Polarization code soft input soft output decoding method, decoding device and communication equipment

Abstract

The invention provides a polarization code soft input soft output decoding method, a decoding device and communication equipment. The decoding method comprises the following steps: (S1) aiming at all special nodes forming a polarization code, fast serial cancellation list decoding under dynamic frozen bit constraint is executed, and the types of the special nodes comprise rate zero, rate one, repetition and single parity check; (S2) after each special node is decoded, calculating the approximation of the posterior probability sum of legal code words which are not accessed under the node; and (S3) utilizing the approximate estimation codebook probability obtained in the step (S2) and calculating bit-level soft information of the output polarization code. Compared with an SO-SCL decoding algorithm, the low-delay soft input and soft output decoding method for the polarization codes, provided by the invention, has the advantages that the degree of parallelism is improved and the decoding delay is remarkably reduced on the premise that the soft output precision is not lost by realizing rapid soft output decoding based on the Rate0, the Rate1, the REP and the SPC nodes.

Description

Technical Field

[0001] The present invention relates to the technical field of channel coding in wireless communications, and in particular to a polar code soft-input soft-output decoding method, a decoding device and a communication device. Background Art

[0002] Polar codes are a type of channel coding technology with deterministic structure and reachable capacity for binary input symmetric discrete memoryless channels. With its outstanding characteristics, polar codes have been selected as the standard channel coding for 5G control channels. Polar codes are usually decoded using the Successive Cancellation List (SCL) algorithm to provide the desired error correction performance. However, the sequential decoding characteristics of the SCL algorithm will lead to a large decoding delay. In order to reduce the delay, some methods implement parallel decoding by directly decoding certain special nodes (sub-polar codes with special structures in the recursive representation of polar codes). However, the above-mentioned polar code decoding algorithms are all hard outputs, that is, they output the decoded codewords, but cannot provide soft outputs, that is, 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. Although algorithms based on Belief Propagation (BP) or Soft Cancellation (SCAN) can provide soft output, they often require internal iteration or cascading of an additional SCL decoder. Even so, the short loops in the factor graph of the polar code will still affect the soft output accuracy of such algorithms. At the 2024 ISIT conference, Yuan et al. proposed a soft-output SCL (SO-SCL) algorithm that can provide relatively accurate soft information output with the help of the SCL decoding tree. However, the SO-SCL algorithm inherits the disadvantage of high decoding delay of the SCL algorithm, so some parallel decoding methods are needed to further reduce the delay without basically losing performance. Summary of the invention

[0003] In view of the problems existing in the prior art, the present invention provides a polar code soft-input soft-output decoding method, a decoding device and a communication device. The decoding method aims to reduce the decoding delay of the polar code without losing the soft information output accuracy.

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

[0005] (S1) performing fast serial cancellation list decoding under dynamic frozen bit constraints for all special nodes constituting a polar code, wherein the types of the special nodes include: rate zero (Rate-Zero, Rate0), rate one (Rate-One, Rate1), repetition (Repetition, REP) and single parity check (SPC);

[0006] (S2) After decoding each special node, calculate the approximate sum of the posterior probabilities of the legal codewords that have not been visited under the node;

[0007] (S3) Using the approximate estimated codebook probability obtained in step (S2), the bit-level soft information of the output polar code is calculated.

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

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

[0010] (S12) For each decoding path, the value of the dynamic frozen bit in the special node is calculated according to the previous decoding result, which specifically includes: for the lth decoding path, at the decoding node Previously, according to the preamble decoding result Calculate the value of the dynamic freeze bit in the node, where Denotes the l-th decoding path sequence u N The estimate, represents the index set {1,2,…,i}. Representation Node The estimate of the bit sequence to be encoded of the corresponding sub-polar code, where the frozen bits are filled with the values ​​of the dynamic frozen bits calculated previously, and the remaining positions are filled with zeros.

