Cross-packet Hybrid Automatic Repeat reQuest Method Based on Multi-level Polar-coded Modulation

Abstract

The present invention is a cross-packet hybrid automatic repeat request method based on multi-level polar code encoding modulation. First, in the multi-level polar code encoding modulation MLPCM transmission, a layer-independent cross-packet hybrid automatic repeat request XP-HARQ transmission mode is adopted, enabling multiple data streams to be independently designed. Then, by utilizing the characteristics of the upper triangular generating matrix of the polar code encoding in the encoding, an encoder and a decoder suitable for the XP-HARQ transmission characteristics are designed, thereby realizing the joint encoding and decoding of multiple data packets during the retransmission process. By further designing the encoding parameters of each data stream, the throughput performance of the system can be maximized. This method combines the advantages of polar codes, multi-level encoding modulation, and XP-HARQ, and can effectively improve the throughput performance of the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of hybrid automatic repeat transmission in wireless communications, and in particular relates to a hybrid automatic repeat transmission method based on polar code coded modulation. Background Art

[0002] Multilevel polar coded modulation (MLPCM) is a coded modulation technique based on polar codes to improve the spectrum efficiency of communication systems. m MLPCM uses digital modulation with an m-ary (m=1, 2, 3, 4, ...) base. It divides the input data stream into m priority levels and decodes them sequentially at the receiving end. The transmitter and receiver each have m encoders and m decoders, respectively. This coding and modulation technique can achieve the desired channel capacity. Another coding and modulation technique based on polar codes is bit-interleaved polar coded modulation (BIPCM). In BIPCM, each data stream has no priority, so the transmitter and receiver each have only one encoder and decoder. BIPCM suffers from significant mutual information loss, and its error rate performance is inferior to MLPCM.

[0003] Hybrid automatic repeat request (HARQ) is a wireless communication protocol that combines automatic repeat request and forward error correction techniques to improve data transmission reliability, reduce latency, and increase throughput in wireless networks. HARQ technology is widely used in modern wireless communication standards, such as 5G.

[0004] Traditional HARQ techniques can be divided into two types based on different coding and decoding strategies: Chase Combining HARQ (CC-HARQ) and incremental redundancy HARQ (IR-HARQ). For CC-HARQ, the sender first encodes the information bits using a forward error correction code and then transmits them. After receiving the information, the receiver will perform decoding. If the decoding is successful, it will send an acknowledgement (ACK) message to the sender; otherwise, it will send a negative acknowledgement (NACK) message to request the retransmission of the data packet. After receiving the NACK, the sender will resend the same codeword. The receiver superimposes and combines all the received codewords for decoding until the decoding is successful or the maximum number of retransmissions is reached, ending the current HARQ cycle. For IR-HARQ, the sender first encodes the information bits using an FEC code to generate a codeword with a lower code rate, and then divides this codeword into multiple sub-codewords according to certain rules. The sender first transmits the sub-codeword containing all the information. Similarly, if the receiver decodes incorrectly, it will feedback a NACK to the sender to request the sender to retransmit. In each retransmission, the sender sends a sub-codeword to the receiver, that is, redundant information. The receiver then combines all the previously received bits to form a codeword with a lower code rate for combined decoding until the decoding is successful or the maximum number of retransmissions is reached, ending the current HARQ cycle. This coding and decoding method can obtain a greater coding gain, thus achieving the purpose of increasing redundancy.

[0005] Research shows that the combination of traditional HARQ technology and polar code encoding modulation technology can further improve the throughput performance of the system, and the HARQ scheme based on MLPCM has better performance than the HARQ scheme based on BIPCM. The HARQ scheme based on MLPCM can be divided into two types: layer-dependent scheme and layer-independent scheme. In the layer-dependent scheme, the data streams of all layers at the transmitter are regarded as a codeword, and the correctness of the codeword is checked by a single cyclic redundancy check (CRC). When the decoding of this codeword fails, the transmitter will retransmit this codeword (CC-HARQ) or the redundant information of this codeword (IR-HARQ). In the layer-independent scheme, each layer transmits an independent codeword, and each codeword also has an independent CRC code. When the codeword of a certain layer is invalid, the codeword (CC-HARQ) or the redundant information of this codeword (IR-HARQ) will be retransmitted during the next transmission on the same layer, while codewords encoded for new information bits will be transmitted on all other upper and lower layers. In this scheme, the receiver will wait until the codeword of a certain layer is correctly decoded before attempting to decode the next layer. Compared with the layer-dependent scheme, the layer-independent scheme only retransmits the incorrect layer codewords, effectively utilizes the channel resources, and improves the system throughput. However, traditional HARQ technology performs encoding and decoding on a fixed information bit data packet during each retransmission process until the retransmission ends and a new cycle starts. This encoding method will waste the channel resources of each retransmission, thereby reducing the system throughput.

[0006] Cross-packet HARQ (XP-HARQ) is a new HARQ technology. It allows new packets to be transmitted during the retransmission of incorrect packets, thereby increasing the system throughput. In cross-packet HARQ, the transmitter can send new packets while waiting for the ACK or NACK of the previously transmitted packets. The receiver can process the new packets and the retransmitted packets simultaneously, thereby reducing the system latency and improving the transmission efficiency. XP-HARQ is particularly suitable for system applications where the packets are small and sensitive to transmission latency. Currently, there is no XP-HARQ design scheme based on polar code encoding modulation. Summary of the Invention

[0007] Technical Problem: In view of the above problems, the present invention proposes a cross-packet hybrid automatic repeat request method based on multi-level polar code encoding modulation, which combines the advantages of polar codes, multi-level encoding modulation, and XP-HARQ, and can effectively improve the throughput performance of the system.

