Method, device and system for decoding polar codes with large cores
Patent Information
- Application Number
- CN202611143755.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-30
- Publication Date
- 2026-09-29
AI Technical Summary
[0004]相比于5G，6G对时延也有更高的要求；然而，无论是极化码还是大核极化码，虽然在串行抵消列表SCL译码（近似最大似然译码）下，纠错能力强，但受限于固有的逐比特串行译码特性，难以实现高的吞吐率和低时延
本发明将高纬度核矩阵的串行Tanner图等价转换为树图，并设计树图辅助的大核极化码快速译码方法，可以在不牺牲纠错能力的前提下，显著降低大核极化码串行SCL译码的时延；此外，由于在设计的树图辅助的大核极化码快速SCL译码过程中，可以并行获取特殊节点对应的若干译码结果，且不用计算整个译码树的所有节点的LLR、部分和信息，有效降低了冗余计算，因此具有更低的译码计算复杂度。
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Figure CN122844858A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of error correction coding technology, specifically to a method, apparatus, and system for decoding large-core polar codes. Background Technology
[0002] Polar codes, as a structured coding scheme theoretically achievable up to the Shannon limit, possess excellent error correction performance and relatively low computational complexity in their encoding and decoding algorithms, making them advantageous for engineering implementation. They have garnered widespread attention from academia and industry and have been adopted by fifth-generation mobile communication systems (5G). However, with the shorter code length requirements of future 6G networks, the channel polarization of polar codes is significantly weakened, thereby drastically reducing their error correction performance. Therefore, improving the polarization capability of polar codes under short code lengths and enhancing their error correction ability remains a challenging research area in polar codes.
[0003] Replacing the second-order polarization kernel matrix of classical polar codes with a higher-order polarization kernel that offers superior polarization performance can fundamentally improve the polarization capability of polar codes, thereby effectively enhancing their error correction capability under short code lengths. Furthermore, by carefully designing the Tanner diagram of the higher-order kernel matrix, large-kernel polar codes can achieve encoding and decoding complexities similar to classical polar codes without sacrificing strong error correction capabilities, thus enabling the practical application of large-kernel polar codes.
[0004] Compared to 5G, 6G has even higher requirements for latency. However, while both polar codes and big-core polar codes have strong error correction capabilities under Serial Cancellation List (SCL) decoding (approximate maximum likelihood decoding), they are limited by their inherent bit-by-bit serial decoding characteristics, making it difficult to achieve high throughput and low latency. Therefore, how to design low-latency big-core polar code SCL decoding to meet the requirements of 6G is a pressing problem that needs to be solved. Summary of the Invention
[0005] The purpose of this invention is to provide a method, apparatus and system for decoding large-core polar codes, with the aim of providing a polar code decoding scheme with strong error correction and low latency under medium-short-long conditions; in addition, since large-core polar codes do not significantly increase the complexity of encoding and decoding, they are still conducive to engineering implementation.
[0006] To achieve the above objectives, the present invention adopts the following technical solution: a big-core polar code decoding method, comprising the following steps: S11. Receive the signal to be decoded. The signal to be decoded is the signal when the big nucleus polar code sent by the transmitter arrives at the receiver. The high-dimensional kernel matrix of the big nucleus polar code can be equivalently converted into a serial kernel Tanner diagram. S12. Design a universal decoding tree graph structure applicable to large-core polar codes of any dimension, and obtain explicit expressions for the partial sum, log-likelihood ratio, and path metric of any node in the universal decoding tree graph structure. S13. Based on the distribution pattern of information bit positions in the leaf nodes of the general decoding tree diagram structure, special node types are summarized. S14. Obtain the fast calculation formula for the partial sum and path metric value corresponding to special nodes in the general decoding tree graph structure; S15. Perform fast decoding of the big-core polar code. For special nodes, directly use their corresponding fast calculation formulas; for non-special nodes, decode normally according to the general decoding tree structure.
