Dual sequence hybrid based secure polar code dynamic encoding method

Abstract

The application provides a dynamic encoding method of a secure polar code based on double-sequence mixing, which comprises the following steps: determining the encoding length N, a shared key k and an agreed number by both parties; encrypting the shared key k by using an encryption algorithm to obtain two pseudo-random sequences by a sending end and a receiving end, and determining a mixed random sequence r according to the agreed number and the two pseudo-random sequences; constructing a bit scrambler and a generation matrix G according to the encoding length N by the sending end, and sequentially inputting a to-be-sent information m and the mixed random sequence r into the bit scrambler, the generation matrix G and a BPSK modulator to obtain a sending code word A; after the sending code word A is transmitted through a wireless channel, a signal B is received by the receiving end, and the signal B and the mixed random sequence r are input into a decoder to obtain original information. The application adopts the stream key technology to mix and encrypt to generate the random sequence, and realizes the changeable code length at the encoding level; and the secret encoding mode is used to realize the channel encoding and decoding which can meet the security requirements.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of communication security technology, in particular to a secure polar code dynamic encoding method based on double sequence mixing, which is applied to a lightweight distributed device platform with high security requirements, and ensures that information has the characteristics of secure transmission while being encoded and decoded in the channel. BACKGROUND

[0002] In the traditional distributed communication scheme, secure communication is often achieved by relying on the separation of the communication layer and the encryption layer. The security of this method mainly depends on the difficulty of breaking the encryption layer. For the implementation of secure communication in a distributed platform, on the one hand, the cost of software and hardware needs to be considered, and on the other hand, it is necessary to prevent the enemy from implementing targeted eavesdropping and large-scale calculation on the encryption layer. For a distributed platform with low cost and reliable security requirements, a secure channel coding scheme is adopted. The encryption for security and the encoding and decoding for reliable transmission can be implemented in the same layer, and the simultaneous transmission of information and random keys is achieved by using the encoding characteristics of polar codes, which greatly helps to confuse the eavesdropper. The mixed stream key further increases the randomness of the stream key and realizes dynamic coding with variable code length. SUMMARY

[0003] In view of the deficiencies in the above background art, the present application proposes a secure polar code dynamic encoding method based on double sequence mixing, which solves the limitation that the security can only rely on the difficulty of breaking the security layer when the encryption and communication are separated in the traditional secure scheme, and realizes channel encoding and decoding that can meet the security requirements through secure coding.

[0004] The technical solution of the present application is as follows:

[0005] A secure polar code dynamic encoding method based on double sequence mixing, the steps of which are as follows:

[0006] The sending end and the legitimate receiving end jointly determine the encoding length N, the shared key k and the agreed number i;

[0007] The sending end uses the rc4 encryption algorithm to encrypt the shared key k to obtain a pseudo-random sequence k A , and the legitimate receiving end uses the A5-1 encryption algorithm to encrypt the shared key k to generate a pseudo-random sequence k B ; and determines a mixed random sequence r according to the agreed number i, the pseudo-random sequence k A and the pseudo-random sequence k B

[0008] The sending end constructs a bit scrambler according to the encoding length N, and inputs the to-be-sent information m and the mixed random sequence r into the bit scrambler to generate a scrambled sequence m';

[0009] ​The sending end determines a generation matrix G according to the encoding length N, inputs the confusion sequence m' into the generation matrix G to obtain a to-be-sent code word, and then performs BPSK modulation on the to-be-sent code word to obtain a sending code word A;

[0010] The sending end sends the sending code word A, and after transmission through a wireless channel, the legal receiving end and the illegal receiving end both receive a signal B;

[0011] The legal receiving end inputs the signal B and the mixed random sequence r into a polar code decoder to decode to obtain the original information;

[0012] The illegal receiving end inputs the signal B and the random sequence r' into the polar code decoder to decode to obtain the error information.

[0013] Preferably, the mixed random sequence r is determined in the following manner: the number i selects the i-th bit of the respective random sequence, and there are 2 2 combination manners, and the combination manners are defined as follows:

[0014] When the combination number is 00, the mixed random sequence r = k A +k B +k0;

[0015] When the combination number is 01, the mixed random sequence r = k B ;

[0016] When the combination number is 10, the mixed random sequence r = k A ;

[0017] When the combination number is 11, the mixed random sequence r = k B +k A +k0; wherein k0 is an all-0 sequence.