[0008] Technical solution: A cross-packet hybrid automatic repeat request method based on multi-level polar code encoding modulation in the present invention. First, in the multi-level polar code encoding modulation MLPCM transmission, a layer-independent cross-packet hybrid automatic repeat request XP-HARQ transmission mode is adopted, enabling multiple data streams to be designed independently. Then, an encoder and a decoder suitable for the XP-HARQ transmission characteristics are designed by utilizing the characteristics of the upper triangular generation matrix of the polar code encoding during encoding, thereby realizing the joint encoding and decoding of multiple data packets during the retransmission process. By further designing the encoding parameters of each data stream, the throughput performance of the system can be maximized.

[0009] The method includes the following steps:

[0010] First step: The sending end confirms the feedback information of the XP-HARQ controller, letting 2 m represent the modulation order, m = 1, 2, 3, 4,...; The MLPCM contains a total of m layers, corresponding to m bit data streams. These data streams all have their own cyclic redundancy check CRC codes and respectively correspond to a mapped bit; The receiving end will wait until the codewords of the previous i - 1 layers are correctly decoded before attempting to decode layer i, i = 1, 2,..., m; The layer performing the decoding operation feeds back the decoding information according to the decoding result. The feedback information includes two types: ACK and NACK. ACK indicates that the decoding of layer i is successful, and NACK indicates that the decoding of layer i fails. The initial feedback information of all layers in the system is ACK;

[0011] Second step: The sending end confirms the HARQ loop status of the current m layers according to the feedback information in the first step. Let K represent the maximum number of transmissions allowed for an XP-HARQ loop in the system, K = 1, 2,...; Let the number of transmissions k = 1, 2,..., K;

[0012] Third step: The sending end generates m source data streams to be encoded. Let R i,k represent the code rate of the new information bit mapped to the i-th bit and in the k-th transmission process. Let the set represent the value set of R i,k , that is, R i,k ∈R s , where represents the code rate interval, d r = 1, 2,..., N. The code rates R i,k of each layer are all fixed and stored in the caches of the sending end and the receiving end; Let N represent the frame length. Let the horizontal vectors u i,k and v i,k respectively represent the new information bit data stream and the source bit data stream mapped to the i-th bit and in the k-th transmission process. The sizes of u i,k and v i,k are NR i,kand N; for u i,k Add N crc bit CRC code to generate a horizontal vector u of length NR i,k +N crc of the horizontal vector u i,k , and let the horizontal vector v i,1:k-1 =(v i,1 ,v i,2 ,...,v i,k-1 ), where v i,k is

[0013]

[0014] In the above formula, A i,k , B i,k , D i,k and C i,k respectively represent the set of new information bit indices, the set of reset information bit indices, the set of information bits to be copied, and the set of frozen bit indices; and respectively represent the sub-vectors formed by the elements with indices A i,k , B i,k , and C i,k in v i,k ; in the sets A i,k , B i,k and C i,k , the intersection of any two is an empty set, and the union of the three is the index set of the entire v i,k , that is, {1, 2,..., N}; represents the sub-vector formed by the elements with index D i,1:k-1 in v i,k ;

[0015] Step 4: The sender performs cross-packet polar code encoding on m source data streams,

[0016] w i,1:k =(w i,1 ,w i,2 ,...,w i,k ) = v i,1:k [G] 1:kN (7)

[0017] In the above formula, the horizontal vector w i,k represents the data stream used to map the i-th bit and in the k-th transmission process, 1:kN represents the index set {1, 2,..., kN}, G is the polar code generation matrix, and [G] 1:kN represents the sub-matrix of size kN formed by the rows and columns with indices 1:kN in G,

[0018]

[0019] In the above formula, F2 is the polarization code core matrix of the second order, is the Kronecker product, and log2(·) represents the logarithmic function with base 2, represents the ceiling function, and the encoder output is w i,k and v i,1:k ;

[0020] Step 5: The transmitting end generates and transmits a symbol frame, maps and modulates the m encoded data streams through set decomposition to generate a symbol frame x, and transmits x to the receiving end;

[0021] Step 6: The receiving end receives and caches the received signal. Let h, y, and z represent the channel gain vector, the received symbol frame, and the complex Gaussian white noise vector respectively. The received signal is expressed as

[0022] y n = h n x n + z n (9)

[0023] In the above formula, h n , x n , y n and z n respectively represent the nth elements of the vectors h, x, y, and z, where n = 1, 2,..., N. The elements in z are independent of each other and follow a complex Gaussian distribution with a mean of 0 and a variance of σ 2 ;

[0024] Step 7: The receiving end uses the multi-stage demodulation method of MLPCM to demodulate and decode each layer i = 1, 2,..., m successively until decoding fails; let represent the received symbol frame in the cache of the receiving end that has not been demodulated for bit i. The number of frames is represented by T i and layer i demodulates and decodes one by one until decoding fails;

[0025] Step 8: Delete the data in the cache of the receiving end. When the cached data frame meets one of the following conditions, delete the data frame and the corresponding demodulated log-likelihood ratio: 1) Any bit data stream contained in the data frame reaches the maximum number of transmissions in the HARQ cycle and decoding fails; 2) All bits contained in the data frame are decoded successfully.

