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CN111130567B - Belief Propagation List Decoding Method for Polar Codes with Added Noise Perturbation and Bit Flip - Google Patents

Belief Propagation List Decoding Method for Polar Codes with Added Noise Perturbation and Bit Flip Download PDF

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CN111130567B
CN111130567B CN202010001330.8A CN202010001330A CN111130567B CN 111130567 B CN111130567 B CN 111130567B CN 202010001330 A CN202010001330 A CN 202010001330A CN 111130567 B CN111130567 B CN 111130567B
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CN111130567A (en
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潘志文
杨与煜
刘楠
尤肖虎
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Southeast University
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    • 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
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Abstract

本发明提供了一种添加噪声扰动和比特翻转的极化码置信传播列表译码方法，包括如下步骤：进行带CRC校验的BPL译码；构造翻转比特集合FBS；进行添加人工噪声扰动和比特翻转的极化码置信传播列表译码。本发明能够在极化码BPL译码方法译码失败的情况下，通过对失败译码结果进行数据分析，进而构造出识别不可靠的信息比特判决的翻转比特集合，置不可靠信息比特的先验对数似然比为无穷值，同时添加了不同的人工噪声加以扰动，以试探性译码的方式纠正BPL译码方法中的错误，显著提高了极化码在BPL译码方法下的误帧率性能。本发明方法能够以较小的译码时延为代价获取误码率性能的增益。

The invention provides a polar code belief propagation list decoding method with added noise disturbance and bit flipping, comprising the following steps: performing BPL decoding with CRC check; constructing flipped bit set FBS; adding artificial noise disturbance and bit flipping Inverted Polar Code Belief Propagation List Decoding. In the case of a polar code BPL decoding failure, the present invention can construct a flip bit set for identifying unreliable information bit judgments by performing data analysis on the failed decoding results, and set the priority of unreliable information bits. The log-likelihood ratio is infinite, and different artificial noises are added for disturbance, and the error in the BPL decoding method is corrected by tentative decoding, which significantly improves the error rate of the polar code under the BPL decoding method. Frame rate performance. The method of the invention can obtain the performance gain of bit error rate at the cost of less decoding time delay.

Description

Polarization code belief propagation list decoding method added with noise disturbance and bit inversion
Technical Field
The invention belongs to the technical field of channel coding in wireless communication, and particularly relates to a polarization code belief propagation list decoding method with added noise disturbance and bit flipping.
Background
The polarization code technology is used as a novel channel coding technology, and when the code length is towards infinity, the transmission rate can reach the channel capacity of a binary input memory-free symmetrical channel. At present, two types of coding modes of polarization codes are mainstream, and one type of coding method based on serial cancellation (SuccessiveCancellation, SC) comprises a coding method based on serial cancellation list (success CancellationList, SCL) of SC coding. The SC-based polar code decoding method belongs to sequential decoding, and the decoded information bits affect the estimation of the subsequent information bits, so that the information bits in the code word must be estimated one by one, thereby generating larger decoding delay. Another class of mainstream decoding methods for polar codes is based on belief propagation (BeliefPropagation, BP) decoding methods, including belief propagation list (BeliefPropagationList, BPL) decoding methods. The BP-based decoding method is applicable to application scenes with higher requirements on time delay because the decoding time delay of the BP-based decoding method is obviously lower than that of the SC-based decoding method due to the property of parallel iterative computation and the BP-based decoding method is insensitive to codeword length. The traditional BP decoding method has poorer error rate and frame error rate performance, the BPL decoding method adopts a plurality of BP decoders based on different factor graphs for decoding, and the error rate and frame error rate performance are improved at the cost of higher calculation complexity and hardware requirements on the basis of the BP decoding method, but compared with the SCL decoding method added with cyclic redundancy check (CylicRedundancyCheck, CRC), the error rate and frame error rate performance of the BPL decoding method are still poorer.
