CN110278002B - Bit-flipping-based polarization code belief propagation list decoding method - Google Patents
Bit-flipping-based polarization code belief propagation list decoding method Download PDFInfo
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- H—ELECTRICITY
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- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/13—Linear codes
- H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
- H03M13/151—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes using error location or error correction polynomials
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/13—Linear codes
- H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
- H03M13/151—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes using error location or error correction polynomials
- H03M13/1545—Determination of error locations, e.g. Chien search or other methods or arrangements for the determination of the roots of the error locator polynomial
Abstract
The invention discloses a polarization code belief propagation list decoding method based on bit flipping, and the used code word is a cascade code formed by CRC (cyclic redundancy check) codes and polarization codes. In the method, under the condition that the BPL decoding result does not pass CRC (cyclic redundancy check), a Flip Bit Set (FBS) is constructed by analyzing the decoding result in the BPL decoding method, information Bits of a polarization code in the FBS are flipped (bit flipping in the invention is realized by setting a prior log-likelihood ratio of the flipped Bits to be infinite), errors in a part of BPL decoders can be corrected, and the error rate and the frame error rate performance of the BPL decoding method are improved.
Description
Technical Field
The invention relates to a bit-reversal-based polar code belief propagation list decoding method, and belongs to the technical field of channel coding in wireless communication.
Background
The polar code technology is a novel channel coding technology, and when the code length tends to be infinite, the transmission rate can reach the channel capacity of a binary input memoryless symmetrical channel. Currently, there are two types of decoding methods for polar codes, one type of decoding method is based on Serial Cancellation (SC), which includes a Serial Cancellation List (SCL) decoding method based on SC decoding, the SC-based polar code decoding method belongs to sequential decoding, and decoded information bits affect the estimation of subsequent information bits, so that the information bits in a codeword must be estimated one by one, thereby generating a large decoding delay. The other mainstream decoding method of the polarization code is based on a Belief Propagation (BP) decoding method, and comprises a Belief Propagation List (BPL) decoding method, and due to the property of parallel iterative computation of the BP decoding method, the decoding time delay of the BP decoding method is significantly lower than that of an SC decoding method and is insensitive to the length of a code word, so that the BP decoding method is suitable for application scenarios with higher requirements on time delay. The traditional BP decoding method has poor error rate and frame error rate performance, the BPL decoding method adopts a plurality of BP decoders based on different factor graphs for decoding, the improvement of the error rate and the frame error rate performance is brought at the cost of higher calculation complexity and hardware requirements on the basis of the BP decoding method, but the error rate and the frame error rate performance of the BPL decoding method are still poor compared with an SCL decoding method added with Cyclic Redundancy Check (CRC). .
Disclosure of Invention
In order to improve the error rate and the frame error rate performance of a BPL decoding method, the invention provides a bit-reversal-based polarized code belief propagation list decoding method, and a used code word is a cascade code formed by a CRC (cyclic redundancy check) code and a polarized code. In the method, under the condition that the BPL decoding result does not pass CRC (cyclic redundancy check), a Flip Bit Set (FBS) is constructed by analyzing the decoding result in the BPL decoding method, information Bits of a polarization code in the FBS are flipped (bit flipping in the invention is realized by setting a prior log-likelihood ratio of the flipped Bits to be infinite), errors in a part of BPL decoders can be corrected, and the error rate and the frame error rate performance of the BPL decoding method are improved.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a bit-reversal-based polar code belief propagation list decoding method, which comprises the following steps of:
the first step, carrying out BPL decoding with CRC check, specifically:
(1) Initialization
For a polar code with a code length of N and a length of K of the original information bit sequence, the received signal is recorded as
The list number in the BPL decoding method is marked as L, and the step (2) is carried out; wherein the original information bit sequence is a CRC-encoded information sequence not filled with frozen bits, y j A jth bit representing the received signal;
(2) Starting L BP decoders simultaneously for decoding