[0007] Furthermore, S12 includes the following steps: S21, for dimension... kernel matrix , For integers greater than 2, construct their corresponding decoding tree graph units, where a single root node is used as the 0th level, and the root node splits downwards into... Each child node is a descendant of the first level, and the root node and its child nodes are considered descendants of the first level. The child nodes together form the kernel matrix. The corresponding decoding tree diagram unit; S22, According to the kernel matrix The corresponding formula for calculating the log-likelihood ratio and the bit-by-bit decoding order are used to calculate the log-likelihood ratio of each child node in the first layer of the decoding tree graph unit from left to right. And perform hard decision on each log-likelihood ratio to obtain the corresponding partial sum value. And return it to the root node, where ; All The partial sums and values of the child nodes are combined to form a sequence. and multiplied by the kernel matrix To obtain parts and sequences And return to the root node, the part and the sequence. The decoding result for the root node; S23. For a given code length Construct a decoding tree graph for the big-core polar code, where the unique root node is used as the first... Layers, splitting downwards The child node is the first Layer; then the first Each node in the layer acts as a parent node and continues to split downwards. The nth child node forms the nth... Layer; and so on, until the first layer is reached. The splitting stops when the layer is reached; record the first layer. The number of nodes in the layer from left to right is Then any node is marked as For any parent node Its child nodes are represented from left to right as follows: ; S24, According to the kernel matrix The corresponding formula for calculating the log-likelihood ratio of the serial core Tanner graph and the bit-by-bit decoding order. Derive any node in the big-core polar code decoding tree graph The explicit expressions for the log-likelihood ratio and the partial sum; S25, the root node of the decoding tree graph has a receive length of... The received sequence is updated according to the explicit expression described in S24, updating the log-likelihood ratio and partial sum information of each node in the decoding tree graph until the first... The partial sums of all leaf nodes in the layer are updated, thus completing the tree graph decoding of the big nucleus polar code.
[0008] Furthermore, in S22, the log-likelihood ratio of the leftmost first node in the first layer of the decoding tree graph unit is calculated. ,right Perform a hard decision operation to obtain the partial sum of the first leftmost node in the first layer of the decoded tree graph unit. and return it to the root node; according to Kernel matrix The corresponding formula for calculating the log-likelihood ratio and the bit-by-bit decoding order are used to calculate the log-likelihood ratio of the second node in the first layer of the decoding tree graph unit. ,right Perform a hard decision operation to obtain the partial sum of the second node in the first layer of the decoded tree graph unit. And return it to the root node; and so on, so that the decoding tree graph units can be obtained sequentially from left to right. The log-likelihood ratio corresponding to each child node and partial sum .
[0009] Furthermore, in S24, for any node in the big-core polar code decoding tree diagram... , its first The soft information log-likelihood ratio of each offspring is expressed as follows: , where the function Represents the kernel matrix The corresponding serial core Tanner graph calculates the first Formula for the log-likelihood ratio of each decoded bit; Representative set The Middle One element; , represent The Middle The set consisting of all elements preceding the first element; Representative function Medium parameters The set of indices; For any node in the big-core polar code decoding tree diagram Parts and sequences It is a length of The bit vector, specifically represented as ,in ,return The remainder, if ,function ,otherwise ; Represents a set The Middle Elements, where the set .
[0010] Furthermore, S13 includes the following steps: S31. Let the root node index of the big-core polar code decoding tree be 1. The second level of the decoding tree... The position indices of the nodes are respectively Similarly, following the order from top to bottom and left to right, the set of indices of all nodes in the big-core polar code decoding tree is: And initialize three empty sets A, B, and F; S32, From the set Starting with the first element, proceed to the right to check the... element The corresponding decoding tree node contains the first Check if all leaf nodes in the layer are either frozen bits, information bits, or a combination of both. If all are frozen bits, proceed to step S33; if all are information bits, proceed to step S34. S33, will elements in Add to set A and update set A, that is... ; S34, will elements in Add to set B and update set B, that is... ; S35. Obtain the indices of all child nodes split from the decoding tree node corresponding to each element in set A, and form set D; obtain the indices of all child nodes split from the decoding tree node corresponding to each element in set B, and form set E; let set And delete the nodes corresponding to sets D and E from the big nucleus polar code decoding tree to obtain a simplified big nucleus polar code decoding tree diagram.
