Polarization coding and decoding method and device for satellite communication

Abstract

This application relates to the field of satellite communications technology and discloses a polarization coding and decoding method and apparatus for satellite communications. The method comprises obtaining K bits to be coded, selecting K sequence numbers from a first sequence, placing the bits to be coded on the polarization channels corresponding to the K sequence numbers, and performing polar code encoding on the K bits to obtain coded bits. The first sequence includes the sequence numbers of N polarization channels, and the first sequence is all or a subsequence of the relevant sequences provided in the specification. This technical solution is applicable to the short message communication system of Beidou satellites. Employing this method can effectively improve the performance of the communication system and reduce its complexity.

Description

Technical Field

[0001] The embodiments of the present application relate to the field of satellite communication technology, and in particular to a Polar code encoding method and apparatus. Background Art

[0002] The Beidou satellite communication system features short message communication, a key feature of the system. These short messages can be thought of as the "short messages" people use on their mobile phones. These messages not only provide positioning information but also display the sender's location. Satellite positioning terminals and Beidou satellites or Beidou ground service stations can exchange information directly via satellite signals in both directions, whereas GPS is limited to one-way communication (the terminal receives location signals from the satellite). Currently, the second-generation Beidou short message system uses Turbo codes for channel coding, but its performance and complexity require further improvement. Summary of the Invention

[0003] The embodiments of the present application provide a polarization coding method and apparatus for a satellite system, which are used to improve the performance and reduce the complexity of a short message communication system.

[0004] The specific technical solutions provided in the embodiments of this application are as follows:

[0005] In a first aspect, a Polar code encoding method is provided. The method includes obtaining K bits to be encoded; selecting K sequence numbers from a first sequence, placing the bits to be encoded in polarized channels corresponding to the K sequence numbers, and performing Polar code encoding on the K bits to be encoded to obtain encoded bits. The first sequence includes sequence numbers of N polarized channels, and the first sequence is all or a subsequence of a sequence shown as sequence Q1 or Q2 in the specification. K is a positive integer, and N is a mother code length of the Polar code, where N=2. n , n is a positive integer, K≤N.

[0006] The solution provided in the embodiments of this application can be used for short message communications on Beidou satellites, and is particularly suitable for channel coding design for outbound short messages. The specially designed information bit determination sequence maximizes performance and reduces complexity. Furthermore, the sequence can be applied to multiple different bit lengths to be encoded. Within the sequence, the channel position sets corresponding to bits of different lengths to be encoded have a nested relationship. This feature can reduce system storage overhead, especially when the mother code length is particularly large.

[0007] In one possible design, the reliability of the polarized channels corresponding to the selected K sequence numbers is higher than the reliability of the polarized channels corresponding to the remaining (NK) sequence numbers in the first sequence.

[0008] In one possible design, the first sequence is pre-stored.

[0009] In one possible design, when the mother code length N is 4096, the number of bits to be encoded K is: 452, 536, 904, 1048, 1808, 2072, 2712 or 3096; or when the mother code length N is 8192, the number of bits to be encoded K is: 235, 470, 940, 1880, 2820 or 3760.

[0010] In one possible design, when the mother code length is 4096, the first sequence is sequence Q1 in the specification; or when the mother code length is 8192, the first sequence is sequence Q2 in the specification.

[0011] In one possible design, the method further includes: performing rate matching on the bits encoded by the Polar code to obtain rate-matched bits.

[0012] In one possible design, the N polarized channels are numbered from 0 to (N-1) or from 1 to N.

[0013] In one possible design, the bits to be encoded include cyclic redundancy check CRC bits.

[0014] In one possible design, the bits to be encoded include parity check bits (PC bits).

[0015] In a second aspect, a polar code decoding method is provided. The method includes receiving bit information to be decoded, where the bit information to be decoded includes K information bits, and the K information bits are carried on polarized channels corresponding to K sequence numbers of a first sequence. The first sequence includes sequence numbers of N polarized channels, and the first sequence is all or a subsequence of a sequence shown as sequence Q1 or Q2 in the specification. K is a positive integer, and N is a mother code length of the polar code, where N=2. n , n is a positive integer, K≤N; performing Polar code decoding according to the bit information to be decoded to obtain the K information bits.

