CN103281166A - Hybrid automatic repeat request transmission method based on polarization code - Google Patents

Abstract

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

A Hybrid Automatic Repeat Request Transmission Method Based on Polar Code

technical field

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.

Background technique

（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 (Polar Codes) is a constructive channel coding method proposed by E.Arikan in 2009 that has been strictly proven to achieve channel capacity. Before polar coding, the channel shown in Figure 1 must be applied to N=2 ⁿ independent binary input channels (or to the N successive 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 a single-step polarization operation on two identical unpolarized channels W: X→Y, where X is the set of channel input symbols (for a binary input channel, X takes the value { 0,1}), Y is the set of channel output symbols. As shown in Figure 1, the input bits marking the polarized channel are respectively u ₁ and u ₂ , and the two input bits get x ₁ through a modulo-two adder, and on the other hand, u ₂ is directly assigned to x ₂ , namely x ₁ =u ₁ ⊕u ₂ , x ₂ =u ₂ , ⊕ is a modulo two addition operation. After x ₁ and x ₂ are respectively sent to the unpolarized channel W, the output obtained is y ₁ and y ₂ . From the input of the channel polarization basic unit (u ₁ and u ₂ ) and the output of the two channels (y ₁ and y ₂ ), the originally independent two unpolarized channels W are combined into a two-input two The output vector channel W ₂ : X ² →Y ² , where X ² =X*X, and the operator * is a Cartesian product. This vector channel contains two subchannels

(input is u ₁ , output is y ₁ y ₂ ) and

(The input is u ₂ and the output is y ₁ y ₂ u ₁ ), 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=2 ⁿ 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.

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 rest of the channels will be 0 (that is, it is completely impossible to transmit bits in other channels). The phenomenon of reliably transmitting bits on the network), 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.

FIG. 2 is a schematic diagram of a recursive structure of a channel polarization device with a length of N, where the minimum unit of recursion (ie when N=1) is the basic unit shown in FIG. 1 .

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 Figure 3, a practical recursive structure of the channel polarization device is introduced. A 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 Figure 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 ...b ₁ ), where, n=log ₂ N, and then reverse the binary sequence to obtain (b ₁ b ₂ …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. The reliability measurement is the DensityEvolution tool or calculated Bhattacharyya (Bhattacharyya) parameters) to carry the bits used to transmit messages, and call this part of the bits information bits and call this part of the channel an information channel (where

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 simply be transmitted ), thus forming 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 (the binary signal obtained after encoding contains number of bits) is equal to the length N of the channel polarizer.

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 (u ₁ ,...,u _N ) composed of information bits and fixed bits and sent to the channel polarization device is the coded code block (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 x ₁ ... x _N passes through N independent channels W, and the received signal sequence is (y ₁ ,...,y _N ).

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=(u ₁ ,…,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, ${\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00003191318700012.png,HDA00003191318700052.png"\; state="\{\{state\}\}">f</figure-callout>}}_2=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]$ superscript

It means to find the Kronecker product of n F ₂ . 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}, the binary representation of (i-1) For (b _n ,b _n-1 ,…,b ₁ ), find a j∈{1,2,…,N} such that the binary representation of (j-1) is (b ₁ ,b ₂ ,…,b _n ), let the i-th row of B _N be equal to the j-th row of I _N.

，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.

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 hole-punching polarization encoding process can also be equivalently described as: multiply the sequence u=(u ₁ ,…,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, ${\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00003191318700012.png,HDA00003191318700052.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right],$

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=( v ₁ ,...,v _M ).

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:

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： $a_N^{\left(i\right)}=a_{N,1}^{\left(i\right)},$ $a_{2k,j}^{(2i-1)}=a_{k,2j-1}^{\left(i\right)}\&CirclePlus;a_{k,2j}^{\left(i\right)},$ $a_{2k,j}^{\left(2i\right)}=a_{k,2j-1}^{\left(i\right)}\&CircleTimes;a_{k,2j}^{\left(i\right)};$ 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 receiver can calculate the log likelihood ratio (LLR) value of each encoded bit according to the received sequence (y ₁ ... 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: $a_N^{\left(i\right)}=a_{N,1}^{\left(i\right)},$ $a_{2k,j}^{(2i-1)}=a_{k,2j-1}^{\left(i\right)}\&CirclePlus;a_{k,2j}^{\left(i\right)},$ $a_{2k,j}^{\left(2i\right)}=a_{k,2j-1}^{\left(i\right)}\&CircleTimes;a_{k,2j}^{\left(i\right)};$ where the operators ⊕ 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

Probability density function of the LLR value corresponding to the jth coded bit, where j=1,2,…,N.

