Polarization code self-isomorphic SC decoding method based on node attributes, medium and equipment

Abstract

The invention discloses a polarization code self-isomorphic SC decoding method based on node attributes, a medium and equipment, and relates to the technical field of channel coding, and the polarization code self-isomorphic SC decoding method based on the node attributes mainly comprises the following steps: according to a minimum information set; obtaining a fixed bit set and a self-isomorphic transformation matrix set by utilizing a partial partial sequence structure and a stabilizer of a single item set; according to the self-isomorphic transformation matrix set, carrying out self-isomorphic transformation on the fixed bit set to obtain a codeword set to be decoded; sC decoding is carried out on the to-be-decoded codeword set to obtain self-isomorphic transformation decoding codewords; and performing inverse self-isomorphic transformation and selection on the self-isomorphic transformation decoding codeword to obtain a decoding result. By implementing the polar code self-isomorphic SC decoding method based on node attributes, the medium and the equipment provided by the invention, the decoding efficiency can be improved.

Description

Technical Field

[0001] The present invention relates to the field of channel coding technology, and more specifically to a node attribute-based polar code automorphic SC decoding method, medium and device. Background Art

[0002] Since 2012, the fifth generation mobile communication (5G) system has gradually become a major research hotspot in the field of mobile communications. A large number of scholars and engineers are committed to pursuing the Shannon capacity limit. Although the performance of Turbo and LDPC codes is very close to the Shannon capacity limit, they have never reached the capacity limit. Polar code is the first coding scheme that can be strictly proved to reach the capacity limit in binary input symmetric discrete memoryless channel (BI-BDC) in theory. Polar code is mainly based on channel polarization theory. Through channel merging and channel splitting, the split channel produces two-level differentiation: one part will become a noiseless channel with a capacity approaching 1, and the other part will become a pure noise channel with a capacity approaching 0. Reliable data transmission can be achieved by simply loading the data to be transmitted into the noiseless channel and not using the pure noise channel.

[0003] Polar code uses the serial cancellation (SC) algorithm in the decoding algorithm. When the code length tends to infinity, the SC decoding algorithm can achieve excellent performance, but when the code length is medium or short, the SC decoding algorithm has serious performance loss. Scholars have proposed the serial cancellation list (SCL) algorithm and used CRC code cascade to achieve better performance. However, the time complexity and memory space of SCL decoding are very high, and it is difficult to implement a high-throughput SCL decoder. Summary of the invention

[0004] The object of the present invention is to provide a polar code automorphic SC decoding method, medium and device based on node attributes, which can improve decoding efficiency.

[0005] The present invention provides a node attribute-based polar code automorphism SC decoding method, comprising the following steps: S1: according to a minimum information set, a partial partial order construction and a stabilizer of a single item set are used to obtain a fixed bit set and an automorphism transformation matrix set; S2: according to the automorphism transformation matrix set, an automorphism transformation is performed on the fixed bit set to obtain a codeword set to be decoded; S3: SC decoding is performed on the codeword set to be decoded to obtain an automorphism transformation decoding codeword; S4: inverse automorphism transformation and selection are performed on the automorphism transformation decoding codeword to obtain a decoding result.

[0006] Specifically, step S1 includes: S11: according to the minimum information set, using partial partial order construction, to obtain a fixed bit set to be decoded, the fixed bit set includes information bits and frozen bits; S12: according to the fixed bit set, using a stabilizer of a single item set, to obtain a block lower triangular transformation matrix; S13: according to the block lower triangular transformation matrix, the block lower triangular transformation matrix includes sub-blocks; transforming the sub-blocks to obtain an automorphic transformation matrix set, the automorphic transformation matrix set includes a permutation matrix set, an upper triangular transformation matrix set and a normal transformation matrix set.

[0007] Specifically, step S11 includes: according to the minimum information set, using partial partial order construction, obtaining a fixed bit set to be decoded, the fixed bit set includes information bits and frozen bits, as shown in the formula: , in, is a fixed bit set, is the code length, and For bits.

[0008] Specifically, step S2 specifically includes: performing automorphic transformation on the fixed bit set according to the automorphic transformation matrix set to obtain the codeword set to be decoded, such as formula:

[0009]

[0010] in, is the codeword to be decoded, is an automorphic fixed bit set, is the automorphism transformation matrix, is a fixed bit set, is a fixed bit set.