Disclosure of Invention
In order to solve the problems, the invention provides a polarization code belief propagation list decoding method added with noise disturbance and bit flipping, and the used code words are cascade codes formed by CRC codes and polarization codes. In the method, under the condition that the BPL decoding result does not pass the CRC check, a Flip Bit Set (FBS) is constructed by analyzing the decoding result in the BPL decoding method, information bits with polarization codes in the FBS are flipped (the bit flipping in the method is realized by setting the prior log likelihood ratio of the flipped bits to infinity), and meanwhile, artificial noise disturbance (the artificial noise disturbance is realized by adding Gaussian white noise with different standard deviations to the received signals) is added, so that errors in part of the BPL decoder can be corrected, and the error rate and the frame error rate performance of the BPL decoding method are improved.
In order to achieve the above purpose, the present invention provides the following technical solutions:
the polarization code belief propagation list decoding method with added noise disturbance and bit flipping comprises the following steps:
the first step: BPL decoding with CRC check
(1) Initialization of
For a polarization code with a code length of N and an original information bit sequence length of K, the received signal is recorded asThe list number in the BPL decoding method is recorded as L, and the list number L represents that L BP decoders adopting different factor graphs are used for decoding in the BPL decoding method, and the step (2) is carried out;
(2) Simultaneously starting L BP decoders to decode
Recording deviceFor the estimation of the information bit sequence by the ith BP decoder, 1.ltoreq.i.ltoreq.L, where +.>Is the ith bit u in the ith BP decoder pair information bit sequence j Estimate of->The value is 0 or 1; record->Estimation of codeword bit sequence for ith BP decoder, wherein +.>Is the ith bit x in the bit sequence of the ith BP decoder pair codeword j Is determined by the estimation of (a); performing BP decoding simultaneously by using L BP decoders; the decoding stopping condition of each BP decoder is that the preset iteration number upper limit is reached or CRC check is met, once the estimation of the BP decoder on the information bit sequence meets the CRC check in the decoding process, the decoding is considered to be successful, the estimation of the BP decoder on the information bit sequence is selected as the decoding output of the method, and the whole decoding flow is ended; otherwise, entering a second step;
and a second step of: constructing a flipped bit set FBS
(1) Initialization of
Initializing a K-row and 2-column all-zero matrix reczero_one_matrix for counting BPL decoding results in the first step, wherein elements of the p-th row and q-th column in the reczero_one_matrix matrix are recorded as rec p,q ,1≤p is less than or equal to K and is less than or equal to 1 and less than or equal to q is less than or equal to 2, the number of elements in FBS is recorded as T, T is less than or equal to 0 and less than or equal to K, T represents the number of bits available for turning, and the step (2) is carried out;
(2) Counting the decoding result of the BPL decoding method in the first step, and writing the decoding result into a matrix reczero_one_matrix;
index is recorded j Is the bit index of the j-th bit in the original information bit sequence with the length of K in the information bit sequence filled with frozen bits, wherein j is more than or equal to 1 and less than or equal to K, and index is more than or equal to 1 j N is less than or equal to; the update rule of reczero_one_matrix is as follows:
wherein rec p,1 Recording index of information bit sequence in L BP decoder p The number of decoders whose bits are translated to 0, rec p,2 Recording index of information bit sequence in L BP decoder p The number of decoders whose bits are translated to 1, go to step (3);
(3) Calculating the ratio of each bit in the original information bit sequence translated to 0 and 1
Definition ratio p P is more than or equal to 1 and K is more than or equal to rec p,1 And rec p,2 The ratio of the smaller value to the larger value in (2) is shifted to the step (4);
(4) Selecting FBS from a set of information bits
The set index_u= { Index 1 ,index 2 ,...,index K The method comprises the steps of (1) sorting elements in index_U according to the sequence from big to small of corresponding ratio, wherein the sorting rule is as follows:
Index_U sorted represents the ordered Index _ U set,represents w in index_U a Individual elements, w a Representing the change in Index caused by ordering, from the ordered set index_U sorted In selecting the first T elements to constructAnd a third step of: polarization code belief propagation list decoding with addition of artificial noise perturbations and bit flipping
(1) Setting a variable t to count the number of times of tentative bit flip decoding, initializing t=1, and turning to the step (2);
