CN103281166B - A kind of mixed automatic retransfer request transmission method based on polarization code - Google Patents

Abstract

Translated fromChinese

一种基于极化码的混合自动重传请求传输方法，是发送端将发送的信息比特序列进行极化编码后得到的编码比特序列进行凿孔后，送入信道传输；接收端对接收信号译码并进行CRC校验；若通过校验，则给发送端反馈ACK信号；否则，发送NACK信号；若发送端接收到NACK信号，则将一部分信息比特不经编码再次发送给接收端，接收端根据第一次接收到的编码比特和新接收的信息比特重新译码；若译码结果仍未通过CRC校验，则发送端将另一部分信息比特不经编码再次发送给接收端，接收端再根据第一次接收到的编码比特、前一次接收到的信息比特和新接收到的信息比特重新译码；持续执行该过程，直到发送端接收到ACK信号，或发送次数达到预设的最大值时，结束一次完整的传输过程。

A hybrid automatic repeat request transmission method based on polar codes, in which the transmitting end performs polar coding on the transmitted information bit sequence and then sends the coded bit sequence into a channel for transmission; the receiving end decodes the received signal code and perform CRC check; if the check is passed, an ACK signal will be fed back to the sending end; otherwise, a NACK signal will be sent; if the sending end receives a NACK signal, a part of the information bits will be sent to the receiving end again without encoding, and the receiving end Re-decode according to the coded bits received for the first time and the newly received information bits; if the decoding result still fails to pass the CRC check, the sender sends another part of the information bits to the receiver without encoding, and the receiver again Re-decode according to the coded bits received for the first time, the previously received information bits and the newly received information bits; continue to perform this process until the sender receives the ACK signal, or the number of transmissions reaches the preset maximum , a complete transmission process ends.

Description

Translated fromChinese

一种基于极化码的混合自动重传请求传输方法A Hybrid Automatic Repeat Request Transmission Method Based on Polar Code

技术领域technical field

本发明涉及一种基于极化码的混合自动重传请求传输方法，用于解决数字通信系统中由于传输信道对通信过程的干扰，使得传输数据出现错误的问题；确切地说，涉及一种采用极化码作为纠错编码的数字通信系统中，通过混合自动重传请求进行信号传输的方法。属于数字通信的信道编码技术领域。The invention relates to a hybrid automatic repeat request transmission method based on polar codes, which is used to solve the problem of errors in transmitted data due to the interference of transmission channels on the communication process in digital communication systems; In digital communication systems where polar codes are used as error-correcting codes, a method for signal transmission through hybrid automatic repeat requests. The invention belongs to the technical field of channel coding of digital communication.

背景技术Background technique

极化码(PolarCodes)是2009年由提出的一种被严格证明可以达到信道容量的构造性的信道编码方法。在进行极化编码之前，先要对N＝2ⁿ个独立的二进制输入信道(或对同一个信道的先后N次使用，即一个信道的N个可用时隙)，应用图1所示的信道极化的基本单元对二进制输入离散信道反复进行极化，其中的n为自然数。最基本的信道极化是对两个相同的未经极化的信道W：进行单步极化操作，其中，是信道输入符号的集合(对于二进制输入信道，取值为{0,1})，是信道输出符号的集合。如图1所示，标记该极化信道的输入比特分别为u₁和u₂，该两个输入比特通过一个模二加法器得到x₁，另一方面将u₂直接赋值给x₂，即x₂＝u₂，为模二加运算。再把x₁和x₂分别送入未经极化信道W后，得到的输出为y₁和y₂。从该信道极化基本单元的输入(u₁和u₂)和两个信道的输出(y₁和y₂)看，原本独立的两个未经极化的信道W被合并成一个两输入两输出的向量信道其中运算符*为笛卡尔积。该向量信道包含两个子信道(输入为u₁、输出为y₁y₂)和(输入为u₂输出为y₁y₂u₁)，这两个子信道即是两个极化信道。经过该单步极化过程，从信道容量上看，其中I(·)表示求信道容量的函数。也就是说：单步极化后，在和容量保持不变的情况下，相比原本未经极化的信道，极化后的信道容量发生了偏离：一个增加，一个减少。如果对两组已经一次极化操作的信道，再在该两组互相独立的转移概率相同的极化信道之间，分别进行单步极化操作，该偏离会更加明显，称这一组单步极化操作为第二层极化操作，前一组单步极化操作被称为第一层极化操作。每多做一层极化操作，需要的信道数就会比原先多一倍。因此，对N＝2ⁿ个信道进行完全的极化，共需要n层极化操作，且每一层极化操作包括了N次单步极化操作。如不加特殊说明，“对N个信道进行极化操作”是指完全极化。Polar Codes (PolarCodes) was developed in 2009 by A constructive channel coding method that is rigorously proven to achieve channel capacity is proposed. Before performing polar coding, the channel shown in Figure 1 must be applied to N=2ⁿ independent binary input channels (or to the N consecutive uses of the same channel, that is, N available time slots of a channel). The basic unit of polarization repeatedly polarizes binary input discrete channels, where n is a natural number. The most basic channel polarization is for two identical unpolarized channels W: Perform a single-step polarization operation, where, is the set of channel input symbols (for binary input channels, takes the value {0,1}), is the set of channel output symbols. As shown in Figure 1, the input bits marking the polarized channel are respectively u₁ and u₂ , and the two input bits get x₁ through a modulo-two adder, and on the other hand, u₂ is directly assigned to x₂ , namely x₂ =u₂ , It is a modulo two addition operation. After x₁ and x₂ are respectively sent to the unpolarized channel W, the output obtained is y₁ and y₂ . From the input of the channel polarization basic unit (u₁ and u₂ ) and the output of the two channels (y₁ and y₂ ), the original independent two unpolarized channels W are combined into a two-input two output vector channel in The operator * is a Cartesian product. This vector channel contains two subchannels (input is u₁ , output is y₁ y₂ ) and (the input is u₂ and the output is y₁ y₂ u₁ ), these two sub-channels are two polarized channels. After this single-step polarization process, from the perspective of channel capacity, Among them, I(·) represents the function of seeking channel capacity. That is to say: after single-step polarization, when the sum capacity remains unchanged, compared with the original unpolarized channel, the capacity of the polarized channel deviates: one increases and the other decreases. If a single-step polarization operation is performed on two sets of channels that have undergone one polarization operation, and then between the two independent polarization channels with the same transition probability, the deviation will be more obvious, and this group is called single-step The polarization operation is the second layer polarization operation, and the previous group of single-step polarization operations is called the first layer polarization operation. For each additional layer of polarization operation, the number of channels required will be doubled. Therefore, to perform complete polarization on N=2ⁿ channels, a total of n layers of polarization operations are required, and each layer of polarization operations includes N times of single-step polarization operations. Unless otherwise specified, "perform polarization operations on N channels" refers to complete polarization.

理论上已经证明，对接近无穷多个信道进行极化操作后，会出现一部分信道的容量为1(即通过其传输的比特一定会被正确接收)，其余信道容量为0(即完全无法在其上可靠地传输比特)的现象，而容量为1的信道占全部信道的比例正好为原二进制输入离散信道的容量。Theoretically, it has been proved that after performing polarization operations on nearly infinite channels, the capacity of some channels will be 1 (that is, the bits transmitted through it will be received correctly), and the capacity of the remaining channels will be 0 (that is, it is completely impossible to transmit bits in other channels). Reliable transmission of bits) phenomenon, and the proportion of the channel with a capacity of 1 to all channels is exactly the capacity of the original binary input discrete channel.

图2所示是长度为N的信道极化装置的递归结构示意图，其中递归的最小单元(即N＝1时)为图1所示的基本单元。FIG. 2 is a schematic diagram of a recursive structure of a channel polarization device with a length of N, wherein the minimum unit of recursion (ie when N=1) is the basic unit shown in FIG. 1 .

参见图3，介绍一个实用的信道极化装置的递归结构，长度为N(对N个信道进行极化)的信道极化装置可以用长度为的信道极化装置作递归操作来表示，递归过程中的最小单元(即N＝2时)就是图1所示的基本单元。图2中的信道极化装置中有一个长度为N的比特反转交织器，其功能是：先将输入端的十进制序号i按二进制表示为(b_nb_n-1…b₁)，其中，n＝log₂N，再将该二进制序列反序，得到(b₁b₂…b_n)，最后重新按十进制表示成θ(i)，作为输入序号i对应的输出序号。比特反转交织器的用处是将输入端序号为i的比特映射到序号θ(i)处。根据编码速率(R)对N个信道进行极化，并选取其中容量最大的K个信道(或者等价地，选取可靠性最高的K个信道，可靠性度量是采用密度进化(DensityEvolution)工具或计算巴塔恰里亚(Bhattacharyya)参数得到的)，以承载用于传输消息的比特，并称该部分比特为信息比特和称该部分信道为信息信道(其中为向下取整运算)，其余未被选中的信道则传输一个约定的比特序列，称其为固定比特序列，并称该部分信道为固定信道(若信道对称，则可简单地传输全零序列)，从而形成一个从承载信息的K个比特到最终送入信道的N个比特的映射关系，这样的一种映射关系即为极化码，其码长(编码后得到的二进制信号所包含的比特数)等于信道极化装置的长度N。Referring to Fig. 3, a practical recursive structure of a channel polarization device is introduced. The channel polarization device with a length of N (to polarize N channels) can be used with a length of The channel polarization device is represented by a recursive operation, and the smallest unit in the recursive process (that is, when N=2) is the basic unit shown in FIG. 1 . In the channel polarization device in Fig. 2, there is a bit inversion interleaver with a length of N, and its function is: first, the decimal number i at the input end is expressed in binary as (b_n b_n-1 ...b₁ ), where, n=log₂ N, and then reverse the binary sequence to obtain (b₁ b₂ …b_n ), and finally re-express it in decimal as θ(i), which is used as the output sequence number corresponding to the input sequence number i. The purpose of the bit reverse interleaver is to map the bit with the sequence number i at the input end to the sequence number θ(i). The N channels are polarized according to the coding rate (R), and the K channels with the largest capacity are selected (or equivalently, the K channels with the highest reliability are selected, and the reliability measurement is performed using the DensityEvolution tool or Calculate Bhattacharyya (Bhattacharyya) parameters) to carry the bits used to transmit messages, and call this part of the bits as information bits and call this part of the channel as an information channel (wherein is a downward rounding operation), and the rest of the unselected channels transmit an agreed bit sequence, which is called a fixed bit sequence, and this part of the channel is called a fixed channel (if the channel is symmetrical, the all-zero sequence can be simply transmitted ), so as to form a mapping relationship from the K bits carrying information to the N bits finally sent to the channel. Such a mapping relationship is a polar code, and its code length (included in the binary signal obtained after encoding The number of bits) is equal to the length N of the channel polarizer.