[0011] Specifically, step S3 includes: S31: obtaining nodes R0, R1 and common nodes according to the codeword set to be decoded; S32: performing butterfly operation of SC decoding on the common nodes; f Operation and g operation are performed to obtain the decoding result of the nth layer of the ordinary root node of the SC decoding tree; S33: SC decoding is performed on the R0 node and the R1 node, R0 is all frozen bits, and the R1 node is decoded according to the maximum likelihood to obtain the decoding result of the nth layer of the SC decoding tree R0 and R1 root nodes; S34: SC decoding is performed according to the decoding result of the nth layer of the SC decoding tree R0 and R1 root nodes to obtain the automorphic transformation decoding codeword.

[0012] Specifically, step S4 includes: S41: performing an inverse automorphism transformation on the automorphism transformed decoding codeword to obtain a decoding codeword result set; S42: obtaining a decoding result according to the decoding codeword result set using the least squares method.

[0013] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of the above-mentioned node attribute-based polar code automorphic SC decoding method are implemented.

[0014] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the above-mentioned node attribute-based polar code automorphic SC decoding method are implemented.

[0015] The present invention also provides a computer program product, including a computer program, characterized in that when the computer program is executed by a processor, the steps of the above-mentioned node attribute-based polar code automorphic SC decoding method are implemented.

[0016] The implementation of the node attribute-based polar code automorphic SC decoding method, medium and device provided by the present invention has the following beneficial effects: The present invention selects part of the bit channels as information bits and frozen bits according to the Polar code automorphism set decoding algorithm by using the UPO structure to obtain an automorphism transformation matrix set; in the automorphism set SC decoding algorithm process, automorphism transformation is performed on the received codeword, and multiple automorphism transformations are performed on the received codeword to obtain a set of received codewords; by referencing the two nodes R0 and R1 in the fast SC decoding algorithm, the number and arrangement of the R0 and R1 nodes after each automorphism transformation are detected, SC decoding is performed, and the codeword is inversely transformed by automorphism to obtain a decoded codeword; by performing the least square method on all the decoded codewords, the optimal result is selected as the decoding result, so as to speed up the automorphism decoding. Set decoding algorithm; that is, the present invention utilizes the self-similar set SC decoding algorithm to exchange and map the data in the codeword to obtain different decoding results, and outputs the optimal result using the least squares method; the algorithm uses two node attributes in the fast decoding algorithm to speed up the decoding speed without reducing the decoding performance too much; compared with the traditional self-similar set SC decoding algorithm, the present invention reduces the SC decoding delay each time by introducing two nodes, and reduces the decoding delay on the basis of almost no reduction in the bit error rate performance; that is, the present invention utilizes two node attributes in the fast decoding algorithm to simplify the calculation, save decoding time, improve the implementation efficiency, and there is no obvious loss in bit error performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which: Figure 1 It is a flow chart of the node attribute-based polar code automorphic SC decoding method provided by the present invention; Figure 2It is a basic processing unit diagram of the SC decoding "butterfly operation" provided by the present invention; Figure 3 is the code length provided by the present invention N =8, number of information bits K =4 complete polar code decoding tree diagram; Figure 4 is the code length provided by the present invention N =8, number of information bits K =4, in which the index 3 bit is swapped with the index 4 bit, and a schematic diagram of the polar code decoding tree after the replacement is completed; Figure 5 It is a comparison diagram of the block error rate provided by the present invention and AE-SC; Figure 6 It is a structural block diagram of the computer device provided by the present invention. DETAILED DESCRIPTION