[0018] Preferably, the generation method of the confusion sequence m' is as follows:

[0019] The mixed random sequence r is transmitted as an input to the bit confusion device as a sequence filled in as a frozen bit;

[0020] The sending end determines a frozen bit mode in the bit confusion device according to the encoding length N and the code rate R;

[0021] In the frozen bit mode, “1” corresponds to an information bit, and the original information is filled in, and “0” corresponds to a frozen bit, and the mixed random sequence is filled in to obtain the confusion sequence m'.

[0022] Preferably, the determination method of the generation matrix G is as follows:

[0023]

[0024] wherein G N represents a polar code encoding matrix, Representation matrix The nth Kronecker product; B N For a sorted matrix, its recursive definition is: I2 = B2, which is a second-order identity matrix; R N To separate odd and even elements, it can be represented as: (u1, u2, u3, ..., u n )·R N =(u1,u3,......u n-1 ,u2,u4......,u n ), matrix B N This involves setting the j-th element of the output sequence to the i'-th element of the original sequence, and converting the original sequence i'∈{1,…,N} into its binary representation i'-1→(b n ,…,b1)→(b1,...,b n →j-1.

[0025] Preferably, the BPSK modulation is f bpsk The transmitted codeword A is f. bpsk (m'*G).

[0026] Preferably, the legitimate receiver inputs signal B and the mixed random sequence r into the polar code decoder, and the method for decoding to obtain the original information is as follows:

[0027] Before decoding begins, the legitimate receiver transmits the mixed random sequence r, signal B, and the frozen bit pattern from the bit mixer to the polar code decoder.

[0028] Step 1: Initialization

[0029] The initialization list contains an empty path, meaning there is only one initial path;

[0030] Initialize the decoding tree by dividing the signal B into different paths, with the root node designated as level 0 and each of the remaining levels representing one bit to be decoded; each set of edges from the root node to a leaf node represents a possible decoding result.

[0031] Step 2: Bit-by-bit decoding

[0032] For each decoding tree node, a hard decision formula is used based on the frozen bit information on the path: Update the node values; where, This indicates the result of the previous bit decoding. This indicates the result of the local decoding. Indicates the bit to be decoded. This represents the received bit string, where count represents the position of that bit in the pseudo-random sequence r, and A f Indicates the freeze bit mode. This represents the posterior probability of the channel to be decoded. This indicates that the bit to be decoded is 0 and all preceding bits have been correctly decoded. This indicates that the bit to be decoded is 1 and all previous bits have been correctly decoded, and l represents the l-th path;

[0033] Based on the updated node values, according to the formula: Calculate the corresponding metric; where δ(x) = 1 / 2(1-sign(x)),

[0034] For each path, based on the metric, the most likely bit value is selected as the decision, and the nodes on the path are updated according to that bit value.

[0035] Step 3: Path Expansion and Sort

[0036] For each path, based on its metric, two sub-paths are extended from its parent path, one assuming the current bit is 0 and the other assuming the current bit is 1;

[0037] Sort all generated sub-paths in ascending order based on the metric value, and select the first L paths, where L is the list size set in the SCL algorithm; if the total number of paths does not reach L, all paths are retained after sorting.

[0038] Step 4: Path pruning

[0039] After each stage, based on the expanded path list, select the top L paths to keep and prune the paths with poor metrics; that is, keep the L paths with the smallest path metrics and prune the rest of the paths.

[0040] Step 5: Iterative Decoding

[0041] Repeat steps 2 to 4 until the decoding performance requirements of the polar code are met or the predetermined number of iterations is reached;

[0042] Step 6: Output the decoding result

[0043] After all layers have completed the calculation iterations, the shortest path is selected from the metric table to provide the decoding, and the final decoding is error-free with the transmitted information.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] 1) This invention, based on polar code channel splitting, transmits random sequences generated by the stream key at positions where fixed bits were originally transmitted. Specifically, information bits are still transmitted at positions with reliable channel capacity, while mixed random sequences are transmitted at positions with poor channel capacity. This achieves secure transmission while maintaining the reliability of the original polar code. Furthermore, the design of the random sequence employs two stream keys to further increase the difficulty of decryption. Without the key between the sender and receiver, an eavesdropper cannot generate the correct random sequence. Moreover, the generation of the random sequence is also related to the current bit combination of both parties. By having each party use their current bit combination, four possible key combinations can be generated. The mixing of random sequences can further obfuscate the frozen bits in the original encoding result by changing the code length. This prior knowledge, which the eavesdropper lacks, makes the eavesdropper's decoding rate almost zero, making it impossible to recover the correct information.