(2) If T is more than T, adding artificial noise disturbance and bit flip BPL decoding method to fail decoding, ending the whole decoding flow; if T is less than or equal to T, turning to the step (3);
(3) The L BP decoders in the BPL method index into the information bit sequence asBit flipping of bits of (2)
Each BP decoder in the BPL decoding method corresponds to a matrix R, R being a matrix of size N× (1+log) 2 N), where N is the length of the polarization code; the first column of R is used to store a priori log likelihood ratios of the information bits; and (3) performing bit flipping: if the ith BP decoder decodes in step (2) in the first step the ith in the sequence of information bitsEstimation of individual bits->1, the corresponding R matrix of the BP decoder is +.>The first column element of the row is assigned to positive infinity; if it is0, R moment corresponding to the BP decoderFirst->Assigning a row first column element to minus infinity; the values of the other elements in R are still assigned according to the traditional BP decoding method; turning to the step (4);
(4) Adding different artificial noise perturbations to L BP decoders in the BPL method
Each BP decoder in the BPL decoding method corresponds to a matrix L, L being a matrix of size N× (1+log) 2 N), where N is the length of the polarization code; the rightmost column of L is used for storing the log-likelihood ratio of the received signal; adding artificial noise disturbance: for BP decoder with serial number i, N-dimensional Gaussian white noise vector with standard deviation of (0.4×i)/L is generatedSuperimposed on the received signal->Taking the superimposed N-dimensional vector as a new receiving signal of the BP decoder to carry out calculation on log likelihood ratio assignment to the rightmost column of the corresponding matrix L of the BP decoder, and turning to the step (5);
(5) BPL decoding using the matrix L and matrix R assigned according to steps (3) and (4)
For the estimation of the information bit sequence by the ith BP decoder, 1.ltoreq.i.ltoreq.L, where +.>Is the ith bit u in the ith BP decoder pair information bit sequence j Estimate of->The value is 0 or 1;Estimating a codeword bit sequence for an ith BP decoder, whereinIs the ith bit x in the bit sequence of the ith BP decoder pair codeword j Is determined by the estimation of (a); performing BP decoding simultaneously by using L BP decoders; the decoding stopping condition of each BP decoder is that the preset iteration number upper limit is reached or CRC check is met, and once the CRC check is met by the estimation of the BP decoder on the information bit sequence in the decoding process, the decoding is considered to be successful; if not, let t=t+1, and go to step (2).
Further, when the BP decoder in the first step (2) decodes, if the estimates of the information bit sequences by the BP decoders meet the CRC check at the same time, the estimate of the information bit sequence by the BP decoder with the smallest sequence number is selected as the decoding output of the method, and the whole decoding process is ended.
Further, in the second step (3), ratio p The calculation rule of (2) is: if rec p,1 ≤rec p,2 ThenIf rec p,1 ＞rec p,2 Then->
Further, in the third step (5), when the BP decoder decodes, if only one BP decoder satisfying the CRC check for the estimation of the information bit sequence in the shortest time, the BP decoder estimates the information bit sequence as the decoding output of the method, and the whole decoding process ends; if the multiple BP decoders meet the CRC check on the estimation of the information bit sequence in the shortest time in parallel, the estimation of the BP decoder with the smallest sequence number on the information bit sequence is selected as the decoding output of the method, and the whole decoding flow is finished.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the polarization code belief propagation list decoding method added with noise disturbance and bit overturn provided by the invention can be used for constructing an overturn bit set for identifying unreliable information bit judgment by carrying out data analysis on a failure decoding result under the condition that the polarization code BPL decoding method fails to decode, setting the prior log likelihood ratio of unreliable information bits as an infinite value, adding different artificial noise to disturb, correcting errors in the BPL decoding method in a heuristic decoding mode, and obviously improving the frame error rate performance of the polarization code under the BPL decoding method. In the middle-high signal-to-noise ratio interval, compared with a BPL decoding method, the method can improve the frame error rate by two orders 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 polarization code belief propagation list decoding method with added noise disturbance and bit flipping provided by the invention.
Detailed Description
The technical scheme provided by the present invention will be described in detail with reference to the following specific examples, and it should be understood that the following specific examples are only for illustrating the present invention and are not intended to limit the scope of the present invention.