[0016] In one possible design, the reliability of the polarized channels corresponding to the selected K sequence numbers is higher than the reliability of the polarized channels corresponding to the remaining (NK) sequence numbers in the first sequence.

[0017] In one possible design, the first sequence is pre-stored.

[0018] In one possible design, when the mother code length N is 4096, the number of information bits K is: 452, 536, 904, 1048, 1808, 2072, 2712 or 3096; or when the mother code length N is 8192, the number of information bits K is: 235, 470, 940, 1880, 2820 or 3760.

[0019] In one possible design, when the mother code length is 4096, the first sequence is sequence Q1 in the specification; or when the mother code length is 8192, the first sequence is sequence Q2 in the specification.

[0020] In one possible design, the N polarized channels are numbered from 0 to (N-1) or from 1 to N.

[0021] In one possible design, the bits to be encoded include cyclic redundancy check CRC bits.

[0022] In one possible design, the bits to be encoded include parity check bits (PC bits).

[0023] In a third aspect, a polarization Polar code encoding apparatus is provided, comprising an acquisition unit configured to acquire K bits to be encoded; a selection unit configured to select K sequence numbers from a first sequence, wherein the polarization channels corresponding to the K sequence numbers are used to place the bits to be encoded; and an encoding unit configured to perform Polar code encoding on the K bits to be encoded to obtain encoded bits. The first sequence includes sequence numbers of N polarization channels, and the first sequence is the entire sequence or a subsequence of a sequence shown as sequence Q1 or Q2 in the specification. K is a positive integer, and N is a mother code length of the Polar code, where N=2. n , n is a positive integer, K≤N.

[0024] In one possible design, the reliability of the polarized channels corresponding to the selected K sequence numbers is higher than the reliability of the polarized channels corresponding to the remaining (NK) sequence numbers in the first sequence.

[0025] In one possible design, the first sequence is pre-stored.

[0026] In one possible design, when the mother code length N is 4096, the number of bits to be encoded K is: 452, 536, 904, 1048, 1808, 2072, 2712 or 3096; or when the mother code length N is 8192, the number of bits to be encoded K is: 235, 470, 940, 1880, 2820 or 3760.

[0027] In one possible design, when the mother code length is 4096, the first sequence is sequence Q1 in the specification; or when the mother code length is 8192, the first sequence is sequence Q2 in the specification.

[0028] In one possible design, the apparatus further includes a rate matching unit configured to perform rate matching on the bits encoded by the Polar code to obtain rate-matched bits.

[0029] In one possible design, the N polarized channels are numbered from 0 to (N-1) or from 1 to N.

[0030] In one possible design, the bits to be encoded include cyclic redundancy check CRC bits.

[0031] In one possible design, the bits to be encoded include parity check bits (PC bits).

[0032] In a fourth aspect, a polarization Polar code decoding apparatus is provided, comprising a receiving unit configured to receive bit information to be decoded, wherein the bit information to be decoded includes K information bits, and the K information bits are carried on polarized channels corresponding to K sequence numbers of a first sequence, wherein the first sequence includes sequence numbers of N polarized channels, and the first sequence is all or a subsequence of a sequence shown as sequence Q1 or Q2 in the specification, wherein K is a positive integer, and N is a mother code length of the Polar code, where N=2. n , n is a positive integer, K≤N, a decoding unit is used to perform Polar code decoding according to the bit information to be decoded to obtain the K information bits.

[0033] In one possible design, the reliability of the polarized channels corresponding to the selected K sequence numbers is higher than the reliability of the polarized channels corresponding to the remaining (NK) sequence numbers in the first sequence.

[0034] In one possible design, the first sequence is pre-stored.