[0011] (S13) Correcting the log-likelihood ratio of the input to the special node according to the value of the dynamic freeze bit, which specifically includes: calculating in is the generator matrix of the polar code, N s =j s -i s +1, and represents the Kronecker product. The LLR sequence α obtained in the correction step (S11) (l) for:

[0012]

[0013] Where ⊙ represents element-by-element multiplication; is the correction amount of the dynamically frozen bit pair sub-polar code codeword.

[0014] (S14) Taking the modified log-likelihood ratio as input, performing conventional fast SCL decoding under the constraint of all-zero frozen bits for the special node, and obtaining a decoded decoding path and a corresponding path metric; this step specifically includes: taking the LLR vector and decoding path The corresponding path metric is the input, is the node Perform the conventional fast SCL decoding under the constraint of all-zero frozen bits, and obtain the decoding node The decoding path after and the corresponding path metric

[0015] (S15) Correcting the decoding path To satisfy the dynamic frozen bit constraint:

[0016]

[0017] in Represents the index set {i s ,i s +1,…,j s}, π(l) represents the existing l-th decoding path From the decoding node The π(l)th decoding path before

[0018] Further, to avoid the calculation in step (S13) , set each special node Most front F d The frozen bits are dynamically frozen, while the rest remain fixed to zero. d The value of should be small enough so that the It is feasible because Total Possibility. d The typical value range is F d ≤3.

[0019] Furthermore, step (S2) specifically includes: if is a Rate0 node, that is, all frozen bits, then the fast SCL algorithm in step (S1) does not perform path extension and selection, and the posterior probability and unvisited legal codewords under this node are

[0020]

[0021] like is a REP node, that is, only the last bit is an information bit, then the fast SCL algorithm in step (S1) can access the node All possible decoding paths are listed below, but some of them are discarded due to the list size limit, so the posterior probability and estimate of the legal codewords not visited under this node are:

[0022]

[0023] Among them: Collection Contains the decoding REP node The decoding path that was later abandoned, is the set of frozen bit indices of the polar code, Representing a collection Path Probability The relationship with the path metric is The corresponding path metric PM(a i ) is output by the fast SCL algorithm of step (S1);

[0024] like is a Rate 1 node, that is, all information bits, then the fast SCL algorithm in step (S1) can only access the node The next possible decoding path, the posterior probability and estimate of all unvisited legal codewords under this node are:

[0025]

[0026] Among them: Collection Contains decoding nodes The decoding paths that have been retained before are combined Contains the decoding Rate1 node The decoding path that remains afterward;

[0027] Similarly, if is an SPC node, that is, 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 posterior probability and estimate of all unvisited legal codewords under this node are:

[0028]

[0029] Where: Path probability Need to node Perform an additional step of the SCL algorithm to decode the frozen bits Get, and collect Contains decoding SPC nodes The decoding path that remains after .

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

[0031] (S31) Given a received sequence y N , calculate the codebook probability as:

[0032]

[0033] Among them: Collection Contains the final decoding path after decoding is completed, the collection Contains the special nodes that make up a polar code, Returns the type of a particular node.

[0034] (S32) Calculate the posterior probability LLR for each code word bit as:

[0035]

[0036] in Probability P C|Y By Channel Calculated.

[0037] The present invention also includes a decoding device, which uses the above decoding method to perform polar code decoding.

[0038] The present invention also includes a communication device, which includes the above-mentioned decoding device.

[0039] The low-latency polar code soft-input and soft-output decoding method proposed in the present invention improves the parallelism compared to the SO-SCL decoding algorithm by realizing fast soft output decoding based on Rate0, Rate1, REP and SPC nodes, and significantly reduces the decoding delay without losing the soft output accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A schematic diagram of a flow chart of a low-latency polar code soft-input soft-output decoding method provided by an embodiment of the present invention.

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

[0042] Figure 3 A comparison diagram of decoding time steps between the low-latency polar code soft-input soft-output decoding method provided by an embodiment of the present invention and other polar code decoding methods.