由信息比特和固定比特组成的、送入信道极化装置的二进制信号序列(u₁,…,u_N)为编码码块(其顺序与其送入的极化信道的序号一致，即u_i送入且序号i为1到N的正整数，表示将N个信道W极化后得到的序号为i的极化信道)。编码码块经过信道极化装置后，得到的x₁…x_N又通过N个独立信道W，接收到的信号序列为(y₁,…,y_N)。The binary signal sequence (u₁ ,…,u_N ) sent to the channel polarization device composed of information bits and fixed bits is coded code blocks (the order of which is consistent with the serial number of the polarized channel sent in, that is, u_i sends enter And the serial number i is a positive integer from 1 to N, Indicates the polarized channel with sequence number i obtained after polarizing N channels W). After the encoded code block passes through the channel polarization device, the obtained x₁ ... x_N passes through N independent channels W, and the received signal sequence is (y₁ ,...,y_N ).

上述过程也可以等价地描述为：将序列u＝(u₁,…,u_N)乘以矩阵G_N，即x＝u·G_N，其中，矩阵N×N的矩阵B_N为比特反序置换矩阵，$F_2=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$的上标表示求n个F₂的克罗内克积。矩阵B_N是将一个N×N的单位方阵的各个行按照比特反序重排才得到的：对每一个序号i∈{1,2,...,N}，(i-1)的二进制表示为(b_n,b_n-1,…,b₁)，找出一个j∈{1,2,…,N}使得(j-1)的二进制表示为(b₁,b₂,…,b_n)，令B_N的第i行等于I_N的第j行。The above process can also be equivalently described as: multiply the sequence u=(u₁ ,...,u_N ) by the matrix G_N , that is, x=u·G_N , where the matrix The N×N matrix B_N is a bit reverse permutation matrix,$f_2=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$ superscript It means to find the Kronecker product of n F₂ . Matrix B_N is obtained by rearranging the rows of an N×N unit square matrix in reverse order of bits: for each sequence number i∈{1,2,...,N}, (i-1) The binary representation is (b_n ,b_n-1 ,…,b₁ ), find a j∈{1,2,…,N} such that the binary representation of (j-1) is (b₁ ,b₂ ,… ,b_n ), let the i-th row of B_N be equal to the j-th row of I_N.

如果极化码码长不为2的幂次。例如：假设码长其中，为向上取整运算。需要先按照以上方法构造一个N维的信道极化变换。该变换需要N个独立信道，其中M个信道是通过对信道W的M次独立使用得到的，剩余的N-M个为与W具有相同输入输出信号集、但信道容量为零的虚拟信道。虚拟信道的排列位置按照以下方法决定：先给定一个N维的向量q，其中前N-M个元素为1，后M个元素为0，即然后，对该向量进行比特反序重排，得到凿孔位置指示序列p＝B_N·q。对序号i∈{1,2,...,N}，若p_i＝1，则表示第i个独立信道为虚拟信道；否则，表示第i个独立信道为信道W的一次独立使用。进行了上述操作以后，与普通极化码一样，从得到的极化信道中选出最可靠的K个信道作为信息信道，用于承载信息比特；其余的信道，则设置为固定信道。通过这种方法得到的极化码称为凿孔极化码。If the code length of the polar code is not a power of 2. For example: assuming code length in, is an upward rounding operation. It is necessary to first construct an N-dimensional channel polarization transformation according to the above method. This transformation requires N independent channels, among which M channels are obtained by using channel W independently for M times, and the remaining NM are virtual channels with the same set of input and output signals as W, but with zero channel capacity. The arrangement position of the virtual channel is determined according to the following method: First, an N-dimensional vector q is given, in which the first NM elements are 1, and the last M elements are 0, namely Then, carry out bit reverse order rearrangement on the vector to obtain the puncture position indication sequence p=B_N ·q. For sequence numbers i∈{1,2,...,N}, if p_i =1, it means that the i-th independent channel is a virtual channel; otherwise, it means that the i-th independent channel is an independent use of channel W. After performing the above operations, as with ordinary polar codes, the obtained polar channel The most reliable K channels are selected as information channels to carry information bits; the rest of the channels are set as fixed channels. The polar codes obtained by this method are called perforated polar codes.

凿孔极化编码过程也可以等价地描述成：将序列u＝(u₁,…,u_N)乘以矩阵G_N，即x＝u·G_N，其中，矩阵B_N为比特反序置换矩阵，$F_2=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right],$表示n个F₂的克罗内克积。然后，将得到的向量x根据凿孔位置指示序列p进行凿孔，其中，p_i＝1表示凿去比特x_i，p_i＝0表示保留比特x_i，得到最终的发送码字v＝(v₁,…,v_M)。The punctured polarization encoding process can also be equivalently described as: multiply the sequence u=(u₁ ,...,u_N ) by the matrix G_N , that is, x=u·G_N , where the matrix B_N is a permutation matrix in reverse order of bits,$f_2=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right],$ Denotes the Kronecker product of n_F2s . Then, the obtained vector x is punctured according to the puncturing position indication sequence p, wherein, p_i =1 means that the bit x_i is punctured, and p_i =0 means that the bit_xi is reserved, and the final transmitted codeword v=( v₁ ,...,v_M ).

在构造极化码时，对二进制删除信道以外的一般信道，都需要使用密度进化工具来计算极化信道的可靠度。下面简单介绍一下使用密度进化计算极化码可靠性的方法：When constructing polar codes, it is necessary to use density evolution tools to calculate the reliability of polar channels for general channels other than binary erasure channels. The following is a brief introduction to the method of calculating the reliability of polar codes using density evolution:

假设发送的信息块为一个K长的全零序列，则其编码后的码字为一个N长的全零序列。经过信道传输，接收端可以根据接收到的序列(y₁…y_N)计算得到各个编码比特的对数似然比(LLR)的值。再用表示第i个极化信道上当发送比特为零时，接收比特的LLR值的概率密度函数。利用极化码的结构，是按照以下方法递归计算得到：$a_N^{\left(i\right)}=a_{N,1}^{\left(i\right)},a_{2k,j}^{(2i-1)}=a_{k,2j-1}^{\left(i\right)}\⊕a_{k,2j}^{\left(i\right)},a_{2k,j}^{\left(2i\right)}=a_{k,2j-1}^{\left(i\right)}\⊗a_{k,2j}^{\left(i\right)};$其中，运算符和分别表示校验节点域卷积和变量节点域卷积。对应每一个k的取值,有i＝1,2,…,k和对应第j个编码比特的LLR值的概率密度函数，其中j＝1,2,…,N。Assuming that the transmitted information block is a K-length all-zero sequence, the encoded codeword is an N-length all-zero sequence. After channel transmission, the receiving end can calculate the value of the logarithmic likelihood ratio (LLR) of each encoded bit according to the received sequence (y₁ ... y_N ). reuse Indicates the i-th polarized channel Above is the probability density function of the LLR value of the received bit when the transmitted bit is zero. Using the polar code structure, is calculated recursively as follows:$a_N^{\left(i\right)}=a_{N,1}^{\left(i\right)},a_{2k,j}^{(2i-1)}=a_{k,2j-1}^{\left(i\right)}\⊕a_{k,2j}^{\left(i\right)},a_{2k,j}^{\left(2i\right)}=a_{k,2j-1}^{\left(i\right)}\⊗a_{k,2j}^{\left(i\right)};$ where the operator and Denote check node domain convolution and variable node domain convolution, respectively. Corresponding to each value of k, there are i=1,2,...,k and The probability density function of the LLR value corresponding to the j-th coded bit, where j=1,2,...,N.

给定一个二进制输入信道W，以及其在输入为比特零时输出LLR值的概率密度函数a，该信道的可靠度可以通过计算其传输出错概率进行评估，传输出错概率计算公式为：由此可以根据得到各个极化信道的可靠性。Given a binary input channel W and the probability density function a of its output LLR value when the input is bit zero, the reliability of the channel can be evaluated by calculating its transmission error probability. The formula for calculating the transmission error probability is: From this it can be based on get each polarized channel reliability.

在信号接收端，极化码译码器任务是根据接收信号序列(y₁,…,y_N)得到发送比特序列(u₁,…,u_N)的一组比特估计序列对于凿孔极化码，(y₁…y_N)中极化码可使用串行抵消SC(successivecancellation)算法，对编码码块中的每个比特按照序号i从1到N依次进行译码：式中，信息比特的判决函数为：其中，$P(y_1,\mathrm{...},y_N|{\hat{u}}_1,\mathrm{...},{\hat{u}}_{i-1},{\hat{u}}_i)=\frac{1}{2^{i-1}}\·W_N^{\left(i\right)}(y_1,\mathrm{...},y_N,{\hat{u}}_1,\mathrm{...},{\hat{u}}_{i-1}|{\hat{u}}_i);$函数为序号为i的极化子信道的转移概率函数，表示发送信号u_i通过信道得到输出y₁…y_N和u₁…u_i-1的概率。At the signal receiving end, the task of the polar code decoder is to obtain a set of bit estimation sequences for the transmitted bit sequence (u₁ ,…,u_N ) according to the received signal sequence (y₁ ,…,y_N ) For the punctured polar code, the polar code in (y₁ …y_N ) can use the serial cancellation SC (successivecancellation) algorithm to decode each bit in the encoded code block in sequence from 1 to N according to the sequence number i: In the formula, the decision function of the information bit is: in,$P({\mathrm{the\; y}}_1,\mathrm{...},{\mathrm{the\; y}}_N|{\hat{u}}_1,\mathrm{...},{\hat{u}}_{i-1},{\hat{u}}_i)=\frac{1}{2^{i-1}}\·W_N^{\left(i\right)}({\mathrm{the\; y}}_1,\mathrm{...},{\mathrm{the\; y}}_N,{\hat{u}}_1,\mathrm{...},{\hat{u}}_{i-1}|{\hat{u}}_i);$ function is the polarization sub-channel with the sequence number i The transition probability function of , which means that the sending signal u_i passes through the channel Get the probabilities of outputs y₁ ...y_N and u₁ ...u_i-1 .

串行抵消译码方法还可以描述为一个码树上的搜索过程(图3为一个简单示例)。串行抵消译码是在码树上逐步扩展，每次从两条候选路径选择其中具有相对大概率值的一条，并在这条路径的基础上，继续进行下一步路径的扩展。The serial cancellation decoding method can also be described as a search process on a code tree (Figure 3 is a simple example). Serial offset decoding is to gradually expand on the code tree, select one of the two candidate paths each time with a relatively high probability value, and continue to expand the next path on the basis of this path.