[0018] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0019] Figure 1 A schematic diagram of the node attribute-based polar code automorphic SC decoding method of this embodiment is shown. In this embodiment, the node attribute-based polar code automorphic SC decoding method includes the following steps: S1: According to the minimum information set, the fixed bit set and the automorphic transformation matrix set are obtained by using the partial partial order construction and the stabilizer of the single item set; Specifically, step S1 includes: S11: According to the minimum information set, a fixed bit set to be decoded is obtained by using a partial partial order construction, where the fixed bit set includes information bits and frozen bits; Specifically, step S11 specifically includes: according to the minimum information set, using partial partial order construction, obtaining a fixed bit set to be decoded, the fixed bit set includes information bits and frozen bits, as shown in the formula: , in, is a fixed bit set, is the code length, and is bit; It should be noted that in step S11, based on the minimum information set, a partial partial order (UPO) is used to obtain a fixed bit set to be decoded, and the fixed bit set includes information bits and frozen bits; a code length is , the length of the information bit is , the dimension is According to the virtual channel index in the codeword , represents their binary reverse expansion, where , if and only if When some partial order conditions are met, it is expressed as i j , the condition is and Only one bit is different, and , ;and and There are two consecutive bits and different, =1, , , According to the iterativeness of the UPO structure, an iterative algorithm is obtained, and the minimum information set is iterated to obtain the index of all information bits, and the other bit indexes should be frozen bits; (1) S12: according to the fixed bit set, using the stabilizer of the single item set, obtain a block lower triangular transformation matrix; It should be noted that in step S12, the automorphism group of the codeword is a set of permutations that keep the properties of the codeword unchanged, that is, each codeword is mapped to a codeword that is not necessarily different. and the maximum untransformed index Automorphism Transformation , keep all the information bit index Stable group A subset of: (2) (3) S13: According to the block lower triangular transformation matrix, the block lower triangular transformation matrix includes sub-blocks; transform the sub-blocks to obtain an automorphic transformation matrix set, the automorphic transformation matrix set includes a permutation matrix set, an upper triangular transformation matrix set and a common transformation matrix set; It should be noted that in step S13, the data S of the stable group can be represented as a set of n×n permutation matrices. For each sub-segment Medium Dimension , corresponding to a block × The block diagonal structure of the automorphic transformation matrix is ​​transformed into a permutation matrix set P for each block structure, and the upper triangular transformation matrix set U is obtained by row addition, and the ordinary transformation matrix A together constitutes an automorphic transformation matrix set, the number of which is M; S2: According to the automorphic transformation matrix set, the fixed bit set is automorphic transformed to obtain the codeword set to be decoded; Specifically, step S2 includes: According to the automorphic transformation matrix set, the fixed bit set is automorphically transformed to obtain the codeword set to be decoded, as shown in the formula:

[0020]

[0021] in, is the codeword to be decoded, is an automorphic fixed bit set, is the automorphism transformation matrix, is a fixed bit set, is a fixed bit set; It should be noted that in step S2, the number of automorphic transformations M can be easily obtained through the information bit index and the frozen bit index and the automorphic transformation matrix set S, and a certain automorphic transformation matrix A is used to transform the received codeword after the automorphic transformation and the fixed bit set after automorphism transformation It can be expressed as follows: (4) S3: Perform SC decoding on the codeword set to be decoded to obtain automorphic transformation decoding codewords; Specifically, step S3 includes: S31: Obtain nodes R0, R1 and common nodes according to the codeword set to be decoded; S32: Butterfly operation for SC decoding of common nodes f Operation and g operation, obtain the decoding result of the nth layer of the common root node of the SC decoding tree; S33: Perform SC decoding on the R0 node and the R1 node, R0 is all frozen bits, and the R1 node is decoded according to the maximum likelihood, and the decoding results of the nth layer of the root nodes of the SC decoding tree R0 and R1 are obtained; S34: According to the decoding results of the nth layer of the root nodes of the SC decoding tree R0 and R1, SC decoding is performed to obtain the automorphic transformation decoding codeword; Formula (6) is used to calculate the SC decoding result, and formula (7) is It should be noted that in step S3, after detecting the R0 and R1 nodes for each received codeword, SC decoding is performed, and the decoded codeword is obtained by inverse automorphism transformation; specifically, the following steps are included: The fixed bit set of the n-th layer N bits after automorphism transformation According to four bits as a unit, determine whether it is an R0 or R1 node, otherwise it is four ordinary nodes; Butterfly operation for SC decoding f Operation, get the SC decoding tree root node Tier i The maximum likelihood ratio LLR is: (5) in, ; Calculate the LLR value of the left leaf node ,in, a 1 is an even number, ; Decoding decision result for: (6) Among them, the frozen bits are bits in the Polar code that are known to both the sender and the receiver; The SC decoding result is calculated, where the hard decision recursive formula is: (7) in, Indicates Layer Node hard decision value; Perform the g operation of the butterfly operation of SC decoding to obtain the root node of the SC decoding tree Tier i The LLR of each is: (8) Calculate the LLR value of the right leaf node , a 2 is an odd number, ; According to formula (6), the judgment result of the child node is obtained; refer to Figure 2 , Figure 2 Diagram of the basic processing unit of "butterfly operation" for SC decoding; It should be noted that the R0 node does not need to be calculated and all bits are frozen. The R1 node is decoded according to the maximum likelihood. The ordinary nodes repeat steps S32 and S33 until the SC decoding result is obtained. , express , The obtained decoding result after the automorphism transformation is obtained from the set of automorphism transformation matrix A, and a set of M candidate decoding codeword results is obtained according to the original automorphism transformation matrix A; refer to Figure 3, Figure 3 The code length of this embodiment N =8, number of information bits K =4, when the code length , the number of information bits When , the information bit index set is , if 0 represents frozen bit and 1 represents information bit, and they are arranged in ascending order by index, then the information bit and frozen bit distribution of the polar code binary tree leaf node is ; refer to Figure 4 , there may be such a Figure 4 Codeword shown: The data with index bit 3 and index bit 4 in the fixed bit set are exchanged. Through the judgment of the 4-bit node, it can be determined as R0 node and R1 node. The decoding process only needs to focus on R1 node and make a hard decision to determine the codeword; S4: performing inverse automorphism transformation and selection on the automorphism transformation decoding codeword to obtain a decoding result; Specifically, step S4 includes: S41: performing an inverse automorphism transformation on the automorphism transformed decoding codeword to obtain a decoding codeword result set; S42: Obtain a decoding result by using a least square method according to the decoding codeword result set; It should be noted that in step S4, the best result is selected as the decoding result according to the least square method from among all the decoding codeword sets; Specifically, according to the obtained set of all decoding codeword results, according to the least square method, the formula is as follows: (9) The least squares sum of the automorphic codewords is calculated by formula (9), the maximum value among the M groups of decoded codewords is compared, and the decoded codeword with the maximum value is output as the decoding result, and the decoding is completed.