The example is illustrated with a code length n=256, and a polarization code of an original information bit sequence length k=136 (including a cyclic redundancy check code length r=8). The construction method of the polarization code in the example is Gaussian approximation, the signal-to-noise ratio of the code word construction is 2.5 dB, and the generation polynomial of the cyclic redundancy check code is g (x) =x 8 +x 6 +x 3 +x 2 +1。
The flow of the polarization code belief propagation list decoding method added with noise disturbance and bit inversion provided by the invention is shown in figure 1, and the method comprises the following steps:
the first step: BPL decoding with CRC check is performed. The method comprises the following steps:
(1) Initializing. For a code length of N, the original informationPolarization code with bit sequence length K, and recording received signal asN=256 in this example. The number of the list in the BPL decoding method is denoted as L (the BPL decoding method is an existing method, and the number of the list L indicates that L BP decoders using different factor graphs are used for decoding in the BPL decoding method), in this example, l=32. And (3) switching to the step (2).
(2) And simultaneously starting L BP decoders to decode. Recording deviceFor the i-th BP decoder (the number of the BP decoder is denoted as i), the information bit sequence is estimated, as the output result of the BP decoder, 1.ltoreq.i.ltoreq.L, wherein +.>Is the ith bit u in the ith BP decoder pair information bit sequence j Estimate of->The value is 0 or 1. Recording deviceEstimation of codeword bit sequence for ith BP decoder, wherein +.>Is the ith bit x in the bit sequence of the ith BP decoder pair codeword j Is a function of the estimate of (2). The BP decoding is performed simultaneously by the L BP decoders. The decoding stop condition of each BP decoder is that the preset iteration number upper limit is reached or CRC check is met. Once the BP decoder estimates the information bit sequence to meet CRC check in the decoding process, the decoding is considered to be successful, the BP decoder estimates the information bit sequence to be used as the decoding output of the method, and the whole decoding process is finished; if multiple BP decoders estimate the information bit sequence while satisfying CRC check, the BP decoder with the smallest sequence number is selected to estimate the information bit sequenceThe estimate is taken as the decoded output of the method,
ending the whole decoding flow; otherwise, the second step is carried out.
And a second step of: the flip bit set FBS is constructed. The method comprises the following steps:
(1) Initializing. Initializing the all-zero matrix reczero_one_matrix of K rows and 2 columns for counting the BPL decoding result in the first step, in this example, k=136. The element of the p-th row and q-th column in the reczero_one_matrix matrix is denoted rec p,q P is more than or equal to 1 and less than or equal to K, q is more than or equal to 1 and less than or equal to 2. The number of elements in FBS is T, T is more than or equal to 0 and less than or equal to K, T represents the number of bits available for turning, and the value of the bit can be determined by an information receiver according to the channel condition. In this example, t=4 is taken. 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 is recorded j Is the bit index of the j-th bit in the original information bit sequence with the length of K in the information bit sequence filled with frozen bits, wherein j is more than or equal to 1 and less than or equal to K, and index is more than or equal to 1 j N is not more than. The update rule of reczero_one_matrix is as follows:
thus rec p,1 Recording index of information bit sequence in L BP decoder p The number of decoders whose bits are translated to 0, rec p,2 Recording index of information bit sequence in L BP decoder p The number of decoders whose bits are translated to 1. And (3) switching to the step (3).
(3) The ratio of each bit in the original information bit sequence translated to 0 and 1 is calculated. Definition ratio p P is more than or equal to 1 and K is more than or equal to rec p,1 And rec p,2 The ratio of the smaller value to the larger value to ensure the ratio p The value of (2) is not more than 1, and the sequencing of the subsequent steps is facilitated. The calculation rule is if rec p,1 ≤rec p,2 ThenIf rec p,1 ＞rec p,2 Thenratio p The larger the bit rate is, the more L BP decoders in the BPL decoding method are to the ratio in the information bit sequence p The larger the decoding difference of the individual bits, the greater the probability that the information bit will have a decoding error. And (4) switching to the step (4).
(4) FBS is selected from the set of information bits. The set index_u= { Index 1 ,index 2 ,...,index K And is a set of bit indices of K original information bits in the information bit sequence after padding with frozen bits. The elements in index_U are ordered according to the sequence from the big to the small of the corresponding ratio, and the ordering rule is as follows:
Index_U sorted representing the ordered index_U set, index wa Represents w in index_U a Individual elements, w a Representing the change in index caused by ordering. From the ordered set index_U sorted In selecting the first T elements to constructFbs= {6,7,13,20} in this example.