[0035] In one possible design, when the mother code length N is 4096, the number of information bits K is: 452, 536, 904, 1048, 1808, 2072, 2712 or 3096; or when the mother code length N is 8192, the number of information bits K is: 235, 470, 940, 1880, 2820 or 3760.

[0036] In one possible design, when the mother code length is 4096, the first sequence is sequence Q1 in the specification; or when the mother code length is 8192, the first sequence is sequence Q2 in the specification.

[0037] In one possible design, the N polarized channels are numbered from 0 to (N-1) or from 1 to N.

[0038] In one possible design, the bits to be encoded include cyclic redundancy check CRC bits.

[0039] In one possible design, the bits to be encoded include parity check bits (PC bits).

[0040] In a fifth aspect, a polar code processing apparatus is provided, comprising a memory for storing a program; and a processor for executing the program stored in the memory. When the program is executed, the processor is configured to execute the method as described in the first aspect or any possible design of the first aspect, or to execute the method as described in the second aspect or any possible design of the second aspect.

[0041] In one possible design, the Polar code encoding device is a chip or an integrated circuit.

[0042] In a sixth aspect, a Polar code processing device is provided, characterized in that it includes an input interface circuit for obtaining bits to be encoded; a logic circuit for executing the method described in the first aspect or any one of the possible designs of the first aspect based on the obtained bits to be encoded to obtain a bit sequence encoded based on the Polar code; or executing the method described in the second aspect or any one of the possible designs of the second aspect to obtain a bit sequence decoded based on the Polar code; and an output interface circuit for outputting the bit sequence.

[0043] In the seventh aspect, a wireless device is provided, characterized in that it includes a processing device, a modem, and a transceiver as described in the fifth aspect: the modem is used to modulate the encoded bit sequence to obtain a modulated sequence, or demodulate the encoded bit information; the transceiver is used to send the modulated sequence, or receive the encoded bit information.

[0044] In one possible design, the wireless device is a terminal or a network device. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A schematic diagram of a wireless communication network scenario to which the embodiments of the present application provide solutions;

[0046] Figure 2 A schematic diagram of a system framework of a wireless communication network applicable to an embodiment of the present application;

[0047] Figure 3 A schematic diagram of a method for determining an information bit position set provided in an embodiment of the present application;

[0048] Figure 4 A schematic diagram of a Polar code encoding method provided in an embodiment of the present application;

[0049] Figure 5 A schematic diagram of a Polar code decoding method provided in an embodiment of the present application;

[0050] Figure 6 A schematic diagram of a Polar code encoding device 600 provided in an embodiment of the present application;

[0051] Figure 7 A schematic diagram of a Polar code encoding device 700 provided in an embodiment of the present application;

[0052] Figure 8 A schematic diagram of a Polar code decoding device 800 provided in an embodiment of the present application;

[0053] Figure 9 A schematic diagram of a Polar code decoding device 900 provided in an embodiment of the present application;

[0054] Figure 10 A schematic diagram of a Polar code encoding device 800 provided in an embodiment of the present application;

[0055] Figure 11 A schematic diagram of a Polar code decoding device 1100 provided in an embodiment of the present application. DETAILED DESCRIPTION

[0056] The terms "first," "second," "third," and "fourth," etc., in the specification and claims of this application and the accompanying drawings are used to distinguish between different objects, rather than to describe a specific order. In addition, the terms "including," "having," and any variations thereof, are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or elements is not limited to the listed steps or elements, but may optionally include steps or elements not listed, or may optionally include other steps or elements inherent to the process, method, product, or apparatus.

[0057] References herein to "embodiments" mean that a particular feature, structure, or characteristic described in connection with the embodiments may be included in at least one embodiment of the present application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it constitute an independent or alternative embodiment that is mutually exclusive of other embodiments. It is understood, both explicitly and implicitly, by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0058] In this application, "at least one (item)" means one or more, "more than one" means two or more, "at least two (items)" means two or three and more, and "and / or" is used to describe the association relationship of associated objects, indicating that three relationships can exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. "At least one of the following items" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or plural.

