A polar code soft-input soft-output decoding method, a decoding device and a communication device

Abstract

The application provides a polar code soft input soft output decoding method, a decoding device and a communication device; the decoding method comprises the following steps: (S1) performing fast serial cancellation list decoding under dynamic frozen bit constraint for all special nodes constituting a polar code; the types of the special nodes comprise rate zero, rate one, repetition and single parity check; (S2) calculating the approximation of the sum of the posterior probabilities of the legal code words not accessed under each special node after decoding; (S3) using the approximation of the code book probability obtained in the step (S2) to calculate the bit level soft information of the output polar code. The low-latency polar code soft input soft output decoding method provided by the application improves the parallelism by realizing fast soft output decoding based on the Rate0, Rate1, REP and SPC nodes, and significantly reduces the decoding latency without losing the soft output precision compared with the SO-SCL decoding algorithm.

Description

Technical Field

[0001] This invention relates to the field of channel coding technology in wireless communication, specifically to a polar code soft-input soft-output decoding method, decoding device, and communication equipment. Background Technology

[0002] Polar codes are a type of channel coding technique with deterministic binary input, symmetric, discrete, memoryless, and achievable channel capacity. Due to their excellent properties, polar codes have been selected as the standard channel coding for 5G control channels. Polar codes are typically decoded using the Successive Cancellation List (SCL) algorithm to provide the desired error correction performance. However, the sequential decoding nature of the SCL algorithm leads to significant decoding latency. To reduce latency, some methods achieve parallel decoding by directly decoding certain special nodes (sub-polar codes with special structures in the recursive representation of the polar code). However, the aforementioned polar code decoding algorithms are all hard output, i.e., they output the decoded codewords, and cannot provide soft output, i.e., the posterior probability log-likelihood ratio of the output codewords. This hinders the application of polar codes in scenarios such as iterative detection and iterative decoding. While algorithms based on Belief Propagation (BP) or Soft Cancellation (SCAN) can provide soft outputs, they often require internal iterations or an additional SCL decoder cascaded. Even so, short loops in the factor graph of polar codes can still affect the accuracy of the soft output of such algorithms. At the 2024 ISIT conference, Yuan et al. proposed a Soft-Output SCL (SO-SCL) algorithm, which can provide relatively accurate soft information output using only the SCL decoding tree. However, the SO-SCL algorithm inherits the high decoding latency of the SCL algorithm, so parallel decoding techniques are needed to further reduce latency without sacrificing performance. Summary of the Invention

[0003] This invention addresses the problems existing in the prior art by providing a polar code soft-input soft-output decoding method, decoding device, and communication equipment. This decoding method aims to reduce the decoding delay of polar codes without sacrificing the accuracy of soft information output.

[0004] The low-latency polar code soft-input soft-output decoding method of the present invention includes:

[0005] (S1) For all special nodes constituting a polar code, perform fast serial cancellation list decoding under dynamic frozen bit constraints. The types of special nodes include: Rate-Zero, Rate0, Rate-One, Rate1, Repetition, REP, and Single Parity Check (SPC).

[0006] (S2) After decoding each special node, calculate the approximate sum of the posterior probabilities of the unvisited legal codewords under that node;

[0007] (S3) Use the approximate estimated codebook probability obtained in step (S2) to calculate the bit-level soft information of the output polar code.

[0008] Furthermore, step (S1) specifically includes:

[0009] (S11) Before decoding a special node, calculate the log-likelihood ratio of the input to that special node in each path. This specifically includes: considering a special node It represents a polar code bit sequence u of length N to be encoded. N =(u1,u2,…,u N The index in ) starts from i s to j s The bit sequence constitutes a special subpolar code (Rate1, Rate0, REP, or SPC). According to the traditional SCL decoding algorithm, the log-likelihood ratio (LLR) of the input to this special node in the l-th decoding path is calculated, denoted as α. (l) ;

[0010] (S12) For each decoding path, calculate the value of the dynamically frozen bits in that special node based on the previous decoding results. Specifically, this includes: for the l-th decoding path, at the decoding node... Based on the previous decoding results Calculate the value of the dynamically frozen bits in this node, where Represents the sequence u of the l-th decoding path pair. N The estimate, Represents the index set {1,2,…,i}. (Using...) Represents a node The estimation of the bit sequence to be encoded for the corresponding subpolar code, wherein the frozen bits are filled with the values ​​of the previously calculated dynamic frozen bits, and the remaining bits are filled with zeros.