And a third step of: polarization code belief propagation list decoding with artificial noise disturbance and bit flipping added is performed. The method comprises the following steps:
(1) Setting a variable t to count the number of times of tentative bit flip decoding, initializing t=1, and turning to step (2).
(2) If T is more than T, adding artificial noise disturbance and bit flip BPL decoding method to fail decoding, ending the whole decoding flow; if T is less than or equal to T, the step (3) is carried out.
(3) The L BP decoders in the BPL method index into the information bit sequence wt The bit of (t element in the FBS set) is bit flipped. Each of the BPL decoding methodsThe BP decoders correspond to a matrix R, R being of size N x (1+log) 2 N), where N is the length of the polarization code. The first column of R is used to store a priori log likelihood ratios of the information bits. The rule of bit flipping is: if the ith BP decoder decodes in step (2) in the first step the ith in the sequence of information bitsEstimation of individual bits->1, the corresponding R matrix of the BP decoder is +.>The first column element of the row is assigned to positive infinity; if->0, the corresponding R matrix of the BP decoder is +.>The row first column element assigns a negative infinity. The values of the remaining elements in R are still assigned according to the conventional BP decoding method. And (4) switching to the step (4).
(4) Different artificial noise perturbations are added to the L BP decoders in the BPL method. Each BP decoder in the BPL decoding method corresponds to a matrix L, L being a matrix of size N× (1+log) 2 N), where N is the length of the polarization code. The right-most column of L is used to store the log-likelihood ratio of the received signal. The rule of adding artificial noise disturbance is: for BP decoder with serial number i, N-dimensional Gaussian white noise vector with standard deviation of (0.4×i)/L is generatedSuperimposed on the received signal->New received signal of BP decoder by superimposed N-dimensional vectorThe number is brought into the right-most column of the calculated log likelihood ratio assignment corresponding to the matrix L of the BP decoder, and the step (5) is carried out.
(5) And (3) performing BPL decoding by using the matrix L and the matrix R which are assigned according to the steps (3) and (4).
For the estimation of the information bit sequence by the ith BP decoder, 1.ltoreq.i.ltoreq.L, where +.>Is the ith bit u in the ith BP decoder pair information bit sequence j Estimate of->The value is 0 or 1.Estimating a codeword bit sequence for an ith BP decoder, whereinIs the ith bit x in the bit sequence of the ith BP decoder pair codeword j Is a function of the estimate of (2). The BP decoding is performed simultaneously by the L BP decoders. The decoding stop condition of each BP decoder is that the preset iteration number upper limit is reached or CRC check is met. Once the estimated information bit sequence of BP decoder meets CRC check in decoding process, the decoding is considered successful. If only one BP decoder for estimating the information bit sequence in the shortest time meets CRC check, the BP decoder estimates the information bit sequence as the decoding output of the method, and the whole decoding flow is ended; if the multiple BP decoders meet the CRC check on the estimation of the information bit sequence in the shortest time in parallel, the estimation of the BP decoder with the smallest sequence number on the information bit sequence is selected as the decoding output of the method, and the whole decoding flow is ended; if not, let t=t+1, and go to step (2).
The technical means disclosed by the scheme of the invention is not limited to the technical means disclosed by the embodiment, and also comprises the technical scheme formed by any combination of the technical features. It should be noted that modifications and adaptations to the invention may occur to one skilled in the art without departing from the principles of the present invention and are intended to be within the scope of the present invention.