Estimation of information bit sequence by ith BP decoder
As a result of the output of the BP decoder, an estimate of the codeword bit sequence by the ith BP decoder is calculated
And receiving signals
Has an Euclidean distance d between i And (4) turning to the step (3); wherein i is more than or equal to 1 and less than or equal to L,
is the ith BP decoder to the jth bit u in the information bit sequence j J is more than or equal to 1 and less than or equal to N,
is the ith BP decoder to the jth bit x in the codeword bit sequence j (ii) an estimate of (d); the information bit sequence is obtained by filling frozen bits in the original information bit sequence, and the code word bit sequence is generated by encoding the information bit sequence by a polar code;
(3) Sequencing decoding results of L BP decoders
Note book
Sorting the components in the decoded _ u according to the following sorting rule to obtain a new vector decoded _ u _ sorted for the vector formed by the estimation of the information bit sequence by the L BP decoders obtained in the step (2), and turning to a step (4):
wherein the content of the first and second substances,
represents the kth in decoded _ u _ sorted m The number of the components is such that,
to represent
And receiving signals
The euclidean distance between them,
to represent
And receiving signals
The euclidean distance between;
(4) CRC (cyclic redundancy check) on decoding results of L BP (back propagation) decoders
Performing CRC on the components in the decoded _ u _ sorted one by one, if the components passing the CRC exist, successfully decoding the BPL decoder with the CRC, outputting the components passing the CRC as decoding, and ending the whole decoding process; if the component passing the CRC does not exist, the decoding of the BPL decoder with the CRC fails, and the second step is carried out;
and secondly, constructing a flipping bit set FBS, specifically comprising:
(A) Initializing a full zero matrix reczero _ one _ matrix of K rows and 2 columns, wherein an element of a qth row and a qth column in the reczero _ one _ matrix is recorded as rec p,q P is more than or equal to 1 and less than or equal to K, and q is more than or equal to 1 and less than or equal to 2; recording the number of elements in the FBS as T, wherein T is more than or equal to 0 and less than or equal to K, and transferring to the step (B);
(B) According to the decoding result of the BPL decoding method in the first step, updating the reczero _ one _ matrix according to the following updating rule, and proceeding to step (C):
therein, index p Is the bit index of the p-th bit in the original information bit sequence with the length of K in the information bit sequence after filling the frozen bits, and is more than or equal to 1 index p ≤N；
(C) Calculating the ratio of each bit in the original information bit sequence to be translated into 0 and 1
If rec p,1 ≤rec p,2 Then rec p,1 And rec p,2 Ratio of smaller value to larger value
If rec p,1 ＞rec p,2 Then, then
Turning to step (D);
(D) Selecting FBS from information bit set
Set Index _ U = { Index = 1 ,index 2 ,...,index K Sorting the elements in the method according to the following sorting rule, selecting the first T elements from the sorted set to construct the FBS, and turning to the third step:
wherein, index _ U sorted Represents the sorted set of Index _ U,
represents Index _ U sorted W of (1) a The number of the elements is one,
thirdly, decoding a polarization code belief propagation list based on bit reversal, specifically comprising the following steps:
(1) initializing t =1, and turning to step (2);
(2) if T is larger than T, the bit flipping-based BPL decoding method fails in decoding, and the whole decoding process is finished; if T is less than or equal to T, switching to the step (3);
(3) in the BPL method, L BP decoders all index into information bit sequence as
Bit flipping is carried out on the bits, and the step (4) is carried out; wherein, each BP decoder in the BPL method corresponds to a size of N × (1 +log) 2 N), the first column of R is used for storing the prior log-likelihood ratio of the information bit, and the rule of bit inversion is as follows: if the ith BP decoder is in the first step, the step (2) decodes the obtained information bit sequence
Estimation of individual bits
If the value is 1, the BP decoder is corresponding to the R-th bit
The row first column element is assigned a positive infinity; if it is
If the value is 0, the BP decoder is set to the corresponding R
Assigning the first row element to negative infinity, and assigning the values of the other elements in the R according to a BP decoding method;
(4) using the R obtained in the step (3), simultaneously starting L BP decoders for decoding, and switching to the step (5);
(5) sequencing the decoding results of the L BP decoders in the step (4) according to the sequencing rule of the step (3) in the first step, and turning to the step (6);
(6) performing CRC on the sequenced decoding results in the step (5) one by one, if the decoding results passing the CRC exist, successfully decoding the bit flipping, outputting the decoding results passing the CRC as decoding, and ending the whole decoding process; if there is no component passing the CRC check, let t = t +1, and proceed to step (2).