[0026] The second step includes the following three cases:

[0027] 1) The feedback information of all layers is ACK: The XP-HARQ status of all layers is the initial transmission, that is, k = 1;

[0028] 2) The first i - 1 layers feedback ACK, layer i feedbacks NACK and has been transmitted k - 1 times: The XP - HARQ state of layer i is the k - th transmission, and the XP - HARQ states of the remaining layers are the first transmissions;

[0029] 3) The first i - 1 layers feedback ACK, layer i feedbacks NACK and has been transmitted K times, and the XP - HARQ states of all layers are the first transmissions.

[0030] The seventh step specifically includes the following processes:

[0031] Step 7.1, layer i demodulates to obtain the log - likelihood ratio vector of the corresponding data stream w represented by r i,k , where j = 1, 2,..., T i,k ; i ;

[0032] Step 7.3, jointly use r i,k and the bit log - likelihood ratio vectors of the previous k - 1 times as the input of the decoder, denoted as r i,1:k =(r i,1 , r i,2 ,..., r i,k ), and use the CRC - assisted serial cancellation list CA - SCL decoding method based on dynamic frozen bits for decoding;

[0033] Step 7.3, according to the decoding CRC check result of Step 7.3, if layer i decodes successfully, feedback ACK; otherwise, feedback NACK, and the receiver ends decoding.

[0034] The R i,k , A i,k , B i,k , D i,k and C i,k , which are used for cross - packet encoding of each layer, and its optimization method includes the following steps:

[0035] The first step: Channel reliability estimation, use the Gaussian approximation method to calculate the reliability of the polarized channel after polarization coding of length kN based on the average mutual information of the channel of layer i, and the calculation result is represented by the vector s i,k , sort the elements in the vector s i,k in descending order, and the sorted vector is represented by , where S i,k represents the index set of the elements in that are the elements in s i,k ;

[0036] The second step: For R i,1 , R i,2 ,..., R i,KTraverse and search all the value cases of R, calculate the throughput of the system and output the corresponding coding parameters; R i,1 , R i,2 ,..., R i,K There are a total of (d r + 1) K value cases;

[0037] Step 3: Output the throughput η i when it is the largest, the R i,1 , R i,2 ,..., R i,K and the corresponding coding parameters.

[0038] The second step described above includes the following processes:

[0039] Step 2.1, calculate the total number of target information bits after k transmissions, denoted as

[0040] Step 2.2, calculate the parameters A i,1 , B i,1 , D i,1 and Ω i,1 , where the set Ω i,k represents the set of the M i,1 most reliable information bit position indices of the polar code of length kN. Let Ω i,1 and A i,1 be the set of the first M i,1 elements in S i,1 . Let B i,1 and D i,1 be empty sets;

[0041] Step 2.3, calculate the coding parameters Ω i,k , A i,k , B i,k , C i,k and D i,k in turn for k = 2, 3,..., K transmissions;

[0042] Step 2.4, generate Ω i,k , A i,k , B i,k , C i,k and D i,k . Select the M i,k smallest elements from the elements with index Ψ in s copy , and generate the set D i,k using the indices of these elements in s i,k . Select the M i,k largest elements from the elements with index Φ in s copy , and use these elements in s i,kThe index generation set Φ * , B i,k = Φ * -(k - 1)N, A i,k is the set of elements that belong to the set Φ-(k - 1)N but do not belong to the set B i,k , C i,k is the set of elements that belong to the set {1, 2,..., N} but do not belong to the set Φ-(k - 1)N, Ω i,k is the set that belongs to the set Ω i,k-1 but does not belong to the set D i,k and the union of the set of elements and the set Φ;

[0043] Step 2.5, simulate and calculate the frame error rate of the polar code of length kN with the information bit set Ω i,k when k = 1, 2,..., K and use CA - SCL decoding, denoted by f i,k ;

[0044] Step 2.6, calculate the throughput,

[0045]

[0046] The said Step 2.3 includes the following processes:

[0047] Generate the parameter M copy and the sets Φ, Ψ. Φ represents the set of position indices used to generate new information bits and reset information bits for the k - th transmission during the polar code encoding of length kN. Ψ represents the set of position indices of the information bits to be copied that are available for selection. M copy represents the number of reset information bits or information bits to be copied; Let Θ represent the set of position indices of the M i,k most reliable information bits of the polar code of length kN, that is, Θ is the set of the first M i,1 elements in S i,1 . First, generate the set of elements that belong to the set Θ but do not belong to the set Ω i,k-1 , denoted by Δ. Φ is the set of elements in Δ whose values are greater than (k - 1)N, and its size is denoted by |Φ|. Ψ is the set of elements that belong to the set Ω i,k-1 but do not belong to the set Θ, and its size is denoted by |Ψ|. M copy takes the minimum value of |Φ| and |Ψ|; Then calculate the difference between the target number of new information bits NR i,k for the k - th transmission and the number of new information bits |Φ|-M copy that can be accommodated under the current parameters, denoted by M diff , M diff = NR i,k -|Φ|+M copy , if Mdiff If it is not equal to 0, then update the total number of information bits M under the current parameters i,k = M i,k + M diff , and execute this step again until M diff = 0.