[0046] 2) Both communicating parties can share a 32-bit raw key and generate two stream keys. By selecting and mixing the stream keys, four different random sequences can be generated, occupying 128 bits and 484 bits respectively. When a legitimate user uses SCL for decoding, the block error rate can be around 7%, while the block error rate of an illegitimate user using the random trial method is 100%.

[0047] 3) It solves the bit vacancy caused by the frozen bits in polar codes, and uses the characteristic of frozen bits in polar codes to transmit random keys, thus meeting the requirements of secure communication while ensuring the code rate remains unchanged.

[0048] 4) It solves the threat of eavesdropping that the original encoding scheme may be subject to due to its fixed encoding method. It adopts stream key technology to generate random sequences through hybrid encryption and achieves variable code length at the encoding level. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0051] 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.

[0052] like Figure 1 As shown, this embodiment of the invention provides a dynamic coding method for secure polar codes based on dual-sequence hybridization, including Alice as the transmitter, Bob as the legitimate receiver, and Eve as the illegitimate receiver. In practical design, the channel capacity of N channels after channel splitting needs to be considered. In a typical BAWGN channel, a Gaussian approximation method is used to estimate the reliability of the channel. The specific implementation steps are as follows:

[0053] The sender and the legitimate receiver jointly determine the encoding length N, the shared key k (0 / 1 bit stream k, length K), and the agreed number i. Based on the same shared key and agreed number i, the sender and the legitimate receiver each use different stream key techniques to generate pseudo-random sequences, and select the corresponding new hybrid random sequence by combining the agreed number.

[0054] The sending end uses the rc4 encryption algorithm to encrypt the shared key k to obtain a pseudo-random sequence k. A The legitimate receiver B uses the A5-1 encryption algorithm to encrypt the shared key k to generate a pseudo-random sequence k. B And based on the agreed number i and the pseudo-random sequence k A and pseudo-random sequence k B Determine the mixed random sequence r.

[0055] The agreed number i is selected from the i-th position of each random sequence, and there are a total of 2 2 There are several combination methods, defined as follows (k0 is a 128-bit sequence of all zeros):

[0056] (0，0) r=k A +k B +k0]]> 384 bit (0，1) r=k B ]] 128 bit (1，0) r=k A ]] 128 bit (1，1) r=k B +k A +k0]]> 384 bit 384 bit

[0057] The transmitting end constructs a bit obfuscator based on the coding length N, and inputs the information to be transmitted m and the mixed random sequence r into the bit obfuscator to generate an obfuscated sequence m'. The bit obfuscator is the process of sorting the capacity after channel splitting. The code rate R means that the first N*R bits with a channel capacity of 1 or close to 1 are selected for information filling, and the last N*R bits are used as frozen bits, finally obtaining m'.

[0058] The specific method for generating the obfuscated sequence m' is as follows:

[0059] A mixed random sequence r is fed as input to a bit obfuscator as the sequence to be filled with frozen bits;

[0060] The sending end determines the freeze bit mode in the bit obfuscator based on the encoding length N and the code rate R;

[0061] In the frozen bit mode, "1" corresponds to the information bit, which is filled with the original information, and "0" corresponds to the frozen bit, which is filled with the mixed random sequence, resulting in the confused sequence m'.

[0062] The sending end determines the generator matrix G based on the encoding length N. N The confused sequence m' is input into the generator matrix G to obtain the codeword to be transmitted. Then, the codeword to be transmitted is modulated by BPSK to obtain the codeword to be transmitted A.

[0063] Generating matrix G N The method for determining it is as follows:

[0064]

[0065] in Representation matrix The nth Kronecker product; B N For a sorted matrix, its recursive definition is: I2 = B2, which is a second-order identity matrix; R N To separate odd and even elements, it can be represented as: (u1, u2, u3, ..., u n )·R N =(u1,u3,......u n-1 ,u2,u4......,u n ), matrix B N This involves setting the j-th element of the output sequence to the i'-th element of the original sequence, and converting the original sequence i'∈{1,…,N} into its binary representation i'-1→(b n ,…,b1)→(b1,…,b n →j-1.

[0066] Define BPSK modulation as f bpsk The transmitted codeword A is f. bpsk (m'*G N ).