As a further technical solution of the present invention,
the value is 0 or 1.
As a further technical scheme of the invention, the value of T can be autonomously determined by an information receiver according to the channel condition.
As a further technical solution of the present invention,
advantageous effects
The polarization code belief propagation list decoding method based on bit inversion can construct an inversion bit set for identifying unreliable information bit judgment by performing data analysis on a failure decoding result under the condition that the decoding of a polarization code BPL decoding method fails, set the prior log likelihood ratio of the unreliable information bit as an infinite value, correct errors in the BPL decoding method in a tentative decoding mode and improve the frame error rate performance of the polarization code under the BPL decoding method. In the interval of medium and high signal-to-noise ratio, compared with a BPL decoding method, the method can improve the frame error rate by one order of magnitude, and meanwhile, the average decoding time delay of the decoding method is similar to that of the BPL decoding method, which shows that the method can obtain the gain of the bit error rate performance at the cost of smaller decoding time delay.
Drawings
Fig. 1 is a flowchart of a polar code belief propagation list decoding method based on bit flipping.
Detailed Description
In the invention, an information sequence with the length of K and which is subjected to CRC coding and is not filled with frozen bits is recorded as an original information bit sequence, an information sequence with the length of N and which is obtained by filling the frozen bits in the original information bit sequence with the length of K is recorded as an information bit sequence, and a bit sequence generated after the information bit sequence is subjected to polarization code coding is called a code word bit sequence.
The bit flipping-based polarization code belief propagation decoding method in the present invention is described by taking a polarization code with a code length N =256 and an original information bit sequence length K =136 (including a cyclic redundancy check code length r = 8) as an example. The construction method of the polarization code in this example is gaussian approximation, the code word construction signal-to-noise ratio is 2.5 db, and the generator polynomial of the cyclic redundancy check code is g (x) = x 8 +x 6 +x 3 +x 2 +1。
As shown in fig. 1, the method comprises the following steps:
the first step is as follows: and carrying out BPL decoding with CRC check. The method comprises the following steps:
(1) And (5) initializing. For a polar code with a code length of N and a length of K of the original information bit sequence, the received signal is recorded as
N =256 in this example. The number of lists in the BPL decoding method is denoted by L (the BPL decoding method is an existing method, and the number of lists L indicates that L BP decoders using different factor graphs are used for decoding in the BPL decoding method), and L =32 in this example. And (4) transferring to the step (2).
(2) And starting L BP decoders for decoding at the same time. Note the book
For the estimation of the information bit sequence by the ith BP decoder, i is more than or equal to 1 and less than or equal to L as the output result of the BP decoder, wherein
J is more than or equal to 1 and less than or equal to N is that the ith BP decoder performs the j bit u in the information bit sequence j Is estimated by the estimation of (a) a,
the value is 0 or 1. Note book
Estimation of codeword bit sequence for the ith BP decoder, wherein
J is more than or equal to 1 and less than or equal to N is that the ith BP decoder performs the operation on the jth bit x in the code word bit sequence j Is estimated. BP decoding is performed simultaneously using L BP decoders. Calculating an estimate of the codeword bit sequence obtained by the ith BP decoder
And receiving signals
Has an Euclidean distance d between i ，
And (4) transferring to the step (3).
(3) And sequencing the decoding results of the L BP decoders. Note the book
And (3) forming a vector by the estimates of the L BP decoders on the information bit sequence obtained in the step (2), wherein each component is the estimate of one BP decoder on the information bit sequence. And sequencing the components in the decoded _ u according to the following rule to obtain a new vector decoded _ u _ sorted:
(4) And performing CRC on the decoding results of the L BP decoders. Performing CRC on the components in the decoded _ u _ sorted one by one, if the components passing the CRC exist, successfully decoding the BPL decoder with the CRC, outputting the components passing the CRC as decoding, and ending the whole decoding process; if no component passing the CRC check exists, the BPL decoder with the CRC check fails in decoding, tentative bit reversal decoding is needed, and the process goes to the second step.