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.

对于凿孔极化码，(y₁…y_N)中极化码可使用串行抵消SC（successive cancellation）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， $P(y_1,\&CenterDot;\&CenterDot;\&CenterDot;,y_N|{\hat{u}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,{\hat{u}}_{i-1},{\hat{u}}_i)=\frac{1}{2^{i-1}}\&CenterDot;W_N^{\left(i\right)}(y_1,\&CenterDot;\&CenterDot;\&CenterDot;,y_N,{\hat{u}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,{\hat{u}}_{i-1}|{\hat{u}}_i);$ 函数 $W_N^{\left(i\right)}(y_1\&CenterDot;\&CenterDot;\&CenterDot;y_N,u_1\&CenterDot;\&CenterDot;\&CenterDot;u_{i-1}|u_i)$ 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 (u ₁ ,…,u _N ) according to the received signal sequence (y ₁ ,…,y _N )

For the punctured polar codes, the polar codes in (y ₁ …y _N ) can use the serial cancellation SC (successive cancellation) algorithm to decode each bit in the encoded code block sequentially from 1 to N according to the sequence number i :

In the formula, the decision function of the information bit is: in, $P({\mathrm{the\; <figure-callout\; id="1"\; label="y"\; filenames="HDA00003191318700012.png,HDA00003191318700013.png"\; state="\{\{state\}\}">y</figure-callout>}}_1,\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;,{\mathrm{the\; y}}_N|{\hat{u}}_1,\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;,{\hat{u}}_{i-1},{\hat{u}}_i)=\frac{1}{2^{i-1}}\&Center\; Dot;W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="1"\; label="y"\; filenames="HDA00003191318700012.png,HDA00003191318700013.png"\; state="\{\{state\}\}">y</figure-callout>}}_1,\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;,{\mathrm{the\; y}}_N,{\hat{u}}_1,\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;,{\hat{u}}_{i-1}|{\hat{u}}_i);$ function $W_N^{\left(i\right)}({\mathrm{the\; <figure-callout\; id="1"\; label="y"\; filenames="HDA00003191318700012.png,HDA00003191318700013.png"\; state="\{\{state\}\}">y</figure-callout>}}_1\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;{\mathrm{the\; y}}_N,u_1\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;u_{i-1}|u_i)$ 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 y ₁ ...y _N and u ₁ ...u _i-1 .

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.

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.

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.

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.

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.

The formula for calculating the throughput rate is:

Referring to Figure 4, a simple example of hybrid automatic repeat request (HARQ) transmission is introduced: when transmitting a certain information block, the sender encodes the information block (transmission sequence 1) and sends it to the channel. After the signal is decoded, it is found that the transmission failed (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 to complete the transmission of the pair of information blocks. HARQ technology has been widely used in existing communication systems (such as WCDMA, LTE and other systems).

In the patent application of the present invention, unless otherwise specified, lowercase English/Greek letters are uniformly used to represent scalars, such as x; cursive uppercase English letters are used to represent sets, such as X; bold lowercase English/Greek letters are used to represent vectors ( or an equivalent sequence), such as x; an element in a vector is represented by a lowercase English/Greek letter (not bold) with the same name, and the serial number of the element in the vector is marked with a subscript, such as the vector x The i-th element is represented by the symbol x _i ; a subvector of the vector x ( _xi ,xi ₊₁ ,…,x _j-1 ,x _j ) is represented by the symbol x _i:j ; it is represented by bold uppercase English letters Represents a square matrix, and marks its size with a subscript, such as X _N represents an N×N square matrix.

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.

Contents of the invention

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 application in actual communication systems, and has good practical prospects.

