A polar code encoding method based on key bit secondary encoding

Abstract

The application belongs to the technical field of channel coding, and particularly relates to a polar code encoding method based on key bit secondary encoding; the method comprises the following steps: setting a transmission frame number m and a single frame code length N according to to-be-encoded data, and calculating a number K of information bits of a new polar code; performing ascending order sorting on a channel according to channel reliability, taking the first K bits as information bit positions, and taking the rest as frozen bit positions; performing polar code encoding on the to-be-encoded data at an encoding end to obtain m frame encoding sequences; dividing the information bit positions into high-reliability information bit positions and low-reliability information bit positions according to the reliability; performing polar code encoding on the low-reliability information bit position information of the m frames to obtain an m+1 frame encoding sequence; the encoding end sends the m frame encoding sequences and the m+1 frame encoding sequence to a receiving end together; and the receiving end decodes the encoding sequences to obtain a decoding result; the application effectively reduces the complexity of polar code decoding and can achieve the effect of reducing the bit error rate through an error correction mechanism.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of channel coding, and particularly relates to a polar code encoding method based on secondary encoding of key bits. BACKGROUND

[0002] Since the polar code was proposed, it has been continuously researched and rapidly developed. Through rigorous mathematical derivation, it is proved that the polar code can approach the Shannon limit under the binary erasure channel (BEC), which provides sufficient theoretical basis for the development of the polar code. The polar code is also determined as the channel coding scheme of the control channel in the 5G enhanced mobile broadband (eMBB) due to its excellent performance. With the development of science and technology, people have put forward the requirements of lower time delay and lower complexity for polar code decoding, which indicates the direction for the future development of the polar code.

[0003] The cascaded encoding mode related to the polar code is the focus of scholars. For the serial cascade, most of them aim to reduce the bit error rate, for example, the existing polar product code encoding and decoding algorithm utilizes the structure of the traditional product code to perform polar encoding and then perform column polar encoding, and such parallel cascade mode can effectively reduce the decoding time delay.

[0004] The longer the code length is, the lower the bit error rate is when the polar code is decoded, but due to the characteristics of the serial decoding, the long code length cannot meet the requirements of the time delay of the 6G system, and the decoding usually adopts the serial cancellation type decoding mode. And because the scheduling mode of the decoding is sequential, there is a problem of high decoding time delay. If the high-parallel decoding method is adopted, it cannot be widely used due to its high complexity and low bit error rate. Therefore, how to reduce the decoding complexity without losing the decoding performance has been a problem that scholars have been studying. In the past, most of the researches on the polar code are on the decoding end, and there is no effective encoding scheme that can balance the complexity and the bit error rate at the encoding end. Although the parallel cascade code represented by the polar product code effectively reduces the decoding delay, it can only have good decoding performance under the condition of long code and high signal-to-noise ratio, and the decoding complexity is not effectively reduced.

[0005] In summary, there is an urgent need for a method that can effectively reduce the complexity and the bit error rate of decoding. SUMMARY

[0006] In view of the deficiencies in the prior art, the application provides a polar code encoding method based on secondary encoding of key bits, which comprises the following steps:

[0007] S1: setting a transmission frame number m and a single frame code length N according to to-be-encoded data, and calculating the number of information bits K of a new polar code according to the transmission frame number and the number of information bits of a standard polar code;

[0008] S2: sorting the channels in ascending order according to the channel reliability, taking the first K bits as information bits, and the rest as frozen bits;

[0009] S3: encoding the to-be-encoded data according to the single-frame code length, the number of information bits, and the number of transmission frames, to obtain m frames of encoded sequences;

[0010] S4: dividing the information bits into high-reliability information bits and low-reliability information bits according to the reliability;

[0011] S5: polar code encoding the low-reliability information bits of the m frames to obtain an (m+1)th frame of encoded sequences;

[0012] S6: the encoding end sends the first m frames of encoded sequences and the (m+1)th frame of encoded sequences to the receiving end together;

[0013] S7: the receiving end decodes the encoded sequences to obtain a decoding result.