The second step is that: a flip bit set FBS is constructed. The method comprises the following steps:
(1) And (6) initializing. Initializing the all-zero matrix reczero _ one _ matrix of K rows and 2 columns is used to count the BPL decoding result in the first step, in this example, K =136. The pth row qth in the reczero _ one _ matrixThe elements of the column are denoted rec p,q P is more than or equal to 1 and less than or equal to K, and q is more than or equal to 1 and less than or equal to 2. The number of elements in the FBS is recorded as T, T is more than or equal to 0 and less than or equal to K, T represents the bit number which can be used for overturning, and the value of the T can be autonomously determined by an information receiver according to the channel condition. In this example, T =4. And (3) switching to the step (2).
(2) And counting the decoding result of the BPL decoding method in the first step, and writing the decoding result into the matrix reczero _ one _ matrix. Index of j Is the bit index of the jth bit in the original information bit sequence with the length of K in the information bit sequence after filling the frozen bits, j is more than or equal to 1 and less than or equal to K, and index is more than or equal to 1 and less than or equal to index j Less than or equal to N. The update rule of reczero _ one _ matrix is as follows:
therefore, rec p,1 Recording the index of the information bit sequence in the L BP decoders p The number of decoders, rec, for each bit to be 0 p,2 Recording the index of the information bit sequence in the L BP decoders p The number of decoders for which a bit is 1. And (4) transferring to the step (3).
(3) The ratio of 0 to 1 for each bit in the original information bit sequence is calculated. Defining ratio p And p is more than or equal to 1 and less than or equal to K is rec p,1 And rec p,2 Ratio of smaller value to larger value in order to ensure ratio p The value of (a) does not exceed 1, facilitating the sequencing of subsequent steps. The calculation rule is if rec p,1 ≤rec p,2 Then, then
If rec p,1 ＞rec p,2 Then, then
ratio p The larger the number of the BPL codes is, the larger the number of the BPL codes is BP decoder for the second ratio in the information bit sequence p The larger the difference in decoding of the individual bits, the greater the probability of decoding error occurring in the information bit. And (5) switching to the step (4).
(4) The FBS is selected from the set of information bits. Memory setAnd Index _ U = { Index = { (Index) } 1 ,index 2 ,...,index K And the K original information bits are set by bit indexes in the information bit sequence after the frozen bits are filled. Sorting the elements in the Index _ U according to the following sorting rule:
Index_U sorted represents the sorted Index _ U set, index wa Represents Index _ U sorted W of (1) a Element of w a Indicating a change in the index due to sorting. From sorted set Index _ U sorted The first T elements of the medium selection are constructed
FBS in this example = {6,7,13,20}.
The third step: and carrying out bit-flipping-based polar code belief propagation list decoding. The method comprises the following steps:
(1) Initializing t =1, counting the number of times of tentative bit reversal decoding by t, and proceeding to step (2).
(2) If T is larger than T, the bit flipping-based BPL decoding method fails in decoding, and the whole decoding process is finished; if T is less than or equal to T, the step (3) is carried out.
(3) All L BP decoders in the BPL method have index in the information bit sequence wt The bit of (the t-th element in the FBS set) is bit flipped. Each BP decoder in the BPL decoding method corresponds to a matrix R, wherein R is a matrix with the size of N x (1 + log) 2 N), where N is the length of the polarization code. The first column of R is used to store the a priori log likelihood ratios of the information bits. The rule of bit flipping is: if the ith BP decoder decodes the ith bit sequence in the information bit sequence obtained in the step (2) in the first step
Estimation of individual bits
1, the first matrix of the R matrix corresponding to the BP decoder
The row first column element is assigned a positive infinity; if it is
0, the first R matrix corresponding to the BP decoder
The row first column element is assigned a negative infinity. The values of the other elements in R are still assigned according to the traditional BP decoding method. And (4) switching to the step.