[0067] The sending end sends out codeword A, which is transmitted through the wireless channel. Both the legitimate and illegitimate receiving ends receive signal B.

[0068] The legitimate receiver inputs signal B and the mixed random sequence r into the polar code decoder to decode the original information. In this embodiment, the SCL decoding algorithm is adopted. The concept of path metric is added to the original SC decoding continuous elimination principle. The path metric measures the state transition probability of different paths. The higher the state transition probability, the smaller the path metric obtained on that path. After all paths are calculated, the one with the smallest metric value is selected as the decoding result.

[0069] Before decoding begins, the legitimate receiver transmits the mixed random sequence r, signal B, and the frozen bit pattern from the bit obfuscator to the polar code decoder.

[0070] The specific decoding steps are as follows:

[0071] Step 1: Initialization

[0072] An initialization list containing an empty path, meaning there is only one initial path.

[0073] Initialize the decoding tree by dividing the entire codeword B into different paths. Let the root node be level 0, and each subsequent level represent a single bit to be decoded. Each set of edges from the root node to a leaf node represents a possible decoding result.

[0074] Step 2: Bit-by-bit decoding

[0075] For each decoding tree node, a hard decision formula is used based on the frozen bit information on the path: Update the node values. Specifically, This indicates the result of the previous bit decoding. This indicates the result of the local decoding. Indicates the bit to be decoded. This represents the received bit string, where count represents the position of that bit in the pseudo-random sequence r, and A f This indicates the freeze bit mode. This represents the posterior probability of the channel to be decoded. This indicates that the bit to be decoded is 0 and all preceding bits have been correctly decoded. This indicates that the bit to be decoded is 1 and all previous bits have been correctly decoded, and l represents the l-th path.

[0076] Based on the updated node values, according to the formula: Calculate the corresponding metric value.

[0077] For each path, based on the metric, the most likely bit value is selected as the decision, and the nodes on the path are updated according to that bit value.

[0078] Step 3: Path Expansion and Sort

[0079] For each path, based on its metric, two sub-paths are extended from its parent path (i.e., the path of the previous stage), one assuming the current bit is 0 and the other assuming the current bit is 1.

[0080] Sort all generated sub-paths in ascending order based on the metric value, and select the top L paths, where L is the list size set in the SCL algorithm (in this embodiment, the list width is L = 16). If the total number of paths is less than L, all paths are retained after sorting.

[0081] Step 4: Path pruning

[0082] After each stage, based on the expanded path list, select the top L paths to retain and prune the paths with poor metrics. That is, keep the L paths with the lowest metrics and prune the rest.

[0083] Step 5: Iterative Decoding

[0084] Repeat steps 2 through 4 until the decoding performance requirements of the polar code are met or the predetermined number of iterations is reached.

[0085] Step 6: Output the decoding result

[0086] After all layers have completed the calculation iterations, the shortest path is selected from the metric table to provide the decoding, and the final decoding is error-free with the transmitted information.

[0087] The unauthorized receiver inputs signal B and a random sequence r' into the polar code decoder, resulting in incorrect information. The eavesdropper, lacking the correct freeze-bit pattern and random sequence, is unable to decode the original information.

[0088] Complexity: When using the SCL decoding algorithm, the decoding complexity is O(L·N·log2 N), where L represents the width of the storage path in the decoder and N represents the code length.

[0089] Reliability Analysis: Since the polarization of polar codes only fully splits when the code length approaches infinity, the SC decoding algorithm suffers from bit errors when used with finite code lengths. The SCL decoding algorithm, based on the original SC decoding, considers path measurement and checks whether previous decoding steps contain missing codes. When L≥2 m m is the number of information bits, which is equivalent to maximum likelihood decoding, but requires a huge amount of extra space. In practice, L = 16 or 8 is often used to reach the upper limit of this decoding, controlling the block error rate to around 5%. Of course, adding CRC check can greatly reduce the block error rate.

[0090] Security Analysis: For the eavesdropping channel W E, The prerequisite for the eavesdropping end to decode is to have the correct channel splitting. In this method, there are two length encodings: 512 bits with a code rate of 0.25 and 256 bits with a code rate of 0.5. Guessing the channel splitting without knowing the channel conditions has The order of magnitude of simple random guessing is extremely large. Moreover, when there is no correct random sequence filled in the frozen bits, the error rate will increase exponentially during the likelihood ratio calculation recursion. Since C(W E ) < C(W), the channel of the eavesdropper is regarded as a degradation of the legitimate transmitter-receiver channel. There will always be a situation where the information bits at the legitimate end are a pure noise channel for the eavesdropping end, so there will always be bit errors and the errors will continue to amplify.

