A Polar Code Encoding and Decoding Method and System Based on Early Stopping Criterion-Based Key Bit Secondary Encoding

Abstract

This invention discloses a polar code encoding and decoding method and system based on the early stopping criterion for key bit secondary encoding. The method is as follows: the encoding end calculates the number of information bits K per frame based on the total number of frames and the bit rate. dynamic Take the first K dynamic One reliable channel is used as the information bit, which is allocated to important data, and the rest are frozen bits to retain other data, resulting in n frame encoded strings. The information bits of each frame are divided into decoding key bits and regular bits, resulting in the (n+1)th frame of the check frame. The first n frame encoded strings and the (n+1)th frame of the check frame are sent to the decoder. The decoder performs decoding, calculates the dynamic threshold ρ of the current signal-to-noise ratio, calculates the partial path metric γ of the information bits, and retains the maximum metric as the bias term. Then, it calculates the relative partial path metric ε of the information bits. If ε is less than ρ, decoding fails, and a retransmission of the encoded frame is requested; otherwise, decoding continues. If all frame decoding results pass the CRC check, decoding is successful. If any frame fails, the flag bit of that frame is activated, and the corresponding frame is backtracked for re-decoding.

Description

Technical Field

[0001] This invention belongs to the field of channel coding and decoding communication technology, and particularly relates to a polar code coding and decoding method and system based on the early stopping criterion for secondary encoding of key bits. Background Technology

[0002] Polar codes are a type of low-complexity channel coding proposed by Turkish professor E. Arikan in 2008. Professor Arikan rigorously derived mathematical results demonstrating that polar codes can achieve the channel capacity of binary discrete memoryless symmetric channels (B-DMC), a proof that laid a solid foundation for polar code research. Due to their simple composition and low complexity, they are used as part of the control channel coding for New Enhanced Mobile Broadband (EMBB) and Ultra-Reliable Low-Latency Communication (URLLC) in fifth-generation mobile communication technology (5G).

[0003] Polar code coding algorithms have attracted widespread attention from scholars, especially in the area of ​​concatenated coding. Currently, the main goal of most concatenated algorithms is often to improve channel capacity and reduce the bit error rate. For example, the polar product code algorithm, by concatenating with product codes, first performs polar coding and then product coding, which can further reduce the system's bit error rate.

[0004] Because polar codes are decoded serially, they suffer from significant decoding delays. Using a highly parallel belief propagation (BP) decoding algorithm results in high decoding complexity. Therefore, minimizing decoding complexity while maintaining a low bit error rate is a major challenge for the decoding end. Correspondingly, there is a lack of an encoding method that can effectively balance complexity and bit error rate at the encoding end. While polar product code algorithms effectively improve decoding performance, the concatenation of two encoding methods increases decoding complexity. Chinese patent application CN202310283865.2, published on June 23, 2023, discloses an invention patent application entitled "A Polar Code Encoding Method Based on Key Bit Secondary Encoding." While this method has its advantages, it suffers from a long decoding cycle in determining whether the current decoding is incorrect and whether the encoded frame needs to be retransmitted. If an effective judgment can be made, theoretically, bits destined to fail in decoding can be determined in advance using an early stopping criterion, thereby enabling earlier retransmission of the encoded frame and further reducing decoding complexity and latency. Therefore, there is an urgent need in this field for a decoding technology that can determine whether decoding has failed using an early stopping criterion. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a polar code encoding and decoding method and system based on the early stopping criterion for secondary encoding of key bits.

[0006] The specific technical solution of the present invention is as follows:

[0007] A polar code encoding and decoding method based on the early stopping criterion and secondary encoding of key bits includes a transmitting end (i.e., the encoding end) and a receiving end (i.e., the decoding end), and its specific steps are as follows:

[0008] S1. The encoding end determines the number of transmission frames n and the code length N of a single frame based on the transmitted data, and calculates the number of information bits K of each frame based on the total number of frames n+1 and the code rate R. dynamic ;

[0009] S2. The channel reliability of each channel is obtained using the polarization weight construction method, and the top K values ​​are taken. dynamic One reliable channel is used as the information bit, and the remaining channels are used as the frozen bit;

[0010] S3. Divide the data into important data and unimportant data. Allocate the important data to the information bit position and leave the unimportant data in the frozen bit position. Perform polar coding on the polar code of the first n frames to obtain the n frame coded string.