In order to achieve the above purpose, the present invention provides a hybrid automatic repeat request (HARQ) transmission method based on polar codes, 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 will 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 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) Determine the following transmission parameters according to the requirements and channel parameters: The transmission purpose is that the signal sender uses a polar code with a code length of N0 within the maximum number of transmissions T, and uses a polar code with a code length of N0 to convert a The K information bit sequence 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 N ₀ is a power of 2, and N ₀ ≥K, the sequence number set of the information channel required for polar coding is A; the bit sequence length of the polar coding bit sequence after puncturing is M, and the puncturing position indication sequence is p, and the information bits to be repeatedly transmitted correspond to The channel number of the channel is stored in a retransmission sequence number sequence r of length QM in turn; after the first, second, ..., T-th transmission, the total number of bits received by the receiving end is: N ₁ , N ₂ ,..., N _T , 0≤N ₁ ≤N ₂ ≤...≤N _T ≤Q;

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) Encode and initialize the transmission sequence: combine the information sequence of length K with the fixed bit sequence of length N ₀ -K known in advance at both the receiving and transmitting ends according to the sequence number set A of the information channel to form A sequence of bits of length N ₀

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 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:MQ ; then set the initial value of the sending times counter t=0;

(3) Send bit sequence: After adding 1 to the value of the number of sending counter t, 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 method to send a sequence of bits:

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 N ₁ 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

:Nt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 y received from the channel after the previous t transmissions.

:Nt carries out polar code decoding, then carries out CRC check to the decoded bit sequence obtained, and judges whether can pass CRC check;

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);

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.

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.

Description of drawings

FIG. 1 is a schematic diagram of a circuit structure of a basic unit of channel polarization.

FIG. 2 is a schematic diagram of a recursive structure of a channel polarization device with a length of N, where the minimum unit of recursion (ie when N=1) is the basic unit shown in FIG. 1 .

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).

4 is a timing diagram of an example of a hybrid automatic repeat request (HARQ) transmission.

FIG. 5 is a flow chart of the operation steps of the polar code-based HARQ transmission method of the present invention.

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.

Figure 7 shows the transmission error probability sequence e, the sequence number set A of the information channel, the puncture position indication sequence p and the retransmission information under the given information sequence length K and the length of the bit sequence after puncturing is m. Flowchart of configuring the channel number sequence r corresponding to the bit.

Fig. 8 is a search flow chart of 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 sequence after puncturing is m.

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.

Fig. 10 is a comparison diagram between the method of the present invention and the HARQ scheme based on LDPC codes and turbo codes.

Detailed ways

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.

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 are 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 a confirmation to the sending end through 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:

Referring to Fig. 5, introduce the concrete operation step of the inventive method:

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 N ₀ 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 N ₀ is a power of 2, and N ₀ ≥ K; the sequence number set of the information channel required for polar coding is A; the length of the bit sequence after the punctured bit sequence of the polar code code is M, and the puncture position indication sequence is p, and the information bits to be repeatedly transmitted The corresponding channel numbers are sequentially stored in a retransmission sequence number sequence r with a length of QM; after the first, second, ..., T-th transmissions, the total number of bits received by the receiving end is: N ₁ , N ₂ , ..., N _T , 0≤N ₁ ≤N ₂ ≤...≤N _T ≤Q.

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 N ₀ and the sequence number set A 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 N ₁ , N ₂ , ..., _NT received by the receiving end after each transmission Item parameters are calculated by performing the following steps (see the search process shown in Figure 6):

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 set parameter set

Optimum throughput rate η _opt =0, optimal bit sequence length m _opt =0 after puncturing, where,

Represents an empty set; and initializes the bit sequence length m=K after puncturing.

(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 A of the corresponding information channel, the puncture position indication sequence p and the channel sequence number sequence r corresponding to the retransmission information bits are obtained . This step includes the following operations (see Figure 7):

其中，括号中的上标i为信道序号，且满足i∈A。(121) According to the value of the bit sequence length m after puncturing, using the traditional puncturing polar coding method, construct a code with the number of information bits K and the code length before puncturing as 1. A perforated polar code with a code length of m after perforation, wherein the sequence number set of the information channel is A, and the perforation position indication sequence is p; then the density evolution calculation is used to obtain the reception of each information channel when the all-zero sequence is sent Probability density function of the log-likelihood ratio (LLR) value of the signal

Among them, the superscript i in the brackets is the channel number, and satisfies i∈A.

(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) For each channel in the sequence number set A belonging to the information channel, calculate the probability of its transmission error $q_i=1-{\&Integral;}_{-\&infin;}^0{a}_{{\mathrm{no}}_0}^{\left(i\right)}\left(x\right)\mathrm{dx},$ And update the transmission error probability sequence $e_k=\underset{i\&Element;A}{\mathrm{\&Sigma;}}{q}_i.$

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 most unreliable information channel at present, that is, select the information channel number i with the largest q _i value from A, then set the channel number r _k =i corresponding to the retransmission information bit, and update the channel number i The probability density function of the corresponding LLR

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.