[0022] The effect of this embodiment refers to Figure 5 ; Figure 5 : is a comparison diagram of the block error rate of this embodiment and AE-SC, as shown in Figure 5 As shown, "The line represents the AE-SC bit error rate curve," The line shows the bit error rate curve of the present invention. When the code length is N=256, the information bit K=128, and the maximum automorphism M=21, it can be seen from the figure that there is almost no big difference in the bit error rate between the two; Table 1 shows the bit operations of the present invention and the AE-SC decoding algorithm. As shown in Table 1, when the code length is N=256, the information bit K=128, and the automorphism M=21, the number of bit operations required for AE-SC to complete the decoding operation is 10240, while the number of bit operations required for the fast AE-SC of the present invention to complete the decoding operation is 6190.

[0023] Table 1: Comparison of the number of bit operations required to complete decoding between this embodiment and AE-SC

[0024] Compared with AE-SC decoding, this embodiment uses node attributes to simplify calculations, greatly improving implementation efficiency and decoding delay, and without significant loss in error performance.

[0025] This embodiment provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned node attribute-based polar code automorphic SC decoding method are implemented. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), a flash memory, a hard disk (HDD) or a solid-state drive (SSD), etc.; the storage medium may also include a combination of the above-mentioned types of memory.

[0026] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the above-mentioned node attribute-based polar code automorphic SC decoding method are implemented.

[0027] like Figure 6As shown, the computer device may include: at least one processor 121, such as a CPU (Central Processing Unit), at least one communication interface 123, a memory 124, and at least one communication bus 122. Among them, the communication bus 122 is used to realize the connection and communication between these components. Among them, the communication interface 123 may include a display screen (Display), a keyboard (Keyboard), and the optional communication interface 123 may also include a standard wired interface and a wireless interface. The memory 124 may be a high-speed RAM memory (Random Access Memory, volatile random access memory), or a non-volatile memory (non-volatile memory), such as at least one disk memory. The memory 124 may also be at least one storage device located away from the aforementioned processor 121. Among them, the memory 124 stores an application program, and the processor 121 calls the program code stored in the memory 124 to perform any of the above method steps. Among them, the communication bus 122 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. The communication bus 122 can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 6Only one line is used to represent it, but it does not mean that there is only one bus or one type of bus. Among them, the memory 124 may include a volatile memory (English: volatile memory), such as a random access memory (English: random-access memory, abbreviated: RAM); the memory may also include a non-volatile memory (English: non-volatile memory), such as a flash memory (English: flash memory), a hard disk drive (English: hard disk drive, abbreviated: HDD) or a solid-state drive (English: solid-state drive, abbreviated: SSD); the memory 124 may also include a combination of the above-mentioned types of memory. Among them, the processor 121 may be a central processing unit (English: central processing unit, abbreviated: CPU), a network processor (English: network processor, abbreviated: NP) or a combination of CPU and NP. Among them, the processor 121 may further include a hardware chip. The above-mentioned hardware chip may be an application-specific integrated circuit (English: application-specific integrated circuit, abbreviated: ASIC), a programmable logic device (English: programmable logic device, abbreviated: PLD) or a combination thereof. The PLD may be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof. Optionally, the memory 124 is also used to store program instructions. The processor 121 may call the program instructions to implement the node attribute-based polar code automorphism SC decoding method of this embodiment.

