A polar code encoding and decoding method and a low-frequency wireless communication system using the same

Abstract

A Polar code encoding and decoding method, the encoding process is: dividing a signal sequence, performing CRC cyclic redundancy encoding; calculating the channel reliability of each polarized channel, selecting the K polarized channels with the highest channel reliability as information bits, and the remaining polarized channels as frozen bits, sequentially placing information bits in the indexes corresponding to the information bits, and placing frozen bits in the indexes corresponding to the frozen bits to obtain a sequence u, multiplying u with a generator matrix of a Polar code to obtain an encoded sequence, and performing 2FSK modulation; the decoding process is: performing 2FSK non-coherent demodulation on the received signal, and decoding according to the obtained log-likelihood ratio (LLR) value. The present application can realize encoding and decoding of Polar codes with any code length based on 2FSK modulation, solve the problems of large attenuation, weak anti-noise performance of a low-frequency wireless communication system, and difficulty of applying Polar codes in the low-frequency wireless communication system, and has high system adaptability and good encoding and decoding effect under low signal-to-noise ratio conditions.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of wireless communication, and particularly relates to a Polar code encoding and decoding method and a low-frequency wireless communication system using the method. BACKGROUND

[0002] In a low-frequency communication system, low-frequency signals can be transmitted across continents due to their super-long wavelength and strong penetration, greatly solving the communication problems in special extreme environments. However, the traditional low-frequency antenna is large in size, expensive in cost, and high in power consumption, which seriously restricts its application environment. In recent years, with the proposal of the "mechanical antenna", the existing system antenna is large in size, complex in equipment, low in radiation efficiency, and large in transmission power and energy consumption, which solves the problems and improves the mobility and flexibility of low-frequency communication applications. However, the attenuation is large in the communication process, and the noise resistance is weak, so how to ensure the reliability of information transmission has become a problem to be solved.

[0003] In order to improve the reliability of the system, various methods need to be used, such as using error correction / detection encoding technology, increasing signal transmission power, etc. Channel coding technology can enhance the ability of data to resist various interference in channel transmission by adding redundant bits after information bits. In channel coding technology, Polar code is the only linear block code that has been proved to achieve the Shannon limit in theory, and has a low-complexity encoding and decoding algorithm. A large number of performance simulation results show that when the encoding block is small, Polar code can outperform Turbo code, low-density parity-check coding and other channel coding technologies when used with cyclic redundancy coding and adaptive successive interference cancellation table decoder. Today, Polar code has been determined as the final solution for 5G short code control channel, greatly improving the reliability of 5G communication system. Polar code can be applied to low-frequency communication system to enhance the anti-noise performance of the system and improve the reliability of information transmission.

[0004] There are some problems in the practical application of Polar code. The channel polarization degree of Polar code is related to the code length, and the signal used in low-frequency wireless communication system is a short code signal. Short code length will lead to insufficient channel polarization, affecting the performance of Polar code. Moreover, the length of Polar code is always fixed at 2 raised to the power of n, which cannot be flexibly adapted to different systems in the actual application process. Therefore, it is a key problem in low-frequency communication to make the code length of Polar code changeable to adapt to different systems and ensure that the code length close to the system requirement can be used as much as possible to make the channel polarization more sufficient under any code length.

[0005] Furthermore, since the existing mechanical antenna modulation mode generally adopts 2FSK modulation, the demodulation mode adopts the traditional non-coherent demodulation, and the non-coherent demodulation directly performs hard decision on the signal after obtaining the demodulation signal. For the Polar code, the application scenario is generally PSK and QAM modulation and demodulation, and the commonly used SC, SCL and CA-SCL decoding methods all need to calculate the log-likelihood ratio of each bit. At present, there is no effective method to calculate the log-likelihood ratio under the condition of 2FSK modulation, and the hard decision obtained by the traditional non-coherent demodulation also affects the decoding performance, so that the error correction code cannot play its due role. These problems show that the traditional Polar code encoding and decoding algorithm is not an ideal method for the low-frequency wireless communication system. SUMMARY

[0006] In order to overcome the above-mentioned defects of the prior art, the purpose of the present application is to provide a Polar code encoding and decoding method and a low-frequency wireless communication system using the method, which is based on 2FSK modulation and can realize Polar code encoding and decoding of any code length, thereby solving the problems of low signal-to-noise ratio of the low-frequency wireless communication system and difficulty of applying Polar code in the low-frequency wireless communication system, and having the characteristics of high system adaptability and good encoding and decoding effect under low signal-to-noise ratio conditions.