[0011] (S13) Correct the log-likelihood ratio of the input to the special node based on the value of the dynamically frozen bits, specifically including: calculating... in Let N be the generator matrix of the polar code. s =j s -i s +1, and This represents the Kronecker product. The LLR sequence α obtained from the correction step (S11) is... (l) for:

[0012]

[0013] Where ⊙ represents element-wise multiplication; It is the correction amount for dynamically frozen bit pairs of subpolar code codes.

[0014] (S14) Using the modified log-likelihood ratio as input, perform regular fast SCL decoding under the all-zero frozen bit constraint for this special node to obtain the decoded path and the corresponding path metric; this step specifically includes: using the LLR vector and decoding path Corresponding path metrics For input, for nodes Perform fast SCL decoding under the constraint of all-zero frozen bits to obtain the decoded node. The subsequent decoding path and the corresponding path metric

[0015] (S15) Correct the decoding path To satisfy the dynamic freeze bit constraint:

[0016]

[0017] in Represents the set of indices {i s i s +1,…,j s}, where π(l) represents the existing l-th decoding path. Originating from decoding nodes The π(l)th decoding path before

[0018] Furthermore, to avoid calculations in step (S13) Matrix multiplication operations at time, setting each special node Most F d One frozen bit is dynamically frozen, while the remaining bits remain fixed at zero. F d The value should be small enough that it can be obtained by looking up a table. It is feasible because Total One possibility. F d The typical range of values ​​for F is d ≤3.

[0019] Furthermore, step (S2) specifically includes: if If the node is Rate0, meaning it consists entirely of frozen bits, then the fast SCL algorithm in step (S1) does not perform path expansion or selection. The sum of the posterior probabilities of the unvisited legal codewords under this node is...

[0020]

[0021] like If it is a REP node, meaning only the last bit is an information bit, then the fast SCL algorithm in step (S1) can access the node. We consider all possible decoding paths, but some are discarded due to list size limitations. Therefore, the posterior probability and estimate of the unvisited valid codewords under this node are:

[0022]

[0023] Where: set Includes decoding REP nodes The decoding path that was later discarded. For the set of frozen bit indices of polar codes, Represents a set Path probability The relationship with path metric is The corresponding path metric PM(a) i The output is from the fast SCL algorithm in step (S1);

[0024] like If the node is Rate1, meaning it consists entirely of information bits, then the fast SCL algorithm in step (S1) can only access the node. The next possible decoding path, the sum of the posterior probabilities of all unvisited legal codewords under this node, is estimated as follows:

[0025]

[0026] Where: set Includes decoding nodes The set of previously retained decoding paths Includes the decoding Rate1 node The remaining decoding path;

[0027] Similarly, if If it is an SPC node, meaning only the first bit is frozen, then the fast SCL algorithm in step (S1) can only access the node. The next possible decoding path, the sum of the posterior probabilities of all unvisited legal codewords under this node, is estimated as follows:

[0028]

[0029] Where: path probability Nodes need to be configured Perform an additional step of the SCL algorithm to decode the frozen bits. Obtain, and set Includes decoding SPC nodes The remaining decoding path.

[0030] Furthermore, step (S3) specifically includes:

[0031] (S31) Given the received sequence y N The codebook probability is calculated as follows:

[0032]

[0033] Where: set This includes the final decoded path that is stored after decoding is completed, a set. It contains special nodes that make up a polar code. Returns the type of a special node.

[0034] (S32) The posterior probability LLR for each codeword bit is calculated as follows:

[0035]

[0036] in probability P C|Y By channel Calculated.

[0037] The present invention also includes a decoding apparatus that performs polar code decoding using the above-described decoding method.

[0038] The present invention also includes a communication device comprising the above-described decoding apparatus.

[0039] The low-latency polar code soft-input soft-output decoding method proposed in this invention improves parallelism compared to the SO-SCL decoding algorithm by implementing fast soft-output decoding based on Rate0, Rate1, REP and SPC nodes, and significantly reduces decoding latency without sacrificing soft-output accuracy. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the low-latency polar code soft-input soft-output decoding method provided in an embodiment of the present invention.