[0091] Specific example:

[0092] Codebook design: Based on negotiating the same shared key and the agreed number i, the transmitter and the receiver each use different stream key technologies to generate pseudo-random sequences, and select the corresponding new mixed random sequence through the combination of the agreed numbers.

[0093] Both parties agree on the shared key k, and k is 32 bits:

[0094] K = [0,0,0,1,1,0,1,0,0,0,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,1]

[0095] The transmitter A uses the rc4 encryption algorithm to generate the random sequence k according to the key k A , k A is 128 bits:

[0096] k A = [0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,

[0097] 1,1,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,1,0,1,1,1,1,0,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,1]

[0098] The receiver B uses the A5-1 encryption algorithm to generate the random sequence k according to the key k B , k B128 bits:

[0099] k B =[0,0,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0 ,1,1,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,1]

[0100] The bit combination is determined based on the random number i. When i = 0, the first bit of each key is selected, and the combination number is 00. At this time, the random sequence k = k A +k B +[0]*128; The following combination code table is obtained:

[0101]

[0102]

[0103] The sender inputs message m, with a code length of 128 bits:

[0104] m=[0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,1,0 ,1,0,1,1,0,1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,1,0,1,1,1, 1,0,1,0,0,1,0,1,1,1,1,0,1,1,1,0,0,1,1,1,1,1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,0,0,0,1,1,1,1]

[0105] The sending end determines the frozen bit mode (frozen_bits) in the bit obfuscator based on the code length N and the code rate R:

[0106] When N = 256 and R = 0.5, frozen_bits = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];

[0107] When N = 512 and R = 0.25, frozen_bits = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0,0,0,|||0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,00,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0];,

[0108] In the frozen bit mode, "1" corresponds to the information bit, which is filled with the original information, and "0" corresponds to the frozen bit, which is filled with a random sequence. The above results are passed into the generator matrix to obtain the codeword to be sent (when i=0 is selected):

[0109] Codeword to be sent = [1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1,0,0,1,1,0,0,0,1,0,0,0,0,1,1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0,1 ,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0,1,1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1 ,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,0,1, 0,0,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1 ,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0,0,1,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,1,0, 0,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0,1,1,1,1,1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,1,1,1,0,0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1],

[0110] BPSK modulation was performed, and the result after modulation is A:

[0111] A＝[-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,-1,1,1,1,-1,-1,1,1,1,1,-1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,1,1,1,-1,1,-1,-1,1,-1,1,-1,1,1,-1,-1,1,1,1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,1,1,1,1,1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,1,1,1,-1,1,-1,-1,1,1,1,-1,-1,-1,-1,1,-1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,1,-1,-1,1,1,1,1,1,-1,-1,1,-1,1,-1,-1,1,1,1,1,-1,1,-1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,1,-1,-1,-1,-1,-1,1,1,-1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,1,1,-1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,1,-1,1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1,-1,-1,1,-1,-1,1,-1,1,1,-1,-1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,1,1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,1,-1,-1,1,1,1,1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,- 1,-1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,1,-1],

[0112] In this example, the wireless channel selected is an additive white Gaussian noise channel, and a set of likelihood ratio information llr is obtained:

[0113] llr＝[-2.0862,-1.6925,4.5727,-2.1815,2.7763,-0.55489,0.4155,-0.92268,-1.5186,-2.6582,-0.94066,1.9094,4.0555,0.18555,-0.95942,-1.4806,-0.36452,3.9305,1.7536,-3.5312,2.1304,1.7145,0.86687,-0.96416,-2.4756,-0.11217,-0.62364,1.1269,0.79543,-1.0308,-0.30682,1.3227,-3.4797,3.8632,-1.7322,3.1286,-0.9618,-0.44104,-3.038,-0.0017246,0.24374,-1.0297,1.3627,-2.4058,-1.3878,0.51452,1.9362,-0.8332,1.893,1.4359,-0.038375,1.6574,-2.2407,-0.025306,-1.6557,-1.8489,1.8267,-0.33562,2.3103,0.058991,0.66675,0.49646,-1.7044,0.15647,3.2261,1.4265,0.83347,-3.4993,2.4307,1.6137,0.10215,1.1637,-3.888,-1.0436,-1.8039,0.46872,-3.2963,-0.3631,1.7657,1.6889,-0.68267,-0.082386,0.23651,0.075506,0.061589,0.23266,-2.4316,2.512,0.23789,2.0063,2.1034,1.7789,-0.88673,0.10837,-0.31642,-1.442,2.504,-2.8231,1.6504,2.6897,2.8616,-1.6911,-3.9184,0.20408,1.8601,2.5848,-1.0019,0.81364,1.2406,-1.4938,2.6745,1.0616,0.18127,-0.72221,-0.27854,0.70914,-2.2509,-0.4646,0.45117,1.9174,0.1659,-2.2889,-2.6032,3.0465,-0.83948,1.8905,-1.2821,0.55069,-0.33464,-1.1488,-1.9136,-1.8174,1.4568,-2.7016,2.5182,3.3376,4.6993,2.2193,0.54945,-1.3319,0.31709,0.81296,-2.4145,-2.6339,2.061,0.18076,-0.74489,-0.58363,-0.27877,1.5592,2.3641,0.68503,-1.5182,1.3609,3.8163,-1.5735,1.0101,4.6446,0.99137,0.87948,-3.1289,-0.58663,-1.0714,-2.5913,2.2987,1.5831,-0.79942,-1.4257,2.4421,-0.035867,-1.3103,-3.5571,2.571,-1.9759,2.4099,-2.2615,-1.1712,2.9119,-0.9074,-0.76601,-0.72191,2.6532,-1.0748,-2.4692,3.4721,-1.4114,-0.4128,-2.8679,-3.3288,2.787,0.82813,0.10957,0.85835,-2.6379,2.6587,-0.98397,1.9655,-1.0615,1.639,-2.7794,-0.90305,-2.6186,0.23544,-2.9371,-0.49019,2.82,-3.7991,1.3985,1.9021,-2.3533,-0.62688,-1.2646,1.3925,-2.2866,2.4372,-0.51569,2.1757,-1.8868,2.7443,-2.7266,1.7667,3.3429,-1.8237,-2.6472,0.86175,-1.8957,-1.0289,0.57321,1.947,-0.99695,1.5906,-1.1744,3.1014,-3.3526,-1.3261,-0.92187,-1.5491,4.0153,2.7697,-1.5936,1.1591,-0.91985,2.9155,-1.5663,3.6178,0.55779,-4.0999,-2.5268,-1.8358,-2.0542,-2.6517,3.2684,-0.44993,0.96573,-2.8052,0.98803,-2.4235,-0.98266,-2.8955,0.55174,1.7122,2.9495,-0.74982,0.68086,0.47909,2.4003,-0.26357,0.080783,-2.2362,1.6155,-1.7893,0.82241,-1.2428,-1.1334,1.1414,1.7515,1.7809,-1.5944,2.4791,1.0026,0.92033,-2.0202,2.2956,-2.594,-3.9176,-1.5179,1.0355,1.9374,1.6914,-0.66699,2.7189,-3.2538,-3.5042,-0.95237,1.9706,-2.7672,3.1427,1.6265,1.7405,-1.24,-0.63545,0.33434,-1.9147,-3.7637,-0.30902,-2.7528,-0.019192,0.84277,0.29277,0.57023,0.18421,-0.38018,-0.13109,2.4417,-1.0337,-1.7653,-2.0149,4.1755,1.1134,1.3454,-2.7667,0.5608,-2.3196,0.56727,1.0934,0.71615,-2.1492,-0.68555,-3.2413,2.3744,-3.2609,-1.7496,-3.8848,-0.91021,-0.71263,-2.4505,-1.1851,-1.3799,3.0441,-1.4233,-0.27629,-1.7319,-2.4011,-1.6327,-1.8358,-0.47494,1.5142,-2.644,-1.7798,3.0812,1.0626,-2.414,2.8237,-1.4575,1.1283,0.65476,-3.4479,-1.3918,1.1858,-1.1834,-3.4186,3.249,-0.97154,-0.38737,2.9157,-2.3246,-1.2044,1.8612,-2.6905,-2.0174,2.2591,-2.0155,-2.3376,-1.0575,-2.4531,-0.73991,-1.3949,-2.8329,-0.53139,2.1823,3.1613,-2.7086,-2.712,-1.1904,-0.74515,-0.54236,-1.5767,-1.8819,2.4067,4.0581,2.6985,1.6913,-2.3082,2.214,0.97544,1.8851,-0.60514,2.7485,2.3253,3.3196,0.74564,-3.9739,-3.8241,-2.7464,-4.1001,1.1353,-2.0084,1.9002,1.9451,-2.4487,-2.6088,-0.58606,1.1041,-3.3111,-1.5719,-1.3279,1.0674,2.4203,-1.3007,-1.8528,1.5295,2.1617,-2.1406,0.25679,1.389,-1.4223,2.2262,-1.6228,1.0091,2.3356,-1.7278,2.6009,-1.6979,1.577,1.4692,0.42512,0.41793,-2.795,0.66207,1.3329,-0.40099,2.0245,3.9256,2.752,-3.1295,1.1729,-0.46238,1.9477,1.2668,1.5246,-0.36879,2.144,-2.7328,1.6471,2.9421,-1.1969,-1.2077,1.3366,-1.7692,1.4551,-1.9388,-1.0898,-0.33825,-3.2185,-3.5009,-0.80309,-3.4828,-0.52935,2.5782,-2.4086,3.1521,-3.2118,0.81147,1.8892,-0.8933,-0.99618,-1.3439,-1.8742,-2.3141,2.1898,-2.0719,-1.0541,-0.21555,-1.2468,0.68681,-2.3806,0.072429,3.5382,-0.26435,1.8076,2.7789,1.3147,2.1971,-1.1683,0.011301,-0.21202,0.39338,1.0329,-1.1528,-1.6584,1.6065,-1.0327,2.1357,0.53032,-3.2309,2.5847,1.3366,-0.76766,-2.6317,2.7128,-0.69815,0.38744].