[0007] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows:

[0008] A Polar code encoding and decoding method, the encoding process is as follows:

[0009] The signal sequence is segmented and CRC cyclic redundancy encoding is performed; the channel reliability of each polarization channel is calculated, the K polarization channels with the highest channel reliability are selected as information bits, and the remaining polarization channels are frozen bits; the information bits are sequentially placed in the indexes corresponding to the information bits, and the frozen bits are placed in the indexes corresponding to the frozen bits, to obtain a sequence u with a length of N; the sequence u is multiplied by the generator matrix G N of the Polar code to obtain an encoding sequence x.

[0010] After the encoding is completed, the encoding sequence x is subjected to 2FSK modulation.

[0011] The decoding process is as follows: the received signal is subjected to 2FSK non-coherent demodulation, the sampling decision in the non-coherent demodulation is optimized to soft decision, and decoding is performed according to the log-likelihood ratio (LLR) value.

[0012] In one embodiment, the encoding process calculates the information bit length according to the code length N, the code rate R and the length crc-len of the CRC check code of the Polar code, segments the signal sequence according to the length, and generates the generator matrix G N of the Polar code according to the size of N, and the formula is as follows:

[0013]

[0014] wherein N is the minimum power of 2 that is greater than or equal to the information code length E, i.e. denotes the n-th Kronecker product of the matrix , and has the recursive formula: B N is a sorting matrix used to complete the bit reverse rearrangement operation, n = log2N.

[0015] In an embodiment, the encoding process uses the polarization weight method to calculate the channel reliability of each polarization channel, as follows:

[0016]

[0017] PW i denotes the channel reliability of the i-th polarization channel, i k is the k-th bit from low to high in the binary expansion of the index value of the i-th polarization channel, i.e. β is a fixed value; the value at the corresponding index of the frozen bit is 0, and the encoding sequence x = uG N .

[0018] In an embodiment, the log-likelihood ratio (LLR) value is calculated by the following method:

[0019] 1) Calculate the log-likelihood ratio (LLR) of each polarization channel, as follows:

[0020]

[0021] W(y|x) is the probability of receiving y for the 2FSK signal transmission x, W(y|x = 0) is the probability of receiving y at the receiving end when the transmitted bit is 0, and W(y|x = 1) is the probability of receiving y at the receiving end when the transmitted bit is 1;

[0022] 2) The noise signal conforms to a Gaussian distribution, and 2FSK demodulation is double-channel demodulation, with the upper branch corresponding to 1 and the lower branch corresponding to 0. Substitute the demodulated y0, y1 into the following formula:

[0023]

[0024] wherein y0 is the output signal after lower branch demodulation, y1 is the output signal after upper branch demodulation, and x is the amplitude value of the transmitted signal;

[0025] 3) Substitute x = A and take the logarithm of the final result to obtain the log-likelihood ratio (LLR) under 2FSK modulation:

[0026]

[0027] where A is the amplitude of the transmitted signal, and σ is the noise variance in the AWGN channel.

[0028] In one embodiment, the decoding process is CA-SCL decoding according to the LLR values, and the method is as follows:

[0029] SCL decoding is performed on the received sequence to obtain L candidate sequences;

[0030] The L sequences obtained are subjected to corresponding CRC checkers, and the bit sequence that successfully passes the CRC check is selected as the decoding output, and if no path passes the CRC check, the first path in the L paths is taken as the decoder output estimation sequence.

[0031] In one embodiment, after obtaining the encoded sequence x, a puncturing operation is performed on it to delete part of the bits so that its length is shortened to the information code length E, wherein the puncturing position is within the frozen bit range; in the decoding process, the log-likelihood ratio (LLR) value of the deleted part in the obtained sequence is zero-padded, and then decoding is performed according to the LLR value; during decoding, the LLR sequence with a length of E is restored to a sequence with a length of N according to the generated puncturing vector pu, that is, 0 is supplemented at the position where pu is 0, and the value at the position where pu is 1 corresponds to the value of the calculated LLR sequence, so that the length of the LLR sequence is restored to N, and then SCL decoding is performed on the restored sequence with a length of N.