[0059] The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0060] The present application provides a polarization encoding and decoding method and device suitable for satellite communications. This application uses the short message communication function of Beidou satellites as an example for illustration; other similar communication systems can also employ the method and device provided herein. A short message workflow is as follows: 1. The short message sender first encrypts a communication request signal containing the recipient's ID number and communication content, and then forwards it via satellite. 2. After receiving the communication request signal, the ground central station decrypts and re-encrypts it, adding it to a continuously broadcast outbound message, which is then broadcast to the user via satellite. 3. The receiving user terminal receives the outbound signal, demodulates and decrypts the outbound message, completing the communication. A specially designed fixed rate matching and nested polarization code information bit determination method can be used to maximize performance and minimize complexity, specifically targeting the number of information bits and code length of Beidou satellites' specific outbound messages (sent from the ground central station to the satellite, and then forwarded by the satellite to the terminal).

[0061] To facilitate understanding of the embodiments of the present application, a brief introduction to polar codes is given below.

[0062] The coding strategy of polar codes is to use noise-free channels to transmit useful information for users, and noisy channels to transmit agreed information or no information, in order to improve the reliability of data transmission and ensure the quality of communication. Polar codes are also linear block codes with low encoding and decoding complexity. Its encoding matrix is , the encoding process is , in is a binary row vector of length (i.e. code length); is a , and . Defined as matrices The above matrix is ​​the Kronecker product of .

[0063] During the encoding process of Polar code, A part of the bits in is used to carry information, which is called the information bit set. The set of indexes of these bits is recorded as The other part of the bits is set to a fixed value agreed upon by the receiving and sending ends, which is called a fixed bit set or a frozen bit set (frozen bits). The complement of The encoding process of Polar code is equivalent to: , here, G N (A) is G N Zhongyou Collection The submatrix G is obtained by taking the rows corresponding to the indices in N (A C ) is G N Zhongyou Collection The submatrix obtained by indexing the rows corresponding to . for The number of information bits in the information bit set is K. Generally, various check bits including but not limited to cyclic redundancy check (CRC) bits and parity check (PC) bits are also included in the information bit set; for The set of fixed bits in , whose number is (NK), are known bits. These fixed bits are usually set to 0, but as long as the receiver and the transmitter agree in advance, the fixed bits can be set arbitrarily. Therefore, the encoded output of the Polar code can be simplified to: ,here for The set of information bits in , is the length The row vector of , Indicates the number of elements in the collection. is the information block size, is a matrix Zhongyou Collection The submatrix obtained by the rows corresponding to the indices in is a The matrix of .

[0064] The construction process of Polar code is the set The selection process determines the performance of Polar codes. The construction process of Polar codes is usually to determine the coexistence of N polarization channels based on the mother code length N, corresponding to the N rows of the coding matrix, calculate the reliability of the polarization channels, and take the indexes of the top K polarization channels with higher reliability as the set The indexes corresponding to the remaining (NK) polarized channels are used as the fixed bit index set. Elements of a set Determines the location of the information bit, the set The polarized channel number is the position index of the information bit or fixed bit. The position index in .

[0065] Polar codes can be constructed online. However, the parameters used in this construction are dependent on the signal-to-noise ratio (SNR). The transmitter and receiver cannot simultaneously obtain accurate SNR parameters (or require additional overhead to obtain), and online construction incurs additional complexity. Furthermore, information bit positions must be stored separately for different code lengths and information bit lengths. Alternatively, a construction method independent of the SNR can be used, such as using the PW (Polarization Weight) value. The PW value ranking sequence itself serves as a reliability ranking sequence for Polar codes and is used to select information bits. Performance can be further improved when the PW is used to select information bit lengths.