[0048] Advantageous effects: The XP-HARQ method based on MLPCM proposed in the present invention is superior to the IR-HARQ and CC-HARQ methods based on MLPCM, the XP-HARQ method based on multi-stage Turbo code coded modulation, and the XP-HARQ method based on bit-interleaved Turbo code coded modulation in terms of throughput performance. Description of the drawings

[0049] Figure 1 is a schematic diagram of cross-packet polar code encoding.

[0050] Figure 2 is the throughput performance of the method proposed in the present invention, the IR-HARQ method based on MLPCM (MLPCM+IR-HARQ), the XP-HARQ method based on multi-stage Turbo code coded modulation (Turbo-MLCM+XP-HARQ), and the XP-HARQ method based on bit-interleaved Turbo code coded modulation (Turbo-BICM+XP-HARQ) under different symbol signal-to-noise ratios. Specific implementation manners

[0051] Taking 16-QAM modulation and code rate interval as an example to illustrate the method of the present invention.

[0052] First step: The transmitting end confirms the feedback information of the XP-HARQ controller. Let 2 m (m = 1, 2, 3, 4,...) represent the modulation order. MLPCM contains a total of m layers, corresponding to m bit data streams. These data streams all have their own CRC codes and each corresponds to a mapped bit. In this solution, the receiving end will wait until the codewords of the first i - 1 (i = 1, 2,..., m) layers are correctly decoded before attempting to decode layer i. The layer performing the decoding operation feeds back decoding information according to the decoding result. The feedback information includes two types: ACK and NACK. ACK indicates that the decoding of layer i is successful. NACK indicates that the decoding of layer i fails. The initial feedback information of all layers of the system is ACK.

[0053] Step 2: The transmitting end confirms the HARQ loop status of the current m layers according to the feedback information in Step 1. Let K denote the maximum number of transmissions allowed for an XP-HARQ loop in the system, where K = 1, 2,.... Let the number of transmissions be k = 1, 2,..., K. This step includes the following two cases: 1) The feedback information of all layers is ACK: The XP-HARQ status of all layers is the initial transmission, i.e., k = 1; 2) The first i - 1 layers feedback ACK, the i-th layer feedbacks NACK and has been transmitted k - 1 times: The XP-HARQ status of the i-th layer is the k-th transmission, and the XP-HARQ status of the remaining layers is the initial transmission; 3) The first i - 1 layers feedback ACK, the i-th layer feedbacks NACK and has been transmitted K times, and the XP-HARQ status of all layers is the initial transmission.

[0054] The above steps are elaborated in detail below. The MLPCM based on 16-QAM includes a total of 4 data streams, each corresponding to a mapped bit. Under the layer-independent XP-HARQ protocol, each data packet of each layer's data stream has a corresponding CRC check bit. Therefore, each data packet under XP-HARQ transmission generates a corresponding CRC check bit before encoding. At the same time, the receiving end decodes layer by layer and only decodes the next layer when the decoding of the current layer is successful. Therefore, after the i-th layer feedbacks NACK, the remaining layers do not feedback information because they have not been decoded. The transmitting end can determine the HARQ loop status of the next transmission for the m layers according to this feedback information.

[0055] Step 3: The transmitting end generates m source data streams to be encoded. Let R i,k denote the code rate of the new information bit mapped to the i-th bit and in the k-th transmission. Let the set denote the value set of R i,k , i.e., R i,k ∈R s , where denotes the code rate interval, and d r = 1, 2,..., N. The code rate R i,k of each layer is fixed and stored in the caches of the transmitting end and the receiving end. Let N denote the frame length. Let the horizontal vectors u i,k and v i,k denote the data stream of the new information bit and the source bit stream used to map the i-th bit and in the k-th transmission, respectively. The sizes of u i,k and v i,k are NR i,k and N, respectively. Add N crc bits of CRC code to u i,k to generate a horizontal vector u i,k of length NR crc + N i,k . Let the horizontal vector v i,1:k-1 =(vi,1 , v i,2 ,..., v i,k-1 ). v i,k is calculated as

[0056]

[0057] In the above formula, A i,k , B i,k , D i,k and C i,k respectively represent the set of new information bit indices, the set of reset information bit indices, the set of information bits to be copied, and the set of frozen bit indices. and respectively represent the sub-vectors formed by the elements with indices A i,k , B i,k , and C i,k in v i,k . In sets A i,k , B i,k , and C i,k , the intersection of any two is an empty set, and the union of the three is the index set of the entire v i,k , that is, {1, 2,..., N}. represents the sub-vector formed by the elements with index D i,1:k-1 in v i,k .

[0058] Step 4: The transmitter performs cross-packet polar code encoding on m source data streams.

[0059] w i,1:k = (w i,1 , w i,2 ,..., w i,k ) = v i,1:k [G] 1:kN (12)

[0060] In the above formula, the horizontal vector w i,k represents the data stream used to map the i-th bit during the k-th transmission after encoding.. 1:kN represents the index set {1, 2,..., kN}. G is the polar code generation matrix, and [G] 1:kN represents a sub-matrix of size kN formed by the rows and columns with indices 1:kN in G. G is calculated as

[0061]

[0062] In the above formula, F2 is the polarization code kernel matrix of order two. is the Kronecker product. log2(·) represents the logarithmic function with base 2. represents the ceiling function. The encoder output w i,k and vi,1:k 。