[0011] Furthermore, S14 includes the following steps: S41. In the simplified big-core polar code decoding tree, the nodes in the decoding trees corresponding to sets A and B are special nodes. The decoding results of their corresponding leaf nodes can be obtained directly, thus avoiding the calculation of the log-likelihood ratio, partial sum, and path metric of their child nodes. When the special node type belongs to A, proceed to S42; when the special node type belongs to B, proceed to S43. S42, length is The partial sum of class A nodes, i.e., the first node in the split decode tree. The decoding results of all leaf nodes of the layer are calculated as follows: ,in Its path metric is calculated as follows: ,in It is the first time that a special node of type A has received this information. The log-likelihood ratio; S42, length is The partial sum of the B-class nodes, i.e., the first node in the split decode tree. The decoding results of all leaf nodes of the layer are calculated as follows: ,in ; It is the first time that a special node of type A has received this information. The log-likelihood ratio; It is a hard decision function, when hour, Returns 0 otherwise; its path metric is calculated as follows: ,in ; It is the first time that a special node of type B has received this information. Log-likelihood ratio It is the first special node corresponding to class B. Each part and value.
[0012] Furthermore, S15 includes the following steps: S51. Perform fast decoding based on the received sequence and the simplified decoding tree diagram. When the current node belongs to class A node, proceed to S52; when the current node belongs to class B node, proceed to S53; when the current node belongs to class F node, proceed to S54. S52. Based on S42, directly obtain the partial sum and path metric value of the special node of type A in the current decoding tree, and then proceed to S54. S53. Based on S43, directly obtain the partial sum and path metric value of the special node of type B in the current decoding tree, and then proceed to S54; S54. Perform big core polar code decoding according to S25.
[0013] A large-core polar code decoding device, comprising: The signal receiving module is used to receive the signal to be decoded, which is the signal when the big nucleus polar code sent by the transmitter arrives at the receiver. The tree graph construction module is used to construct a general decoding tree graph structure applicable to large-kernel polar codes of any dimension, and to determine the expressions for the log-likelihood ratio, partial sum, and path metric of any node in the general decoding tree graph. The node classification module is used to summarize the special node types in the decoding tree diagram based on the distribution pattern of information bit positions of leaf nodes in the decoding tree diagram; The fast calculation module is used to determine the partial sum and path metric value of special nodes using a fast calculation formula. The decoding execution module is used to perform fast decoding of big-core polar codes. For special nodes, it directly uses their corresponding fast calculation formulas for processing, while for non-special nodes, it performs normal decoding according to the decoding tree structure.
[0014] A large-core polar code decoding system, comprising: Memory, used to store computer programs; A processor for executing a computer program to implement the steps of the big-core polar code decoding method as described in any one of claims 1-7.
[0015] The beneficial effects of this invention are: This invention converts the serial Tanner graph of the high-dimensional kernel matrix into an equivalent tree graph and designs a tree graph-assisted fast decoding method for large kernel polar codes. This method can significantly reduce the latency of serial SCL decoding of large kernel polar codes without sacrificing error correction capability. Furthermore, since several decoding results corresponding to special nodes can be obtained in parallel during the tree graph-assisted fast SCL decoding process of large kernel polar codes, and the LLR, partial sum information of all nodes in the entire decoding tree does not need to be calculated, redundant calculations are effectively reduced, thus resulting in lower decoding computational complexity. Attached Figure Description
[0016] Figure 1 A flowchart of a large-core polar code decoding method provided in an embodiment of the present invention; Figure 2 The equivalent transformation between the serial kernel Tanner graph and the tree graph corresponding to the high-dimensional polarization kernel matrix provided in the embodiments of the present invention; Figure 3 This is the basic unit of the decoding tree diagram for arbitrary-dimensional big-kernel polar codes provided in the embodiments of the present invention; Figure 4 This is a decoding tree diagram of a large-core polar code provided in an embodiment of the present invention; Figure 5 This is a special node type of the big nucleus polar code provided in the embodiments of the present invention; Figure 6 A simplified decoding tree diagram of a large-core polar code provided in an embodiment of the present invention; Figure 7 A comparison of the error correction capabilities of the big-core polar codes and classical second-order polar codes provided in the embodiments of the present invention at different code lengths; Figure 8 This paper compares the error correction capabilities of the fast SCL decoding of big-core polar codes provided in this embodiment of the invention with those of existing fast decoding of big-core polar codes at different code lengths. Detailed Implementation
[0017] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
[0018] For a big-core polar code with a code length of N and a transmission of K information bits, the big-core polar coding technique also uses a Tanner diagram to polarize N independent and identically distributed channels into N bit channels. Of these N bit channels, the K most reliable ones are called information bit channels, used to transmit the information bits of the big-core polar code; the other NK bit channels are called frozen bit channels, and the bits transmitted on the frozen bit channels are called frozen bits. Therefore, before decoding a big-core polar code, it is necessary to obtain its Tanner diagram and information bit position indices in advance.