[0066] As can be seen from the coding matrix, the original Polar code (mother code) has a code length that is an integer power of 2. In practical applications, rate matching is required to achieve Polar codes of arbitrary code lengths. Puncturing or shortening is used to achieve rate matching. During encoding, mother codes exceeding the target code length are punctured or shortened to reach the target code length. During decoding, padded code is restored to the mother code length. For the specific number of outbound information bits and code length for Beidou outbound traffic (sent from the ground central station to the satellite, and then forwarded by the satellite to the terminal), a fixed rate matching method and information bit position can be used as the code design solution.

[0067] Before introducing the specific solution, a brief introduction is first given to the scenario and system architecture applicable to the solution provided by the embodiment of the present application.

[0068] Figure 1 Schematic diagram of wireless communication network scenario applicable to the solution provided by the embodiment of the present application. The solution provided by the present application can be applied to NTN communication system, such as Figure 1 As shown, the communication system 100 may be composed of a terminal device 101 , a satellite (or satellite base station) 102 , and a ground station (or gateway) 103 .

[0069] The terminal device 101 may also be referred to as user equipment (UE), terminal, or terminal device. A terminal device is a device, chip, or communication system with wireless transceiver capabilities. It can be deployed on land, including indoors or outdoors, handheld, wearable, or vehicle-mounted; on water, such as on ships; or in the air, such as on airplanes, balloons, or satellites. A terminal device may be a mobile phone, tablet computer, computer with wireless transceiver capabilities, virtual reality (VR) terminal device, augmented reality (AR) terminal device, wireless terminal in industrial control, wireless terminal in self-driving, wireless terminal in remote medical care, wireless terminal in smart grid, wireless terminal in transportation safety, wireless terminal in smart city, wireless terminal in smart home, and so on. It is understandable that the terminal device may also be a terminal device in a future 5G network or a terminal device in a future evolved public land mobile network (PLMN), etc. For ease of description, the following will take the terminal device as an example to illustrate the method involved in the embodiment of the present application.

[0070] Optional, Figure 1 In the communication system shown, terminal devices can communicate with each other through communication technologies such as device-to-device (D2D), vehicle-to-everything (V2X) or machine-to-machine (M2M). The embodiments of the present application do not limit the communication method between terminal devices.

[0071] Among them, the satellite 102 can provide wireless access services for terminal devices, dispatch wireless resources to the accessed terminal devices, and provide reliable wireless transmission protocols and data encryption protocols. Satellites can be base stations that use artificial earth satellites and high-altitude aircraft as wireless communication, such as evolutionary NodeBs (eNBs) and 5G base stations (gNBs). Alternatively, the satellite can also serve as a relay for these base stations, transparently transmitting the wireless signals of these base stations to the terminal devices. In this case, the ground station can be regarded as a base station for wireless communication. Therefore, in some embodiments, such as in the satellite regeneration scenario, the network device can be Figure 1In other embodiments, such as in a satellite transparent transmission scenario, the network device can be Figure 1 For ease of description, the method involved in this application is described below by taking the network device as a base station as an example.

[0072] In the embodiments provided in the present application, the network device may include but is not limited to the satellite base station shown above. For example, the network device may also be a base station in a future communication system such as a sixth-generation communication system. Optionally, the network device may also be an access node, a wireless relay node, a wireless backhaul node, etc. in a wireless local area network (wireless fidelity, WiFi) system. Optionally, the network device may also be a wireless controller in a cloud radio access network (CRAN) scenario. Optionally, the network device may also be a wearable device or a vehicle-mounted device, etc. Optionally, the network device may also be a small station, a transmission reception point (TRP) (or also referred to as a transmission reception point), etc. It is understandable that the network device may also be a base station in a future evolved PLMN, etc.

[0073] Optionally, the satellite 102 may be a geostationary earth orbit (GEO) satellite, a medium earth orbit (MEO) satellite or a low earth orbit (LEO) satellite of a non-geostationary earth orbit (NGEO), or a high altitude platform station (HAPS), etc.