Claims (4)

1.添加噪声扰动和比特翻转的极化码置信传播列表译码方法，其特征在于，包括如下步骤：1. A polar code confidence propagation list decoding method with added noise perturbation and bit flipping, characterized by comprising the following steps: 第一步：进行带CRC校验的BPL译码Step 1: Perform BPL decoding with CRC check (1)初始化(1) Initialization 对于码长为N，原始信息比特序列长为K的极化码，记接收信号为BPL译码方法中的列表数记为L，列表数L表示BPL译码方法中使用L个采用不同因子图的BP译码器进行译码，转入步骤(2)；For a polar code of length N and original information bit sequence length K, let the received signal be denoted as . The number of lists in the BPL decoding method is denoted as L. The number of lists L indicates that the BPL decoding method uses L BP decoders with different factor graphs for decoding. Proceed to step (2). (2)同时启动L个BP译码器进行译码(2) Simultaneously start L BP decoders for decoding. 记为第i个BP译码器对信息比特序列的估计，作为该BP译码器的输出结果，1≤i≤L，其中是第i个BP译码器对信息比特序列中第j个比特uj的估计，取值为0或1；记为第i个BP译码器对码字比特序列的估计，其中是第i个BP译码器对码字比特序列中第j个比特xj的估计；利用L个BP译码器同时进行BP译码；每个BP译码器的译码停止条件为达到预设的迭代次数上限或满足CRC校验，译码过程中一旦有BP译码器对信息比特序列的估计满足CRC校验，则认为译码成功，选择该BP译码器对信息比特序列的估计作为本方法的译码输出，整个译码流程结束；否则进入第二步；remember Let be the estimate of the information bit sequence for the i-th BP decoder, and be the output of the BP decoder, 1≤i≤L, where It is the estimate of the j-th bit u<sub>j</sub> in the information bit sequence by the i-th BP decoder. The value can be 0 or 1; denoted as Let be the estimate of the codeword bit sequence for the i-th BP decoder, where This is the estimate of the j-th bit xj in the codeword bit sequence by the i-th BP decoder; BP decoding is performed simultaneously using L BP decoders; the decoding stopping condition for each BP decoder is reaching the preset upper limit of the number of iterations or satisfying the CRC check. During the decoding process, once a BP decoder's estimate of the information bit sequence satisfies the CRC check, the decoding is considered successful, and the estimate of the information bit sequence by that BP decoder is selected as the decoding output of this method, and the entire decoding process ends; otherwise, proceed to the second step. 第二步：构造翻转比特集合FBSStep 2: Construct the Flipped Bit Set (FBS) (1)初始化(1) Initialization 初始化K行2列的全零矩阵reczero_one_matrix用于统计第一步中BPL译码结果，reczero_one_matrix矩阵中第p行第q列的元素记为recp,q,1≤p≤K,1≤q≤2，FBS中元素个数记为T,0≤T≤K,T表示可用于翻转的比特数，转入步骤(2)；Initialize a K-row, 2-column all-zero matrix reczero_one_matrix to count the BPL decoding results in the first step. The element in the p-th row and q-th column of the reczero_one_matrix matrix is denoted as rec p,q , 1≤p≤K, 1≤q≤2. The number of elements in FBS is denoted as T, 0≤T≤K, where T represents the number of bits that can be flipped. Proceed to step (2). (2)统计第一步中BPL译码方法的译码结果，写入矩阵reczero_one_matrix中；(2) Calculate the decoding results of the BPL decoding method in the first step and write them into the matrix reczero_one_matrix; 记indexj是长为K的原始信息比特序列中第j个比特在填充冻结比特后的信息比特序列中的比特索引,1≤j≤K,1≤indexj≤N；reczero_one_matrix的更新规则如下：Let index j be the bit index of the j-th bit in the original information bit sequence of length K after filling with frozen bits, 1≤j≤K, 1≤index j≤N ; the update rule of reczero_one_matrix is as follows: 其中，recp,1记录L个BP译码器中将信息比特序列中第indexp个比特译为0的译码器数目，recp,2记录L个BP译码器中将信息比特序列中第indexp个比特译为1的译码器数目，转入步骤(3)；Where rec p,1 records the number of L BP decoders that decode the p -th bit of the information bit sequence to 0, and rec p,2 records the number of L BP decoders that decode the p- th bit of the information bit sequence to 1. Proceed to step (3). (3)计算原始信息比特序列中每个比特被译为0和1的比例(3) Calculate the proportion of each bit in the original information bit sequence that is translated into 0 and 1. 