[0011] S4. Based on whether the information bits are important to the decoding, divide the information bits of each of the first n frames into decoding key bits and decoding regular bits.

[0012] S5. Encode all the key bits set of decoding in the first n frames using polar codes to obtain the (n+1)th frame of the check frame.

[0013] S6. The encoding end sends the encoded strings of the first n frames and the check frame of the (n+1)th frame to the decoding end.

[0014] S7. The decoder decodes the received encoded data and calculates the dynamic threshold ρ at the current signal-to-noise ratio.

[0015] S8. Calculate the partial path metric value γ corresponding to each information bit, and retain the largest metric value as the bias term.

[0016] S9. During the decoding process, calculate the relative partial path metric ε. If the metric corresponding to the current information bit is less than the dynamic threshold, the decoding fails and a retransmission of the encoded frame is requested directly. Otherwise, continue decoding the next information bit.

[0017] S10. If all frame decoding results pass the CRC check, the decoding is successful and the decoding ends; if any frame fails the CRC check, the flag bit of that frame is activated, and the decoding is reverted to the corresponding frame.

[0018] This invention reduces the number of invalid traversals and lowers the overall complexity of the decoding algorithm.

[0019] Preferably, in step S1, the number of information bits K for each frame is recalculated. dynamicThe formula is as follows:

[0020]

[0021] Among them, K inf This indicates the number of information bits in the initial polar code. This represents the floor function.

[0022] Preferably, the bit length of each frame is consistent, and the bit rate is consistent in the first n frames.

[0023] As a preferred option, a CRC check bit is added to each frame.

[0024] As a preferred approach, information bits with low reliability (i.e. reliability below the threshold) are used as key bits for decoding, and the remaining information bits are used as regular bits for decoding. The sum of all key bits in n frames plus the CRC of a single frame must not exceed the total code length of a single frame.

[0025] As a preferred option, the formula for calculating the dynamic threshold ρ under the current signal-to-noise ratio is as follows:

[0026] ρ = ln(FER / 1000)

[0027] FER represents the frame error rate.

[0028] In the In the context of a set of independent and uniformly distributed random variables, which correspond to the system's variables, Chernoff bounds can be applied. Inequality to obtain the correct bit u i The conclusion is that the probability of the relative partial path metric value being lower than the dynamic threshold ρ decreases exponentially as ρ decreases. Setting the performance loss at 0.1 × FER, Monte Carlo simulations were conducted to obtain the linear relationship between FER and ρ for different polarization code lengths N (256, 512, 1024), code rates R (1 / 3, 1 / 2, 2 / 3), and decoder list lengths L (1, 2, 4) in the low signal-to-noise ratio range, i.e., FER = 0.1 to 0.001. Figure 3 As shown. To ensure that the performance loss of most codewords is within an acceptable range, this invention derives the empirical formula above by analyzing the relevant data: ρ = ln(FER / 1000). Given the signal-to-noise ratio (SNR), polar code length N, code rate R, and decoder list length L, ρ can be directly calculated.

[0029] As a preferred embodiment, in step S8, the formula for calculating the partial path metric of the current decoded bit i is as follows:

[0030]

[0031] in, Represents the path metric. The transmission probability of the transmitted signal. The bias term B is taken as the metric for the largest portion of the path. i .

[0032] Preferably, in step S9, the formula for calculating the relative partial path metric of the current decoded bit i is as follows:

[0033]

[0034] in, B represents a partial path metric. i This indicates the bias term.

[0035] Preferably, during the decoding process, the relative partial path metric value corresponding to each decoded bit is calculated. If the current If the value is less than the set threshold ρ, the subsequent decoding is immediately terminated, and the encoded frame containing the current bit is directly retransmitted. Otherwise, the current decoding process continues.

[0036] Preferably, in step S10, if the decoding results of all n encoded frames pass the CRC check, the decoding is considered successful, the decoding ends, and no further decoding and verification frames are performed. If any frame decoding fails, the flag bit of that frame is activated. i =1, and decode the verification frame for error detection.