[0032] In one embodiment, the puncturing operation is performed as follows:

[0033] The number of puncturing positions S is calculated, S = N-E;

[0034] A vector p with a length of N*(1-R) is defined, that is, the length of the frozen bits, and the elements are all 1, that is, p = (1...11...1), the first S elements of the vector are set to 0, and the vector becomes p = (0...01...1), and R is the code rate of the Polar code;

[0035] Bit flipping is performed on p to obtain p', and the length of p' is the length of the frozen bits;

[0036] A puncturing vector pu with a length of N is generated, and the elements are all 1, the value at the position corresponding to the frozen bit index in pu is corresponding to the vector p', and the positions corresponding to the information bits in pu are all 1;

[0037] The puncturing operation is performed, and the coded bit sequence x is corresponding to the puncturing vector pu, the corresponding bits are deleted at the position where pu is 0, and the corresponding bits are retained at the position where pu is 1, to obtain a transmission bit sequence with a length of E.

[0038] In one embodiment, the obtained sequence is subjected to SCL decoding, and the method is as follows:

[0039] SC decoding is performed on each bit, the left sub-tree is decoded according to the LLR value, the right sub-tree is decoded according to the decoded information, and the process is repeated; a candidate path with the minimum path metric value PM is reserved while performing the bit-by-bit decoding, and the path metric value PM of each candidate path is calculated; during the recursive decoding, the PM is gradually increased in each step of calculation, and finally L candidate sequences are obtained.

[0040] In one embodiment, the calculation formula of the path metric value PM is as follows:

[0041]

[0042] denotes the jth polarized channel in the N polarized channels, denotes the log-likelihood ratio value of the jth polarized channel;

[0043] During the recursive decoding, the calculation formula of the PM is as follows:

[0044]

[0045] denotes the path metric value after the (i-1)th bit in the lth path is decoded, denotes the path metric value after the ith bit in the lth path is decoded;

[0046] The In the formula, when the decision result of the path is the same as the result indicated by the likelihood ratio, the first formula is used for calculation, that is, the path metric value is unchanged; when the decision result is opposite to the result indicated by the likelihood ratio, the second formula is used for calculation, that is, the path metric value is increased When the decision result is opposite to the result indicated by the likelihood ratio and the bit is a frozen bit, the decoding path is completely wrong, and the path metric value is increased to infinity.

[0047] Another object of the present application is to protect a low-frequency wireless communication system of the Polar code encoding and decoding method, wherein the Polar code encoding and decoding method is applied to the channel encoding and channel decoding processes of the low-frequency wireless communication system.

[0048] Compared with the prior art, the present application has the following beneficial effects:

[0049] 1) The Polar channel reliability estimation method based on polarization weight can calculate the reliability of each polarized channel offline, and the reliability is only related to the index of the polarized channel and is not related to other factors, so that the real-time change in transmission is not required, and the implementation complexity in actual application is reduced.

[0050] 2) The application adopts a method of quasi-uniform puncturing of frozen bit positions to change the code length of the Polar code, and sets the puncturing positions in the frozen bit range, thereby realizing the compatibility of the Polar code with different code length systems under the condition of ensuring that the information bits are not affected.

[0051] 3) The application adopts a new calculation method of log-likelihood ratio based on 2FSK modulation and demodulation, so that the Polar code decoding scheme can be applied to a low-frequency wireless communication system. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 is the implementation flowchart of the method of the application.

[0053] Figure 2 is the binary tree principle diagram of Polar code encoding.

[0054] Figure 3 is the implementation flowchart of 2FSK demodulation in the application.

[0055] Figure 4 is the implementation flowchart of CA-SCL decoding.

[0056] Figure 5 is the SCL decoding flowchart.

[0057] Figure 6 is the SC decoding principle diagram. DETAILED DESCRIPTION

[0058] The embodiments of the application will be described in detail below with reference to the accompanying drawings and examples.

[0059] The Polar code encoding and decoding method proposed by the application includes an encoding part, a modulation and demodulation part, and a decoding part, and uses the characteristics of the Polar code to improve the reliability of information transmission.As shown in the figure, the specific scheme includes the following steps: Figure 1

[0060] Parameter setting and calculation:

[0061] According to the code length E of the system transmission information, the code length N of the Polar code is set, N is the smallest power of 2 value greater than or equal to the information code length E, that is, The code rate R of the Polar code, the length crc-len of the cyclic redundancy check code, and the corresponding generator and checker are set. The reserved path number L of the CA-SCL decoding at the decoding end is set. The generator matrix of the Polar code is generated according to the size of N.