[0043] Figure 4 This is a comparison chart of decoding performance between the low-latency polar code soft-input soft-output decoding method provided by an embodiment of the present invention and other polar code soft-output decoding methods.

[0044] Figure 5 This is a comparison chart of decoding performance in a multiple-input multiple-output system between the low-latency polar code soft-input soft-output decoding method provided by an embodiment of the present invention and other polar code soft-output decoding methods. DETAILED DESCRIPTION

[0045] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0046] Consider a polar code with a code length of N and a bit sequence to be encoded as u N =(u1,u2,…,u N ), after polarization transformation, the codeword c is obtained N =u N G N ,in is the generator matrix of the polar code, represents the Kronecker product. N Index in collection The bits in are frozen bits, and their values ​​are calculated as in represents the index set {1,2,…,i-1}. For the commonly used static frozen bits, For the dynamic freezing bit, u i and The value of Since the polar code with a code length of N can be expressed as the polarization of two polar codes with a code length of N / 2, the sequence It can correspond to a sub-polarization code with a special structure, and the sub-code word is in Represents an index collection N s =j s -i s +1. Such a sub-polarization code is called a special node and is recorded as In particular, the Rate0 node represents The bits in the middle are all frozen bits, and the Rate1 node indicates The REP node represents Only the last bit is the information bit, and the SPC node indicates Only the first bit is a frozen bit. Since the polar code with a code length of 2 must be one of the Rate0 node, Rate1 node, REP node or SPC node, any polar code with a code length of N can be fully represented by these four nodes. The set of special nodes that constitute the polar code is recorded as

[0047] The embodiment of the present invention provides a low-latency soft-input soft-output decoding method for the above polar code, and the specific implementation process is as follows: Figure 1 As shown, the description is as follows:

[0048] (S1) For a special node set Nodes in By index i s Decode in order from small to large For a specific node First, fast SCL decoding under dynamic frozen bit constraints is performed, including:

[0049] (S11) Before decoding a special node, the log likelihood ratio of the input of the special node in each path is calculated, which specifically includes: according to the traditional SCL decoding algorithm, the log likelihood ratio of the input node in the lth decoding path is calculated. The LLR of (l) ;

[0050] (S12) For each decoding path, the value of the dynamic frozen bit in the special node is calculated according to the previous decoding result, which specifically includes: for the lth decoding path, at the decoding node Previously, according to the preamble decoding result Calculate the value of the dynamic freeze bit in the node, where Denotes the l-th decoding path sequence u N Since the frozen bits are all before the information bits in the four nodes considered, it can be estimated in the decoding The dynamic frozen bits are calculated before. Representation Node The estimate of the bit sequence to be encoded of the corresponding sub-polar code, where the frozen bits are filled with the values ​​of the dynamic frozen bits calculated previously, and the remaining positions are filled with zeros.

[0051] (S13) Correcting the log-likelihood ratio of the input to the special node according to the value of the dynamic freeze bit, which specifically includes: calculating in is the generator matrix of the polar code, and represents the Kronecker product. The LLR sequence α obtained in the correction step (S11) (l) for:

[0052]

[0053] Where ⊙ represents element-by-element multiplication; is the correction amount of the dynamically frozen bit pair sub-polar code codeword.

[0054] (S14) Taking the modified log-likelihood ratio as input, performing conventional fast SCL decoding under the constraint of all-zero frozen bits for the special node, and obtaining a decoded decoding path and a corresponding path metric; this step specifically includes: taking the LLR vector and decoding path The corresponding path metric is the input, is the node Perform fast SCL decoding under the conventional all-zero frozen bit constraint. For a detailed implementation, refer to "Fast and Flexible Successive-CancellationList Decoders for Polar Codes" by SA Hashemi, C. Condo, and WJ Gross in IEEE Transaction on Signal Processing. The algorithm outputs the decoding node. The decoding path after and the corresponding path metric

[0055] (S15) Correcting the decoding path To satisfy the dynamic frozen bit constraint, the expression is:

[0056]

[0057] in: Represents the index set {i s ,i s +1,…,j s}, π(l) represents the existing l-th decoding path From the decoding node The π(l)th decoding path before

[0058] Further, to avoid the calculation in step (S13) The present invention proposes to set each special node Most front F d The frozen bits are dynamically frozen, while the rest remain fixed to zero. d The value of should be small enough so that the It is feasible because Total In some embodiments, F d The value range is F d ≤3.