[0037] As a preferred method, the decoding process for the verification frame is as follows: For f i The frame corresponding to =0 retains its result, for f i For frames with a value of 1, the key bit is treated as an information bit and the check frame is decoded using traditional polar code. If the result fails the CRC check, the decoding fails and ends. Conversely, the key bit is used to perform a backtracking operation on the check frame, which is treated as a frozen bit, and the information frame is decoded again. If the CRC check passes, the error correction is successful; otherwise, the error correction fails.

[0038] This invention also discloses a polar code encoding and decoding system based on the early stopping criterion for secondary encoding of key bits, used to execute the above method. The system includes an encoding end and a decoding end, wherein:

[0039] Encoding end: Determine the number of transmission frames n and the code length N of a single frame based on the transmitted data, and calculate the number of information bits K of each frame based on the total number of frames n+1 and the code rate R. dynamic ;

[0040] The channel reliability of each channel is obtained using the Gaussian construction method, and the top K values ​​are selected. dynamic One reliable channel is used as the information bit, and the remaining channels are used as the frozen bit;

[0041] The data is divided into important data and unimportant data. Important data is allocated to information bits, and unimportant data is kept in frozen bits. Polar coding is performed on the polar codes of the first n frames to obtain n frame encoded strings.

[0042] Based on the importance of information bits to decoding, the information bits of each frame in the first n frames are divided into decoding key bits and decoding regular bits.

[0043] Encode all the key bits set of decoding in the first n frames using polar codes to obtain the (n+1)th frame of the check frame.

[0044] Send the first n frame encoded strings and the (n+1)th check frame to the decoder;

[0045] Decoding end: Decodes the received encoded data and calculates the dynamic threshold ρ at the current signal-to-noise ratio;

[0046] Calculate the partial path metric γ corresponding to each information bit, and retain the largest metric as the bias term;

[0047] During the decoding process, the relative partial path metric ε is calculated. If the metric ε corresponding to the current information bit is less than the dynamic threshold ρ, the decoding fails and a retransmission of the encoded frame is requested directly. Otherwise, the decoding of the next information bit continues.

[0048] If all frame decoding results pass the CRC check, the decoding is successful and the decoding ends; if any frame fails the CRC check, the flag bit of that frame is activated, and the decoding process is restarted from the corresponding frame.

[0049] Compared with the prior art, the advantages of the present invention are:

[0050] This invention relates to a polar code encoding and decoding method and system based on the early stopping criterion of secondary encoding of key bits. During the decoding process at the decoding end, by calculating the dynamic threshold under the current signal-to-noise ratio and the relative partial path metric value corresponding to each decoded bit, if the relative partial path metric value of the current decoded bit is less than the dynamic threshold under the current signal-to-noise ratio, a decoding error is identified, and the information frame is directly retransmitted. This achieves the requirement of early stopping and enables the decoding result to be judged before CRC check, further reducing the complexity and latency of polar code decoding. Attached Figure Description

[0051] Figure 1 This is a flowchart of a polar code encoding and decoding method based on the early stopping criterion for secondary encoding of key bits, according to a preferred embodiment of the present invention.

[0052] Figure 2 In the preferred embodiment of the present invention, the coding portion is in N=1024, K dynamic Structure diagram when m=563 and m=10.

[0053] Figure 3 This is a preferred embodiment of the invention. For different N, R, L, and SNR values, in P... loss The dynamic threshold ρ is displayed at ≤0.1×FER; each star point corresponds to a different quadruple combination (N,R,L,SNR).

[0054] Figure 4 In the preferred embodiment of the present invention, N=1024, K dynamic Simulation comparison of bit error rate with traditional polar code under different decoding methods when m=563 and m=10.

[0055] Figure 5 In the preferred embodiment of the present invention, N=1024, K dynamic The simulation comparison of the complexity of the polar code with m=563 and m=10 is shown in the figure.