[0041] Figure 2This is a schematic diagram of a decoding tree for fast soft-output SCL decoding of Rate0, Rate1, REP and SPC nodes of length 4, provided in an embodiment of the present invention.

[0042] Figure 3 This is a comparison chart of the decoding time steps of the low-latency polar code soft-input soft-output decoding method provided in this embodiment of the invention with other polar code decoding methods.

[0043] Figure 4 This is a comparison chart of the decoding performance of the low-latency polar code soft-input soft-output decoding method provided in this embodiment of the invention with other polar code soft-output decoding methods.

[0044] Figure 5 The graph shows a comparison of the decoding performance of the low-latency polar code soft-input soft-output decoding method provided in this embodiment of the invention with other polar code soft-output decoding methods in a multiple-input multiple-output system. Detailed Implementation

[0045] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0046] Consider a polar code of length N, with the bit sequence to be encoded being u. N =(u1,u2,…,u N The codeword c is obtained after polarization transformation. N =u N G N ,in This is the generator matrix of the polar code. This represents the Kronecker product. N Index in a collection The value in the middle is the frozen bit, which is calculated as follows: in This represents the index set {1, 2, ..., i-1}. For commonly used statically frozen bits, As for dynamically frozen bits, u i and The value is related to, for example Since a polar code of length N can be represented as the polarization of two polar codes of length N / 2, the sequence... It can correspond to a subpolar code with a special structure, the subcodeword being: in Represents the set of indices N s =j s -i s +1. Such a subpolar code is called a special node, denoted as . Specifically, the Rate0 node represents The middle part is all frozen bits, represented by the Rate1 node. The entire string consists of information bits, represented by the REP node. Only the last bit is an information bit, and the SPC node represents... Only the first bit is a frozen bit. Since a polar code of length 2 must be one of the Rate0 node, Rate1 node, REP node, or SPC node, any polar code of length N can be completely represented by these four types of nodes. Let the set of special nodes constituting this polar code be denoted as .

[0047] Embodiments of the present invention provide a low-latency soft-input soft-output decoding method for the above-mentioned polar codes. The specific implementation process is as follows: Figure 1 As shown, the description is as follows:

[0048] (S1) For special node sets Nodes in By index i s Decode in ascending order For a special node First, fast SCL decoding under dynamic frozen bit constraints is performed, specifically including:

[0049] (S11) Before decoding a special node, calculate the log-likelihood ratio of the input to that special node in each path. Specifically, this includes: calculating the input node in the l-th decoding path according to the traditional SCL decoding algorithm. The LLR, denoted as α (l) ;

[0050] (S12) For each decoding path, calculate the value of the dynamically frozen bits in that special node based on the previous decoding results. Specifically, this includes: for the l-th decoding path, at the decoding node... Based on the previous decoding results Calculate the value of the dynamically frozen bits in this node, where Represents the sequence u of the l-th decoding path pair. N The estimation. Since the frozen bits are all before the information bits in all four types of nodes considered, it is possible to estimate them during decoding. The dynamically frozen bits were calculated beforehand. (Using...) Represents a node The estimation of the bit sequence to be encoded for the corresponding subpolar code, wherein the frozen bits are filled with the values ​​of the previously calculated dynamic frozen bits, and the remaining bits are filled with zeros.

[0051] (S13) Correct the log-likelihood ratio of the input to the special node based on the value of the dynamically frozen bits, specifically including: calculating... in Let be the generator matrix of the polar code, and This represents the Kronecker product. The LLR sequence α obtained in the correction step (S11) is... (l) for:

[0052]

[0053] Where ⊙ represents element-wise multiplication; It is the correction amount for dynamically frozen bit pairs of subpolar code codes.