[0074] Ground station 103 can be used to connect the satellite and the core network. For example, when the satellite serves as a wireless communication base station, the ground station can transparently transmit signaling between the satellite and the core network. Alternatively, the ground station can serve as a wireless communication base station, and the satellite can transparently transmit signaling between a terminal device and the ground station. For example, during communication, the ground station can send signaling from the core network to the satellite via a feedback link (also known as a feeder link). The satellite then sends this signaling to the terminal device via a service link between the satellite and the terminal device. Conversely, the terminal device can also send signaling to the satellite via the service link, and the satellite can send this signaling to the core network via the ground station.

[0075] Understandable, Figure 1Only one satellite and one ground station are shown. In actual use, a multi-satellite and / or multi-ground station architecture may be adopted as needed. Each satellite may provide services to one or more terminal devices, each satellite may correspond to one or more ground stations, each ground station may correspond to one or more satellites, and so on. This application does not specifically limit this. Figure 1 In the communication scenario shown, in the embodiments of the present application, the polar code encoding and decoding method can be performed by the aforementioned ground station or terminal. When the network device or terminal acts as a transmitter to send data or information, this polar code encoding method can be used. Correspondingly, when the network device or terminal acts as a receiver to receive data or information, this polar code decoding method can be used.

[0076] Figure 2 A schematic diagram of a system framework of a wireless communication network for which the embodiments of the present application provide a solution is provided, such as Figure 2 As shown, after the transmitting end determines the information bits to be encoded, it performs Polar encoding on the information bits to be encoded, and after rate matching, sends them out. The encoded information is transmitted through the channel. The receiving end receives the information from the channel, derates it, and decodes it. After decoding, the decoded information bits are output. The solution provided in this application can be applied to existing communication systems, especially satellite communication scenarios, to replace the existing codec or serve as an enhancement solution to existing codec.

[0077] The polar code encoding and decoding method provided in the embodiments of the present application is described in detail below.

[0078] Figure 3 Schematic diagram of a method for determining an information bit position set provided in an embodiment of the present application, wherein the maximum mother code length of the Polar code is N max , when the information bit length is K, the bit length after encoding (after rate matching or output) is M, and the mother code length of the Polar code corresponding to the current information bit is N=2^ceil(log2(M)). The solution provided in the embodiment of the present application involves how to improve the performance of the code and reduce the complexity under the given number of information bits and code length (mother code length, code length after rate matching, or other specified output code length). The solution provided in the embodiment of the present application can be used for short message communication of Beidou satellites, and is particularly suitable for the channel coding design of outbound short messages. Through specially designed fixed rate matching and information bit determination methods, the performance is maximized and the complexity is reduced. At this time, the number of bits that need to be rate matched (punctured or shortened) is (NM), and the rate matching position set is fixed. The rate matching position set records the rate matching position sequence number (optional, the sequence number starts from 0 and the maximum is N max-1), the information bit position set is determined based on the rate matching position set. Since multiple information bit lengths can exist when the number of bits M after outbound encoding is fixed, and the channel position sets corresponding to information bits of different lengths are nested, system storage overhead can be reduced, especially when the mother code length is very large. The information bit sequence number sets of different lengths K1, K2, and K3 in the figure are subsets of the information bit sequence number set of length K4. Subsetting can be done from back to front or from front to back. The illustrated subsetting method is for example only.

[0079] based on Figure 1 The wireless communication network scenario shown and Figure 2 The communication system framework shown in Figure 4 The embodiment of the present application provides a Polar code encoding method, and the specific process is as follows:

[0080] Step 401: Obtain K bits to be encoded.

[0081] Step 402: Select K sequence numbers from the first sequence, and place the to-be-coded bits on polarized channels corresponding to the K sequence numbers.

[0082] Step 403: Perform Polar code encoding on the K bits to be encoded to obtain encoded bits.

[0083] The first sequence includes the sequence numbers of N polarized channels. The first sequence is the entire sequence or a subsequence of the sequence shown in the sequence Q1 or Q2 in the specification. K is a positive integer, and N is the mother code length of the Polar code, N=2. n , n is a positive integer, K≤N. The first sequences Q1 and Q2 refer to the relevant parts in the latter part of the specification and will not be described in detail below.