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A、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) Determine whether k<Qm is true, if true, set k=k+1, and return to step (123); otherwise, follow the formula

Set the last element in the transmission error probability sequence, and record the obtained transmission error probability sequence e, the sequence number set A of the information channel, the puncture position indication sequence p and the value of the channel sequence number r corresponding to the retransmission information bit, and end the calculation process.

(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> _ηopt is established , if yes, execute the subsequent step (14); otherwise, skip to execute step (15). The search operation in this step includes the following (see Figure 8):

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) Set a temporary set T ₁ =S, and set n=m;

(133) Judging whether n∈S is true, if true, jump to step (137); otherwise, execute subsequent step (134);

(134) Set the temporary set T ₂ =S∪{n}, then arrange the elements in the set T ₂ from small to large, and then assign values to n ₁ , n ₂ ,..., n _l in turn;

(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 n ₁ , Estimated value of throughput at n ₂ ,...,n _l $\mathrm{\&rho;}=\frac{K\&times;(1-e_{{\mathrm{no}}_l-m+1})}{{\mathrm{\&Sigma;}}_{t=1}^l{\mathrm{no}}_t\&times;(e_{{\mathrm{no}}_{t-1}-m+1}-e_{{\mathrm{no}}_t-m+1})+{\mathrm{no}}_l\&times;e_{{\mathrm{no}}_l-\mathrm{<figure-callout\; id="1"\; label="m\; +"\; filenames="HDA00003191318700012.png,HDA00003191318700013.png"\; state="\{\{state\}\}">m</figure-callout>}+1}};$ 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) Determine whether ρ>η holds true, if so, set T ₁ =S∪{n}, and record η=ρ; otherwise, directly execute step (137);

(137) Determine whether n<Q holds true, if so, set n=n+1, and return to step (133); otherwise, go to step (138).

(138) Record the optimal configuration parameter set S=T ₁ and its corresponding throughput estimation value η when the number of elements in S is l;

(139) Determine whether l<T is true, if so, set l=l+1, and return to step (132); otherwise, end the search process of step (13).

(14) Record and update the configured transmission parameters: S _opt = S, η _opt = η, m _opt = m;

(15) Determine whether m<Q is true, if so, set m=m+1, and then return to step (12); otherwise, execute subsequent step (16);

其中，表示向上取整操作。(16) Arrange and output the parameters of the optimal configuration scheme: Arrange the elements in S _opt from small to large, and assign them to N ₁ , N ₂ , ..., _{NT in turn} ; then set M=m _opt and

in, Indicates a round up operation.

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 N ₀ -K known in advance at both the receiving and transmitting ends according to the sequence number set A of the information channel to form A sequence of bits of length N ₀

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 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 to t=0.

Step 3, send the bit sequence: after adding 1 to the value t of the sending times 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:

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 N ₁ 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

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;

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;

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.

In step 4, the path metric calculation operations required to execute the decoding algorithm include the following:,

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 $W_N^{\left(i\right)}({\mathrm{the\; y}}_{1:m},u_{1:i-1}|u_i)$ 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 bits u _i , the received signal is the probability of y _1:M and u _1:i-1 .

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) Initialize the conditional probability And set the serial number offset value j=1.

(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, $P\left({\mathrm{the\; y}}_{{m+1:N}_t}\right|{\hat{u}}_{1:i})=\frac{1}{2}\&times;P\left({\mathrm{the\; y}}_{{m+1:N}_t}\right|{\hat{u}}_{1:i})\&times;(W\left({\mathrm{the\; y}}_{m+j}\right|0)+W\left({\mathrm{the\; y}}_{m+j}\right|1)).$

(423) Determine whether j<N _t -M is true, if true, set j=j+1, and return to the execution step (422); otherwise, execute the subsequent step (424).

(424) records obtained value and end the calculation process.

的路径度量。(43) According to the formula $P\left({\mathrm{the\; y}}_{{1:N}_t}\right|{\hat{u}}_{1:i})=P\left({\mathrm{the\; y}}_{1:m}\right|{\hat{u}}_{1:i})P\left({\mathrm{the\; y}}_{{m+1:N}_t}\right|{\hat{u}}_{1:i})$ 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.

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. Comparison of throughput estimates and actual values

Under the binary input additive white Gaussian noise (BAWGN) channel, the symbol signal-to-noise ratio SNR={-3.0,0.0,3.0}dB, the information sequence length K=1024, and the polar code encoding output sequence length M after puncturing 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, N ₁ =M When , the amount of simulation is at least 1000000 information blocks. The calculation and simulation results are shown in Figure 9.