[0019] By converting the Tanner graph corresponding to the XOR structure into a tree graph structure, classical polar codes can be decoded quickly using SCL, thereby reducing decoding complexity and latency. Similarly, the core Tanner graph of big-core polar codes can also be converted into a tree graph, thus enabling fast SCL decoding. Figure 2 When the kernel matrix dimension is 6, the kernel matrix The corresponding equivalent transformation between the serial core Tanner graph and the tree graph, where Figure 2 (a) in the diagram is the Tanner plot of the serial core. Figure 2 (b) in the diagram represents a tree diagram. Of course, different kernel matrix dimensions will result in different tree diagrams. Figure 2 A universal decoding tree unit applicable to big-kernel polar codes of arbitrary dimensions is presented, where the parent node receives the LLR value sequence, corresponding to the LLR value of the output node of the serial kernel Tanner graph, which can then be obtained using a bit-by-bit serial decoding formula. The LLR values and partial sums of the child nodes.
[0020] Once the basic decoding tree units of the big-core polar code are obtained, the complete decoding tree structure can be easily derived. For example... Figure 4 The diagram shown is a decoding tree diagram for a large-kernel polar code with a kernel matrix size of 6 and a code length N=36. The decoding tree diagram starts from the root node at the top and is divided into several parts. Layer, in which The size of the nucleus. (Excluding the...) Except for the leaf nodes of the first layer, any node in any other layer splits into... There are child nodes. If the child node is... The number of nodes in the layer from left to right is used Let's represent it as... Then, any node in the decoding tree can be labeled as... Therefore, for any parent node Its child nodes can be represented from left to right as follows: .
[0021] Unlike classical polar code SCL decoding, big-core polar code tree graph decoding does not perform bit-by-bit decoding in ascending order, but rather follows the decoding order corresponding to the core Tanner graph. The decision is made. Specifically, the SCL decoding order assisted by the big-core polar code tree diagram is as follows:
[0022] in, yes The first in Each element. Figure 2 (a) Taking the core Tanner diagram as an example, its bit-by-bit serial decoding formula is calculated as follows:
[0023]
[0024]
[0025]
[0026]
[0027]
[0028] in for Corresponding kernel Tanner graph input node The LLR value, Yes The partial sum value obtained by performing a hard decision operation. It can be seen that... The bit-by-bit decoding order is .therefore, Figure 3 The bit-by-bit decoding order of the large-core polar code decoding tree diagram is as follows:
[0029] In the tree-structured decoding of big-core polar codes, the soft information LLR value passed from the parent node to the child node is included, as well as the partial sum passed from the child node to the parent node estimated by hard decision. Unlike the classical polar code decoding tree, in the big-core polar code decoding tree structure, each parent node no longer splits into left and right child nodes, but instead splits into... Offspring. Assume Figure 3 Middle parent node Located in the decoding tree The stage, and received a length of LLR sequences .according to The formula for the first decoded bit of the kernel Tanner diagram can be used to calculate... Figure 3 The leftmost child node The LLR sequence. For nodes The LLR performs a hard decision and returns partial sum information to the parent node. At this point, it can be done through And the formula for the second decoding bit of the kernel Tanner diagram is used to calculate the result. Figure 3 The LLR sequence corresponding to the second child node. And so on, we can obtain... The LLR sequence corresponding to each child node is used to return a partial sum sequence to the parent node. In fact, the parent node... The returned partial sum sequence is equivalent to the coded codewords generated by the kernel Tanner graph.