[0063] The above steps are elaborated in detail below. The above steps introduce the process of cross-packet polar code encoding for layer i. Figure 1 is the cross-packet encoding model for layer i, where S / P represents serial-to-parallel conversion. R i,k The value set of is R s = {0, 1 / 16, 1 / 8,..., 15 / 16, 1}. During the HARQ cycle, the initial transmission (i.e., k = 1) only contains one information bit packet of size NR i,1 Each retransmission adds a new information bit packet. After cross-packet encoding, two data streams are generated. One is the encoded data stream w i,k , which is used for subsequent modulation processes. The other is the source data stream v i,1:k , which will be used for the encoding process of the next retransmission. Four encoding parameters are included in the encoding process: A i,k , B i,k , D i,k and C i,k , representing the set of new information bit indices, the set of reset information bit indices, the set of information bits to be copied, and the set of frozen bit indices respectively. The positions with indices in A i,k in the source data stream v i,k will be used to store new packets. The information bits that have been transmitted at the positions with indices in D i,1:k-1 in the source data stream v i,k will be copied to the positions with indices in B i,k in the new source data stream v i,k . can be regarded as dynamic frozen bits. The positions with the remaining indices in v i,k are all frozen bits.

[0064] Step 5: The transmitter generates and sends a symbol frame. The m encoded data streams are modulated through set decomposition mapping to generate a symbol frame x, and x is sent to the receiver.

[0065] Step 6: The receiver receives and caches the received signal. This scheme mainly targets complex Gaussian channels and Rayleigh fast-fading channels. Let h, y, and z represent the fast Rayleigh fading channel gain vector, the received symbol frame, and the complex Gaussian white noise vector respectively. The received signal is expressed as

[0066] y n = h n x n + z n (14)

[0067] In the above formula, h n , x n , yn and z n represent the n-th (n = 1, 2, ..., N) elements of the vectors h, x, y, and z respectively. The elements in z are independent of each other and follow a complex Gaussian distribution with a mean of 0 and a variance of σ 2 . In the complex Gaussian channel, all elements in h take the value of 1. In the Rayleigh fast fading channel, the elements in h are independent of each other and follow a complex Gaussian distribution with a mean of 0 and a variance of 1.

[0068] Step 7: The receiving end uses the multi-level demodulation method of MLPCM to successively demodulate and decode each layer i = 1, 2, ..., m until decoding fails. Let represent the received symbol frame in the receiving end buffer that has not been demodulated for bit i, and the number of frames is represented by T i . Layer i demodulates and decodes one by one until decoding fails, which specifically includes the following processes:

[0069] (1) Layer i demodulates (j = 1, 2, ..., T i ) to obtain the bit log-likelihood ratio vector of the corresponding data stream w i,k , which is represented by r i,k .

[0070] (2) Combine r i,k and the previous k - 1 bit log-likelihood ratio vectors as the input to the decoder, denoted as r i,1:k =(r i,1 , r i,2 , ..., r i,k ), and use the CRC-aided successive cancellation list (CA-SCL) decoding method based on dynamic frozen bits for decoding.

[0071] (3) According to the decoding CRC check result in (3), if layer i decodes successfully, feedback ACK; otherwise, feedback NACK, and the receiving end ends decoding.

[0072] Step 8: Delete the data in the receiving end buffer. When the buffered data frame meets one of the following conditions, delete the data frame and the corresponding demodulated log-likelihood ratio: 1) Any one of the bit data streams contained in the data frame reaches the maximum number of transmissions in the HARQ cycle and decoding fails; 2) All bits contained in the data frame are decoded successfully.

[0073] The above steps are elaborated in detail below. The receiving end uses the multi-level demodulation method of MLPCM to successively demodulate and decode each layer \(i = 1, 2, \cdots, m\) until the decoding fails. According to the second step, after the decoding of layer \(i - 1\) fails, layer \(i\) will not be decoded, and the next transmission mode of layer \(i\) is the initial transmission of the XP-HARQ cycle. Therefore, before starting to decode layer \(i\), there are multiple received data frames for which the \(i\)-th mapped bits have not been demodulated. These data frames need to be cached at the receiving end until the decoding of layer \(i\) starts and are deleted after meeting the deletion conditions of the ninth step. When decoding the data stream included in the \(k\)-th transmission of an XP-HARQ cycle for layer \(i\), the previous demodulation results, that is, \(r\) i ,1: k =(r i,1 ,r i,2 ,\(\cdots\),r i,k ). The decoder will successively output the decoding results of the data packets \(u\) i,k ,u i,k-1 ,\(\cdots\),u i,1 . When any one of the data packets fails to pass the corresponding CRC check, the decoding ends and a NACK is fed back.

[0074] The optimization method for the parameters (i.e., \(R\) i,k , \(A\) i,k , \(B\) i,k , \(D\) i,k and \(C\) i,k ) used for cross-packet coding of each layer includes the following steps:

[0075] The first step: Channel reliability estimation. Use the Gaussian approximation method to calculate the reliability of the polarized channel after polarization coding with a length of \(kN\) based on the average mutual information of the channel of layer \(i\), and the calculation result is represented by the vector \(s\) i,k . Arrange the elements in the vector \(s\) i,k in descending order, and the arranged vector is represented by , where \(S\) i,k represents the index set of the elements in \(s\) in i,k .