[0056] Figure 6 This is a block diagram of a polar code encoding and decoding system based on the early stopping criterion for secondary encoding of key bits, according to a preferred embodiment of the present invention. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] like Figure 1 As shown, this embodiment proposes a polar code encoding and decoding method based on the early stopping criterion and secondary coding of key bits. Taking a polar code with a length of 1024 and a code rate of 0.5, and 10 frames transmitted as an example, this embodiment provides the following specific implementation steps:

[0059] Step 1: At the encoding end, based on the transmitted data, determine the number of transmission frames (10) and the single frame code length (1024), resulting in a total of 11 frames. Recalculate the number of information bits per frame based on the total number of frames and the bitrate.

[0060]

[0061] Among them, K inf This indicates the number of information bits in the initial polar code. This represents the floor function.

[0062] All information bits in the 11 frames of polar codes with a code length of 1024 and a code rate of 0.5 are compressed into 10 frames, with each frame containing 563 polar codes. At this point, each of the first 10 frames becomes a polar code with a code length of 1024 and a code rate of 0.55, but the total code rate of the 10 frames is 0.5.

[0063] Step 2: Obtain the channel reliability of each channel using the polarization weight construction method, and take the top K... dynamic One reliable channel is used as the information bits, and the rest are used as frozen bits.

[0064] The specific process of polar weight construction method: Assuming a polar code of code length N, the index of each bit sub-channel is 0≤j≤N-1. Expanding j in binary yields the expression {j... n-1 j n-2 , ..., j0), where n = log2N, j n-1 It is the highest bit, polarization channel. The formula for calculating the polarization weight PW is as follows:

[0065]

[0066] Where β = 2 1 / 4 After obtaining all N polarization channels The PW values ​​are then sorted from largest to smallest. Bits listed earlier in the order correspond to more reliable channels, and the channel with the earlier bits is selected for information transmission. The following demonstration uses a polar code with a code length of N = 8 as an example:

[0067] The sub-channel numbers are (W1, W2, W3, W4, W5, W6, W7, W8), and the corresponding sub-channel bit indices are (0, 1, 2, 3, 4, 5, 6, 7). Each sub-channel bit index is expanded into binary to obtain (000, 001, 010, 011, 100, 101, 110, 111). Finally, the binary expansion results are substituted into the PW calculation formula to obtain the polarization weight of each sub-channel (0.000, 1.000, 1.189, 2.189, 1.414, 2.414, 2.603, 3.603). After sorting the PW values ​​in descending order, the channel reliability from high to low is (W8, W7, W6, W4, W5, W3, W2, W1).

[0068] Specifically, in this embodiment, the sub-channels are sorted in ascending order according to their polarization weight, and the first 563 sub-channels are selected, i.e. (W 128 W 190 , ..., W 1022 W 1023 ) represents the information bits; the remaining 461 sub-channels, namely (W1, W2, ..., W... 1008 W1024 ) represents the frozen bits. Where W i This represents the i-th sub-channel.

[0069] Step 3: Allocate important data to information bits and leave unimportant data in frozen bits. Perform polar coding on the first 10 frames of polar codes to obtain 10 frame encoded strings.

[0070] Assume the encoded sequence of the i-th frame is u i Then the encoded sequence x i =u i ·G 10 Among them, G 10 It is a 10th-order Kronecker product.

[0071] Step 4: Based on the importance of the information bits to the decoding, divide the information bits of each of the first n frames into key decoding bits and regular decoding bits.

[0072] The information bits in the first 10 frames of the encoded string are further divided into decoding key bits and decoding regular bits based on the magnitude of the polarization weight. The number of decoding key bits is 100, and the specific sub-channel number is (W). 915 W 916 , ..., W 1022 W 1023 The regular number of bits is 563-100=463, and the specific sub-channel number is (W 128 W 190 , ..., W 913 W 914 ).

[0073] Encode the key bits of each of the first 10 frames and add them to the check frame, then add a 16-bit CRC code at the end. The requirement is that the sum of the total length of the key bits of the 10 frames plus the 16-bit CRC is less than the total code length and less than 1024 bits. Therefore, on average, each frame can only receive [a certain amount of code]. Number of key bits.

[0074] Step 5: Encode all the key bits set of decoding in the first n frames using polar codes to obtain the (n+1)th frame of the check frame.