[0062] In an embodiment of the invention, E = 112, N = 128 (the smallest power of 2 greater than or equal to 112 is 128), R = 0.5, and L = 4. Based on the magnitude of N, the generator matrix G of the Polar code is generated. N Its generation method is as follows:

[0063]

[0064] in Represents a matrix The nth Kronecker product has a recursive formula B N It is a sorting matrix used to perform bit reversal operations, n = log2N.

[0065] Setting `crc-len=24` results in a generator named `24A`, whose expression is:

[0066] D 24 +D 23 +D 18 +D 17 +D 14 +D 11 +D 10 +D 7 +D 6 +D 5 +D 4 +D 3 +D+1(2)

[0067] Encoding section:

[0068] Step 1: Calculate the information bit length A based on the Polar code length N, code rate R, and CRC check code length crc-len. In this embodiment, A = 40. Divide the signal sequence according to this length, and perform CRC cyclic redundancy encoding on the divided sequence (2) to obtain 64 bits of information.

[0069] Step 2: Based on the generated information bit index set, frozen bit index set, and generator matrix GN, complete the Polar code encoding.

[0070] Specifically, the reliability of each polarization channel is first calculated. Based on the code length and code rate, an information bit index set and a frozen bit index set are generated. Bits with high reliability are designated as information bits, and bits with low reliability are designated as frozen bits. The K polarization channels with the highest reliability are selected as information bits for Polar code encoding, and the remaining polarization channels are designated as frozen bits. Figure 2 The encoding process is as follows when N=8, and the encoding process of this invention is similar.

[0071] In the embodiment of the present application, the channel reliability of each polarized channel is calculated using the polarization weight method, and the calculation method is as follows:

[0072]

[0073] PW i represents the channel reliability of the i-th polarized channel, i k is the k-th bit from low to high in the binary expansion of the index value of the i-th polarized channel, that is, β is a fixed value, and through a large number of simulation calculation and verification, β = 2 can be obtained as the performance optimization index. 0.25 .

[0074] The PW value obtained by using this method represents the reliability of each polarized channel, and the larger the PW value, the higher the reliability of the polarized channel. After calculating the PW value of each polarized channel, K polarized channels with the largest PW are selected as information bits to transmit information, and the K bits are defined as information bits; the remaining N-K polarized channels are used as frozen bits to transmit and receive fixed bits agreed by both parties, which generally transmit 0, and the N-K bits are defined as frozen bits.

[0075] According to the result from small to large, the last K polarized channels are selected as information bits, and the information bits, i.e. the information to be transmitted, are placed in the index corresponding to the information bits in turn, and the remaining polarized channels are frozen bits, and the frozen bits are placed in the index corresponding to the frozen bits to obtain the original bit sequence u before encoding with a length of N, and the value in the index corresponding to the frozen bit is 0.

[0076] The obtained sequence u is multiplied by the generator matrix G N of the Polar code as follows:

[0077] x = uG N (4)

[0078] The encoded bit sequence, i.e. the encoding sequence x, is obtained, and the Polar code encoding is completed.

[0079] Modulation and demodulation part:

[0080] Step 3: According to the set 2FSK related parameters, the 2FSK modulation is performed on the encoding sequence x.

[0081] In the embodiment of the present application, two different frequency carriers are generated according to formula (5), the frequency f1 corresponds to 1, and the frequency f2 corresponds to 0, and the 2FSK modulation is performed.

[0082]

[0083] Step 4: The received signal is 2FSK non-coherent demodulated as shown in formula (6). Figure 3 ​

[0084] The modulation process, i.e., step 3, can be part of encoding, and the demodulation process, i.e., step 4, can be part of decoding.

[0085] Decoding part:

[0086] Step 5: Optimize the sample decision (hard decision) in the non-coherent demodulation into a soft decision, and decode according to the log-likelihood ratio (LLR) value.