作为串行抵消译码的一个改良型，串行抵消列表译码允许保留多条候选路径，而不是仅仅一条，以此扩大搜索范围，并减小在搜索过程中离开正确路径的概率。其具体方法是：将所有的候选路径与其对应的可靠性度量值都存储于一个列表中。该列表中的所有候选路径都被同步扩展，所以每次扩展后，该列表中的候选路径数量就会翻倍。接着，丢弃那些可靠性度量值较小的部分候选路径，以保证候选路径数始终不大于列表大小的一半。并在译码结束时，从表中找出可靠性度量值最大的那条路径，其对应的比特估计序列即为译码结果。As an improved version of serial cancellation decoding, serial cancellation list decoding allows to keep multiple candidate paths instead of only one, so as to expand the search range and reduce the probability of leaving the correct path during the search process. The specific method is: storing all candidate paths and their corresponding reliability measurement values in a list. All candidate paths in the list are expanded synchronously, so after each expansion, the number of candidate paths in the list doubles. Then, some candidate paths with smaller reliability metric values are discarded to ensure that the number of candidate paths is always no more than half the size of the list. And at the end of decoding, find out the path with the largest reliability measure value from the table, and its corresponding bit estimation sequence is the decoding result.

串行抵消译码的另外一个改良为串行抵消堆栈译码。它是使用一个有序堆栈，用于存储候选路径，而不是列表。串行抵消堆栈译码的过程中，每次都只基于可靠性度量最大的那一条候选路径(位于堆栈栈顶)进行扩展。当出现栈顶路径到达码树的某一个叶子节点时，就停止译码过程，并且将该路径所对应的比特估计序列输出，作为译码结果。Another modification of serial cancellation decoding is serial cancellation stack decoding. It uses an ordered stack for storing candidate paths instead of a list. In the process of serial offset stack decoding, only the candidate path (located at the top of the stack stack) with the largest reliability measure is expanded each time. When a stack top path arrives at a certain leaf node of the code tree, the decoding process is stopped, and the bit estimation sequence corresponding to the path is output as a decoding result.

如果信息块包含了循环冗余信息，即信息块序列的循环冗余校验结果为全零序列，就可以使用循环冗余校验辅助的串行抵消列表/堆栈译码算法进行译码。采用这种译码方法，有限码长极化码的抗噪性能可以得到很大幅度的提高。If the information block contains cyclic redundancy information, that is, the cyclic redundancy check result of the information block sequence is an all-zero sequence, it can be decoded by using the serial offset list/stack decoding algorithm assisted by the cyclic redundancy check. Using this decoding method, the anti-noise performance of the finite code length polar code can be greatly improved.

在对系统延时不敏感的通信应用中，混合自动重传请求(HARQ)是一种常用的用以提高系统吞吐率的传输方法。In communication applications that are not sensitive to system delay, hybrid automatic repeat request (HARQ) is a commonly used transmission method to improve system throughput.

其吞吐率的计算公式为：The formula for calculating the throughput rate is:

参见图4，介绍混合自动重传请求(HARQ)传输的一个简单示例：在传输某一个信息块时，发送端将信息块(发送序列1)编码后送入信道，如果接收端对接收到的信号进行译码后，发现传输失败(如无法通过循环冗余校验)。此时，接收端就会通过一个反馈链路传输一个不确认(NACK)消息给发送端，发送端就会将该信息块重新编码发送(发送序列2…T)。这个过程会一直持续到接收端正确译码，此时，接收端会发送一个确认(ACK)消息给发送端，从而完成该对信息块的传输。HARQ技术已经被广泛用于已有通信系统(如WCDMA、LTE等系统)中。Referring to Figure 4, a simple example of hybrid automatic repeat request (HARQ) transmission is introduced: when transmitting a certain information block, the sending end encodes the information block (sending sequence 1) and sends it to the channel, if the receiving end is correct for the received After the signal is decoded, it is found that the transmission fails (such as failing to pass the cyclic redundancy check). At this time, the receiving end will transmit a non-acknowledgment (NACK) message to the sending end through a feedback link, and the sending end will re-encode and send the information block (sending sequence 2...T). This process will continue until the receiving end decodes correctly. At this time, the receiving end will send an acknowledgment (ACK) message to the sending end, thereby completing the transmission of the pair of information blocks. The HARQ technology has been widely used in existing communication systems (such as WCDMA, LTE and other systems).

本发明专利申请中，除非有特殊说明，统一使用小写的英文/希腊字母表示标量，如x；用花体大写的英文字母表示集合，如用粗体小写的英文/希腊字母表示向量(或等价的序列)，如x；向量中的某一个元素，则采用与其同名的小写英文/希腊字母(非粗体)表示，并用下标标记该元素在向量中的序号，如向量x的第i个元素用符号x_i表示；向量x的一个子向量(x_i,x_i+1,…,x_j-1,x_j)用符号x_i:j表示；用粗体大写的英文字母表示方阵，并用下标标记其大小，如X_N表示一个N×N的方阵。In the patent application of the present invention, unless otherwise specified, lowercase English/Greek letters are uniformly used to represent scalar quantities, such as x; uppercase English letters are used to represent sets, such as A vector (or an equivalent sequence) is represented by a bold lowercase English/Greek letter, such as x; an element in a vector is represented by a lowercase English/Greek letter (not bold) with the same name and marked with a subscript The serial number of the element in the vector, for example, the i-th element of vector x is represented by symbol x_i ; a subvector of vector x (_xi ,_xi+1 ,…,x_j-1 ,x_j ) is represented by symbol x_{i: j} means; use bold uppercase English letters to indicate a square matrix, and use a subscript to mark its size, such as X_N means an N×N square matrix.

上述现有技术的缺点是：因为实用的编码系统的码长不可能无限长，而对于有限数量的信道进行极化操作后，仍会存在一部分传输性能不是特别好、也不是特别差的信道。所以，在现有的译码方法下，有限码长的极化码取得的抗噪性能并不理想。因此，直接将极化码应用于实际系统中，并不能获得非常理想的吞吐率。另一方面，已经应用于实际系统的HARQ系统大多是基于turbo码或者LDPC码的，受到码构造方法的限制，其码长的调节范围受限，从而导致系统吞吐率与信道容量仍然有较大的距离。The disadvantage of the above-mentioned prior art is that because the code length of a practical coding system cannot be infinitely long, after performing polarization operations on a limited number of channels, there will still be some channels whose transmission performance is not particularly good or not particularly bad. Therefore, under the existing decoding methods, the anti-noise performance obtained by polar codes with limited code length is not ideal. Therefore, directly applying the polar code to an actual system cannot obtain a very ideal throughput rate. On the other hand, most of the HARQ systems that have been used in practical systems are based on turbo codes or LDPC codes. Due to the limitation of the code construction method, the adjustment range of the code length is limited, resulting in a large system throughput and channel capacity. distance.

发明内容Contents of the invention

有鉴于此，本发明的目的是提供一种基于极化码的混合自动重传请求传输方法，以便能够大大提高采用极化码作为信道编码的通信系统的吞吐率，并提高比特正确译码的概率，从而使得本发明基于极化码的HARQ方案能够得到最大限度的优化。而且，本发明方法操作简便，特别适合应用于实际通信系统中，具有很好的实用化前景。In view of this, the purpose of the present invention is to provide a hybrid automatic repeat request transmission method based on polar codes, so that the throughput rate of the communication system using polar codes as channel coding can be greatly improved, and the probability of correct bit decoding can be improved. probability, so that the polar code-based HARQ scheme of the present invention can be optimized to the greatest extent. Moreover, the method of the invention is easy to operate, is particularly suitable for being applied in an actual communication system, and has a good practical prospect.

为了达到上述目的，本发明提供了一种基于极化码的混合自动重传请求(HARQ)传输方法，其特征在于：信号发送端将准备发送的信息比特序列进行一次极化编码，得到的编码比特经过凿孔后，被送入信道进行传输；信号接收端对接收信号进行译码，并对译码结果进行循环冗余码(CRC)校验；若校验通过，则信号接收端经由反馈链路给发送端发送确认(ACK)信号；否则，给发送端发送非确认(NACK)信号；若发送端接收到NACK信号，则将其中部分信息比特不经过编码再次通过信道发送给接收端，接收端则根据第一次接收到的编码比特和新接收到的信息比特重新译码；若译码结果依然不能通过CRC校验，则发送端接收到NACK信号后，将另一部分信息比特不经过编码再次通过信道发送给接收端，接收端再根据第一次接收到的编码比特、前一次接收到的信息比特和新接收到的信息比特重新译码；上述过程持续执行，直到发送端接收到ACK信号，或者发送次数达到预设的最大值时，才结束一次完整的传输过程；该方法包括下述操作步骤：In order to achieve the above object, the present invention provides a hybrid automatic repeat request (HARQ) transmission method based on a polar code, which is characterized in that: the signal sending end performs a polar coding on the information bit sequence to be sent, and the obtained code After the bits are punctured, they are sent to the channel for transmission; the signal receiving end decodes the received signal, and performs a cyclic redundancy code (CRC) check on the decoding result; if the verification is passed, the signal receiving end passes the feedback The link sends an acknowledgment (ACK) signal to the sending end; otherwise, a non-acknowledgment (NACK) signal is sent to the sending end; if the sending end receives a NACK signal, some of the information bits are sent to the receiving end through the channel again without encoding. The receiving end re-decodes according to the encoded bits received for the first time and the newly received information bits; if the decoding result still fails to pass the CRC check, the sending end will pass another part of the information bits after receiving the NACK signal. The code is sent to the receiving end through the channel again, and the receiving end re-decodes according to the coded bits received for the first time, the information bits received last time and the newly received information bits; the above process continues until the sending end receives ACK signal, or when the number of transmissions reaches a preset maximum value, a complete transmission process is ended; the method includes the following steps:

(1)根据需求及信道参数确定下述各项传输参数：传输目的是信号发送端在最大发送次数T以内，使用码长为N₀的极化码，将一个包含有CRC校验比特、长度为K的信息比特序列经由二进制输入无记忆信道W传输至信号接收端，且在T次发送次数内，总共允许发送的最大比特数为Q；其中，正整数N₀为2的幂，且N₀≥K，极化编码所需的信息信道的序号集合为极化码编码比特序列经过凿孔后的比特序列长度为M，其凿孔位置指示序列为p，预备重复传输的信息比特对应的信道序号依次存储于一个长度为Q-M的重传序号序列r；在第1次、第2次、……、第T次发送后，接收端接收到的总比特数依次为：N₁、N₂、……、N_T，0≤N₁≤N₂≤…≤N_T≤Q；(1) Determine the following transmission parameters according to the requirements and channel parameters: the purpose of transmission is to use a polar code with a code length of N₀ within the maximum number of transmissions T at the signal sending end, and convert a polar code containing CRC check bits, length The information bit sequence of K is transmitted to the signal receiving end through the binary input memoryless channel W, and within T times of sending times, the maximum number of bits allowed to be sent in total is Q; where the positive integer N₀ is a power of 2, and N₀ ≥ K, the sequence number set of the information channel required for polar coding is The bit sequence length of the polar code coded bit sequence after puncturing is M, the puncturing position indication sequence is p, and the channel sequence numbers corresponding to the information bits to be repeatedly transmitted are sequentially stored in a retransmission sequence number sequence r of length QM; After the 1st, 2nd, ..., T-th transmissions, the total number of bits received by the receiver is: N₁ , N₂ , ...,_NT , 0≤N₁ ≤N₂ ≤... ≤ N_T ≤ Q;