定义ratiop,1≤p≤K为recp,1和recp,2中的较小值对较大值的比值，转入步骤(4)；Define ratio p ,1≤p≤K as the ratio of the smaller value of rec p,1 and rec p,2 to the larger value, and proceed to step (4); (4)从信息比特集合中选出FBS(4) Select FBS from the set of information bits 记集合Index_U＝{index1,index2,...,indexK}为K个原始信息比特在填充冻结比特后的信息比特序列中的比特索引组成的集合，对Index_U中的元素按照对应的ratio从大到小的顺序进行排序，排序规则为：Let the set Index_U = {index 1 ,index 2 ,...,index K } be the set of bit indices of the K original information bits in the information bit sequence after filling with frozen bits. The elements in Index_U are sorted in descending order according to their corresponding ratios, with the following sorting rule: Index_Usorted表示经过排序后的Index_U集合，表示Index_U中的第wa个元素，wa表示由排序引起的索引的变化，从排序后的集合Index_Usorted中选择前T个元素构建第三步：进行添加人工噪声扰动和比特翻转的极化码置信传播列表译码Index_U sorted represents the sorted set of Index_U. This represents the w- th element in Index_U, where w_a represents the index change caused by sorting. The sorted set Index_U is constructed by selecting the first T elements from the sorted set . Step 3: Perform polar code belief propagation list decoding with added artificial noise perturbation and bit flipping. (1)设置变量t对试探性比特翻转译码的次数进行计数，初始化t＝1，转入步骤(2)；(1) Set variable t to count the number of times the trial bit flip decoding is performed, initialize t=1, and go to step (2); (2)若t＞T，则添加人工噪声扰动和比特翻转的BPL译码方法译码失败，整个译码流程结束；若t≤T，转入步骤(3)；(2) If t > T, the BPL decoding method with added artificial noise perturbation and bit flipping fails to decode and the entire decoding process ends; if t ≤ T, proceed to step (3). (3)BPL方法中的L个BP译码器都对信息比特序列中索引为的比特进行比特翻转BPL译码方法中的每个BP译码器都对应一个矩阵R，R是一个大小为N×(1+log2 N)的矩阵，其中N是极化码的长度；R的第一列用于存储信息比特的先验对数似然比；进行比特翻转：若第i个BP译码器在第一步中步骤(2)译码得到的对信息比特序列中第个比特的估计为1，则将该BP译码器对应的R矩阵的第行第一列元素赋值为正无穷；若为0，则将该BP译码器对应的R矩阵的第行第一列元素赋值为负无穷；R中其余元素的值仍按传统BP译码方法赋值；转入步骤(4)；(3) In the BPL method, all L BP decoders are located at index 1 in the information bit sequence. In the BPL decoding method, each BP decoder corresponds to a matrix R, which is an N×(1+log 2 N) matrix, where N is the length of the polar code; the first column of R is used to store the prior log-likelihood ratio of the information bits; bit flipping is performed: if the i-th BP decoder in step (2) of the first step, the first bit of the information bit sequence is flipped. Estimation of bits If the value is 1, then the first element of the R matrix corresponding to the BP decoder is... The element in the first column of the row is assigned the value of positive infinity; if If the value is 0, then the first element of the R matrix corresponding to the BP decoder is... The first element in the first column is assigned the value of negative infinity; the values of the remaining elements in R are still assigned according to the traditional BP decoding method; proceed to step (4); (4)对BPL方法中的L个BP译码器添加不同的人工噪声扰动(4) Add different artificial noise perturbations to the L BP decoders in the BPL method. BPL译码方法中的每个BP译码器都对应一个矩阵L，L是一个大小为N×(1+log2 N)的矩阵，其中N是极化码的长度；L的最右侧一列用于存储接收信号的对数似然比；添加人工噪声扰动：对序号为i的BP译码器，生成标准差为(0.4×i)÷L的N维高斯白噪声向量叠加上接收信号由叠加后的N维向量作为该BP译码器的新的接收信号带入计算对数似然比赋值给该BP译码器对应矩阵L的最右侧一列，转入步骤(5)；Each BP decoder in the BPL decoding method corresponds to a matrix L, which is an N×(1+log 2 N) matrix, where N is the length of the polar code; the rightmost column of L is used to store the log-likelihood ratio of the received signal; artificial noise perturbation is added: for the BP decoder with index i, an N-dimensional Gaussian white noise vector with a standard deviation of (0.4×i)÷L is generated. Superimposed with the received signal The superimposed N-dimensional vector is used as the new received signal of the BP decoder and is used to calculate the log-likelihood ratio. The value is assigned to the rightmost column of the matrix L corresponding to the BP decoder, and then proceed to step (5). (5)使用按照步骤(3)和(4)赋值后的矩阵L和矩阵R进行BPL译码(5) Use the matrices L and R, which have been assigned values according to steps (3) and (4), to perform BPL decoding. 