decoding sub-matrix;

performing a decoding operation on the fourth decoding matrix to generate a unit matrix with a diagonal coefficient of 1;

When performing a decoding operation on the fourth decoding matrix, a synchronous decoding operation is performed on the data to be decoded to generate the k source data blocks.
The method according to any one of claims 13-14, wherein forming the first decoding matrix and the second decoding matrix according to the low-order domain coding coefficient matrix, comprising:

According to the low-order domain coding coefficient matrix, the first decoding matrix, the second decoding matrix and the third decoding matrix are formed, wherein the third decoding matrix corresponds to the high-order finite field The coding coefficients form the third higher-order domain coding coefficient group, and the finite field of the third higher-order domain coding coefficient group is the coding coefficients corresponding to the sixth coded data block divided by the first higher-order finite field coding coefficients group and the finite fields of other coding coefficients other than the second higher-order finite field coding coefficient group, the finite field order corresponding to the third higher-order finite field coding coefficient group is higher than the highest-order finite field order supported by the receiving end ;

A decoding operation is performed on the third decoding matrix to generate a zero matrix.
The method according to any one of claims 10-15, wherein the method further comprises:

For k said source data blocks, where k is a positive integer,

When the following conditions are met, the w fourth encoded packets are decoded, including:

in,
for
Matrix, the high-order domain coding coefficient matrix is G, the high-order domain coding coefficient matrix is composed of the coding coefficients of the high-order finite field, and the low-order domain coding coefficient matrix H, w are positive integers.
The method according to any one of claims 10-16, wherein the second decoding mode is used to perform a decoding operation on the one or more fourth encoded packets to generate the k' Source data blocks, including:

In the highest-order finite field corresponding to the coding coefficients of the sixth coded data block, the sixth coded data block is decoded, so that the matrix composed of the coding coefficients of the sixth coded data block is decoded to obtain a unit matrix;

When a decoding operation is performed on the matrix formed by the encoding coefficients of the sixth encoded data block, a synchronous decoding operation is performed on the sixth encoded data block to generate the k' source data blocks.
A network device, comprising:

A processor, configured to perform encoding processing on k source data blocks by using the first encoding coefficient matrix to generate one or more first encoding data blocks, the first encoding data block and one of the first encoding coefficient matrices Corresponding to the group coding coefficient, k is a positive integer;

The processor is further configured to generate one or more first encoded packets according to the one or more first encoded data blocks, where the first encoded packets include one or more of the first encoded data a block, and a set of coding coefficients in the first coding coefficient matrix corresponding to one or more of the first coded data blocks;

The first coding coefficient matrix includes coding coefficients of a first finite field and coding coefficients of a second finite field, and the first finite field and the second finite field are finite fields with a nested structure, and the The order of the second finite field is higher than that of the first finite field, and the finite field with the nested structure satisfies the following relationship: the order has a multiple relationship, and the characteristic numbers are consistent;

A receiver, configured to send the one or more first encoded messages.
The network device of claim 18, wherein:

The source data block is: p j , where j is a positive integer, 1≤j≤k;

The coding coefficients of the first finite field and the coding coefficients of the second finite field are α n,k , and n is a positive integer;

One or more of the first encoded data blocks include: c n , wherein,
The network device according to claim 18 or 19, characterized in that:

The coding coefficients of the first finite field are carried in the network layer or the data link layer of the first coded message;

The coding coefficients of the second finite field are carried in the transport layer of the first coded message.
A limited field coding network device, characterized in that, the network device comprises:

The processor is configured to perform encoding processing on the k source data blocks by using the second encoding coefficient matrix to generate one or more second encoding data blocks, the second encoding data block and one of the second encoding coefficient matrices Corresponding to the group coding coefficient, k is a positive integer;

The processor is further configured to perform encoding processing on the one or more second encoded data blocks and the k source data blocks by using a third encoding coefficient matrix to generate g third encoded data blocks, the The three encoded data blocks correspond to a group of encoding coefficients in the third encoding coefficient matrix, and g is a positive integer;

The processor is further configured to generate one or more second encoded packets according to the one or more second encoded data blocks and the g third encoded data blocks, one of the second encoded packets comprising: one or more of the third encoded data blocks and one or more encoding coefficients of the third encoded data blocks;

Wherein, the second encoding coefficient matrix includes encoding coefficients of a third finite field, the third encoding coefficient matrix includes encoding coefficients of a fourth finite field, and the third finite field and the fourth finite field have embedded The finite field of the nested structure, and the order of the fourth finite field is higher than the third finite field, and the finite field with the nested structure satisfies the following relationship: the order has a multiple relationship, and the characteristic number is one to;

A transceiver, configured to send one or more of the second encoded messages.
The network device according to claim 21, wherein the second encoded message further comprises:

at least one said second encoded data block, and, at least one encoded coefficient of said second encoded data block,