[0075] Encode the key bits of the decoding in each of the first 10 frames and add them to the check frame. Then add a 16-bit CRC code at the end to form a check frame with a code length of 1024, an information bit count of 1016, and a frozen bit count of 8.

[0076] Step 6: The encoded strings of the first n frames and the check frame of the (n+1)th frame are sent from the encoder to the decoder.

[0077] The first 10 frames and the 11th frame are transmitted together to the decoding end through an additive white Gaussian noise (AWGN) channel.

[0078] Step 7: The decoder decodes the received encoded data and calculates the dynamic threshold ρ at the given signal-to-noise ratio.

[0079] Assuming a current signal-to-noise ratio of 1.5dB, N = 1024, and R = 0.5, the FER performance of a conventional polar code decoder with a serial cancellation list SCL-4 (list size 4) at 1.5dB is approximately 5 × 10⁻⁶. -2 Then the dynamic threshold ρ = ln(5 × 10) -2 ( / 1000)≈-9.90.

[0080] Step 8: Calculate the partial path metric γ corresponding to each information bit, and retain the largest metric as the bias term.

[0081] The first 10 frames of encoded strings are decoded. In this embodiment, only the decoding of 8 bits of information in a single frame is demonstrated. If the signal received by the decoder is: From the formula The channel log-likelihood ratio (LLR) value was obtained as follows:

[0082]

[0083] According to the formula in, This represents the LLR value corresponding to the j-th decoded bit in the total code length N. The calculated channel path metric (PM) value is as follows:

[0084]

[0085] Finally, substitute into the formula in, Represents the path metric. To determine the transmission probability of the transmitted signal, the partial path metric value for each decoded bit is obtained. as follows:

[0086] (0.04, 1.57, 6.18, 9.42, 12.73, 12.73, 12.73, 12.73)

[0087] Take the path metric value with the largest number of decoded bits as the bias term B. i Then B i =12.73.

[0088] Step 9: During the decoding process, calculate the relative partial path metric ε. If the metric corresponding to the current information bit is less than the dynamic threshold, the decoding is considered to have failed, and a retransmission of the encoded frame is requested directly. Otherwise, continue decoding the next information bit.

[0089] According to the formula The relative partial path metric for the current decoded bit i is calculated as follows:

[0090]

[0091] If the relative path metric of the first and second information bits is less than the set dynamic threshold ρ, the current bit decoding is considered to have failed, and the encoded frame is retransmitted directly.

[0092] Step 10: If all frame decoding results pass the CRC check, the decoding is considered successful and the decoding ends. If any frame fails, the flag bit corresponding to that frame in the decoding frame is activated, and the decoding check frame is used for error correction.

[0093] If decoding fails, the flag bit of that frame in the check frame will be activated. i =1, for f i The frame corresponding to =0 retains its result, for f i For frames with a value of 1, the key bit is treated as an information bit and the check frame is decoded using traditional polar code. If the result fails the CRC check, the decoding fails and ends. Conversely, the key bit is used to perform a backtracking operation on the check frame, which is treated as a frozen bit, and the information frame is decoded again. If the CRC check passes, the error correction is successful; otherwise, the error correction fails, and a request is made to retransmit the encoded frame.

[0094] The following is in conjunction with the appendix Figure 4 , 5 This embodiment demonstrates the superiority of the polar code encoding and decoding method based on the early stopping criterion for key secondary coding.

[0095] Figure 4 A preferred embodiment of the present invention provides a polar code decoding method based on the early stopping criterion for key secondary coding in N=1024, K dynamic The simulation comparison of bit error rate between the proposed method and traditional polar codes under different decoding methods when m=563 and m=10 is shown. The curves with triangles and rhombuses on the solid lines represent the decoding method proposed in this invention. Figure 4 Therefore, with the same decoding list length L, the method of the present invention has almost no loss in decoding performance compared with the key bit secondary encoding method using traditional SCL decoding. Figure 5 This is a comparison graph of complexity. The curves with triangles and diamonds on the solid lines represent the decoding method proposed in this invention. It can be seen that under medium to low signal-to-noise ratios and with the same decoding list length L, the decoding complexity of the method proposed in this invention is significantly reduced compared to the traditional SCL decoding method. The complexity is reduced by about 9.3% at 1.5dB.