(2)对传输序列进行编码和初始化：将长度为K的信息序列与收、发两端都预先已知的长度为N₀-K的固定比特序列根据信息信道的序号集合进行组合，构成一个长度为N₀的比特序列再将该比特序列送入一个传统极化码编码器进行极化编码，并根据凿孔位置指示序列p进行凿孔后，得到M个比特v_1:M；然后，将这些比特与根据重传序号序列r确定的Q-M个重传信息比特z_1:Q-M组合在一起，构成一个长度为Q的待发送序列x_1:Q；其中，自然数下标k是重传信息比特向量中的元素序号，其最大值是Q-M，且待发送序列长度x_1:Q的前M个元素分别与v_1:M相等，即x_1:M＝v_1:M，后Q-M个元素分别与z_1:Q-M相等，即x_M+1:Q＝z_1:M-Q；再设置发送次数计数器的初始值t＝0；(2) Coding and initializing the transmission sequence: the information sequence of length K and the fixed bit sequence of length N₀ -K known in advance at both the receiving and transmitting ends are set according to the serial number of the information channel Combine to form a bit sequence of length N₀ then the bit sequence It is sent to a traditional polar code encoder for polar encoding, and after puncturing according to the puncturing position indication sequence p, M bits v_1:M are obtained; then, these bits are combined with the QM retransmission information bits z_1:QM are combined to form a sequence x_{1:Q to be sent with a length of Q} ; wherein, The natural number subscript k is the element sequence number in the retransmission information bit vector, and its maximum value is QM, and the first M elements of the sequence length x_1:Q to be sent are respectively equal to v_1:M , that is, x_1:M =v_1:M , the latter QM elements are equal to z_1:QM respectively, i.e. x_M+1:Q =z_1:MQ ; then the initial value t=0 of the number of sending counter is set;

(3)发送比特序列：将发送次数计数器的值t加1后，判断t＞T是否成立，若是，则终止传输过程，宣告传输失败，结束该方法全部操作；否则，信号发送端按照下述方法发送一个比特序列：(3) Send bit sequence: After adding 1 to the value t of the number of sending counter, judge whether t>T is established, if so, terminate the transmission process, declare the transmission failure, and end all operations of the method; otherwise, the signal sending end follows the following steps method to send a sequence of bits:

若t＝1，则顺序发送待发送比特序列的前N₁个比特否则，顺序发送待发送比特序列的第N_t-1+1到第N_t个比特，即If t=1, then send the first N₁ bits of the bit sequence to be sent sequentially Otherwise, sequentially send the N_t-1 +1 to N_t bits of the bit sequence to be sent, namely

(4)接收比特序列：信号接收端采用串行抵消译码算法对经过前t次传输从信道中总共接收到的信号序列进行极化码译码，再对得到的译码比特序列进行CRC校验，并判断是否能够通过CRC校验；(4) Receiving bit sequence: The signal receiving end adopts the serial cancellation decoding algorithm to analyze the total signal sequence received from the channel after the previous t transmissions Perform polar code decoding, and then perform CRC check on the obtained decoded bit sequence, and judge whether it can pass the CRC check;

若CRC校验失败，则接收端通过反馈链路发送一个NACK信号给发送端，返回执行步骤(3)；If the CRC check fails, the receiving end sends a NACK signal to the sending end through the feedback link, and returns to step (3);

若CRC校验通过，则接收端通过反馈链路发送一个ACK信号给发送端，成功完成本次传输过程。If the CRC check passes, the receiving end sends an ACK signal to the sending end through the feedback link, and the transmission process is successfully completed.

与现有技术相比较，本发明方法的创新优点是：本发明通过对部分信息信道承载的比特进行重传，提高了该部分比特正确译码的概率。本发明通过对极化码进行凿孔，并对部分信息比特进行重复传输的序列长度的进行调节，且调节步长仅仅为1比特，同时又可以准确地估计吞吐率，使得本发明基于极化码的HARQ方案能够得到最大限度地优化。再者，本发明方法是对普通极化码进行凿孔、重复传输等简单操作步骤实现的，操作简便，而且，极化码本身的编码、译码复杂度就非常低，从而使得本发明方法操作的整体复杂度与现有的各种传输系统有明显地降低。因此，本发明更适合于实际通信系统中的应用，具有很好的推广应用前景。Compared with the prior art, the innovative advantage of the method of the present invention is: the present invention increases the probability of correct decoding of the part of bits by retransmitting the bits carried by part of the information channel. The present invention punctures the polar code, and adjusts the sequence length of repeated transmission of part of the information bits, and the adjustment step is only 1 bit, and at the same time can accurately estimate the throughput rate, so that the present invention is based on polarization The HARQ scheme of the code can be optimized to the greatest extent. Furthermore, the method of the present invention is realized by simple operation steps such as punching holes and repeated transmissions to ordinary polar codes, and the operation is simple and convenient. Moreover, the complexity of encoding and decoding of the polar code itself is very low, so that the method of the present invention The overall complexity of operation is significantly lower than that of various existing transmission systems. Therefore, the present invention is more suitable for application in actual communication systems, and has good prospects for popularization and application.

附图说明Description of drawings

图1是信道极化的基本单元电路结构示意图。FIG. 1 is a schematic diagram of a circuit structure of a basic unit of channel polarization.

图2是长度为N的信道极化装置的递归结构示意图，其中递归的最小单元(即N＝1时)为图1所示的基本单元。FIG. 2 is a schematic diagram of a recursive structure of a channel polarization device with a length of N, wherein the minimum unit of recursion (ie when N=1) is the basic unit shown in FIG. 1 .

图3是一个码长N＝4的极化码的码树示意图。图中的黑实线指示了一条串行抵消译码得到的路径，其对应的比特估计序列为(0110)。FIG. 3 is a schematic diagram of a code tree of a polar code with code length N=4. The black solid line in the figure indicates a path obtained by serial cancellation decoding, and the corresponding bit estimation sequence is (0110).

图4是混合自动重传请求(HARQ)传输示例的时序图。4 is a timing diagram of an example hybrid automatic repeat request (HARQ) transmission.

图5是本发明基于极化码的混合自动重复请求传输方法操作步骤流程图。FIG. 5 is a flow chart of the operation steps of the polar code-based HARQ transmission method of the present invention.

图6是给定信息序列长度K、最大传输次数T和最多传输比特数Q后，最优传输参数配置的搜索流程图。Fig. 6 is a flow chart of searching for the optimal transmission parameter configuration given the information sequence length K, the maximum number of transmission times T and the maximum number of transmission bits Q.

图7是在给定的信息序列长度K、凿孔后的比特序列长度取值为m的条件下，传输出错概率序列e、信息信道的序号集合凿孔位置指示序列p与重传信息比特对应的信道序号序列r的配置流程图。Figure 7 is a set of sequence numbers of transmission error probability sequence e and information channel under the condition of given information sequence length K and bit sequence length after puncturing as m A flow chart of configuring the channel sequence number r corresponding to the puncture position indication sequence p and the retransmission information bits.

图8是当信息序列长度为K、凿孔后序列长度为m时的最佳配置参数集合与最佳配置下的吞吐率估计值η的搜索流程图。Figure 8 is the optimal configuration parameter set when the length of the information sequence is K and the length of the sequence after puncturing is m Flowchart of the search with the throughput estimate η under the optimal configuration.

图9是本发明方法的吞吐率估计值与仿真实施例得到的实际值的比较图。FIG. 9 is a graph comparing the estimated value of the throughput rate of the method of the present invention with the actual value obtained by the simulation embodiment.

图10是本发明方法与基于LDPC码及turbo码的HARQ方案比较图。Fig. 10 is a comparison diagram between the method of the present invention and the HARQ scheme based on LDPC codes and turbo codes.

具体实施方式detailed description

为使本发明的目的、技术方案和优点更加清楚，下面结合附图对本发明作进一步的详细描述。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings.

本发明基于凿孔极化码的混合自动重传请求(HARQ)传输方法的操作内容是：信号发送端将准备发送的信息比特序列进行一次极化编码，得到的编码比特经过凿孔后，被送入信道进行传输；信号接收端对接收信号进行译码，并对译码结果进行循环冗余码(CRC)校验；若校验通过，则信号接收端经由反馈链路给发送端发送确认(ACK)信号；否则，给发送端发送非确认(NACK)信号；若发送端接收到NACK信号，则将其中部分信息比特不经过编码、直接通过信道发送给接收端，接收端则根据第一次接收到的编码比特和新接收到的信息比特重新进行译码；若译码结果依然不能通过CRC校验，则发送端接收到NACK信号后，将另一部分信息比特不经过编码再次通过信道发送给接收端，接收端再根据第一次接收到的编码比特、前一次接收到的信息比特和新接收到的信息比特重新进行译码；上述过程持续执行，直到发送端接收到ACK信号，或者发送次数达到预设的最大值时，才结束一次完整的传输过程。该方法包括下述操作步骤：The operation content of the hybrid automatic repeat request (HARQ) transmission method based on the puncturing polar code of the present invention is: the signal transmitting end performs a polar coding on the information bit sequence to be sent, and the obtained coded bits are punctured and then transmitted Send it into the channel for transmission; the signal receiving end decodes the received signal, and performs a cyclic redundancy code (CRC) check on the decoding result; if the verification is passed, the signal receiving end sends an acknowledgment to the sending end via the feedback link (ACK) signal; otherwise, send a non-acknowledgment (NACK) signal to the sending end; if the sending end receives the NACK signal, part of the information bits will be sent directly to the receiving end through the channel without encoding, and the receiving end will send it to the receiving end according to the first Re-decode the encoded bits received for the first time and the newly received information bits; if the decoding result still fails to pass the CRC check, after receiving the NACK signal, the sender sends another part of the information bits through the channel again without encoding To the receiving end, the receiving end re-decodes according to the coded bits received for the first time, the previously received information bits and the newly received information bits; the above process continues until the sending end receives the ACK signal, or A complete transmission process will end only when the number of sending times reaches the preset maximum value. The method comprises the following steps:

参见图5，介绍本发明方法的具体操作步骤：Referring to Fig. 5, introduce the concrete operation step of the inventive method:

步骤1，根据需求及信道参数确定下述各项传输参数：传输目的是信号发送端在最大发送次数T以内，使用码长为N₀的极化码，将一个包含有CRC校验比特、长度为K的信息比特序列经由二进制输入无记忆信道W传输至信号接收端，且在T次发送次数内，总共允许发送的最大比特数为Q；其中，正整数N₀为2的幂，且N₀≥K；极化编码所需的信息信道的序号集合为极化码编码比特序列经过凿孔后的比特序列长度为M，其凿孔位置指示序列为p，预备重复传输的信息比特对应的信道序号依次存储于一个长度为Q-M的重传序号序列r；在第1次、第2次、……、第T次发送后，接收端接收到的总比特数依次为：N₁、N₂、……、N_T，0≤N₁≤N₂≤…≤N_T≤Q。Step 1. Determine the following transmission parameters according to the requirements and channel parameters: The transmission purpose is that the signal sending end uses a polar code with a code length of N₀ within the maximum number of transmissions T, and uses a polar code that includes CRC check bits, length The information bit sequence of K is transmitted to the signal receiving end through the binary input memoryless channel W, and within T times of sending times, the maximum number of bits allowed to be sent in total is Q; where the positive integer N₀ is a power of 2, and N₀ ≥ K; the sequence number set of the information channel required for polar coding is The bit sequence length of the polar code coded bit sequence after puncturing is M, the puncturing position indication sequence is p, and the channel sequence numbers corresponding to the information bits to be repeatedly transmitted are sequentially stored in a retransmission sequence number sequence r of length QM; After the 1st, 2nd, ..., T-th transmissions, the total number of bits received by the receiver is: N₁ , N₂ , ...,_NT , 0≤N₁ ≤N₂ ≤... ≤ N_T ≤ Q.