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. Compared with the HARQ scheme based on LDPC code and turbo code

Under the binary input additive white Gaussian noise (BAWGN) channel, the information sequence length K=1024, the maximum number of transmissions 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.

Table 1 The optimal transmission parameter configuration obtained by searching

SNR(dB) m N ₁ N ₂ N ₃ N ₄ N ₅ N ₆ -4.0 3262 3262 3348 3477 3666 3940 4874 -3.0 2729 2729 2800 2906 3059 3283 4033 -2.0 2272 2272 2326 2410 2531 2713 3322 -1.0 1922 1922 1961 2026 2121 2263 2739 -0.0 1665 1665 1699 1752 1829 1949 2351 1.0 1472 1472 1497 1536 1599 1693 2014 2.0 1310 1310 1332 1363 1410 1482 1741 3.0 1200 1200 1217 1241 1276 1335 1540 4.0 1120 1120 1133 1150 1172 1218 1375 5.0 1059 1059 1064 1075 1089 1121 1227 6.0 1036 1036 1041 1048 1057 1076 1144 7.0 1027 1027 1029 1032 1038 1050 1099 8.0 1024 1024 1025 1027 1030 1036 1063 9.0 1024 1024 1025 1027 1029 1032 1047 10.0 1024 1024 1025 1026 1027 1029 1036

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.

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)

1. A hybrid automatic repeat request (HARQ) transmission method based on polar codes, characterized in that: the signal sending end performs a polar coding on the information bit sequence to be sent, and the obtained coded bits are punctured and then 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 a confirmation to the sending end through 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 use 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) Determine the following transmission parameters according to the requirements and channel parameters: The transmission purpose is that the signal sender uses a polar code with a code length of N ₀ within the maximum number of transmissions T, and uses 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 N ₀ is a power of 2, and N ₀ ≥ K; the sequence number set of the information channel required for polar coding is A; the length of the bit sequence after the punctured bit sequence of the polar code code is M, and the puncture position indication sequence is p, and the information bits to be repeatedly transmitted The corresponding channel numbers are sequentially stored in a retransmission sequence number sequence r with a length of QM; after the first, second, ..., T-th transmissions, the total number of bits received by the receiving end is: N ₁ , N ₂ ,..., _NT , 0≤N ₁ ≤N ₂ ≤... _≤NT ≤Q; (2) Encode and initialize the transmission sequence: combine the information sequence of length K with the fixed bit sequence of length N ₀ -K known in advance at both the receiving and transmitting ends according to the sequence number set A of the information channel to form A sequence of bits of length N ₀ , and 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 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; (3) Send bit sequence: After adding 1 to the value of the number of sending counter t, 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 method to send a sequence of bits: If t=1, then send the first N ₁ 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) Receiving bit sequence: The signal receiving end uses the serial offset 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; 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); 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. 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 transmitted Q, including The polar code length N ₀ , the sequence number set A 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 bits received by the receiving end after each transmission The parameters of the numbers N ₁ , N ₂ , ..., _NT are obtained by performing the following steps: (11) Initialize the set parameter set Optimum throughput rate η _opt =0, optimal bit sequence length m _opt =0 after puncturing, where,

Represents an empty set; and initializes the bit sequence length m=K after puncturing; (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} when the value is selected, the probability value of transmission error under the serial offset decoding algorithm; at the same time, the sequence number set A of the corresponding information channel, the punching position indication sequence p and the retransmission sequence number sequence r are obtained; (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> _ηopt is established , if yes, perform the next step (14); otherwise, skip to step (15); (14) Record and update the configured transmission parameters: S _opt = S, η _opt = η, m _opt = m; (15) Determine whether m<Q is true, if so, set m=m+1, and then return to step (12); otherwise, execute subsequent step (16); (16) Arrange and output the parameters of the optimal configuration scheme: Arrange the elements in S _opt from small to large, and assign them to N ₁ , N ₂ , ..., _{NT in turn} ; then set M=m _opt and

in,

Indicates a round up operation. 3. The method according to claim 2, characterized in that the step (12) includes the following operations: (121) According to the value of the bit sequence length m after puncturing, using the traditional puncturing polar coding method, construct a code with the number of information bits K and the code length before puncturing as