[0114] Upon receiving the corresponding codeword, i.e., the aforementioned llr signal, the legitimate receiver simultaneously determines the random sequence (the sequence with the frozen bits filled in during decoding) fz_value according to the shared key and the agreed-upon number:

[0115] fz_value=[0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0 ,0,0,1,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,1,1,0,1,1,1,1,0,1,0,1,1, 0,1,1,1,0,1,0,1,1,0,0,0,1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1 ,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0 ... ,0 ...

[0116] The receiver passes llr and fz_value to the decoder (using the SCL decoding algorithm). The decoder determines the likelihood ratio execution layer number llr_layer and the bit execution layer number bit_layer based on the code length.

[0117] llr_layer=[0,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,6,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,7,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,6,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,8,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,6,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,7,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,6,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,5,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,4,0,1,0,2,0,1,0,3,0,1,0,2,0,1,0],

[0118] bit_layer=[0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,4,4,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,5,5,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,4,4,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,6,6,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,4,4,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,5,5,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,4,4,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,7,7,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,4,4,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,5,5,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,4,4,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,6,6,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,4,4,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,5,5,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,4,4,0,0,1,1,0,0,2,2,0,0,1,1,0,0,3,3,0,0,1,1,0,0,2,2,0,0,1,1,0,0,8,8],

[0119] In the decoder, a list L=16 is created to store the metrics of 16 paths. When a path with a smaller metric value than the one in the list is found, the list is updated. After all the execution layer operations are completed, the path with the smallest metric value is selected and the result is output. Finally, it is determined that the decoded information is correct with the sent information.