该步骤1中，预设的参数只有三个：信息序列长度K、最大传输次数T和传输的最大比特数Q，而其余的参数，包括极化码码长N₀、信息信道的序号集合经过凿孔后的比特序列长度M、凿孔位置指示序列p、重传序号序列r、以及每次传输后接收端接收到的总比特数N₁、N₂、……、N_T的各项参数都是执行下述步骤计算得到的(参见图6所示的搜索流程)：In this step 1, there are only three preset parameters: the information sequence length K, the maximum number of transmission times T and the maximum number of bits transmitted Q, while the remaining parameters include the polar code length N₀ and the sequence number set of the information channel The bit sequence length M after puncturing, the puncturing position indication sequence p, the retransmission sequence number sequence r, and the total number of bits N₁ , N₂ , ...,_NT received by the receiving end after each transmission The parameters are calculated by performing the following steps (see the search process shown in Figure 6):

(11)初始化设置参数集合最佳吞吐率η_opt＝0，最优凿孔后的比特序列长度m_opt＝0，其中，表示空集；并初始化设置凿孔后的比特序列长度m＝K。(11) Initialize the setting parameter set Optimal throughput η_opt =0, optimal bit sequence length after puncturing m_opt =0, where, represents an empty set; and initializes the bit sequence length m=K after puncturing.

(12)根据信息序列长度K和凿孔后的比特序列长度m，计算得到长度为Q-m+1的传输出错概率序列e，用于存储发送比特总数n在{m,m+1,…,Q}中取值时，在串行抵消译码算法下传输出错的概率值；同时得到相应的信息信道的序号集合凿孔位置指示序列p和重传信息比特对应的信道序号序列r。该步骤包括下列操作内容(参见图7所示)：(12) According to the information sequence length K and the bit sequence length m after puncturing, calculate the transmission error probability sequence e with a length of Q-m+1, which is used to store the total number of transmitted bits n in {m, m+1,... ,Q}, the probability value of transmission error under the serial offset decoding algorithm; at the same time, the sequence number set of the corresponding information channel is obtained The puncture position indication sequence p and the channel sequence number sequence r corresponding to the retransmission information bits. This step includes the following operations (see Figure 7):

(121)根据凿孔后的比特序列长度m的值，采用传统凿孔极化编码方法，构造一个信息比特数为K、凿孔前码长为凿孔后码长为m的凿孔极化码，其中，信息信道的序号集合为凿孔位置指示序列为p；再利用密度进化计算得到发送全零序列时，各个信息信道的接收信号的对数似然比(LLR)值的概率密度函数其中，括号中的上标i为信道序号，且满足(121) According to the value of the bit sequence length m after puncturing, adopt the traditional puncturing polarization coding method to construct a code with the number of information bits K and the code length before puncturing as A punctured polar code with a code length of m after puncturing, where the sequence number set of the information channel is The drill hole position indication sequence is p; and then use the density evolution calculation to obtain the probability density function of the logarithmic likelihood ratio (LLR) value of the received signal of each information channel when the all-zero sequence is sent Among them, the superscript i in the brackets is the channel number, and satisfies

(122)分别初始化设置传输出错概率序列e和重传信息比特对应的信道序号序列r为一个长度为Q-m+1的全零序列和一个长度为Q-m的全零序列，并令重传信息比特对应的信道序号k＝1。(122) Initially set the transmission error probability sequence e and the channel sequence number sequence r corresponding to the retransmission information bits as an all-zero sequence with a length of Q-m+1 and an all-zero sequence with a length of Q-m, and make the retransmission information The channel number k=1 corresponding to the bit.

(123)对归属于信息信道的序号集合中的每个信道，分别计算其传输出错的概率$q_i=1-{\∫}_{-\mathrm{\∞}}^0{a}_{n_0}^{\left(i\right)}\left(x\right)dx,$并更新传输出错概率序列$e_k=\underset{i\∈A}{\Σ}{q}_i.$(123) Set of sequence numbers belonging to the information channel For each channel in , calculate the probability of its transmission error$q_i=1-{\∫}_{-\mathrm{\∞}}^0{a}_{{\mathrm{no}}_0}^{\left(i\right)}\left(x\right)dx,$ And update the transmission error probability sequence$e_k=\underset{i\∈A}{\Σ}{q}_i.$

(124)找出当前最不可靠的信息信道，即从中选出使得q_i值最大的信息信道序号i，再设置重传信息比特对应的信道序号r_k＝i，并更新该信道所对应的LLR的概率密度函数其中，a为通过信道W传输比特0时，接收信号的LLR值的概率密度函数，运算表示卷积。(124) Find out the current least reliable information channel, that is, from Select the information channel number i that makes the value of q_i the largest, and then set the channel number r_k =i corresponding to the retransmission information bit, and update the probability density function of the LLR corresponding to the channel Among them, a is the probability density function of the LLR value of the received signal when bit 0 is transmitted through the channel W, and the operation Indicates convolution.

(125)判断k＜Q-m是否成立，若成立，则设置k＝k+1后，返回执行步骤(123)；否则，按照公式设置传输出错概率序列中的最后一个元素，并记录得到的传输出错概率序列e、信息信道的序号集合凿孔位置指示序列p和重传信息比特对应信道序号序列r的数值，并结束计算过程。(125) judge whether k＜Qm is set up, if set up, after then setting k=k+1, return execution step (123); Otherwise, according to formula Set the last element in the transmission error probability sequence, and record the obtained transmission error probability sequence e and the sequence number set of the information channel The puncture position indication sequence p and the value of the channel sequence number sequence r corresponding to the retransmission information bits, and the calculation process ends.

(13)搜索并得到当信息序列长度为K、凿孔后的比特序列长度为m时的最佳配置参数集合S与最佳配置下的吞吐率估计值η；并判断η＞η_opt是否成立，若是，则执行后续步骤(14)；否则，跳转执行步骤(15)。该步骤中的搜索操作包括下列内容(参见图8所示)：(13) Search and obtain the optimal configuration parameter set S and the estimated throughput value η under the optimal configuration when the length of the information sequence is K and the length of the bit sequence after puncturing is m; and judge whether η > η_opt is established , if yes, execute the subsequent step (14); otherwise, skip to execute step (15). The search operation in this step includes the following contents (seeing as shown in Figure 8):

(131)初始化设置在信息序列长度为K、凿孔后序列长度为m时的最佳配置参数集合最佳配置下的吞吐率估计值η＝0，且传输次数序号l＝1；(131) Initialize and set the optimal configuration parameter set when the information sequence length is K and the sequence length after drilling is m The estimated throughput rate under the optimal configuration η=0, and the number of transmission times l=1;

(132)设置一个临时集合并设置n＝m；(132) Set up a temporary collection and set n=m;

(133)判断是否成立，若成立，则跳转执行步骤(137)；否则，执行后续步骤(134)；(133) Judgment Whether it is established, if established, then jump to the execution step (137); otherwise, perform the subsequent step (134);

(134)设置临时集合然后将集合中的元素从小到大顺序排列后，依次赋值给n₁、n₂、……、n_l；(134) Set temporary collection and then set the After the elements in are arranged in ascending order, they are assigned to n₁ , n₂ ,..., n_l in sequence;

(135)根据传输出错概率序列e，计算当信息序列长度为K、凿孔后序列长度为m、最多进行l次传输、且每次传输后接收端收到的总比特数依次为n₁、n₂、……、n_l时的吞吐率估计值式中，自然数变量t为传输次数序号的临时数值，其最大值为l；(135) According to the transmission error probability sequence e, calculate when the length of the information sequence is K, the length of the sequence after puncturing is m, the maximum number of transmissions is l, and the total number of bits received by the receiving end after each transmission is n₁ , Estimated value of throughput at n₂ ,...,n_l In the formula, the natural number variable t is the temporary value of the number of transmission times, and its maximum value is 1;

(136)判断ρ＞η是否成立，若是，则设置并记录η＝ρ；否则，直接执行步骤(137)；(136) Determine whether ρ>η is established, if so, set And record η=ρ; Otherwise, directly execute step (137);

(137)判断n＜Q是否成立，若是，则设置n＝n+1，返回执行步骤(133)；否则，执行步骤(138)。(137) Determine whether n<Q holds true, if so, set n=n+1, return to execute step (133); otherwise, execute step (138).

(138)记录中元素个数为l时的最佳配置参数集合及其对应的吞吐率估计值η；(138) records The optimal configuration parameter set when the number of elements in is l and its corresponding estimated throughput η;

(139)判断l＜T是否成立，若是，则设置l＝l+1，返回执行步骤(132)；否则，结束该步骤(13)的搜索过程。(139) Determine whether l<T is established, if so, set l=l+1, and return to step (132); otherwise, end the search process of step (13).

(14)记录并更新所配置的传输参数：η_opt＝η，m_opt＝m；(14) Record and update the configured transmission parameters: η_opt = η, m_opt = m;

(15)判断m＜Q是否成立，若是，则设置m＝m+1，然后返回执行步骤(12)；否则，执行后续步骤(16)；(15) judge whether m＜Q is set up, if so, then set m=m+1, then return to execution step (12); Otherwise, carry out follow-up step (16);

(16)整理并输出最优配置方案的参数：将S_opt中的元素从小到大顺序排列，依次赋值给N₁、N₂、……、N_T；再设置M＝m_opt和其中，表示向上取整操作。(16) Organize and output the parameters of the optimal configuration scheme: Arrange the elements in S_opt from small to large, and assign them to N₁ , N₂ , ...,_NT in turn; then set M=m_opt and in, Indicates a round up operation.