[0014] Preferably, the formula for calculating the number of information bits K of the new polar code is:

[0015]

[0016] wherein K' represents the number of information bits of the standard polar code, and [·] represents the integer function.

[0017] Preferably, all the encoded sequences contain CRC check bits at the end.

[0018] Preferably, the code lengths of the encoded sequences of each frame are the same.

[0019] Preferably, the low-reliability information bits are key bits, the length of the single-frame key bits is not fixed, and the total length of the m frames of key bits and the length of the single-frame CRC are not higher than the total code length of the check frames.

[0020] Preferably, the decoding process of the encoded sequences includes: taking the (m+1)th frame of encoded sequences as a check frame; decoding the first m frames of encoded sequences, if the decoding results of the m frames of encoded sequences all pass the CRC check, it is considered as decoding success, and the correct decoding result is obtained; otherwise, the check frame is used for error correction.

[0021] Further, the process of error correction using the check frame includes:

[0022] The check frame is decoded by taking the check frame key bit corresponding to the successfully decoded coded sequence as a dynamic frozen bit, otherwise, taking the check frame key bit as an information bit; if the decoding result passes the CRC check, the key bit is extracted from the check frame and backtracked to the corresponding bit in the original error coded sequence, and the error coded sequence is decoded again by taking the key bit as a dynamic frozen bit; if the decoding result passes the CRC check, the decoding is successful, otherwise, the decoding fails and retransmission is requested.

[0023] The application has the advantages that the polar code encoding method based on key bit secondary encoding re-encodes the key bits of the first m blocks of code as dynamic frozen bits and re-transmits the m+1 block as a check block to check the key information bits in the first m blocks and correct errors; the dynamic frozen bit technology is used to increase the code rate and effectively reduce the complexity of polar code decoding when the channel condition is good and the signal-to-noise ratio is high. In addition, when an error occurs, the application can reduce the bit error rate through the error correction mechanism. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 The polar code encoding method based on key bit secondary encoding in the application is a flowchart.

[0025] Figure 2 The structural diagram when N=1024, K=563, and m=10 in the application is shown.

[0026] Figure 3 The bit error rate simulation comparison diagram of the application and the traditional polar code under different decoding modes when N=1024, K=563, and m=10 is shown.

[0027] Figure 4 The complexity simulation comparison diagram of the application and the traditional polar code when N=1024, K=563, and m=10 is shown.

[0028] Figure 5 The bit error rate simulation diagram of the application under different code lengths when m=10 and SCL, L=4 decoding is shown. DETAILED DESCRIPTION

[0029] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0030] The application provides a polar code encoding method based on key bit secondary encoding, as shown in Figure 1As shown, the method includes the following:

[0031] S1: Set the number of transmission frames m and the single frame code length N according to the data to be encoded, and calculate the number of information bits K of the new polar code according to the number of transmission frames and the number of information bits of the standard polar code.

[0032] For example, such as Figure 2 As shown, if the polar code length N is 1024 and the number of transmission frames m is 10, the last 8 bits of the CRC code length are reserved before encoding and included in the information bits. The standard polar code is represented as P(1024, 512). This invention recalculates the number of information bits K of the new polar code based on the number of information bits of the standard polar code, and evenly distributes the total number of information bits of the first m+1 frames to the first m frames, as shown below:

[0033]

[0034] Where K′ represents the number of information bits in the standard polar code, and [∈] represents the floor function.

[0035] The total number of information bits in the traditional polar code P(1024,512) is 512×11=5632, which is divided equally among the first 10 frames to form a single frame P(1024,563) polar code, so as to ensure that the total number of information bits remains unchanged; its total number of information bits is 5630, and the total code rate R is 1 / 2.

[0036] S2: Sort the channels in ascending order according to their reliability, take the first K bits as information bits, and the rest as frozen bits.