[0059] (S2) After decoding a node Calculate the approximate sum of the posterior probabilities of the legal codewords that have not been visited under the node, including:

[0060] like If it is a Rate0 node (rate zero node), that is, all bits are frozen, the fast SCL algorithm in step (S1) does not perform path extension and selection. Figure 2 The figure shows the SCL decoding tree diagram of the polar code, where each node represents a possible partial decoding path, the left child of the node indicates that the next bit is decoded as 0, and the right child indicates that it is decoded as 1. The decoding of the Rate0 node is as follows: Figure 2 As shown in (a), the sum of the posterior probabilities of the legal codewords that have not been visited under this node is:

[0061]

[0062] in: represents a polar code bit sequence u with a length of N N =(u1,u2,…,u N ) index from i s to s The bit sequence of constitutes a special sub-polarization code, i.e., a special node; Indicates that given a special node The desired posterior probability and the node type;

[0063] like is a REP node (repeated node), that is, only the last bit is an information bit, then the fast SCL algorithm in step (S1) can access the node All possible decoding paths are listed, but some of them are discarded due to the size limit of the list, such as Figure 2 (b) As shown. So the posterior probability and estimate of the legal codewords that have not been visited under this node are:

[0064]

[0065] Among them: Collection Contains the decoding REP node The decoding path that was later abandoned, is the set of frozen bit indices of the polar code, Representing a collection Path Probability The relationship with the path metric is The corresponding path metric PM(a i ) is output by the fast SCL algorithm of step (S1);

[0066] like is a Rate 1 node (rate 1 node), that is, all information bits, then the fast SCL algorithm in step (S1) can only access the node The next part of the possible decoding path is Figure 2 (c) The posterior probability and estimate of all unvisited legal codewords under this node are

[0067]

[0068] The collection Contains decoding nodes The decoding paths that have been retained before are combined Contains the decoding Rate1 node The decoding path that remains afterward;

[0069] Similarly, if is an SPC node (single parity check node), that is, only the first bit is frozen, then the fast SCL algorithm in step (S1) can only access the node The next part of the possible decoding path is Figure 2 (d) The posterior probability and estimate of all unvisited legal codewords under this node are

[0070]

[0071] Where: Path probability Need to node Perform an additional step of the SCL algorithm to decode the frozen bits Get, and collect Contains decoding SPC nodes The decoding path that remains after .

[0072] (S3) decoding all special nodes, using the approximate estimated codebook probability obtained in step (S2) and calculating the outputted bit-level soft information of the polar code, specifically including:

[0073] (S31) Given a received sequence y N , calculate the codebook probability as:

[0074]

[0075] Among them: Collection Contains the final decoding path after decoding is completed, the collection Contains the special nodes that make up a polar code, Returns the type of a particular node.

[0076] (S32) Calculate the posterior probability LLR for each code word bit:

[0077]

[0078] in: Probability P C|Y By Channel Calculated.

[0079] An embodiment of the present invention further provides a polar code soft-input and soft-output decoding device, which uses the above algorithm to perform low-latency polar code soft-output decoding.

[0080] An embodiment of the present invention further provides a communication device, the device comprising the decoding device according to claim 6

[0081] Figure 3 The figure shows the comparison of the decoding time step of the low-latency soft-input and soft-output polar code decoding method of this patent with the SO-SCL method and the fast SCL (FSCL) method of hard output under different code lengths N and information bit numbers K. It can be seen from the figure that the decoding method provided by this patent can save at least 76% of the time step compared with the SO-SCL method, but can provide soft output at the expense of a little decoding delay compared with the FSCL method. Figure 4 The decoding performance comparison chart of the low-latency polar code soft input and soft output decoding method of this patent and other polar code soft output decoding methods is shown. It can be seen from the figure that the decoding method provided by this patent can achieve performance comparable to that of the SO-SCL method and is superior to other methods.