为第i个BP译码器对信息比特序列的估计，作为该BP译码器的输出结果，1≤i≤L，其中是第i个BP译码器对信息比特序列中第j个比特uj的估计，取值为0或1；为第i个BP译码器对码字比特序列的估计，其中是第i个BP译码器对码字比特序列中第j个比特xj的估计；利用L个BP译码器同时进行BP译码；每个BP译码器的译码停止条件为达到预设的迭代次数上限或满足CRC校验，译码过程中一旦存在BP译码器对信息比特序列的估计满足CRC校验，则认为译码成功；否则令t＝t+1，转入步骤(2)。 Let be the estimate of the information bit sequence for the i-th BP decoder, and be the output of the BP decoder, 1≤i≤L, where It is the estimate of the j-th bit u<sub>j</sub> in the information bit sequence by the i-th BP decoder. The value can be 0 or 1; Let be the estimate of the codeword bit sequence for the i-th BP decoder, where It is the estimate of the j-th bit xj in the codeword bit sequence by the i-th BP decoder; BP decoding is performed simultaneously by L BP decoders; the decoding stopping condition of each BP decoder is to reach the preset upper limit of the number of iterations or to satisfy the CRC check. If the BP decoder's estimate of the information bit sequence satisfies the CRC check during the decoding process, the decoding is considered successful; otherwise, let t = t + 1 and proceed to step (2). 2.根据权利要求1所述的添加噪声扰动和比特翻转的极化码置信传播列表译码方法，其特征在于，所述第一步步骤(2)中BP译码器进行译码时，若有多个BP译码器对信息比特序列的估计同时满足CRC校验，则选取序号最小的BP译码器对信息比特序列的估计作为本方法的译码输出，整个译码流程结束。2. The polar code confidence propagation list decoding method with added noise perturbation and bit flipping according to claim 1, characterized in that, when the BP decoder performs decoding in the first step (2), if the estimation of the information bit sequence by multiple BP decoders simultaneously satisfies the CRC check, the estimation of the information bit sequence by the BP decoder with the smallest sequence number is selected as the decoding output of this method, and the entire decoding process ends. 3.根据权利要求1所述的添加噪声扰动和比特翻转的极化码置信传播列表译码方法，其特征在于，所述第二步步骤(3)中，ratiop的计算规则为：若recp,1≤recp,2，则若recp,1＞recp,2，则 3. The polar code belief propagation list decoding method with added noise perturbation and bit flipping according to claim 1, characterized in that, in the second step (3), the calculation rule for ratio p is: if rec p,1 ≤ rec p,2 , then If rec p,1 > rec p,2 , then 4.根据权利要求1所述的添加噪声扰动和比特翻转的极化码置信传播列表译码方法，其特征在于，所述第三步步骤(5)中，BP译码器译码时，若在最短时间内对信息比特序列的估计满足CRC校验的BP译码器只有一个，则该BP译码器对信息比特序列的估计作为本方法的译码输出，整个译码流程结束；若有多个BP译码器以并列的最短时间对信息比特序列的估计满足CRC校验，则选取序号最小的BP译码器对信息比特序列的估计作为本方法的译码输出，整个译码流程结束。4. The polar code confidence propagation list decoding method with added noise perturbation and bit flipping according to claim 1, characterized in that, in the third step (5), when the BP decoder decodes, if there is only one BP decoder whose estimation of the information bit sequence satisfies the CRC check in the shortest time, then the estimation of the information bit sequence by that BP decoder is used as the decoding output of this method, and the entire decoding process ends; if multiple BP decoders satisfy the CRC check in the shortest time in parallel, then the estimation of the information bit sequence by the BP decoder with the smallest sequence number is selected as the decoding output of this method, and the entire decoding process ends.
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