And/or, at least one of the source data blocks, and, the coding coefficients of at least one of the source data blocks, the coding coefficients of at least one of the source data blocks are corresponding elements in the unit matrix, and the size of the unit matrix is determined by The number of the second encoded data blocks and the number of the source data blocks are determined, and the encoding coefficients of the source data blocks belong to the fourth finite field.
The network device according to claim 21 or 22, characterized in that:

The coding coefficients of the third finite field are carried in the transport layer of the second coded message;

The coding coefficients of the fourth finite field are carried in the network layer or the data link layer of the second coded message.
The network device according to any one of claims 21-23, wherein the second coding coefficient matrix further comprises coding coefficients of a fifth finite field, the fifth finite field and the third finite field Having a nested structure, the order of the fifth finite field is different from the order of the third finite field.
A finite field recoding network device, characterized in that the network device comprises:

a transceiver, configured to receive one or more third encoded packets, where the third encoded packets include g' fourth encoded data blocks and encoding coefficients corresponding to the g' fourth encoded data blocks , g' is a positive integer;

a processor, configured to perform encoding processing on the g' fourth encoded data blocks by using the fourth encoding coefficient matrix to generate one or more fifth encoded data blocks, the fifth encoded data blocks and the fourth encoded data blocks A set of coding coefficients in the coefficient matrix corresponds to;

The processor is further configured to generate one or more re-encoded messages according to the one or more fifth encoded data blocks, where the re-encoded messages include one or more of the fifth encoded data blocks, and a set of encoding coefficients in the fourth encoding coefficient matrix corresponding to one or more of the fifth encoded data blocks;

Wherein, the finite field of the coding coefficients in the fourth coding coefficient matrix and the finite field of the coding coefficients included in the third coding message have a nested structure, and the finite field with the nested structure satisfies the following relationship: The order has a multiple relationship, and the number of features is consistent;

The transceiver is further configured to send one or more of the recoded packets.
The network device of claim 25, wherein:

The finite field order of the coding coefficients in the fourth coding coefficient matrix is equal to the lowest order of the finite field in the network where the intermediate node is located;

Or, the finite field order of the coding coefficients in the fourth coding coefficient matrix is less than or equal to the highest order of the finite field in the network where the intermediate node is located;

Or, the finite field order of the coding coefficients in the fourth coding coefficient matrix is greater than or equal to the lowest order of the finite field in the network where the intermediate node is located.
The network device according to any one of claims 25-26, characterized in that,

The fourth encoded data block is Xi, 1≤i≤u, i is a positive integer, and u is a positive integer;

The fourth coding coefficient is γ u,v , where v is a positive integer greater than 1;

The fifth encoded data block is Y v , wherein,
Among them, 1≤j≤v.
A finite field decoding network device, characterized in that the network device comprises:

a transceiver, configured to receive one or more fourth encoded messages, where the fourth encoded message includes t' sixth encoded data blocks and encoding coefficients corresponding to the t' sixth encoded data blocks, t ' is a positive integer;

a processor, configured to perform a decoding operation on the one or more fourth encoded messages in a low-order finite field and a high-order finite field by using the first decoding method, and generate k source data blocks, where k is a positive integer;

The low-order finite field is the finite field with the lowest order in the network where the receiving end is located, the high-order finite field is any high-order finite field of the coding coefficients corresponding to the sixth encoded data block, and the high-order finite field is The order of the finite field is higher than the order of the lower-order finite field, and the lower-order finite field and the higher-order finite field have a nested structure, wherein the finite field with the nested structure satisfies the following relationship: The order has a multiple relationship, and the number of features is consistent;

or,

The processor is further configured to perform a decoding operation on the one or more fourth encoded packets in the highest-order finite field of the encoding coefficients corresponding to the sixth encoded data block by using the second decoding method, and generate There are k' source data blocks, the highest-order finite field is the highest-order finite field of the coding coefficients corresponding to the sixth coded data block, and k' is a positive integer.
The network device of claim 28, wherein:

The processor is specifically configured to perform a first decoding operation on the one or more fourth encoded packets in the low-order finite field;

The processor is specifically configured to perform a second decoding operation on the result obtained by the first decoding operation in the high-order finite field to generate the k source data blocks.
The network device of claim 29, wherein:

The processor is specifically configured to determine, according to the encoding coefficients corresponding to the sixth encoded data block in the one or more fourth encoded packets, the encoding coefficients of the low-order finite field and the high-order finite field the coding coefficients;

The processor is specifically configured to form a low-order domain coding coefficient matrix from the coding coefficients of the low-order finite field;

The processor is specifically configured to form a first decoding matrix and a second decoding matrix according to the low-order domain encoding coefficient matrix, wherein the encoding coefficients of the first decoding matrix correspond to the high-order finite The coding coefficients of the domain form the first high-order domain coding coefficient group, and the finite field of the first high-order domain coding coefficient group is the lowest order among all the high-order finite fields of the coding coefficients corresponding to the sixth coded data block. finite field;