[0082] The low-latency polar code soft-input soft-output decoding method provided by this patent can also be applied to the multiple-input multiple-output (MIMO) system with iterative detection and decoding. Figure 5The decoding performance comparison chart of the low-latency polar code soft input and soft output decoding method of this patent in a 2-transmit 2-receive MIMO system and other polar code soft output decoding methods is shown. As can be seen from the figure, the decoding method provided by this patent has the same performance as the SO-SCL method and is better than other methods.

Claims

1. A polar code soft-input soft-output decoding method, characterized in that: (S1) performing fast serial cancellation list decoding under dynamic frozen bit constraints for all special nodes constituting a polar code, wherein the types of the 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 legal codewords that have not been visited under the node; (S3) Using the approximate estimated codebook probability obtained in step S2, bit-level soft information of the output polar code is calculated.

2. The polar code soft-input soft-output decoding method according to claim 1, characterized in that: The fast SCL decoding under the dynamic frozen bit constraint in step S1 includes: (S11) before decoding a special node, calculating the log-likelihood ratio of each path inputting the special node; (S12) for each decoding path, calculating the value of the dynamic frozen bit in the special node according to the previous decoding result; (S13) modifying the log-likelihood ratio input to the special node according to the value of the dynamic freeze bit; (S14) taking the modified log-likelihood ratio as input, performing conventional fast SCL decoding under the constraint of all-zero frozen bits for the special node, and obtaining a decoded decoding path and a corresponding path metric; (S15) Modify the decoding path to meet the dynamic frozen bit constraint.

3. The polar code soft-input soft-output decoding method according to claim 2, characterized in that: In the process of fast SCL decoding under dynamic frozen bit constraint, the maximum number of first F in each special node is set. d The frozen bits are dynamically frozen, while the rest remain fixed to zero; d The value range is F d ≤3, so that the result of the matrix multiplication when calculating the correction amount of the dynamic frozen bit to the sub-polar code word in step S13 is obtained by the table lookup method.

4. 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 the node in step S2 specifically includes: For the rate zero node, the required posterior probability sum is: in: represents a polar code bit sequence u with a length of N N =(u1,u2,…,u N ) index from i s to h s The bit sequence of constitutes a special sub-polarization code, i.e., a special node; Indicates that given a special node The desired posterior probability and the node type; For repeated nodes, the posterior probability and estimate required are: Among them: Collection Contains the decoding REP node The decoding path that was later abandoned, is the set of frozen bit indices of the polar code, Representing a collection Path Probability The relationship with the path metric is The corresponding path metric PM(a i ) is output by the fast serial cancellation list decoding algorithm under the dynamic frozen bit constraint of step S1; For a rate one node, the desired posterior probability and estimate is: Among them: Collection Contains decoding nodes The decoding path that remains before, and the collection Contains the decoding Rate1 node The decoding path that remains afterward; For a single parity check node, the required posterior probability and estimate are: Where: Path probability Need to node Perform an additional step of the SCL algorithm to decode the frozen bits Get, and collect Contains decoding SPC nodes The decoding path that remains after .

5. The polar code soft-input soft-output decoding method according to claim 1, characterized in that: The codebook probability in step S3 is estimated as: Where: y N To receive the sequence, set Contains the final decoding path after decoding is completed, the collection Contains the special nodes that make up a polar code, Returns the type of a special node; The bit-level soft information in step S3 is calculated as: Where: u∈{1,2,…,N}, Probability P C|Y By Channel Calculated.

6. A decoding device, characterized in that: Polar decoding is performed using the method described in any one of claims 1 to 5.

7. A communication device, characterized in that: Includes the decoding device as described in claim 6.

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