[0030] by Figure 2 The decoding tree diagram in (b) will be used as an example for illustration. When the code length N=6, Figure 2 In (b), the parent node (1,1) receives an LLR sequence of length 6. Based on the first decoded bit The LLR calculation formula can be reformulated as a function. It can calculate the LLR value of child node (1,0). for
[0031] right By executing a hard decision, one obtains... Figure 2 The partial sum of the leftmost child node (1,0) in (b) is also the decoding result. . It will return to the parent node (1,1) and calculate... Figure 2 The LLR value of the second child node (2,0) in (b) can be specifically represented as:
[0032] right By executing a hard decision, one obtains... Figure 2 (b) Partial sum of node (2,0) .Will Returning the value to node (1,1) allows us to calculate the LLR value for node (3,0):
[0033] Similarly, the LLR values of child nodes (4,0), (5,0), and (6,0) are calculated as follows:
[0034]
[0035]
[0036] Next, based on the partial sums of the 6 child nodes and the kernel matrix... It can calculate partial sums and sequences:
[0037]
[0038]
[0039]
[0040] And return it to the parent node (0,1), where for Corresponding kernel Tanner graph output node The encoded bits. This completes the process. Figure 2 (b) The entire information transmission and decoding process of the big nucleus polar code decoding tree graph.
[0041] Figure 4 For a big-kernel polar code decoding tree with a kernel matrix size of 6 and a code length of N=36, the information bit position index set is... When we look at the data, we can see that all the leaf nodes covered by node (1,1) are frozen bits. These special nodes are called Rate-0 nodes. Note that a leaf node is a node in the big-kernel polar code decoding tree that no longer splits into offspring, i.e., the [missing information - likely a specific node or node]. All nodes in the layer. The generalized structure of a Rate-0 node is as follows: Figure 5 As shown in (a), its All leaf nodes are frozen bits. For decoding the Rate-0 node, instead of following the original decoding tree (i.e., instead of enumerating and calculating the information of all child nodes split from the Rate-0 node), the partial sums and path metrics of all its leaf nodes can be directly obtained through S42. Specifically, the length is... The partial sum of class A nodes, i.e., the first node in the split decode tree. The decoding results of all leaf nodes of the layer are calculated as follows: ,in Additionally, the length is The path metric of the A-class node, i.e., the path metric of the split-out decoder tree. The path metric of the last leaf node in the layer is calculated as follows: ,in It is the first time that a special node of type A has received this information. One LLR value.
[0042] and Figure 4 Unlike node (1,1), node (6,1) covers all leaf nodes that are information bits. This special type of node is called a Rate-1 node. The generalized structure of a Rate-1 node is as follows: Figure 5 As shown in (b), its All leaf nodes are information bits. For decoding the Rate-1 node, instead of following the original decoding tree (i.e., instead of enumerating and calculating the information of all child nodes split from the Rate-1 node), the partial sums and path metrics of all its leaf nodes can be directly obtained through S43. Specifically, the length is... The partial sum of the B-class nodes, i.e., the first node in the split decode tree. The decoding results of all leaf nodes of the layer are calculated as follows: ,in ; It is the first time that a special node of type A has received this information. One LLR value; It is a hard decision function, specifically, when hour, Returns 0 otherwise. Additionally, the length is... The path metric of the A-class node, i.e., the path metric of the split-out decoder tree. The path metric of the last leaf node in the layer is calculated as follows: ,in , It is the first time that a special node of type B has received this information. One LLR value, It is the first special node corresponding to class B. Each part and its value. In summary, big-core polar codes can be derived from... Figure 6The simplified decoding tree shown is used for fast decoding. For special nodes, decoding is performed according to the fast calculation formulas in S42 and S43, while for other non-special nodes, decoding is performed according to the normal decoding tree process in S25.
[0043] Figure 7 The error rate comparison between the big-core polar code decoding method of this invention and the SCL decoding in the 5G standard is shown. It can be seen that when the kernel matrix dimension is greater than or equal to 15, the error correction capability of the big-core polar code decoding method of this invention is significantly better than that of the SCL decoding in the 5G standard.
[0044] Figure 8 The presentation compares the frame error rates of the big-kernel polar code decoding method of this invention with those of existing fast-SC big-kernel polar code decoding. It can be seen that, under different dimensional kernel matrices, the error correction capability of the big-kernel polar code decoding method of this invention is significantly superior to existing fast big-kernel polar code decoding schemes.