[0087] In an embodiment of the application, the log-likelihood ratio (LLR) of each polar channel is calculated according to formula (6) using the output information:

[0088]

[0089] W(y|x) is the probability of receiving y when the 2FSK signal x is transmitted, which essentially calculates the influence of noise on the signal, W(y|x=0) is the probability of receiving y when the transmitted bit is 0, and W(y|x=1) is the probability of receiving y when the transmitted bit is 1. The noise signal conforms to a Gaussian distribution, and the 2FSK demodulation is a double-channel demodulation, the upper branch corresponds to 1, and the lower branch corresponds to 0. Therefore, substitute the demodulated y0 and y1 (y0 is the signal output after lower branch demodulation, and y1 is the signal output after upper branch demodulation) into formula (7), where x is the amplitude value of the transmitted signal. Regardless of whether the transmitted bit is 0 or 1, the amplitude value of the transmitted signal is A, so x=A is substituted, and the logarithm of the final result is taken to obtain the log-likelihood ratio (LLR) under 2FSK modulation:

[0090]

[0091]

[0092] In the formula, A is the amplitude value of the transmitted signal, and sigma is the noise variance in the AWGN channel.

[0093] The log-likelihood ratio calculation method of the application is applicable to 2FSK modulation and demodulation, so that the decoding scheme of the Polar code can be applied to the 2FSK modulation and demodulation system, and the compatibility problem of the Polar code and the low-frequency wireless communication system is solved.

[0094] In an embodiment of the application, the decoding adopts the CA-SCL decoding scheme, and the decoding flow chart is as shown in Figure 4 The method is as follows:

[0095] 1) SCL decoding is performed on the obtained sequence to obtain L candidate sequences.

[0096] The SCL decoding flow is as shown in Figure 5 SC decoding is performed on each bit, and the decoding principle is as shown in Figure 6As shown, the left subtree is first translated based on the LLR value, and then the right subtree is translated based on the already translated information. After obtaining the values ​​of the left and right child nodes, the two nodes are subjected to the same calculations as the encoding transformation to obtain the estimated value of the root node. It then returns the parent node for use by the root node at that level; its recursive process is the same as the depth-first traversal algorithm for a binary tree. And so on; the calculation methods for the functions f and g in the diagram are:

[0097]

[0098] L1 represents the likelihood ratio for the bits in the left subtree, and L2 represents the likelihood ratio for the bits in the right subtree. This represents the bits translated from the left subtree.

[0099] While performing bit-by-bit decoding, the L candidate paths with the smallest path metrics are retained, and the path metric PM of each candidate path is calculated. The simplified calculation formula is as follows:

[0100]

[0101] This represents the j-th polarization channel out of N polarization channels. This represents the log-likelihood ratio of the j-th polarization channel.

[0102] During the recursive decoding process, PM is incremented step by step in each calculation, as shown in the following formula:

[0103]

[0104] This represents the path metric value after decoding the (i-1)th bit in the l-th path. This represents the path metric value after the i-th bit in the l-th path is decoded.

[0105] exist In the formula, when the decision result of the path is the same as the result indicated by the likelihood ratio, the first formula is used, meaning the path metric remains unchanged (i.e., it can be judged as 0 or 1, and both paths are retained, but the likelihood ratio indicator only has one result: 0 or 1, so the absolute value of the likelihood ratio is not added when the decision value is the same as the likelihood ratio indicator value, but is added at different times); when the decision result is opposite to the result indicated by the likelihood ratio, the second formula is used, meaning the path metric increases. When the decision result is the opposite of the result shown by the likelihood ratio and the bit is a frozen bit, the decoding path is completely wrong, and the path metric increases to infinity.

[0106] Finally, L candidate sequences are obtained, and these L candidate sequences are sorted according to the path metric.

[0107] The obtained L sequences are subjected to corresponding CRC checkers, and the bit sequence successfully passing the CRC check is selected as the decoding output. If none of the L paths passes the CRC check, the first path in the L paths, i.e., the path with the minimum path metric value, is selected as the decoder output estimation sequence.

[0108] In an embodiment of the present application, after obtaining the encoded sequence x, the encoding part performs puncturing operation on x to delete some bits, so that the length of x is shortened to the information code length E, wherein the puncturing positions are within the frozen bit range. Correspondingly, in the decoding part, the log-likelihood ratio (LLR) values of the deleted positions in the obtained sequence are subjected to zero padding, and then the decoding is performed according to the LLR values.

[0109] The puncturing operation method in the embodiment is as follows:

[0110] 1) Calculate the number of puncturing positions S, S=N-E. In the embodiment, S=16.

[0111] 2) Define a puncturing vector p with a length of N*(1-R), i.e., the length of the frozen bits, and all the elements are 1, i.e., p=(1...11...1). Set the first S elements of the vector p to 0, so that p=(0...01...1), and R is the code rate of the Polar code. In the embodiment, the length of the vector p is 64.