[0096] like Figure 6As shown, this embodiment discloses a polar code encoding and decoding system based on the early stopping criterion for secondary encoding of key bits, used to execute the above method. The system includes an encoding end and a decoding end, wherein:

[0097] Encoding end: Determine the number of transmission frames n and the code length N of a single frame based on the transmitted data, and calculate the number of information bits K of each frame based on the total number of frames n+1 and the code rate R. dynamic ;

[0098] The channel reliability of each channel is obtained using the polarization weight construction method, taking the top K values. dynamic One reliable channel is used as the information bit, and the remaining channels are used as the frozen bit;

[0099] The data is divided into important data and unimportant data. Important data is allocated to information bits, and unimportant data is kept in frozen bits. Polar coding is performed on the polar codes of the first n frames to obtain n frame encoded strings.

[0100] Based on the importance of information bits to decoding, the information bits of each frame in the first n frames are divided into decoding key bits and decoding regular bits.

[0101] Encode all the key bits set of decoding in the first n frames using polar codes to obtain the (n+1)th frame of the check frame.

[0102] Send the first n frame encoded strings and the (n+1)th check frame to the decoder;

[0103] Decoding end: Decodes the received encoded data and calculates the dynamic threshold ρ at the current signal-to-noise ratio;

[0104] Calculate the partial path metric γ corresponding to each information bit, and retain the largest metric as the bias term;

[0105] During the decoding process, the relative partial path metric ε is calculated. If the metric ε corresponding to the current information bit is less than the dynamic threshold ρ, the decoding fails and a retransmission of the encoded frame is requested directly. Otherwise, the decoding of the next information bit continues.

[0106] If all frame decoding results pass the CRC check, the decoding is successful and the decoding ends; if any frame fails the CRC check, the flag bit of that frame is activated, and the decoding process is restarted from the corresponding frame.

[0107] Other aspects of this embodiment can be found in the above method embodiments.

[0108] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A polar code encoding and decoding method based on the early stopping criterion of secondary encoding of key bits, characterized in that, Includes the following steps: S1. The encoding end determines the number of transmission frames n and the code length N of a single frame based on the transmitted data, and calculates the number of information bits K of each frame based on the total number of frames n+1 and the code rate R. dynamic ; S2. The channel reliability of each channel is obtained using the polarization weight construction method, and the top K values ​​are taken. dynamic One reliable channel is used as the information bit, and the remaining channels are used as the frozen bit; S3. Divide the data into important data and unimportant data. Allocate the important data to the information bits and keep the unimportant data in the frozen bits. Perform polar coding on the polar codes of the first n frames to obtain the n-frame encoded string. S4. Based on the importance of information bits to decoding, divide the information bits of each frame in the first n frames into decoding key bits and decoding regular bits. In this step, information bits with reliability below the threshold are used as decoding key bits, and the remaining information bits are used as decoding regular bits. The sum of all key bits in n frames plus the CRC check bits of a single frame does not exceed the total code length of a single frame. S5. Encode all the key bits set of decoding in the first n frames using polar codes to obtain the (n+1)th frame of the check frame. S6. The encoding end sends the encoded strings of the first n frames and the check frame of the (n+1)th frame to the decoding end. S7. The decoding end decodes the received encoded data and calculates the dynamic threshold ρ at the current signal-to-noise ratio. The formula for calculating the dynamic threshold ρ at the current signal-to-noise ratio is as follows: ρ=ln(FER / 1000) Where FER represents the frame error rate; S8. Calculate the partial path metric value corresponding to each information bit. The largest metric value is retained as the bias term; in this step, the formula for calculating the partial path metric value of the current decoded bit i is as follows: in, Represents the path metric. The transmission probability of the transmitted signal; the bias term B is taken as the metric of the largest portion of the path. i ; S9. During the decoding process, calculate the relative partial path metric value. If the metric value corresponding to the current information bit is less than the dynamic threshold ρ, the decoding fails and a retransmission of the encoded frame is requested directly. Otherwise, continue decoding the next information bit. S10. If all frame decoding results pass the CRC check, the decoding is successful and the decoding ends; if any frame fails the CRC check, the flag bit of that frame is activated, and the decoding is reverted to the corresponding frame.