[0045] This invention is not limited to the preferred embodiments described above. Anyone can derive other forms of products under the guidance of this invention. However, regardless of any changes made in their shape or structure, any technical solution that is the same as or similar to this application falls within the protection scope of this invention.
Claims
1. A big-core polar code decoding method, characterized in that, Includes the following steps: S11. Receive the signal to be decoded. The signal to be decoded is the signal when the big nucleus polar code sent by the transmitter arrives at the receiver. The high-dimensional kernel matrix of the big nucleus polar code can be equivalently converted into a serial kernel Tanner diagram. S12. Design a universal decoding tree graph structure applicable to large-core polar codes of any dimension, and obtain explicit expressions for the partial sum, log-likelihood ratio, and path metric of any node in the universal decoding tree graph structure. S13. Based on the distribution pattern of information bit positions in the leaf nodes of the general decoding tree diagram structure, special node types are summarized. S14. Obtain the fast calculation formula for the partial sum and path metric value corresponding to special nodes in the general decoding tree graph structure; S15. Perform fast decoding of the big-core polar code. For special nodes, directly use their corresponding fast calculation formulas; for non-special nodes, decode normally according to the general decoding tree structure.
2. The big-core polar code decoding method according to claim 1, characterized in that, S12 includes the following steps: S21, for dimension... kernel matrix , For integers greater than 2, construct their corresponding decoding tree graph units, where a single root node is used as the 0th level, and the root node splits downwards into... Each child node is a descendant of the first level, and the root node and its child nodes are considered descendants of the first level. The child nodes together form the kernel matrix. The corresponding decoding tree diagram unit; S22, According to the kernel matrix The corresponding formula for calculating the log-likelihood ratio and the bit-by-bit decoding order are used to calculate the log-likelihood ratio of each child node in the first layer of the decoding tree graph unit from left to right. And perform hard decision on each log-likelihood ratio to obtain the corresponding partial sum value. And return it to the root node, where ; All The partial sums and values of the child nodes are combined to form a sequence. and multiplied by the kernel matrix To obtain parts and sequences And return to the root node, the part and the sequence. The decoding result for the root node; S23. For a given code length Construct a decoding tree graph for the big-core polar code, where the unique root node is used as the first... Layers, splitting downwards The nth child node is the Layer; then the first Each node in the layer acts as a parent node and continues to split downwards. The nth child node forms the nth... Layer; and so on, until the first layer is reached. The splitting stops when the layer is reached; record the first layer. The number of nodes in the layer from left to right is Then any node is marked as For any parent node Its child nodes are represented from left to right as follows: ; S24, According to the kernel matrix The corresponding formula for calculating the log-likelihood ratio of the serial core Tanner graph and the bit-by-bit decoding order. Derive any node in the big-core polar code decoding tree graph The explicit expressions for the log-likelihood ratio and the partial sum; S25, the root node of the decoding tree graph has a receive length of... The received sequence is updated according to the explicit expression described in S24, updating the log-likelihood ratio and partial sum information of each node in the decoding tree graph until the first... The partial sums of all leaf nodes in the layer are updated, thus completing the tree graph decoding of the big nucleus polar code.
3. The big-core polar code decoding method according to claim 2, characterized in that: In step S22, the log-likelihood ratio of the leftmost first node in the first layer of the decoding tree graph unit is calculated. ,right Perform a hard decision operation to obtain the partial sum of the first leftmost node in the first layer of the decoded tree graph unit. and return it to the root node; according to Kernel matrix The corresponding formula for calculating the log-likelihood ratio and the bit-by-bit decoding order are used to calculate the log-likelihood ratio of the second node in the first layer of the decoding tree graph unit. ,right Perform a hard decision operation to obtain the partial sum of the second node in the first layer of the decoded tree graph unit. And return it to the root node; and so on, so that the decoding tree graph units can be obtained sequentially from left to right. The log-likelihood ratio corresponding to each child node and partial sum .
4. The big-core polar code decoding method according to claim 2, characterized in that: In S24, for any node in the big-core polar code decoding tree diagram... , its first The soft information log-likelihood ratio of each offspring is expressed as follows: , where the function Represents the kernel matrix The corresponding serial core Tanner graph calculates the first Formula for the log-likelihood ratio of each decoded bit; Representative set The Middle One element; , represent The Middle The set consisting of all elements preceding the first element; Representative function Medium parameters The set of indices; For any node in the big-core polar code decoding tree diagram Parts and sequences It is a length of The bit vector, specifically represented as ,in ,return The remainder, if ,function ,otherwise ; Represents a set The Middle Elements, where the set .