[0112] 3) Perform bit flipping operation on p to obtain p', and the length of p' is the length of the frozen bits.

[0113] 4) Generate a puncturing vector pu with a length of N, and all the elements are 1. Set the value corresponding to the frozen bit index in pu to correspond to the vector p', and the positions corresponding to the information bits in pu are all 1. In the embodiment, the length of the puncturing vector pu is 128.

[0114] 5) Perform puncturing operation on the encoded bit sequence x, and delete the corresponding bits at the positions where pu is 0, and keep the corresponding bits at the positions where pu is 1, to obtain a transmission bit sequence with a length of E. In the embodiment, E=112 bits.

[0115] At this time, when decoding, the calculated LLR sequence with a length of E needs to be restored to a sequence with a length of N according to the generated puncturing vector pu, and then SCL decoding is performed. That is, 0 is padded at the positions where pu is 0 (the positions deleted by the transmission end), and the values at the positions where pu is 1 (the positions kept by the transmission end) correspond to the values of the calculated LLR sequence, so that the length of the LLR sequence is restored to N.

[0116] Finally, the redundant part of CRC is removed, and the information sequence obtained at the receiving end is spliced in order to complete the information transmission process.

[0117] The application adopts the polarization weight method to estimate the reliability of the polarization channel when Polar code is encoded, and solves the compatibility problem between the Polar code and different code length systems and the problem of high algorithm complexity when estimating the reliability of the polarization channel by using the method of quasi-uniform puncturing of the frozen bit position.

[0118] The Polar code encoding and decoding method of the application is suitable for a low-frequency wireless communication system, and the main implementation process of the low-frequency wireless communication system is to generate source information, source encoding, encryption, channel encoding, digital modulation, channel, digital demodulation, channel decoding, decryption, source decoding, and obtain sink information. The encoding and decoding method of the Polar code is mainly applied to the channel encoding and channel decoding process of the low-frequency wireless communication system. The Polar code utilizes the channel polarization principle, so that the channel capacities of the polarization channels present a polarization trend, the capacities of a part of the polarization channels tend to 1, close to noiseless channels, and the reliability is extremely high, and the capacities of the remaining polarization channels tend to 0, close to all-noise channels, and the reliability is extremely low. The information bits are transmitted on the channels with extremely high reliability, and the redundant information agreed by both parties is transmitted on the channels with extremely low reliability, so that the original information transmitted by the sending end can be recovered by relying on some prior information when there is part of error at the receiving end.

[0119] The existing low-frequency wireless communication system does not use the Polar code as an encoding and decoding scheme, so that the ability to process noise in the signal is limited. The application introduces the Polar code into the low-frequency wireless communication system, adds redundant information to the signal during signal transmission, utilizes the channel polarization theory of the Polar code and the assistance of the CRC code, and improves the reliability of information transmission of the system under the condition of low signal-to-noise ratio.

Claims

1. A Polar code encoding and decoding method, characterized in that, The encoding process is as follows: The signal sequence is segmented and subjected to CRC cyclic redundancy coding. The channel reliability of each polarization channel is calculated using the polarization weight method, as follows: Indicates the first i Channel reliability of individual polarization channels For the first i The binary expansion of the index values ​​of the polarization channels, from low to high, is the first... k Position, that is , The value is fixed, and the value at the corresponding index of the frozen bit is 0; Choose the channel with the highest reliability. K One polarization channel is used as the information bit, and the remaining polarization channels are used as the freeze bits. The information bits are sequentially placed at their corresponding indices, and the freeze bits are placed at their corresponding indices, resulting in a length of... N sequence u , convert the sequence u With the generator matrix of Polar codes G N Multiply to obtain the encoded sequence x Among them, based on the code length of the Polar code N Bitrate R And the length of the CRC checksum, crc-len, is used to calculate the information bit length, and the signal sequence is segmented according to this length; and based on N The size of the generator matrix for Polar codes. G N The formula is as follows: in, N It is the smallest power of 2 value that is greater than or equal to the information code length E, i.e. , Represents a matrix of n The Kronecker product has a recursive formula: , It is a sorting matrix used to perform bit reversal operations. ; After encoding is completed, the encoded sequence is processed. x Perform 2FSK modulation; The decoding process is as follows: The received signal undergoes 2FSK incoherent demodulation; the sampling decision in the incoherent demodulation is optimized into a soft decision; and decoding is performed based on the log-likelihood ratio (LLR) value. The LLR value is calculated using the following method: 1) Calculate the log-likelihood ratio for each polarization channel. LLR The formula is as follows: Send 2FSK signal x Received y The probability, Let y be the probability that the receiver receives y when the transmitted bit is 0. Let y be the probability that the receiver receives y when the transmitted bit is 1. 2) The noise signal conforms to a Gaussian distribution. 2FSK demodulation uses dual-channel demodulation, with the upper branch corresponding to 1 and the lower branch corresponding to 0. The demodulated signal... Substitute into the following formula: in, This is the signal output after demodulation by the lower branch. This is the signal output after demodulation by the upper branch. x The amplitude value of the transmitted signal; 3) Substitute x = A And by taking the logarithm of the final result, the log-likelihood ratio (LLR) under 2FSK modulation is obtained: In the formula, A The amplitude of the transmitted signal. Let V be the noise variance in the AWGN channel.