[0076] The second step: Traverse all the value cases of \(R\) i,1 , \(R\) i,2 , \(\cdots\), \(R\) i,K , calculate the throughput of the system and output the corresponding coding parameters. \(R\) i,1 , \(R\) i,2 , \(\cdots\), \(R\) i,K has a total of \((d\) r + 1) K value cases. This step includes the following processes:

[0077] (1) Calculate the total number of target information bits after k transmissions, denoted as

[0078] (2) Calculate the parameters A i,1 , B i,1 , D i,1 and Ω i,1 , where the set Ω i,k represents the set of indices of the M i,1 most reliable information bit positions of the polar code of length kN. Let Ω i,1 and A i,1 be the set of the first M i,1 elements in S i,1 . Let B i,1 and D i,1 be empty sets.

[0079] (3) Calculate the encoding parameters Ω i,k , A i,k , B i,k , C i,k and D i,k successively for k = 2, 3,..., K transmissions. This step includes the following processes:

[0080] (a) Generate the parameters M copy and the sets Φ, Ψ. Φ represents the set of indices of the positions for generating new information bits and resetting information bits in the encoding process of the polar code of length kN. Ψ represents the set of indices of the positions of the information bits to be copied that are available for selection. M copy represents the number of reset information bits or information bits to be copied. Let Θ represent the set of indices of the M i,k most reliable information bit positions of the polar code of length kN, that is, Θ is the set of the first M i,1 elements in S i,1 . First, generate the set of elements that belong to the set Θ but not to the set Ω i,k-1 , denoted as Δ. Φ is the set of elements in Δ that have values greater than (k - 1)N, and its size is denoted as |Φ|. Ψ is the set of elements that belong to the set Ω i,k-1 but not to the set Θ, and its size is denoted as |Ψ|. M copy takes the minimum value of |Φ| and |Ψ|. Then calculate the difference between the number of target new information bits NR i,k for the kth transmission and the number of new information bits |Φ| - M copy that can be accommodated under the current parameters, denoted as M diff . M diff = NR i,k - |Φ| + M copy . If M diffIf it is not equal to 0, update the total number of information bits M under the current parameters i,k = M i,k + M diff , and execute this step again until M diff = 0

[0081] (b) Generate Ω i,k , A i,k , B i,k , C i,k and D i,k . Select M i,k the smallest elements from the elements with index Ψ in s copy , and use the indices of these elements in s i,k to generate the set D i,k . Select M i,k the largest elements from the elements with index Φ in s copy , and use the indices of these elements in s i,k to generate the set Φ * . B i,k = Φ * -(k - 1)N. A i,k is the set of elements that belong to the set Φ-(k - 1)N but do not belong to the set B i,k . C i,k is the set of elements that belong to the set {1, 2,..., N} but do not belong to the set Φ-(k - 1)N. Ω i,k is the union of the set of elements that belong to the set Ω i,k-1 but do not belong to the set D i,k and the set Φ

[0082] (4) Calculate the frame error rate of the polar code with information bit set Ω i,k of length kN for k = 1, 2,..., K and use CA - SCL decoding, denoted by f i,k .

[0083] (5) Calculate the throughput

[0084]

[0085] Step 3: Output the R i when the throughput η i,1 is the largest, R i,2 , R i,K and the corresponding coding parameters

[0086] The above steps are elaborated in detail below. The set of possible values of R i,k R s = {0, 1 / 16, 1 / 8,..., 15 / 16, 1} has a total of d r + 1 = 17 values. Therefore, Ri,1 , R i,2 ,..., R i,K There are 17 K value cases. From the second step, the k - 1 transmitted codewords after k - 1 transmissions in layer i form a polar code of length (k - 1)N, and the number of information bits contained is The information bit position index set is Ω i,k-1 . Ω i,k-1 contains the set D i,k , that is, the information bits with index D i,k will be copied and used for the generation of the source data stream during the kth transmission. D i,k contains a total of M copy elements. During the kth transmission, there are a total of NR i,k new information bits and M copy bits copied from the information bits transmitted in the previous k - 1 times. Therefore, the generated set Φ must satisfy |Φ| = M copy + NR i,k , and step (a) in the second step must be continuously executed until M diff = 0. In step (b) of the second step, M copy indices of the least reliable channels are selected from the set Ψ to generate the set D i,k , M copy indices of the most reliable channels are selected from the set Φ to generate the set B i,k , and the remaining indices in Φ generate the set A i,k . Finally, Ω i,k is generated. Step (9) calculates the probability of NACK feedback for the kth transmission in layer i, and this value can be estimated by the bit error rate of the polar code of length kN with the information bit set as Ω i,k and the rest being frozen bits. Step (10) gives the calculation formula for the system throughput. Finally, through exhaustive search, the R i when the throughput η i,1 , R i,2 ,..., R i,K is maximized and the corresponding coding parameters can be obtained.

[0087] The method proposed in the present invention is compared with the IR - HARQ method based on MLPCM, the XP - HARQ method based on multi - level Turbo - coded modulation, and the XP - HARQ method based on bit - interleaved Turbo - coded modulation in terms of throughput performance at different symbol signal - to - noise ratios (unit: decibel (dB)), and the results are as Figure 2 shown. Among them, the modulation method is 16 - QAM, the channel is a fast Rayleigh fading channel, and the frame length is 128. At Figure 2MLPCM+IR-HARQ, Turbo-MLCM+XP-HARQ, and Turbo-BICM+XP-HARQ respectively represent the IR-HARQ method based on MLPCM, the XP-HARQ method based on multi-stage Turbo-coded modulation, and the XP-HARQ method based on bit-interleaved Turbo-coded modulation. Figure 2 It shows that the method proposed in the present invention has throughput performance advantages of up to 5 dB, 3.5 dB, and 5 dB respectively compared with the IR-HARQ method based on MLPCM, the XP-HARQ method based on multi-stage Turbo-coded modulation, and the XP-HARQ method based on bit-interleaved Turbo-coded modulation, verifying the effectiveness of the proposed method.