步骤2，对传输序列进行编码和初始化：将长度为K的信息序列与收、发两端都预先已知的长度为N₀-K的固定比特序列根据信息信道的序号集合进行组合，构成一个长度为N₀的比特序列再将该比特序列送入一个传统极化码编码器进行极化编码，并根据凿孔位置指示序列p进行凿孔后，得到M个比特v_1:M；然后，将这些比特与根据重传序号序列r确定的Q-M个重传信息比特z_1:Q-M组合在一起，构成一个长度为Q的待发送序列x_1:Q；其中，自然数下标k是重传信息比特向量中的元素序号，其最大值是Q-M，且待发送序列长度x_1:Q的前M个元素分别与v_1:M相等，即x_1:M＝v_1:M，后Q-M个元素分别与z_1:Q-M相等，即x_M+1:Q＝z_1:Q-M；再设置发送次数计数器的初始值t＝0。Step 2, encode and initialize the transmission sequence: combine the information sequence of length K with the fixed bit sequence of length N₀ -K known in advance at both the receiving and transmitting ends according to the sequence number of the information channel Combine to form a bit sequence of length N₀ then the bit sequence It is sent to a traditional polar code encoder for polar encoding, and after puncturing according to the puncturing position indication sequence p, M bits v_1:M are obtained; then, these bits are combined with the QM retransmission information bits z_1:QM are combined to form a sequence x_{1:Q to be sent with a length of Q} ; wherein, The natural number subscript k is the element sequence number in the retransmission information bit vector, and its maximum value is QM, and the first M elements of the sequence length x_1:Q to be sent are respectively equal to v_1:M , that is, x_1:M =v_1:M , the last QM elements are respectively equal to z_1:QM , that is, x_M+1:Q =z_1:QM ; then set the initial value of the sending times counter t=0.

步骤3，发送比特序列：将发送次数计数器的值t加1后，判断t＞T是否成立，若是，则终止传输过程，宣告传输失败，结束该方法全部操作；否则，信号发送端按照下述方法发送一个比特序列：Step 3, send the bit sequence: After adding 1 to the value t of the number of sending counter, judge whether t>T is true, if so, terminate the transmission process, declare the transmission failure, and end all operations of the method; otherwise, the signal sending end follows the following steps method to send a sequence of bits:

若t＝1，则顺序发送待发送比特序列的前N₁个比特否则，顺序发送待发送比特序列的第N_t-1+1到第N_t个比特，即If t=1, then send the first N₁ bits of the bit sequence to be sent sequentially Otherwise, sequentially send the N_t-1 +1 to N_t bits of the bit sequence to be sent, namely

步骤4，接收比特序列：信号接收端采用串行抵消译码算法对经过前t次传输从信道中总共接收到的信号序列进行极化码译码，再对得到的译码比特序列进行CRC校验，并判断是否能够通过CRC校验；Step 4, receiving the bit sequence: the signal receiving end uses the serial cancellation decoding algorithm to analyze the total signal sequence received from the channel after the previous t transmissions Perform polar code decoding, and then perform CRC check on the obtained decoded bit sequence, and judge whether it can pass the CRC check;

若CRC校验失败，则接收端通过反馈链路发送一个NACK信号给发送端，返回执行步骤3；If the CRC check fails, the receiving end sends a NACK signal to the sending end through the feedback link, and returns to step 3;

若CRC校验通过，则接收端通过反馈链路发送一个ACK信号给发送端，成功完成本次传输过程。If the CRC check passes, the receiving end sends an ACK signal to the sending end through the feedback link, and the transmission process is successfully completed.

该步骤4中，执行译码算法所需的路径度量计算操作包括下列内容：，In step 4, the path metric calculation operations required to execute the decoding algorithm include the following:,

(41)用序列表示某一条译码路径，且与传统的凿孔极化码的译码方法相同，根据第1次传输时的接收信号序列y_1:M及序号为i的极化子信道的信道转移函数计算条件概率$P\left(y_{1:M}\right|{\hat{u}}_{1:i})=\frac{W_N^{\left(i\right)}(y_{1:M},{\hat{u}}_{1:i-1}|{\hat{u}}_i)}{2^{i-1}};$式中，转移函数为通过信道发送比特u_i时，接收信号为y_1:M与u_1:i-1的概率。(41) with sequence Indicates a certain decoding path, and is the same as the decoding method of the traditional punctured polar code, according to the received signal sequence y_1:M and the channel transfer function of the polar sub-channel with the serial number i during the first transmission Computing conditional probabilities$P\left({\mathrm{the\; y}}_{1:m}\right|{\hat{u}}_{1:i})=\frac{W_N^{\left(i\right)}({\mathrm{the\; y}}_{1:m},{\hat{u}}_{1:i-1}|{\hat{u}}_i)}{2^{i-1}};$ In the formula, the transfer function for pass channel When sending bits u_i , the received signal is the probability of y_1:M and u_1:i-1 .

(42)根据第2次到第t次传输时得到的接收信号序列与信道W的转移概率函数W(y|x)，计算条件概率其中，转移概率函数W(y|x)为通过信道W发送比特x时，接收信号为y的概率。该步骤包括下列操作内容：(42) According to the received signal sequence obtained from the second to the tth transmission Calculate the conditional probability with the transition probability function W(y|x) of the channel W Wherein, the transition probability function W(y|x) is the probability that the received signal is y when the bit x is transmitted through the channel W. This step includes the following operations:

(421)初始化设置条件概率并设置序号偏置值j＝1。(421) Initialize conditional probability And set the serial number offset value j=1.

(422)判断r_j≤i是否成立，若成立，则否则，$P\left(y_{M+1:N_t}\right|{\hat{u}}_{1:i})=\frac{1}{2}\&times;P\left(y_{M+1:N_t}\right|{\hat{u}}_{1:i})\&times;\left(W\right(y_{M+j}|0)+W(y_{M+j}|1\left)\right).$(422) Judging whether r_j ≤ i is true, if true, then otherwise,$P\left({\mathrm{the\; y}}_{m+1:N_t}\right|{\hat{u}}_{1:i})=\frac{1}{2}\&times;P\left({\mathrm{the\; y}}_{m+1:N_t}\right|{\hat{u}}_{1:i})\&times;\left(W\right({\mathrm{the\; y}}_{m+j}|0)+W({\mathrm{the\; y}}_{m+j}|1\left)\right).$

(423)判断j＜N_t-M是否成立，若成立，则设置j＝j+1，并返回执行步骤(422)；否则，执行后续步骤(424)。(423) Determine whether j<N_t -M is true, if true, set j=j+1, and return to step (422); otherwise, execute subsequent step (424).

(424)记录得到的值，并结束计算过程。(424) record obtained value and end the calculation process.

(43)按照公式计算当发送信号为时接收信号为的概率，并用该条件概率值表示长度为i的路径的路径度量。(43) According to the formula Calculate when sending a signal as When the received signal is , and use this conditional probability value to represent a path of length i path metrics.

本发明已经进行了多次仿真实施例的实验和模拟使用，下面就仿真实施例的试验结果，详细介绍本发明的实施过程及性能分析：The present invention has carried out experiment and simulation use of simulation embodiment for many times, below with regard to the test result of simulation embodiment, introduce implementation process and performance analysis of the present invention in detail:

1.吞吐率估计值与实际值的比较1. Comparison of throughput estimates and actual values

在二进制输入加性白高斯噪声(BAWGN)信道下，以符号信噪比SNR＝{-3.0,0.0,3.0}dB、信息序列长度K＝1024、极化码编码输出凿孔后序列长度M分别等于{2656,1640,1184}为实施例的试验参数，通过仿真比较吞吐率估计值与实际值的差别，每次重传30比特，即N_t+1-N_t＝30，N₁＝M时，仿真量至少为1000000个信息块。计算及仿真结果如图9所示。Under the binary input additive white Gaussian noise (BAWGN) channel, the signal-to-noise ratio SNR={-3.0,0.0,3.0}dB, the length of the information sequence K=1024, and the length M of the sequence after polar code encoding output puncture are respectively Equal to {2656, 1640, 1184} is the experimental parameter of the embodiment, compare the difference between the estimated value of the throughput rate and the actual value through simulation, and retransmit 30 bits each time, that is, N_t+1 -N_t =30, N₁ =M When , the amount of simulation is at least 1000000 information blocks. The calculation and simulation results are shown in Figure 9.

可以看到，发送估计值是实际值的一个非常准确的下界。因此，用这样的估计值去进行传输方案参数配置的选择，可以达到非常好的优化效果。As you can see, the send estimate is a very accurate lower bound on the actual value. Therefore, using such an estimated value to select the parameter configuration of the transmission scheme can achieve a very good optimization effect.

2.与基于LDPC码及turbo码的HARQ方案比较2. Compared with the HARQ scheme based on LDPC code and turbo code

在二进制输入加性白高斯噪声(BAWGN)信道下，信息序列长度K＝1024，最大传输次数T＝6，最大传输比特数Q＝16384。搜索得到传输参数配置如下表1所示，采用串行抵消译码算法，吞吐率曲线如图10所示。Under the binary input additive white Gaussian noise (BAWGN) channel, the information sequence length K=1024, the maximum number of transmission times T=6, and the maximum number of transmission bits Q=16384. The configuration of the transmission parameters obtained from the search is shown in Table 1 below, and the serial cancellation decoding algorithm is adopted, and the throughput rate curve is shown in Figure 10.

表1搜索得到的最优传输参数配置Table 1 The optimal transmission parameter configuration obtained by searching

SNR(dB)SNR(dB)MmN₁N₁N₂N₂N₃N₃N₄N₄N₅N₅N₆N₆-4.0-4.032623262326232623348334834773477366636663940394048744874-3.0-3.027292729272927292800280029062906305930593283328340334033-2.0-2.022722272227222722326232624102410253125312713271333223322-1.0-1.019221922192219221961196120262026212121212263226327392739-0.0-0.0166516651665166516991699175217521829182919491949235123511.01.0147214721472147214971497153615361599159916931693201420142.02.0131013101310131013321332136313631410141014821482174117413.03.0120012001200120012171217124112411276127613351335154015404.04.0112011201120112011331133115011501172117212181218137513755.05.0105910591059105910641064107510751089108911211121122712276.06.0103610361036103610411041104810481057105710761076114411447.07.0102710271027102710291029103210321038103810501050109910998.08.0102410241024102410251025102710271030103010361036106310639.09.01024102410241024102510251027102710291029103210321047104710.010.010241024102410241025102510261026102710271029102910361036

参见图10所示的本发明方案与基于LDPC码及turbo码的HARQ方案比较图，从吞吐率的比较曲线可以看到：本发明方法能够与目前已知的采用LDPC或Turbo码的最好技术方案获得几乎相当的吞吐率，在中、高信噪比条件下，甚至能获得更好的吞吐率。另外，由于接收端采用低复杂度的串行抵消译码算法，并且重传比特的选择规则简单，其构造和接收复杂度都要远远低于基于LDPC和Turbo码的方案。Referring to the comparison diagram of the present invention's scheme shown in Figure 10 and the HARQ scheme based on LDPC codes and turbo codes, it can be seen from the comparison curve of throughput that the present invention's method can be compared with the currently known best technology using LDPC or Turbo codes The scheme achieves almost the same throughput rate, and even better throughput rate under medium and high signal-to-noise ratio conditions. In addition, since the receiving end adopts a low-complexity serial offset decoding algorithm, and the selection rule of retransmission bits is simple, its construction and reception complexity are far lower than those based on LDPC and Turbo codes.