2. The Polar code encoding and decoding method according to claim 1, characterized in that, The decoding process involves CA-SCL decoding based on the LLR value, as follows: The received sequence is SCL decoded to obtain L candidate sequences; The obtained L sequences are passed through the corresponding CRC checkers. The bit sequence that successfully passes the CRC check is selected as the decoded output. If no path passes the CRC check, the first path in the L paths is used as the decoder output estimated sequence.

3. The Polar code encoding and decoding method according to claim 2, characterized in that, The encoding process, in order to obtain the encoded sequence x Then, a puncturing operation is performed to delete some bits, shortening its length to the information code length E, wherein the puncturing positions are within the frozen bit range; in the decoding process, the log-likelihood ratio (LLR) value of the deleted portion in the obtained sequence is padded with zeros, and then decoding is performed based on the LLR value; during decoding, the generated puncturing vector is first used as the basis for decoding. pu The calculated LLR sequence of length E is restored to a sequence of length E. N The sequence, that is, in pu Fill the positions with 0s. pu The value at the position that is 1 corresponds to the value of the calculated LLR sequence, thus restoring the length of the LLR sequence to its original value. N Then, the length of the recovered value is... N The sequence is then SCL decoded.

4. The Polar code encoding and decoding method according to claim 3, characterized in that, The method for drilling is as follows: Calculate the number of holes S , S = N - E ; Define a vector p , length is N *(1- R ), which is the length of the frozen bits, where all elements are 1, i.e. Before the vector S Set each element to 0, and it becomes , R The code rate of the Polar code; right p Perform a bit flip operation to obtain p ', p The length of ' is the length of the frozen bits; Generate length is N Punch vector pu All elements are 1, pu The value and vector at the position corresponding to the frozen bit index p Correspondingly, pu All bits corresponding to the information bits in the middle are 1; Perform a puncturing operation to convert the encoded bit sequence x With the punch vector pu Correspondingly, in pu Delete the corresponding bit at the position where it is 0. pu The corresponding bit at the position of 1 is reserved to obtain a transmission bit sequence of length E.

5. The Polar code encoding and decoding method according to claim 2, 3, or 4, characterized in that, The method for performing SCL decoding on the obtained sequence is as follows: For each bit, perform SC decoding. First, decode the left subtree based on the LLR value, then decode the right subtree based on the already decoded information, and so on. While decoding bit by bit, retain the L candidate paths with the smallest path metric values ​​and calculate the path metric value PM for each candidate path. During the recursive decoding process, PM is gradually increased in each step of the calculation, and finally L candidate sequences are obtained.

6. The Polar code encoding and decoding method according to claim 5, characterized in that, The formula for calculating the path metric PM is as follows: express N The first polarization channel j One polarization channel, Indicates the first j The log-likelihood ratio of each polarization channel; During the recursive decoding process, the PM is calculated using the following formula: Indicates the first l The first path The path metric value after each bit is translated. Indicates the first l The first path i The path metric value after each bit is translated; The In the formula, when the decision result for the path is the same as the result shown by the likelihood ratio, the first formula is used, meaning the path metric remains unchanged; when the decision result is opposite to the result shown by the likelihood ratio, the second formula is used, meaning the path metric increases. When the decision result is opposite to the result shown by the likelihood ratio and the bit is a frozen bit, the decoding path is completely wrong and the path metric increases to infinity.

7. A low-frequency wireless communication system utilizing the Polar code encoding and decoding method described in claim 1.

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