[0088] The specific embodiments described in this article are only illustrative of the spirit of the present invention. Those skilled in the art to which the present invention pertains can make various modifications or supplements to the described specific embodiments or use similar ways to replace them, but will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A cross-packet hybrid automatic repeat request method based on multi-level polar code encoding and modulation, characterized in that First, in the multi-level polar code coded modulation MLPCM transmission, a layer-independent cross-packet hybrid automatic repeat request XP-HARQ transmission mode is adopted, enabling multiple data streams to be independently designed. Then, by utilizing the characteristics of the upper triangular generating matrix of the polar code coding in the coding process, an encoder and a decoder suitable for the XP-HARQ transmission characteristics are designed, thus realizing the joint encoding and decoding of multiple data packets during the retransmission process. By further designing the coding parameters of each data stream, the throughput performance of the system can be maximized; The method includes the following steps: Step 1: The transmitting end confirms the feedback information of the XP-HARQ controller, making 2 m denotes the modulation order, m = 1, 2, 3, 4, …; MLPCM consists of m layers in total, corresponding to m bit data streams, and these data streams all have their own cyclic redundancy check (CRC) codes and respectively correspond to a mapped bit; The receiving end will wait until the codewords of the previous i - 1 layers are correctly decoded before attempting to decode layer i, i = 1, 2, ..., m; The layer that performs the decoding operation feeds back decoding information according to the decoding result. The feedback information includes two types: ACK and NACK. ACK indicates that the decoding of layer i is successful, and NACK indicates that the decoding of layer i fails. The initial feedback information for all layers of the system is ACK; Step 2: The sending end confirms the HARQ loop status of the current m layers according to the feedback information in Step 1. Let K denote the maximum number of transmissions allowed for an XP-HARQ loop in the system, where K = 1, 2,...; Let the number of transmissions k = 1, 2,..., K; Step 3: The sender generates m source data streams to be encoded, and let R i,k denote the code rate of the new information bit mapped to the i-th bit and in the k-th transmission. Let the set denote the value set of R i,k , that is, R i,k ∈R s , where denotes the code rate interval, d r = 1, 2,..., N. The code rate R i,k of each layer is fixed and stored in the caches at the sender and the receiver; Let N denote the frame length, and let the horizontal vectors u i,k and v i,k respectively represent the new information bit data stream and the source bit data stream for mapping the i-th bit during the k-th transmission. The sizes of u i,k and v i,k are NR i,k and N respectively; add an N i,k -bit CRC code to u crc to generate a horizontal vector u i,k of length NR crc ++N i,k . Let the horizontal vector v i,1:k-1 =(v i,1 , v i,2 ,..., v i,k-1 ), where v i,k is In the above formula, A i,k , B i,k , D i,k and C i,k respectively represent the set of new information bit indices, the set of reset information bit indices, the set of information bits to be copied, and the set of frozen bit indices; and respectively represent the sub-vectors formed by the elements with indices A i,k , B i,k , and C i,k in v i,k ; in sets A i,k , B i,k , and C i,k , the intersection of any two is an empty set, and the union of the three is the index set of the entire v i,k , that is, {1, 2,..., N}; represents the sub-vector formed by the elements with index D i,1:k-1 in v i,k ; Step 3: The sending end performs cross-packet polar coding on the m source data streams, w i,1:k = (w i,1 , w i,2 ,..., w i,k ) = v i,1:k [G] 1:kN + (2) In the above formula, the horizontal vector w i,k represents the data stream used for mapping the i-th bit after encoding and during the k-th transmission. 1:kN represents the index set {1, 2,..., kN}, G is the polarization code generation matrix, and [G] 1:kN represents a sub-matrix of size kN formed by the rows and columns with indices 1:kN in G. In the above formula, F2 is the polarization code kernel matrix of the second order, is the Kronecker product, log2(·) represents the logarithmic function with base 2, represents the ceiling function, and the encoder outputs w i,k and v i,1:k ; Step 4: The sending end generates and sends a symbol frame, generates a symbol frame x by modulating the m encoded data streams through set partitioning mapping, and sends x to the receiving end; Step 5: The receiving end receives and caches the received signal. Let h, y, and z denote the channel gain vector, the received symbol frame, and the complex Gaussian white noise vector respectively. The received signal is expressed as y n = h n x n + z n (4) In the above formula, h n , x n , y n and z n respectively represent the n-th elements of vectors h, x, y, and z, where n = 1, 2,..., N. The elements in z are independent of each other and follow a complex Gaussian distribution with a mean of 0 and a variance of σ 2 . Step 7: The receiving end uses the multi-level demodulation method of MLPCM to demodulate and decode each layer i = 1, 2,..., m successively until decoding fails; let denote the received symbol frame in the receiving end buffer that has not been demodulated for bit i, and the number of frames is denoted by T i indicating that layer i is demodulated and decoded one by one until decoding fails; Step 6: Delete the data cached at the receiving end. When the cached data frame meets one of the following conditions, delete the data frame and the corresponding demodulated log-likelihood ratio: 1) The HARQ loop of any bit data stream contained in the data frame reaches the maximum number of transmissions and the decoding fails; 2) All bits contained in the data frame are decoded successfully; The said R i,k , A i,k , B i,k , D i,k and C i,k , which are used for cross-packet encoding at each level, and its optimization method includes the following steps: + Step 1: Channel reliability estimation. Use the Gaussian approximation method to calculate the reliability of the polarized channel after polar coding of length kN based on the average mutual information of the channel in layer i. The calculation result is represented by vector s i,k Denote. For the elements in vector s i,k Arrange them in descending order. The arranged vector is represented by Denote, where S i,k Denote The elements in are the index set of the elements in s i,k ; Step 2: Traverse all the value cases of R i,1 , R i,2 ,..., R i,K , calculate the throughput of the system and output the corresponding coding parameters; R i,1 , R i,2 ,..., R i,K There are a total of (d r + 1) K value cases; Step 3: Output throughput η i when R is maximum i,1 , R i,2 ,..., R i,K and the corresponding coding parameters; The second step includes the following processes: Step 2.1, calculate the total number of target information bits after k transmissions, denoted as Step 2.2, calculate the parameters A when k = 1 i,1 , B i,1 , D i,1 and Ω i,1 , where the set Ω i,k represents the set of the M i,1 most reliable information bit position indices of the polar code of length kN. Let Ω i,1 and A i,1 be the set of the first M i,1 elements in S i,1 . Let B i,1 and D i,1 be empty sets; Step 2.3, calculate the coding parameters Ω, A, B, C, and D in the k-th transmission for k = 2, 3,..., K in sequence; i,k A i,k B i,k C i,k D i,k ; Step 2.4, generate Ω i,k , A i,k , B i,k , C i,k and D i,k , select M i,k of the smallest elements from the elements with index Ψ in s copy , and generate set D i,k using the indices of these elements in s i,k , select M i,k of the largest elements from the elements with index Φ in s copy , and generate set Φ i,k using the indices of these elements in s * , B i,k = Φ * - (k - 1)N, A i,k is the set of elements that belong to Φ - (k - 1)N but do not belong to set B i,k , C i,k is the set of elements that belong to {1, 2,..., N} but do not belong to Φ - (k - 1)N, Ω i,k is the union of the set of elements that belong to set Ω i,k-1 but do not belong to set D i,k and set Φ; Step 2.5, perform simulation calculations on the bit error rate of the polar code of length kN with the information bit set Ω for k = 1, 2,..., K and using CA-SCL decoding, denoted by f i,k ; i,k Represent; Step 2.6, calculate the throughput, The step 2.3 includes the following processes: Generation parameter M copy and sets Φ and Ψ, where Φ represents the set of position indices for generating new information bits and resetting information bits for the k-th transmission during the polarization code encoding process of length kN, Ψ represents the set of position indices of information bits to be copied that are available for selection, and M copy represents the number of reset information bits or information bits to be copied; let Θ represent the set of position indices of the M i,k most reliable information bits of the polarization code of length kN, that is, Θ is the set of the first M i,1 elements in S i,1 First, generate the set of elements that belong to set Θ but not to set Ω i,k-1 , denoted by Δ. Φ is the set of elements that belong to set Δ but have values greater than (k - 1)N, and its size is denoted by |Φ|. Ψ is the set of elements that belong to set Ω i,k-1 but not to set Θ, and its size is denoted by |Ψ|. M copy takes the minimum value of |Φ| and |Ψ|; then calculate the target number of new information bits NR i,k for the k-th transmission and the difference between the number of new information bits |Φ| - M copy that can be accommodated under the current parameters, denoted by M diff , M diff = NR i,k - |Φ| + M copy . If M diff ≠ 0, then update the total number of information bits M i,k under the current parameters to M i,k + M diff , and execute this step again until M diff = 0.