[0028] This embodiment provides a computer program product, including a computer program, characterized in that when the computer program is executed by a processor, the steps of the above-mentioned node attribute-based polar code automorphic SC decoding method are implemented.

[0029] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A node attribute-based polar code automorphism SC decoding method, characterized in that: The following steps are involved: S1: According to the minimum information set, the fixed bit set and the automorphic transformation matrix set are obtained by using the partial partial order construction and the stabilizer of the single item set; S2: performing an automorphic transformation on the fixed bit set according to the automorphic transformation matrix set to obtain a codeword set to be decoded; S3: Perform SC decoding on the codeword set to be decoded to obtain automorphic transformation decoding codewords; S4: performing inverse automorphism transformation and selection on the automorphism transformation decoding codeword to obtain a decoding result.

2. The node attribute-based polar code automorphism SC decoding method according to claim 1, characterized in that: Step S1 specifically includes: S11: According to the minimum information set, a fixed bit set to be decoded is obtained by using a partial partial order construction, where the fixed bit set includes information bits and frozen bits; S12: according to the fixed bit set, using a stabilizer of a single item set, obtaining a block lower triangular transformation matrix; S13: According to a block lower triangular transformation matrix, the block lower triangular transformation matrix includes sub-blocks; transform the sub-blocks to obtain an automorphic transformation matrix set, the automorphic transformation matrix set includes a permutation matrix set, an upper triangular transformation matrix set and a normal transformation matrix set.

3. The node attribute-based polar code automorphic SC decoding method according to claim 2, characterized in that: Step S11 specifically includes: according to the minimum information set, using partial partial order construction, obtaining a fixed bit set to be decoded, wherein the fixed bit set includes information bits and frozen bits, as shown in the formula: ， in, is a fixed bit set, is the code length, and For bits.

4. The node attribute-based polar code automorphic SC decoding method according to claim 1, characterized in that: Step S2 specifically includes: performing an automorphic transformation on the fixed bit set according to the automorphic transformation matrix set to obtain a codeword set to be decoded, such as formula: in, is the codeword to be decoded, is an automorphic fixed bit set, is the automorphism transformation matrix, is a fixed bit set, is a fixed bit set.

5. The node attribute-based polar code automorphic SC decoding method according to claim 1, characterized in that: Step S3 specifically includes: S31: Obtaining a node R0 node, a node R1 node and a common node according to the codeword set to be decoded; S32: performing butterfly operation of SC decoding on the common node f Operation and g operation, obtain the decoding result of the nth layer of the common root node of the SC decoding tree; S33: Perform SC decoding on the R0 node and the R1 node, R0 is all frozen bits, and the R1 node is decoded according to the maximum likelihood, to obtain the decoding results of the nth layer of the root nodes of the SC decoding tree R0 and R1; S34: Perform SC decoding according to the decoding results of the nth layer of the root nodes R0 and R1 of the SC decoding trees to obtain an automorphic transformation decoding codeword.

6. The node attribute-based polar code automorphic SC decoding method according to claim 1, characterized in that: Step S4 specifically includes: S41: performing an inverse automorphism transformation on the automorphism transformed decoding codeword to obtain a decoding codeword result set; S42: Obtain a decoding result using a least square method according to the decoding codeword result set.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the node attribute-based polar code automorphism SC decoding method are implemented as described in any one of claims 1 to 6.

8. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the node attribute-based polar code automorphic SC decoding method are implemented as described in any one of claims 1 to 6.

9. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the node attribute-based polar code automorphism SC decoding method according to any one of claims 1 to 6 are implemented.

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