5. The big-core polar code decoding method according to claim 2, characterized in that, S13 includes the following steps: S31. Let the root node index of the big-core polar code decoding tree be 1. The second level of the decoding tree... The position indices of the nodes are respectively Similarly, following the order from top to bottom and left to right, the set of indices of all nodes in the big-core polar code decoding tree is: And initialize three empty sets A, B, and F; S32, From the set Starting with the first element, proceed to the right to check the... element The corresponding decoding tree node contains the first Check if all leaf nodes in the layer are either frozen bits, information bits, or a combination of both. If all are frozen bits, proceed to step S33; if all are information bits, proceed to step S34. S33, will elements in Add to set A and update set A, that is... ; S34, will elements in Add to set B and update set B, that is... ; S35. Obtain the indices of all child nodes split from the decoding tree node corresponding to each element in set A, and form set D; obtain the indices of all child nodes split from the decoding tree node corresponding to each element in set B, and form set E; let set And delete the nodes corresponding to sets D and E from the big nucleus polar code decoding tree to obtain a simplified big nucleus polar code decoding tree diagram.
6. The big-core polar code decoding method according to claim 5, characterized in that, S14 includes the following steps: S41. In the simplified big-core polar code decoding tree, the nodes in the decoding trees corresponding to sets A and B are special nodes. The decoding results of their corresponding leaf nodes can be obtained directly, thus avoiding the calculation of the log-likelihood ratio, partial sum, and path metric of their child nodes. When the special node type belongs to A, proceed to S42; when the special node type belongs to B, proceed to S43. S42, length is The partial sum of class A nodes, i.e., the first node in the split decode tree. The decoding results of all leaf nodes of the layer are calculated as follows: ,in Its path metric is calculated as follows: ,in It is the first time that a special node of type A has received this information. The log-likelihood ratio; S42, length is The partial sum of the B-class nodes, i.e., the first node in the split decode tree. The decoding results of all leaf nodes of the layer are calculated as follows: ,in ; It is the first time that a special node of type A has received this information. The log-likelihood ratio; It is a hard decision function, when hour, Returns 0 otherwise; its path metric is calculated as follows: ,in ; It is the first time that a special node of type B has received this information. Log-likelihood ratio It is the first special node corresponding to class B. Each part and value.
7. The big-core polar code decoding method according to claim 5, characterized in that, S15 includes the following steps: S51. Perform fast decoding based on the received sequence and the simplified decoding tree diagram. When the current node belongs to class A node, proceed to S52; when the current node belongs to class B node, proceed to S53; when the current node belongs to class F node, proceed to S54. S52. Based on S42, directly obtain the partial sum and path metric value of the special node of type A in the current decoding tree, and then proceed to S54. S53. Based on S43, directly obtain the partial sum and path metric value of the special node of type B in the current decoding tree, and then proceed to S54; S54. Perform big core polar code decoding according to S25.
8. A large-core polar code decoding device, characterized in that, include: The signal receiving module is used to receive the signal to be decoded, which is the signal when the big nucleus polar code sent by the transmitter arrives at the receiver. The tree graph construction module is used to construct a general decoding tree graph structure applicable to large-kernel polar codes of any dimension, and to determine the expressions for the log-likelihood ratio, partial sum, and path metric of any node in the general decoding tree graph. The node classification module is used to summarize the special node types in the decoding tree diagram based on the distribution pattern of information bit positions of leaf nodes in the decoding tree diagram; The fast calculation module is used to determine the partial sum and path metric value of special nodes using a fast calculation formula. The decoding execution module is used to perform fast decoding of big-core polar codes. For special nodes, it directly uses their corresponding fast calculation formulas for processing, while for non-special nodes, it performs normal decoding according to the decoding tree structure.
9. A large-core polar code decoding system, characterized in that, include: Memory, used to store computer programs; A processor for executing a computer program to implement the steps of the big-core polar code decoding method as described in any one of claims 1-7.