2. The cross-packet hybrid automatic repeat request method based on multi-level polar code encoding modulation according to claim 1, wherein The second step includes the following three cases: 1) The feedback information of all layers is ACK: The XP-HARQ status of all layers is the initial transmission, that is, k = 1; 2) The first i - 1 layers feedback ACK, the i-th layer feedbacks NACK and has been transmitted k - 1 times: The XP-HARQ status of the i-th layer is the k-th transmission, and the XP-HARQ status of the remaining layers is the initial transmission; 3) The first i - 1 layers feedback ACK, the i-th layer feedbacks NACK and has been transmitted K times, and the XP-HARQ status of all layers is the initial transmission.

3. The cross-packet hybrid automatic repeat request method based on multi-level polar code encoding and modulation according to claim 1, characterized in that The seventh step specifically includes the following processes: Step 7.1, layer i pairs demodulates to obtain the corresponding data stream w i,k of the log-likelihood ratio vector, denoted by r i,k , where j = 1, 2,..., T i ; Step 7.3, combine r i,k and the bit log-likelihood ratio vectors of the previous k - 1 times as the input to the decoder, denoted as r i,1:k =(r i,1 , r i,2 ,..., r i,k ), and perform decoding using the CRC-aided serial cancellation list CA-SCL decoding method based on dynamic frozen bits; Step 7.3, according to the decoding CRC check result in step 7.3, if the i-th layer is decoded successfully, feedback ACK; Otherwise, feedback NACK, and the receiving end ends the decoding.

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