[0037] Calculate the Bavarian parameters of the channel. A smaller Bavarian parameter indicates a more reliable channel. Sort the channels in ascending order of reliability, taking the first K bits as information bits and the rest as frozen bits. Using a traditional Gaussian construction as an example, N = (N0, N1...N...). 460 ) represents frozen bits, N = (N 461 N 462 ...N 1023 () represents information bits.

[0038] S3: The encoding end performs polar code encoding on the data to be encoded according to the single frame code length, the number of information bits and the number of transmission frames to obtain an m-frame encoding sequence; wherein, the code length of each frame encoding sequence is the same.

[0039] S4: Divide information bits into high-reliability information bits and low-reliability information bits according to their reliability.

[0040] Each block (frame) of information bits is further divided into two parts based on reliability: a set of high-reliability information bits A. i This can be represented as N = (N 561 N 562 ...N1023 ), a set of low-reliability information bits i , which can be expressed as N = (N 461 , N 462 , …, N 560 ) here; CRC check bits are added at the end of the CRC check code of each encoding sequence, so the total number of bits of the m-frame B set should not exceed the total code length N of a single block, i.e. B1+B2+…+B m +CRC < N, where subscript i represents that the set belongs to the polar code of the i-th frame transmission, i≤m.

[0041] The low-reliability information bits are key bits. Preferably, the length of the key bits of a single frame is not fixed, and the total length of the key bits of m frames plus the length of the CRC of a single frame is not higher than the total code length of the check frame; preferably, the number of key bits of all frames is the same; when m = 10, N = 1024, and CRC = 8, then (N-CRC) / m key bits per frame, the calculation result is rounded down to 101, for convenience of calculation, the first 100 key bits with lower reliability can be taken.

[0042] S5: Polar code encoding is performed on the low-reliability information bit information of the m frames to obtain an encoding sequence of the (m+1)-th frame.

[0043] The unreliable information bits of the first m frames are transmitted again after being combined with the new polar code information bits of the (m+1)-th frame; the new polar code is represented as P(N, K check ); where K check = B1+B2+…+B m +CRC, i.e. P(1024, 1008), where the length of CRC is 8.

[0044] S6: The encoding end sends the encoding sequences of the first m frames and the encoding sequence of the (m+1)-th frame to the receiving end together.

[0045] S7: The receiving end decodes the encoding sequence to obtain a decoding result.

[0046] The decoding process of the encoding sequence includes:

[0047] The encoding sequence of the (m+1)-th frame is used as a check frame; the first m encoding sequences are decoded, and if the decoding results of the m encoding sequences all pass the CRC check, it is considered that the decoding is successful, and the correct decoding result is obtained; otherwise, the check frame is used for error correction.

[0048] The process of error correction using the check frame includes:

[0049] The check frame key bit corresponding to the successfully decoded coded sequence is regarded as a dynamic frozen bit, the check frame key bit corresponding to the failed decoding coded sequence is regarded as an information bit, and the check frame is decoded; the failed decoding coded sequence is regarded as an error coded sequence;

[0050] If the decoding result passes the CRC check, the key bit (a low reliability information bit set B i ) is extracted from the check frame, the corresponding bit in the original error coded sequence i is traced back, and the key bit is regarded as a dynamic frozen bit, and the error coded sequence is decoded again; if the decoding result passes the CRC check, the decoding is successful, otherwise, the decoding fails, and retransmission is requested.

[0051] The application is evaluated as follows:

[0052] As shown in Figure 3 , it can be seen that the error rate of the application and the traditional polar code both decrease obviously at high signal-to-noise ratio, and the turning point of the signal-to-noise ratio gradually decreases with the improvement of the decoding accuracy of the decoding method. This is because under the condition of high signal-to-noise ratio and high decoding success rate, most code blocks can be directly decoded successfully, so the code rate in the check frame is often low, so the check frame decoding success rate is high, and the check frame decoding success rate is high. After tracing back to the original code block, the code rate can be reduced, and the error rate can be reduced.