(4) And (4) carrying out BPL decoding by using the matrix R assigned according to the step (3).
For the estimation of the information bit sequence by the ith BP decoder, i is more than or equal to 1 and less than or equal to L as the output result of the BP decoder, wherein
J is more than or equal to 1 and less than or equal to N is that the ith BP decoder performs bit u in the information bit sequence j The estimation of (a) is performed,
the value is 0 or 1.
Estimation of codeword bit sequence for the ith BP decoder, wherein
J is more than or equal to 1 and less than or equal to N is that the ith BP decoder performs the operation on the jth bit x in the code word bit sequence j Is estimated. BP decoding is performed simultaneously using L BP decoders. Calculating the codeword estimate from the ith BP decoder
And receiving signals
Has an Euclidean distance d between i ，
And (5) switching to the step.
(5) And sequencing the decoding results of the L BP decoders. Note the book
And (4) forming a vector by the estimates of the L BP decoders on the information bits obtained in the step (4), wherein each component is the estimate of a BP decoder on the information bit sequence. And sequencing the components in the decoded _ u according to the formula (1) to obtain a new vector decoded _ u _ sorted. And (6) switching to the step.
(6) And performing CRC on the decoding results of the L BP decoders. Performing CRC on the components in the decoded _ u _ decoded one by one, if the components passing the CRC exist, successfully decoding the bit flipping, outputting the components passing the CRC as a decoding, and ending the whole decoding process; if there is no component passing the CRC check, let t = t +1, and proceed to step (2).
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (4)
1. The polar code belief propagation list decoding method based on bit reversal is characterized by comprising the following steps of:
the first step, carrying out BPL decoding with CRC check, specifically:
(1) Initialization
For a polar code with a code length of N and a length of K of the original information bit sequence, the received signal is recorded as
The list number in the BPL decoding method is marked as L, and the step (2) is carried out; wherein the original information bit sequence is a CRC-encoded information bit sequence not filled with frozen bits, y j J is more than or equal to 1 and less than or equal to N, and represents the jth bit of the received signal;
(2) Starting L BP decoders simultaneously for decoding
Estimation of information bit sequence by ith BP decoder
As a result of the output of the BP decoder, an estimate of the codeword bit sequence by the ith BP decoder is calculated
And receiving signals
Has an Euclidean distance d between i And (4) turning to the step (3); wherein i is more than or equal to 1 and less than or equal to L,
is the ith BP decoder to the jth bit u in the information bit sequence j J is more than or equal to 1 and less than or equal to N,
is the ith BP decoder to the jth bit x in the codeword bit sequence j (ii) is estimated; the information bit sequence is obtained by filling frozen bits in the original information bit sequence, and the code word bit sequence is generated by encoding the information bit sequence by a polar code;
(3) Sequencing decoding results of L BP decoders
Note the book
For the L BP decoder pairs obtained in step (2)And (4) a vector formed by estimation of the information bit sequence is sorted according to the following sorting rule to obtain a new vector sorted _ u _ sorted, and the step is carried out:
wherein the content of the first and second substances,
represents the kth in decoded _ u _ sorted m The number of the components is such that,
to represent
And receiving signals
The euclidean distance between them,
to represent
And receive the signal
The euclidean distance therebetween;
(4) CRC (cyclic redundancy check) is carried out on decoding results of L BP (back propagation) decoders
Performing CRC on the components in the decoded _ u _ sorted one by one, if the components passing the CRC exist, successfully decoding the BPL decoder with the CRC, outputting the components passing the CRC as a decoding, and ending the whole decoding process; if the component passing the CRC does not exist, the decoding of the BPL decoder with the CRC fails, and the second step is carried out;
and secondly, constructing a flipping bit set FBS, specifically comprising:
(A) Initializing a full zero matrix reczero _ one _ matrix of K rows and 2 columns, wherein an element of a qth row and a qth column in the reczero _ one _ matrix is recorded as rec p,q P is more than or equal to 1 and less than or equal to K, and q is more than or equal to 1 and less than or equal to 2; recording the number of elements in the FBS as T, wherein T is more than or equal to 0 and less than or equal to K, and transferring to the step (B);
(B) According to the decoding result of the BPL decoding method in the first step, updating the rezero _ one _ matrix according to the following updating rule, and proceeding to step (C):
therein, index p Is the bit index of the p-th bit in the original information bit sequence with the length of K in the information bit sequence after filling the frozen bits, and is more than or equal to 1 index p ≤N；
(C) Calculating the ratio of each bit in the original information bit sequence to be translated into 0 and 1
If rec p,1 ≤rec p,2 Then rec p,1 And rec p,2 Ratio of smaller value to larger value
If rec p,1 ＞rec p,2 Then, then
Turning to step (D);
(D) Selecting FBS from information bit set
Set Index _ U = { Index = 1 ,index 2 ,...,index K Sorting the elements in the FBS according to the following sorting rule, selecting the first T elements from the set obtained by sorting to construct the FBS, and turning to the third step:
wherein, index _ U sorted Represents the sorted set of Index _ U,
represents Index _ U sorted W of (1) a The number of the elements is one,
thirdly, decoding a polarization code belief propagation list based on bit reversal, specifically comprising the following steps:
(1) initializing t =1, and turning to step (2);
(2) if T is larger than T, the bit flipping-based BPL decoding method fails in decoding, and the whole decoding process is finished; if T is less than or equal to T, switching to the step (3);
(3) in the BPL method, L BP decoders all index into information bit sequence as
Bit flipping is carried out on the bits, and the step (4) is carried out; wherein, each BP decoder in the BPL method corresponds to a decoder with a size of N x (1 + log) 2 N), the first column of R is used for storing the prior log-likelihood ratio of the information bit, and the rule of bit inversion is as follows: if the ith BP decoder is in the first step, the step (2) decodes the obtained information bit sequence
Estimation of individual bits
If the BP decoder is 1, the corresponding R in the BP decoder is the second
The row first column element is assigned a positive infinity; if it is
If the value is 0, the BP decoder is set to the corresponding R
Assigning the first row element to negative infinity, and assigning the values of the other elements in the R according to a BP decoding method;
(4) using the R obtained in the step (3), simultaneously starting L BP decoders for decoding, and switching to the step (5);
(5) sequencing the decoding results of the L BP decoders in the step (4) according to the sequencing rule of the step (3) in the first step, and turning to the step (6);
(6) performing CRC on the sequenced decoding results in the step (5) one by one, if the decoding results passing the CRC exist, successfully decoding the bit flipping, outputting the decoding results passing the CRC as decoding, and ending the whole decoding process; if there is no component passing the CRC check, let t = t +1, and proceed to step (2).
2. The bit-reversal based polar-code belief-propagation list decoding method of claim 1, wherein the bit-reversal based polar-code belief-propagation list decoding method,
the value is 0 or 1.
3. The bit flipping-based polar code belief propagation list decoding method of claim 1, wherein a value of T is autonomously determined by an information receiver according to a channel condition.
4. The bit flipping-based polar code belief propagation list decoding method of claim 1,
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| CN110492974B (en) * | 2019-08-19 | 2020-08-07 | 北京邮电大学 | Parallel polar code decoding method and device |
| CN110620588B (en) * | 2019-10-25 | 2023-08-25 | 网络通信与安全紫金山实验室 | BPL decoding method and device based on polarization code |
| CN110798284B (en) * | 2019-11-25 | 2022-01-21 | 安徽大学 | Polarization code transmission method based on double BP decoding graph parallel decoding technology |
| CN110932824B (en) * | 2020-02-11 | 2020-06-26 | 网络通信与安全紫金山实验室 | Polarization code belief propagation method based on bidirectional graph with bit reversal |
| CN111416624B (en) * | 2020-03-27 | 2023-05-26 | 网络通信与安全紫金山实验室 | Polarization code belief propagation decoding method, equipment and storage medium |
| CN111541517B (en) * | 2020-04-17 | 2022-03-25 | 北京交通大学 | List polarization code propagation decoding method |
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