以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本发明保护的范围之内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the present invention. within the scope of protection.

Claims (6)

Translated fromChinese

1.一种基于极化码的混合自动重传请求(HARQ)传输方法，其特征在于：信号发送端将准备发送的信息比特序列进行一次极化编码，得到的编码比特经过凿孔后，被送入信道进行传输；信号接收端对接收信号进行译码，并对译码结果进行循环冗余码(CRC)校验；若校验通过，则信号接收端经由反馈链路给发送端发送确认(ACK)信号；否则，给发送端发送非确认(NACK)信号；若发送端接收到NACK信号，则将其中部分信息比特不经过编码再次通过信道发送给接收端，接收端则根据第一次接收到的编码比特和新接收到的信息比特重新译码；若译码结果依然不能通过CRC校验，则发送端接收到NACK信号后，将另一部分信息比特不经过编码再次通过信道发送给接收端，接收端再根据第一次接收到的编码比特、前一次接收到的信息比特和新接收到的信息比特重新译码；上述过程持续执行，直到发送端接收到ACK信号，或者发送次数达到预设的最大值时，才结束一次完整的传输过程；该方法包括下述操作步骤：1. A hybrid automatic repeat request (HARQ) transmission method based on polar codes, characterized in that: the signal transmitting end carries out a polar coding on the information bit sequence to be sent, and the coded bits obtained are punctured and then punctured. Send it into the channel for transmission; the signal receiving end decodes the received signal, and performs a cyclic redundancy code (CRC) check on the decoding result; if the verification is passed, the signal receiving end sends an acknowledgment to the sending end via the feedback link (ACK) signal; otherwise, send a non-acknowledgment (NACK) signal to the sending end; if the sending end receives the NACK signal, part of the information bits will be sent to the receiving end again through the channel without encoding, and the receiving end will send it to the receiving end according to the first time The received encoded bits and the newly received information bits are re-decoded; if the decoding result still fails to pass the CRC check, after receiving the NACK signal, the sender sends another part of the information bits to the receiver through the channel again without encoding. end, the receiving end re-decodes according to the encoded bits received for the first time, the information bits received last time and the newly received information bits; the above process continues until the sending end receives the ACK signal, or the number of sending times reaches When the preset maximum value is reached, a complete transmission process is completed; the method includes the following steps:(1)根据需求及信道参数确定下述各项传输参数：传输目的是信号发送端在最大发送次数T以内，使用码长为N₀的极化码，将一个包含有CRC校验比特、长度为K的信息比特序列经由二进制输入无记忆信道W传输至信号接收端，且在T次发送次数内，总共允许发送的最大比特数为Q；其中，正整数N₀为2的幂，且N₀≥K；极化编码所需的信息信道的序号集合为极化码编码比特序列经过凿孔后的比特序列长度为M，其凿孔位置指示序列为p，预备重复传输的信息比特对应的信道序号依次存储于一个长度为Q-M的重传序号序列r；在第1次、第2次、……、第T次发送后，接收端接收到的总比特数依次为：N₁、N₂、……、N_T，0≤N₁≤N₂≤…≤N_T≤Q；(1) Determine the following transmission parameters according to the requirements and channel parameters: the purpose of transmission is to use a polar code with a code length of N₀ within the maximum number of transmissions T at the signal sending end, and convert a polar code containing CRC check bits, length The information bit sequence of K is transmitted to the signal receiving end through the binary input memoryless channel W, and within T times of sending times, the maximum number of bits allowed to be sent in total is Q; where the positive integer N₀ is a power of 2, and N₀ ≥ K; the sequence number set of the information channel required for polar coding is The bit sequence length of the polar code coded bit sequence after puncturing is M, the puncturing position indication sequence is p, and the channel sequence numbers corresponding to the information bits to be repeatedly transmitted are sequentially stored in a retransmission sequence number sequence r of length QM; After the 1st, 2nd, ..., T-th transmissions, the total number of bits received by the receiver is: N₁ , N₂ , ...,_NT , 0≤N₁ ≤N₂ ≤... ≤ N_T ≤ Q;(2)对传输序列进行编码和初始化：将长度为K的信息序列与收、发两端都预先已知的长度为N₀-K的固定比特序列根据信息信道的序号集合进行组合，构成一个长度为N₀的比特序列再将该比特序列送入一个传统极化码编码器进行极化编码，并根据凿孔位置指示序列p进行凿孔后，得到M个比特v_1:M；然后，将这些比特与根据重传序号序列r确定的Q-M个重传信息比特z_1:Q-M组合在一起，构成一个长度为Q的待发送序列x_1:Q；其中，自然数下标k是重传信息比特向量中的元素序号，其最大值是Q-M，且待发送序列长度x_1:Q的前M个元素分别与v_1:M相等，即x_1:M＝v_1:M，后Q-M个元素分别与z_1:Q-M相等，即x_M+1:Q＝z_1:Q-M；再设置发送次数计数器的初始值t＝0；(2) Coding and initializing the transmission sequence: the information sequence of length K and the fixed bit sequence of length N₀ -K known in advance at both the receiving and transmitting ends are set according to the serial number of the information channel Combine to form a bit sequence of length N₀ then the bit sequence It is sent to a traditional polar code encoder for polar encoding, and after puncturing according to the puncturing position indication sequence p, M bits v_1:M are obtained; then, these bits are combined with the QM retransmission information bits z_1:QM are combined to form a sequence x_{1:Q to be sent with a length of Q} ; wherein, The natural number subscript k is the element sequence number in the retransmission information bit vector, and its maximum value is QM, and the first M elements of the sequence length x_1:Q to be sent are respectively equal to v_1:M , that is, x_1:M =v_1:M , the latter QM elements are equal to z_1:QM respectively, i.e. x_M+1:Q =z_1:QM ; then set the initial value t=0 of the number of sending counter;(3)发送比特序列：将发送次数计数器的值t加1后，判断t＞T是否成立，若是，则终止传输过程，宣告传输失败，结束该方法全部操作；否则，信号发送端按照下述方法发送一个比特序列：(3) Send bit sequence: After adding 1 to the value t of the number of sending counter, judge whether t>T is established, if so, terminate the transmission process, declare the transmission failure, and end all operations of the method; otherwise, the signal sending end follows the following steps method to send a sequence of bits:若t＝1，则顺序发送待发送比特序列的前N₁个比特否则，顺序发送待发送比特序列的第N_t-1+1到第N_t个比特，即If t=1, then send the first N₁ bits of the bit sequence to be sent sequentially Otherwise, sequentially send the N_t-1 +1 to N_t bits of the bit sequence to be sent, namely(4)接收比特序列：信号接收端采用串行抵消译码算法对经过前t次传输从信道中总共接收到的信号序列进行极化码译码，再对得到的译码比特序列进行CRC校验，并判断是否能够通过CRC校验；(4) Receiving bit sequence: The signal receiving end adopts the serial cancellation decoding algorithm to analyze the total signal sequence received from the channel after the previous t transmissions Perform polar code decoding, and then perform CRC check on the obtained decoded bit sequence, and judge whether it can pass the CRC check;若CRC校验失败，则接收端通过反馈链路发送一个NACK信号给发送端，返回执行步骤(3)；If the CRC check fails, the receiving end sends a NACK signal to the sending end through the feedback link, and returns to step (3);若CRC校验通过，则接收端通过反馈链路发送一个ACK信号给发送端，成功完成本次传输过程。If the CRC check passes, the receiving end sends an ACK signal to the sending end through the feedback link, and the transmission process is successfully completed.2.根据权利要求1所述的方法，其特征在于：所述步骤(1)中，预设的参数只有三个：信息序列长度K、最大传输次数T和传输的最大比特数Q，而包括极化码码长N₀、信息信道的序号集合经过凿孔后的比特序列长度M、凿孔位置指示序列p、重传序号序列r、以及每次传输后接收端接收到的总比特数N₁、N₂、……、N_T的各项参数都是执行下述步骤得到的：2. The method according to claim 1, characterized in that: in the step (1), there are only three preset parameters: the information sequence length K, the maximum number of transmission times T and the maximum number of bits Q transmitted, and include Polar code length N₀ , sequence number set of information channel The bit sequence length M after puncturing, the puncturing position indication sequence p, the retransmission sequence number sequence r, and the total number of bits N₁ , N₂ , ...,_NT received by the receiving end after each transmission The parameters are obtained by performing the following steps:(11)初始化设置参数集合最佳吞吐率η_opt＝0，最优凿孔后的比特序列长度m_opt＝0，其中，表示空集；并初始化设置凿孔后的比特序列长度m＝K；(11) Initialize the setting parameter set Optimal throughput η_opt =0, optimal bit sequence length after puncturing m_opt =0, where, Represent an empty set; and initialize and set the length of the bit sequence m=K after puncturing;(12)根据信息序列长度K和凿孔后的比特序列长度m，计算得到长度为Q-m+1的传输出错概率序列e，用于存储发送比特总数n在{m,m+1,…,Q}中取值时，在串行抵消译码算法下传输出错的概率值；同时得到相应的信息信道的序号集合凿孔位置指示序列p和重传序号序列r；(12) According to the information sequence length K and the bit sequence length m after puncturing, calculate the transmission error probability sequence e with a length of Q-m+1, which is used to store the total number of transmitted bits n in {m, m+1,... ,Q}, the probability value of transmission error under the serial offset decoding algorithm; at the same time, the sequence number set of the corresponding information channel is obtained Puncture position indication sequence p and retransmission sequence number sequence r;(13)搜索并得到当信息序列长度为K、凿孔后的比特序列长度为m时的最佳配置参数集合S与最佳配置下的吞吐率估计值η；并判断η＞η_opt是否成立，若是，则执行后续步骤(14)；否则，跳转执行步骤(15)；(13) Search and obtain the optimal configuration parameter set S and the estimated throughput value η under the optimal configuration when the length of the information sequence is K and the length of the bit sequence after puncturing is m; and judge whether η > η_opt is established , if so, execute subsequent step (14); otherwise, jump to execute step (15);(14)记录并更新所配置的传输参数：η_opt＝η，m_opt＝m；(14) Record and update the configured transmission parameters: η_opt = η, m_opt = m;(15)判断m＜Q是否成立，若是，则设置m＝m+1，然后返回执行步骤(12)；否则，执行后续步骤(16)；(15) judge whether m＜Q is set up, if so, then set m=m+1, then return to execution step (12); Otherwise, carry out follow-up step (16);(16)整理并输出最优配置方案的参数：将S_opt中的元素从小到大顺序排列，依次赋值给N₁、N₂、……、N_T；再设置M＝m_opt和其中，表示向上取整操作。