The coding coefficients corresponding to the high-order finite field in the coding coefficients of the second decoding matrix form a second high-order field coding coefficient group, and the finite field of the second high-order field coding coefficient group is the sixth coding The finite field of other coding coefficients except the first high-order finite field coding coefficient group in the coding coefficients corresponding to the data block, and the finite field order of the second high-order field coding coefficient group is less than or equal to the receiving end the highest order finite field order supported;

The processor is specifically configured to perform a decoding operation on the second decoding matrix to generate a first decoding sub-matrix and a second decoding sub-matrix, wherein the first decoding sub-matrix is a zero matrix, The second decoding matrix is an identity matrix;

The processor is specifically configured to perform a synchronous decoding operation on the first decoding matrix when the second decoding matrix performs a decoding operation to generate a third decoding sub-matrix and a fourth decoding sub-matrix, The number of rows of the third decoding sub-matrix is consistent with the number of rows of the first decoding sub-matrix, and the number of rows of the fourth decoding sub-matrix is the same as the number of rows of the second decoding sub-matrix The number of columns is the same, or, the number of columns of the third decoding sub-matrix is the same as the number of columns of the first decoding sub-matrix, and the number of columns of the fourth decoding sub-matrix is the same as the number of columns of the second decoding sub-matrix The number of columns of the submatrix is the same;

The processor is specifically configured to perform a synchronous decoding operation on the sixth encoded data block to generate data to be decoded when the first decoding matrix performs a decoding operation.
The network device of claim 30, wherein:

The result obtained by the first decoding operation includes the third decoding sub-matrix, the fourth decoding sub-matrix, and the data to be decoded,

The processor is specifically configured to determine a fifth decoding sub-matrix corresponding to the fourth decoding sub-matrix according to the fourth decoding sub-matrix, and the fifth decoding sub-matrix is determined by the higher-order finite The coding coefficient composition of the domain;

The processor is specifically configured to generate a sixth decoding sub-matrix according to the fourth decoding sub-matrix and the fifth decoding sub-matrix, wherein the vectors in the sixth decoding sub-matrix are determined by the A set of coding coefficients of the fifth decoding sub-matrix and a set of coding coefficients of the fourth decoding sub-matrix are obtained by addition in the finite field corresponding to the fifth decoding sub-matrix;

The processor is specifically configured to form a fourth decoding matrix according to the third decoding sub-matrix and the sixth decoding sub-matrix;

The processor is specifically configured to perform a decoding operation on the fourth decoding matrix to generate a unit matrix;

The processor is specifically configured to perform a synchronous decoding operation on the data to be decoded to generate the k source data blocks when performing a decoding operation on the fourth decoding matrix.
The network device according to any one of claims 28-31, wherein,

The processor is specifically configured to form the first decoding matrix, the second decoding matrix and the third decoding matrix according to the low-order domain coding coefficient matrix, wherein the third decoding matrix The coding coefficients corresponding to the high-order finite field in the above form a third high-order field coding coefficient group, and the finite field of the third high-order field coding coefficient group is divided by the coding coefficients corresponding to the sixth coded data block. The finite field of the coding coefficients other than the first high-order finite field coding coefficient group and the second high-order finite field coding coefficient group, and the finite field order corresponding to the third high-order field coding coefficient group is higher than that of the receiving end the highest order finite field order supported;

The processor is specifically configured to perform a decoding operation on the third decoding matrix to generate a zero matrix.
The network device according to any one of claims 28-32, wherein the network device further comprises:

For the k source data blocks, when the following conditions are met, the processor is further configured to decode the w fourth encoded packets, including:

in,
for
matrix, the high-order domain coding coefficient matrix is G, the high-order domain coding coefficient matrix is composed of the coding coefficients of the high-order finite field, and the low-order domain coding coefficient matrix H, w are positive integers.
The network device according to any one of claims 28-33, wherein,

The processor is specifically configured to decode the sixth coded data block in the highest-order finite field corresponding to the coding coefficients of the sixth coded data block, so that the coding coefficients of the sixth coded data block consist of The matrix is decoded to obtain the identity matrix;

The processor is specifically configured to perform a synchronous decoding operation on the sixth encoded data block when the matrix composed of the encoding coefficients of the sixth encoded data block is subjected to a decoding operation to generate the k' pieces of source data Piece.
A computer-readable storage medium, characterized in that the computer-readable storage medium has program instructions, and when the program instructions are directly or indirectly executed, make such as claims 1-3, and/or claim 4 -7, and/or, the method of any one of claims 8-10, and/or, claims 11-17 is implemented.
A chip system, characterized in that the chip system includes one or more processors and a memory, the memory stores program instructions, and when the program instructions are executed in the one or more processors, A method as claimed in any of claims 1-3, and/or, claims 4-7, and/or, claims 8-10, and/or, claims 11-17, is caused to be implemented.