[0054] (S14) Using the modified log-likelihood ratio as input, perform regular fast SCL decoding under the all-zero frozen bit constraint for this special node to obtain the decoded path and the corresponding path metric; this step specifically includes: using the LLR vector and decoding path Corresponding path metrics For input, for nodes Perform fast SCL decoding under the standard all-zero frozen bit constraint. For a detailed implementation, refer to "Fast and Flexible Successive-CancellationList Decoders for Polar Codes" published in *IEEE Transactions on Signal Processing* by SAHashemi, C. Condo, and WJ Gross. The algorithm outputs the decoding node. The subsequent decoding path and the corresponding path metric

[0055] (S15) Correct the decoding path To satisfy the dynamic bit freeze constraint, its expression is:

[0056]

[0057] in: Represents the set of indices {i s i s +1,…,j s}, where π(l) represents the existing l-th decoding path. Originating from decoding nodes The π(l)th decoding path before

[0058] Furthermore, to avoid calculations in step (S13) In matrix operations at the time, this invention proposes setting each special node. Most F d One frozen bit is dynamically frozen, while the remaining bits remain fixed at zero. F d The value should be small enough that it can be obtained by looking up a table. It is feasible because Total One possibility. In some embodiments, F d The range of values ​​for F is d ≤3.

[0059] (S2) After decoding each node Calculating an approximation of the sum of posterior probabilities of unvisited legal codewords under this node includes:

[0060] like If the node is Rate0 (rate zero node), meaning it consists entirely of frozen bits, then the fast SCL algorithm in step (S1) will not perform path expansion and selection. Figure 2 The diagram illustrates the SCL decoding tree for polar codes, where each node represents a possible partial decoding path. The left child of a node indicates that the next bit will be decoded as 0, while the right child indicates that the next bit will be decoded as 1. The decoding of the Rate0 node is shown below. Figure 2 As shown in (a), the sum of the posterior probabilities of the unvisited legal codewords under this node is:

[0061]

[0062] in: U represents the bit sequence to be encoded of a polar code of length N. N =(u1,u2,…,u N The index in ) starts from i s to j s The bit sequence forms a special subpolar code, namely a special node; Indicates a given special node The sum of the posterior probabilities for that node type;

[0063] like If it is a REP node (repeated node), meaning only the last bit is an information bit, then the fast SCL algorithm in step (S1) can access the node. This lists all possible decoding paths, but some are discarded due to list size limitations, such as... Figure 2 As shown in (b), the posterior probability and estimate of the unvisited legal codewords under this node are:

[0064]

[0065] Where: set Includes decoding REP nodes The decoding path that was later discarded. For the set of frozen bit indices of polar codes, Represents a set Path probability The relationship with path metric is The corresponding path metric PM(a) i The output is from the fast SCL algorithm in step (S1);

[0066] like If it is a Rate1 node (a node consisting entirely of information bits), then the fast SCL algorithm in step (S1) can only access the node. The next possible decoding path, such as Figure 2 As shown in (c), the posterior probability sum of all unvisited legal codewords under this node is estimated as follows:

[0067]

[0068] The set Includes decoding nodes The set of previously retained decoding paths Includes the decoding Rate1 node The remaining decoding path;

[0069] Similarly, if If it is an SPC node (single parity check node), meaning only the first bit is frozen, then the fast SCL algorithm in step (S1) can only access the node. The next possible decoding path, such as Figure 2 As shown in (d), the posterior probability sum of all unvisited legal codewords under this node is estimated as follows:

[0070]

[0071] Where: path probability Nodes need to be configured Perform an additional step of the SCL algorithm to decode the frozen bits. Obtain, and set Includes decoding SPC nodes The remaining decoding path.

[0072] (S3) After decoding all special nodes, the approximate codebook probability obtained in step (S2) is used to calculate the bit-level soft information of the output polar code, specifically including:

[0073] (S31) Given the received sequence y N The codebook probability is calculated as follows:

[0074]

[0075] Where: set This includes the final decoded path that is stored after decoding is completed, a set. It contains special nodes that make up a polar code. Returns the type of a special node.

[0076] (S32) Calculate the posterior probability LLR for each codeword bit.

[0077]

[0078] in: probability P C|Y By channel Calculated.

[0079] Embodiments of the present invention also provide a polar code soft-input soft-output decoding apparatus, which uses the above-described algorithm to perform low-latency polar code soft-output decoding.

[0080] Embodiments of the present invention also provide a communication device, which includes the decoding device as described in claim 6.