[0120] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A dynamic coding method for secure polar codes based on dual-sequence hybridization, characterized in that, The steps are as follows: The sending end and the legitimate receiving end jointly determine the encoding length N, the shared key k, and the agreed number i; The sending end uses the rc4 encryption algorithm to encrypt the shared key k to obtain a pseudo-random sequence k. A The legitimate receiving end uses the A5-1 encryption algorithm to encrypt the shared key k to generate a pseudo-random sequence k. B And based on the agreed number i and the pseudo-random sequence k A and pseudo-random sequence k B Determine the mixed random sequence r; The mixed random sequence r is determined as follows: A conventional number i is selected from the i-th element of each random sequence, resulting in a total of 2... 2 There are several ways to combine them, and the combination methods are defined as follows: When the number of combinations is 0, the mixed random sequence r = k A +k B +k0; When the number of combinations is 0 or 1, the mixed random sequence r = k B ; When the number of combinations is 10, the mixed random sequence r = k A ; When the number of combinations is 11, the mixed random sequence r = k B +k A +k0; where k0 is a sequence of all zeros; The transmitting end constructs a bit obfuscator based on the encoding length N, and inputs the information to be transmitted m and the mixed random sequence r into the bit obfuscator to generate an obfuscated sequence m'. The method for generating the confusing sequence m' is as follows: A mixed random sequence r is fed as input to a bit obfuscator as the sequence to be filled with frozen bits; The sending end determines the freeze bit mode in the bit obfuscator based on the encoding length N and the code rate R; In the frozen bit mode, "1" corresponds to the information bit, which is filled with the original information, and "0" corresponds to the frozen bit, which is filled with the mixed random sequence to obtain the confused sequence m'. The transmitting end determines the generator matrix G based on the coding length N, and inputs the confusion sequence m' into the generator matrix G to obtain the codeword to be transmitted. Then, the codeword to be transmitted is BPSK modulated to obtain the transmitted codeword A. The sender transmits codeword A, which is transmitted through the wireless channel. Both the legitimate and illegitimate receivers receive signal B. The legitimate receiver inputs signal B and the mixed random sequence r into the polar code decoder to decode and obtain the original information. An illegitimate receiver inputs signal B and a random sequence r' into a polar code decoder, which decodes to obtain an error message.

2. The dynamic coding method for secure polar codes based on dual-sequence hybridization according to claim 1, characterized in that, The method for determining the generating matrix G is as follows: Among them, G N Represents the polar code encoding matrix. Representation matrix The nth Kronecker product; B N For a sorted matrix, its recursive definition is: I2 = B2, which is a second-order identity matrix; R N To separate odd and even elements, it can be represented as: (u1, u2, u3, ..., u n )·R N =(u1,u3,......u n-1 ,u2,u4......,u n ), matrix B N This involves setting the j-th element of the output sequence to the i'-th element of the original sequence, and converting the original sequence i'∈{1,…,N} into binary representation. i'-1→(b n ,...,b1)→(b1,...,b n )→j-1.

3. The dynamic coding method for secure polar codes based on dual-sequence hybridization according to claim 2, characterized in that, The BPSK modulation is f bpsk The transmitted codeword A is f. bpsk (m'*G).

4. The dynamic coding method for secure polar codes based on dual-sequence hybridization according to claim 1, characterized in that, The legitimate receiver inputs signal B and mixed random sequence r into the polar code decoder. The method for decoding to obtain the original information is as follows: before decoding begins, the legitimate receiver inputs the mixed random sequence r, signal B, and the frozen bit pattern in the bit mixer into the polar code decoder. Step 1: Initialization The initialization list contains an empty path, meaning there is only one initial path; Initialize the decoding tree by dividing the signal B into different paths, with the root node designated as level 0 and each of the remaining levels representing one bit to be decoded; each set of edges from the root node to a leaf node represents a possible decoding result. Step 2: Bit-by-bit decoding For each decoding tree node, a hard decision formula is used based on the frozen bit information on the path: Update the node values; where, This indicates the result of the previous bit decoding. This indicates the result of the local decoding. Indicates the bit to be decoded. This represents the received bit string, where count represents the position of that bit in the pseudo-random sequence r, and A f Indicates the freeze bit mode. This represents the posterior probability of the channel to be decoded. This indicates that the bit to be decoded is 0 and all preceding bits have been correctly decoded. This indicates that the bit to be decoded is 1 and all previous bits have been correctly decoded, and l represents the l-th path; Based on the updated node values, according to the formula: Calculate the corresponding metric value; where, For each path, based on the metric, the most likely bit value is selected as the decision, and the nodes on the path are updated according to that bit value. Step 3: Path Expansion and Sort For each path, based on its metric, two sub-paths are extended from its parent path, one assuming the current bit is 0 and the other assuming the current bit is 1; Sort all generated sub-paths in ascending order based on the metric value, and select the first L paths, where L is the list size set in the SCL algorithm; if the total number of paths does not reach L, all paths are retained after sorting. Step 4: Path pruning After each stage, based on the expanded path list, select the top L paths to keep and prune the paths with poor metrics; that is, keep the L paths with the smallest path metrics and prune the rest of the paths. Step 5: Iterative Decoding Repeat steps 2 to 4 until the decoding performance requirements of the polar code are met or the predetermined number of iterations is reached; Step 6: Output the decoding result After all layers have completed the calculation iterations, the shortest path is selected from the metric table to provide the decoding, and the final decoding is error-free with the transmitted information.

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