(16) Organize and output the parameters of the optimal configuration scheme: Arrange the elements in S_opt from small to large, and assign them to N₁ , N₂ , ...,_NT in turn; then set M=m_opt and in, Indicates a round up operation.3.根据权利要求2所述的方法，其特征在于，所述步骤(12)包括下列操作内容：3. method according to claim 2, is characterized in that, described step (12) comprises following operation content:(121)根据凿孔后的比特序列长度m的值，采用传统凿孔极化编码方法，构造一个信息比特数为K、凿孔前码长为凿孔后码长为m的凿孔极化码，其中的信息信道的序号集合为凿孔位置指示序列为p；再利用密度进化计算得到发送全零序列时，各个信息信道的接收信号的对数似然比LLR值的概率密度函数其中，括号中的上标i为信道序号，且满足(121) According to the value of the bit sequence length m after puncturing, adopt the traditional puncturing polarization coding method to construct a code with the number of information bits K and the code length before puncturing as After puncturing, the code length of the punctured polar code is m, and the sequence number set of the information channel is The drill hole position indication sequence is p; then use the density evolution calculation to obtain the probability density function of the logarithmic likelihood ratio LLR value of the received signal of each information channel when the all-zero sequence is sent Among them, the superscript i in the brackets is the channel number, and satisfies(122)分别初始化设置传输出错概率序列e和重传信息比特对应的信道序列r为一个长度为Q-m+1的全零序列和一个长度为Q-m的全零序列，并令重传信息比特对应的信道序号k＝1；(122) Initially set the transmission error probability sequence e and the channel sequence r corresponding to the retransmission information bits as an all-zero sequence with a length of Q-m+1 and an all-zero sequence with a length of Q-m, and make the retransmission information bits The corresponding channel number k=1;(123)对归属于信息信道的序号集合中的每个信道，分别计算其传输出错的概率并更新传输出错概率序列(123) Set of sequence numbers belonging to the information channel For each channel in , calculate the probability of its transmission error And update the transmission error probability sequence(124)找出当前最不可靠的信息信道，即从中选出使得q_i值最大的信息信道序号i，再设置重传信息比特对应的信道序号r_k＝i，并更新该信道所对应的LLR的概率密度函数其中，a为通过信道W传输比特0时，接收信号的LLR值的概率密度函数，运算表示卷积；(124) Find out the current least reliable information channel, that is, from Select the information channel number i that makes the value of q_i the largest, and then set the channel number r_k =i corresponding to the retransmission information bit, and update the probability density function of the LLR corresponding to the channel Among them, a is the probability density function of the LLR value of the received signal when bit 0 is transmitted through the channel W, and the operation Indicates convolution;(125)判断k＜Q-m是否成立，若成立，则设置k＝k+1后，返回执行步骤(123)；否则，按照公式设置传输出错概率序列中的最后一个元素，并记录得到的传输出错概率序列e、信息信道的序号集合凿孔位置指示序列p和重传序号序列r的数值，并结束计算过程。(125) judge whether k＜Qm is set up, if set up, after then setting k=k+1, return execution step (123); Otherwise, according to formula Set the last element in the transmission error probability sequence, and record the obtained transmission error probability sequence e and the sequence number set of the information channel The puncture position indicates the sequence p and the value of the retransmission sequence number sequence r, and ends the calculation process.4.根据权利要求2所述的方法，其特征在于，所述步骤(13)中的搜索操作包括下列内容：4. The method according to claim 2, characterized in that the search operation in the step (13) comprises the following:(131)初始化设置在信息序列长度为K、凿孔后序列长度为m时的最佳配置参数集合最佳配置下的吞吐率估计值η＝0，且传输次数序号l＝1；(131) Initialize and set the optimal configuration parameter set when the information sequence length is K and the sequence length after drilling is m The estimated throughput rate under the optimal configuration η=0, and the number of transmission times l=1;(132)设置一个临时集合并设置n＝m；(132) Set up a temporary collection and set n=m;(133)判断是否成立，若成立，则跳转执行步骤(137)；否则，执行后续步骤(134)；(133) Judgment Whether it is established, if established, then jump to the execution step (137); otherwise, perform the subsequent step (134);(134)设置临时集合然后将集合中的元素从小到大顺序排列后，依次赋值给n₁、n₂、……、n_l；(134) Set temporary collection and then set the After the elements in are arranged in ascending order, they are assigned to n₁ , n₂ ,..., n_l in turn;(135)根据传输出错概率序列e，计算当信息序列长度为K、凿孔后序列长度为m、最多进行l次传输、且每次传输后接收端收到的总比特数依次为n₁、n₂、……、n_l时的吞吐率估计值式中，自然数变量t为传输次数序号的临时数值，其最大值为l；(135) According to the transmission error probability sequence e, calculate when the length of the information sequence is K, the length of the sequence after puncturing is m, the maximum number of transmissions is l, and the total number of bits received by the receiving end after each transmission is n₁ , Estimated value of throughput at n₂ ,...,n_l In the formula, the natural number variable t is the temporary value of the number of transmission times, and its maximum value is 1;(136)判断ρ＞η是否成立，若是，则设置并记录η＝ρ；否则，直接执行步骤(137)；(136) Determine whether ρ>η is established, if so, set And record η=ρ; Otherwise, directly execute step (137);(137)判断n＜Q是否成立，若是，则设置n＝n+1，返回执行步骤(133)；否则，执行步骤(138)；(137) judge whether n＜Q is set up, if so, then set n=n+1, return execution step (133); Otherwise, execution step (138);(138)记录中元素个数为l时的最佳配置参数集合及其对应的吞吐率估计值η；(138) records The optimal configuration parameter set when the number of elements in is l and its corresponding estimated throughput η;(139)判断l＜T是否成立，若是，则设置l＝l+1，返回执行步骤(132)；否则，结束该步骤(13)的搜索过程。(139) Determine whether l<T is established, if so, set l=l+1, and return to step (132); otherwise, end the search process of step (13).5.根据权利要求1所述的方法，其特征在于，所述步骤(4)中，执行译码算法所需的路径度量计算操作包括下列内容：5. method according to claim 1, is characterized in that, in described step (4), the required path metric calculation operation of carrying out decoding algorithm comprises the following content:(41)用序列表示某一条译码路径，且与传统的凿孔极化码的译码方法相同，根据第1次传输时的接收信号序列y_1:M及序号为i的极化子信道的信道转移函数计算条件概率$P\left(y_{1:M}\right|{\hat{u}}_{1:i})=\frac{W_N^{\left(i\right)}(y_{1:M},{\hat{u}}_{1:i-1}|{\hat{u}}_i)}{2^{i-1}};$式中，转移函数为通过信道发送比特u_i时，接收信号为y_1:M与u_1:i-1的概率；(41) with sequence Indicates a certain decoding path, and is the same as the decoding method of traditional punctured polar codes, according to the received signal sequence y_1:M in the first transmission and the channel transfer function of the polar sub-channel with the number i Computing conditional probabilities$P\left({\mathrm{the\; y}}_{1:m}\right|{\hat{u}}_{1:i})=\frac{W_N^{\left(i\right)}({\mathrm{the\; y}}_{1:m},{\hat{u}}_{1:i-1}|{\hat{u}}_i)}{2^{i-1}};$ In the formula, the transfer function for pass channel When sending bit u_i , the probability that the received signal is y_1:M and u_1:i-1 ;(42)根据第2次到第t次传输时得到的接收信号序列与信道W的转移概率函数W(y|x)，计算条件概率其中，转移概率函数W(y|x)为通过信道W发送比特x时，接收信号为y的概率；(42) According to the received signal sequence obtained from the second to the tth transmission Calculate the conditional probability with the transition probability function W(y|x) of the channel W Among them, the transition probability function W(y|x) is the probability that the received signal is y when the bit x is sent through the channel W;(43)按照公式$P\left(y_{1:N_t}\right|{\hat{u}}_{1:i})=P\left(y_{1:M}\right|{\hat{u}}_{1:i})\&CenterDot;P\left(y_{M+1:N_t}\right|{\hat{u}}_{1:i})$计算当发送信号为时接收信号为的概率，并用该条件概率值表示长度为i的路径的路径度量。(43) According to the formula$P\left({\mathrm{the\; y}}_{1:N_t}\right|{\hat{u}}_{1:i})=P\left({\mathrm{the\; y}}_{1:m}\right|{\hat{u}}_{1:i})\&CenterDot;P\left({\mathrm{the\; y}}_{m+1:N_t}\right|{\hat{u}}_{1:i})$ Calculate when sending a signal as When the received signal is , and use this conditional probability value to represent a path of length i path metrics.6.根据权利要求5所述的方法，其特征在于，所述步骤(42)包括下列操作内容：6. method according to claim 5, is characterized in that, described step (42) comprises following operation content:(421)初始化设置条件概率并设置序号偏置值j＝1；(421) Initialize conditional probability And set the serial number offset value j=1;(422)判断r_j≤i是否成立，若成立，则$P\left(y_{M+1:N_t}\right|{\hat{u}}_{1:i})=P\left(y_{M+1:N_t}\right|{\hat{u}}_{1:i})\&CenterDot;W\left(y_{M+j}\right|{\hat{u}}_{r_k});$否则，$P\left(y_{M+1:N_t}\right|{\hat{u}}_{1:i})=\frac{1}{2}\&times;P\left(y_{M+1:N_t}\right|{\hat{u}}_{1:i})\&times;\left(W\right(y_{M+j}|0)+W(y_{M+j}|1\left)\right);$(422) Judging whether r_j ≤ i is true, if true, then$P\left({\mathrm{the\; y}}_{m+1:N_t}\right|{\hat{u}}_{1:i})=P\left({\mathrm{the\; y}}_{m+1:N_t}\right|{\hat{u}}_{1:i})\&CenterDot;W\left({\mathrm{the\; y}}_{m+j}\right|{\hat{u}}_{r_k});$ otherwise,$P\left({\mathrm{the\; y}}_{m+1:N_t}\right|{\hat{u}}_{1:i})=\frac{1}{2}\&times;P\left({\mathrm{the\; y}}_{m+1:N_t}\right|{\hat{u}}_{1:i})\&times;\left(W\right({\mathrm{the\; y}}_{m+j}|0)+W({\mathrm{the\; y}}_{m+j}|1\left)\right);$(423)判断j＜N_t-M是否成立，若成立，则设置j＝j+1，并返回执行步骤(422)；否则，执行后续步骤(424)；(423) judge whether j＜N_t -M is established, if established, then set j=j+1, and return to execution step (422); Otherwise, carry out follow-up step (424);(424)记录得到的值，并结束计算过程。(424) record obtained value and end the calculation process.