[0081] Figure 3 The diagram illustrates a comparison of the decoding time steps of the low-latency polar code soft-input soft-output decoding method of this patent with the SO-SCL method and the hard-output Fast SCL (FSCL) method under different code lengths N and information bit counts K. As can be seen from the diagram, the decoding method provided by this patent can save at least 76% of the time step compared to the SO-SCL method, but provides soft output at the cost of a slight reduction in decoding latency compared to the FSCL method. Figure 4 The diagram shows a performance comparison between the low-latency polar code soft-input soft-output decoding method of this patent and other polar code soft-output decoding methods. As can be seen from the diagram, the decoding method provided by this patent achieves performance comparable to the SO-SCL method and outperforms other methods.

[0082] The low-latency polar code soft-input soft-output decoding method provided in this patent can also be applied to iterative detection and decoding multiple-input multiple-output (MIMO) systems. Figure 5The figure shows a performance comparison between the low-latency polar code soft-input soft-output decoding method of this patent and other polar code soft-output decoding methods in a 2-transmit 2-receive MIMO system. As can be seen from the figure, the decoding method provided by this patent performs comparably to the SO-SCL method and outperforms other methods.

Claims

1. A polar code soft-input soft-output decoding method, characterized in that: (S1) For all special nodes that constitute a polar code, perform fast serial cancellation list decoding under dynamic frozen bit constraints. The types of special nodes include: rate zero, rate one, repetition and single parity check. (S2) After decoding each special node, calculate the approximate sum of the posterior probabilities of the unvisited legal codewords under that node; (S3) Use the approximate estimated codebook probability obtained in step S2 and calculate the bit-level soft information of the output polar code. The fast SCL decoding under dynamic frozen bit constraints in step S1 includes: (S11) Before decoding a special node, calculate the log-likelihood ratio of the input to that special node in each path; (S12) For each decoding path, calculate the value of the dynamically frozen bit in the special node based on the previous decoding result; (S13) Correct the log-likelihood ratio of the input to the special node based on the value of the dynamically frozen bits; (S14) Using the modified log-likelihood ratio as input, perform fast SCL decoding under the constraint of all-zero frozen bits for this special node to obtain the decoded path and the corresponding path metric. (S15) Modify the decoding path to meet the dynamic frozen bit constraint. In the process of fast SCL decoding under dynamic frozen bit constraints, the maximum number of the first F bits in each special node is set. d One of the frozen bits is dynamically frozen, while the remaining bits remain fixed at zero; F d The range of values ​​for F is d ≤3, so that the result of matrix multiplication when calculating the correction amount of the dynamically frozen bit pair subpolar code codeword in step S13 can be obtained by looking up a table.

2. The polar code soft-input soft-output decoding method according to claim 1, characterized in that: The process of calculating the approximate sum of the posterior probabilities of the unvisited legal codewords under this node in step S2 specifically includes: For the velocity zero node, the sum of the posterior probabilities is: in: U represents the bit sequence to be encoded of a polar code of length N. N =(u1,u2,…,u N The index in ) starts from i s to j s The bit sequence forms a special subpolar code, namely a special node; Indicates a given special node The sum of the posterior probabilities for that node type; For repeated nodes, the estimated posterior probability sum is: Where: set Includes decoding REP nodes The decoding path that was later discarded. For the set of frozen bit indices of polar codes, Represents a set Path probability The relationship with path metric is The corresponding path metric PM(a) i The output is from the fast serial cancellation list decoding algorithm under the dynamic frozen bit constraint in step S1. For a velocity node, the estimated posterior probability sum is: Where: set Includes decoding nodes The previously retained decoding path, and the set Includes the decoding Rate1 node The remaining decoding path; For a single parity check node, the estimated posterior probability sum is: Where: path probability Nodes need to be configured Perform an additional step of the SCL algorithm to decode the frozen bits. Obtain, and set Includes decoding SPC nodes The remaining decoding path.

3. The polar code soft-input soft-output decoding method according to claim 1, characterized in that: The codebook probability estimate in step S3 is as follows: Where: y N For receiving sequences, set This includes the final decoded path that is stored after decoding is completed, a set. It contains special nodes that make up a polar code. Returns the type of a special node; The bit-level soft information calculation in step S3 is as follows: in: probability P C|Y By channel Calculated.

4. A decoding device, characterized in that, Polarization decoding is performed using the method described in any one of claims 1 to 3.

5. A communication device, characterized in that, Includes the decoding device as described in claim 4.

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