[0053] As shown in Figure 4 , the code rate is increased by the first decoding, but in most cases at high signal-to-noise ratio, the decoding is successful, and the error correction mechanism does not need to be started, and the same information needs to be decoded m+1 times, but the application only needs m times. Therefore, under the premise of ensuring the success rate, the complexity of the application is reduced.

[0054] As shown in Figure 5 , like the traditional polar code, the error rate of the application gradually decreases with the increase of the code length, and the decoding effect is better.

[0055] As described above, taking N=1024, K=512, i.e. P(1024,512), decoding using SCL, L=4, and signal-to-noise ratio of 2dB as an example, the error frame rate is about 5‰ in such an environment, i.e. only 5 frames are wrong in 1000 frames, so only a small part of the key bits that have not been successfully decoded need to be re-decoded. In the check frame, the known result is regarded as a dynamic frozen bit, so in the check frame, the code rate is often low, the check frame decoding success rate is high, and the check frame decoding success rate is high. After tracing back to the original code block, the code rate can be reduced, and the error rate can be reduced. Similarly, since the code rate is increased by the first decoding, but in most cases the decoding is successful, and the error correction mechanism does not need to be started, and the same information needs to be decoded m+1 times, but now only m times. Therefore, under the premise of ensuring the success rate, the complexity is reduced.

[0056] The above examples further illustrate the objects, technical solutions and advantages of the present application. It should be understood that the above examples are merely preferred embodiments of the present application and are not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made to the present application within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A polar code encoding method based on key bit secondary encoding, characterized in that, include: S1: Set the number of transmission frames m and the single frame code length N according to the data to be encoded. Calculate the number of information bits K of the new polar code based on the number of transmission frames and the number of information bits in the standard polar code. The formula for calculating the number of information bits K of the new polar code is: Among them, K ′ This indicates the number of information bits in the standard polar code, and [·] represents the floor function; S2: Sort the channels in ascending order according to their reliability, take the first K bits as information bits, and the rest as frozen bits; S3: The encoding end performs polar code encoding on the data to be encoded according to the single frame code length, the number of information bits and the number of transmission frames to obtain an m-frame encoded sequence; S4: Divide the information bits into high-reliability information bits and low-reliability information bits according to their reliability; S5: Polar code encoding is performed on the low reliability information bits of frame m to obtain the encoding sequence of frame m+1. S6: The encoding end sends the encoded sequence of the first m frames and the encoded sequence of the (m+1)th frame together to the receiving end; S7: The receiver decodes the encoded sequence to obtain the decoding result.

2. The polar code encoding method based on key bit secondary encoding according to claim 1, characterized in that, All encoded sequences contain a CRC check bit at the end.

3. The polar code encoding method based on key bit secondary encoding according to claim 1, characterized in that, The code length of each frame's encoded sequence is the same.

4. The polar code encoding method based on key bit secondary encoding according to claim 1, characterized in that, The low-reliability information bits are critical bits. The length of the critical bits in a single frame is not fixed. The sum of the total length of the critical bits in m frames and the CRC length in a single frame is not higher than the total code length of the check frame.

5. The polar code encoding method based on key bit secondary encoding according to claim 1, characterized in that, The process of decoding the encoded sequence includes: using the (m+1)th frame encoded sequence as a check frame; The first m frames of the encoded sequence are decoded. If the decoding results of all m frames of the encoded sequence pass the CRC check, the decoding is considered successful and the correct decoding result is obtained; otherwise, a check frame is used for error correction.

6. The polar code encoding method based on key bit secondary encoding according to claim 5, characterized in that, The process of error correction using check frames includes: The key bits of the verification frame corresponding to the successfully decoded encoded sequence are treated as dynamically frozen bits; otherwise, they are treated as information bits, and the verification frame is decoded. If the decoding result passes the CRC check, the key bits are extracted from the verification frame and traced back to the corresponding bits in the original erroneous encoded sequence. These key bits are then treated as dynamically frozen bits, and the erroneous encoded sequence is decoded again. If the decoding result passes the CRC check, the decoding is successful; otherwise, the decoding fails, and a retransmission is requested.

Images