1. A perforated polar code with a code length of m after perforation, in which the sequence number set of the information channel is A, and the perforation position indication sequence is p; and then the density evolution calculation is used to obtain the reception of each information channel when the all-zero sequence is sent. The probability density function of the log-likelihood ratio LLR value of the signal

Among them, the superscript i in the brackets is the channel number, and satisfies i∈A; (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) For each channel in the sequence number set A belonging to the information channel, calculate the probability of its transmission error $q_i=1-{\&Integral;}_{-\&infin;}^0{a}_{{\mathrm{no}}_0}^{\left(i\right)}\left(x\right)\mathrm{dx},$ And update the transmission error probability sequence $e_k=\underset{i\&Element;A}{\mathrm{\&Sigma;}}{q}_i;$ (124) Find out the most unreliable information channel at present, that is, select the information channel number i with the largest q _i value from A, then set the channel number r _k =i corresponding to the retransmission information bit, and update the channel number i The probability density function of the corresponding LLR

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) Determine whether k<Qm is true, if true, set k=k+1, and return to step (123); otherwise, follow the formula

Set the last element in the transmission error probability sequence, and record the values of the obtained transmission error probability sequence e, information channel sequence number set A, punching position indication sequence p and retransmission sequence number sequence r, and end the calculation process. 4. The method according to claim 2, characterized in that the search operation in the step (13) includes the following: (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) Set a temporary set T ₁ =S, and set n=m; (133) Judging whether n∈S is true, if true, jump to step (137); otherwise, execute subsequent step (134); (134) Set the temporary set T ₂ =S∪{n}, then arrange the elements in the set T ₂ from small to large, and then assign values to n ₁ , n ₂ ,..., n _l in turn; (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 n ₁ , Estimated value of throughput at n ₂ ,...,n _l $\mathrm{\&rho;}=\frac{K\&times;(1-e_{{\mathrm{no}}_l-m+1})}{{\mathrm{\&Sigma;}}_{t=1}^l{\mathrm{no}}_t\&times;(e_{{\mathrm{no}}_{t-1}-m+1}-e_{{\mathrm{no}}_t-m+1})+{\mathrm{no}}_l\&times;e_{{\mathrm{no}}_l-m+1}};$ 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) Determine whether ρ>η holds true, if so, set T ₁ =S∪{n}, and record η=ρ; otherwise, directly execute step (137); (137) Determine whether n<Q holds true, if so, set n=n+1, and return to step (133); otherwise, go to step (138). (138) Record the optimal configuration parameter set S=T ₁ and its corresponding throughput estimation value η when the number of elements in S is l; (139) Determine whether l<T is true, if so, set l=l+1, and return to step (132); otherwise, end the search process of step (13). 5. The method according to claim 1, characterized in that, in the step (4), the path metric calculation operations required to execute the decoding algorithm include the following: (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 $W_N^{\left(i\right)}({\mathrm{the\; y}}_{1:m},u_{1:i-1}|u_i)$ Computing conditional probabilities $P\left({\mathrm{the\; y}}_{1:m}\right|{\hat{u}}_{1:i})=\frac{W_N^{\left(i\right)}({\mathrm{the\; y}}_{1:m},{\hat{u}}_{1:i}|{\hat{u}}_i)}{2^{i-1}};$ 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) 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) 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. The method according to claim 5, characterized in that the step (42) includes the following operations: (421) Initialize the conditional probability

And set the serial number offset value j=1; (422) Judging whether r _j ≤ i is true, if true, then $P\left({\mathrm{the\; y}}_{m+1:N_t}\right|{\hat{u}}_{1:i})=P\left({\mathrm{the\; y}}_{m+1:N_t}\right|{\hat{u}}_{1:i})\&Center\; Dot;W\left({\mathrm{the\; y}}_{m+j}\right|{\hat{u}}_{r_k});$ otherwise, $P\left({\mathrm{the\; y}}_{{m+1:N}_t}\right|{\hat{u}}_{1:i})=\frac{1}{2}\&times;P\left({\mathrm{the\; y}}_{{m+1:N}_t}\right|{\hat{u}}_{1:i})\&times;(W\left({\mathrm{the\; y}}_{m+j}\right|0)+W\left({\mathrm{the\; y}}_{m+j}\right|1));$ (423) Determine whether j<N _t -M is true, if true, set j=j+1, and return to the execution step (422); otherwise, execute the subsequent step (424); (424) records obtained

value and end the calculation process.

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