2. The polar code encoding and decoding method based on the early stopping criterion and secondary encoding of key bits according to claim 1, characterized in that, In step S1, the number of information bits K for each frame is recalculated. dynamic The formula is as follows: Among them, K inf This indicates the number of information bits in the initial polar code. This represents the floor function.

3. The polar code encoding and decoding method based on the early stopping criterion and secondary encoding of key bits according to claim 1, characterized in that, In step S1, the bit length is consistent in each frame, and the bit rate is consistent in the first n frames.

4. The polar code encoding and decoding method based on the early stopping criterion and secondary encoding of key bits according to claim 1, characterized in that, In steps S3 and S5, CRC check bits are added to each frame.

5. The polar code encoding and decoding method based on the early stopping criterion and secondary encoding of key bits according to claim 1, characterized in that, In step S9, the formula for calculating the relative partial path metric of the current decoded bit i is as follows: in, B represents a partial path metric. i Indicates the bias term; During the decoding process, the relative partial path metric value corresponding to each decoded bit is calculated. If the current If the value is less than the set threshold ρ, the subsequent decoding is immediately terminated and the encoded frame containing the current bit is directly retransmitted; otherwise, the current decoding process continues.

6. The polar code encoding and decoding method based on the early stopping criterion of secondary encoding of key bits according to any one of claims 1-5, characterized in that, In step S10, if the decoding results of all n encoded frames pass the CRC check, the decoding is considered successful, the decoding ends, and no further decoding and verification frames are required. If any frame decoding CRC check fails, the flag bit of that frame is activated. i =1, and perform error detection on the decoded verification frame.

7. The polar code encoding and decoding method based on the early stopping criterion and secondary encoding of key bits according to claim 6, characterized in that, The decoding process for the check frame is as follows: For f i The frame corresponding to =0 retains its result, for f i For frames with a value of 1, the key bits are treated as information bits and the check frame is decoded using traditional polar codes. If the result fails the CRC check, the decoding fails and ends. Conversely, the key bits are used to perform a backtracking operation on the check frame as frozen bits to decode the information frame again. If the CRC check passes, the error correction is successful; otherwise, the error correction fails and the decoding ends.

8. A polar code encoding and decoding system based on the early stopping criterion for secondary encoding of key bits, used to perform the method as described in any one of claims 1-7, characterized in that, The system includes an encoder and a decoder, wherein: Encoding end: Determine the number of transmission frames n and the code length N of a single frame based on the transmitted data, and calculate the number of information bits K of each frame based on the total number of frames n+1 and the code rate R. dynamic ; The channel reliability of each channel is obtained using the polarization weight construction method, taking the top K values. dynamic One reliable channel is used as the information bit, and the remaining channels are used as the frozen bit; The data is divided into important data and unimportant data. Important data is allocated to information bits, and unimportant data is kept in frozen bits. Polar coding is performed on the polar codes of the first n frames to obtain n frame encoded strings. Based on the importance of information bits to decoding, the information bits of each frame in the first n frames are divided into decoding key bits and decoding regular bits. Encode all the key bits set of decoding in the first n frames using polar codes to obtain the (n+1)th frame of the check frame. Send the first n frame encoded strings and the (n+1)th check frame to the decoder; Decoding end: Decodes the received encoded data and calculates the dynamic threshold ρ at the current signal-to-noise ratio; Calculate the partial path metric value corresponding to each information bit. The largest metric value is retained as the bias term; During the decoding process, the relative path metric is calculated. If the metric corresponding to the current information bit is less than the dynamic threshold ρ, the decoding fails and a retransmission of the encoded frame is requested directly. Otherwise, the decoding of the next information bit continues. If all frame decoding results pass the CRC check, the decoding is successful and the decoding ends; if any frame fails the CRC check, the flag bit of that frame is activated, and the decoding process is restarted from the corresponding frame.

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