[0084] The first sequence or subsequence described herein is arranged by reliability, forming a ranking relationship. The reliability of polarized channels can be calculated using the aforementioned method. Sequences can be sorted from low to high reliability, from high to low reliability, or divided into two or more groups, with reliability arranged from low to high or from high to low within each group. The specific grouping method can be based on the magnitude of the polarized channel sequence numbers or other methods based on congruent sequence numbers (for example, grouping into three groups, where sequence numbers that are congruent after divisibility by 3 are grouped together), without specific limitation. The same terminology applies hereinafter.

[0085] Optionally, the first sequence is pre-stored.

[0086] Optionally, when the mother code length N is 4096, the number K of bits to be encoded is: 452, 536, 904, 1048, 1808, 2072, 2712 or 3096; or when the mother code length N is 8192, the number K of bits to be encoded is: 235, 470, 940, 1880, 2820 or 3760.

[0087] Optionally, the K may fluctuate based on the above values, for example, a K value that is increased or decreased by 10, 12, 15 or 20. More specifically, based on 452, the number K of information bits may be an integer between 432 and 472: 433, 434, 435, 436, 437, 438, 439, 440, ..., 470, 471, 472. Similarly, based on 536, the number K of information bits may be an integer between 516 and 556: 516, 517, ..., 555, 556. Based on 3096, the number K of information bits may be an integer between 3076 and 3116: 3076, 3077, ..., 3115, 3116. Based on 235, the number K of information bits may be an integer between 215 and 255: 215, 216, ..., 254, 255. Based on 470, the number K of information bits may be an integer between 450 and 490: 450, 451, ..., 489, 490; 940 as the basis, the number K of the information bits can be an integer between 920 and 960: 920, 921, ..., 959, 960, and other K values ​​are also applicable.

[0088] Optionally, when the mother code length is 4096, the first sequence is sequence Q1 in the specification; or when the mother code length is 8192, the first sequence is sequence Q2 in the specification.

[0089] Optionally, the method further includes: performing rate matching on the bits encoded by the Polar code to obtain rate-matched bits. For example, puncturing the sequence encoded by the Polar code according to the target code length. If the sequence numbers in the first sequence provided in this application are set as rate matching (puncturing or shortening) positions, the sequence number or numbers will be skipped. Optionally, rate matching can be performed in ascending order of sequence numbers, such as puncturing. The number of bits to be punctured can be determined based on the difference between the mother code length and the target code length. For example, if the mother code length is 8192 and the target code length to be transmitted is 7520, the number of bits to be punctured is 672 (8192-7520). Optionally, rate matching can also be performed based on the shortening position set S1 provided later in the specification.

[0090] It is understood that, assuming that the first sequence after excluding punctured or shortened bit positions has M elements, the polarization channel reliabilities corresponding to the selected K sequence numbers are higher than the polarization channel reliabilities corresponding to the remaining (MK) sequence numbers in the sequence. Preferably, the sequence includes the sequence numbers of M polarization channels, which are arranged in the sequence according to their reliabilities, where M is a positive integer. However, it is understood that the reliability ordering in the sequence may be discontinuous due to rate matching, excluding bit positions requiring puncturing or shortening in advance. Furthermore, adjustments to certain positions in the sequence do not affect the reliability of channel transmission in this scenario. For example, interchanging the selected K sequence numbers does not affect the selection of those K sequence numbers; the only requirement is that the polarization channel reliabilities corresponding to the selected K sequence numbers are higher than the polarization channel reliabilities corresponding to the remaining (MK) sequence numbers in the sequence. Optionally, the selected K sequence numbers are the last K sequence numbers in the first sequence, or the selected K sequence numbers are the first K sequence numbers in the first sequence.

[0091] Optionally, the bits to be encoded include cyclic redundancy check CRC bits.

[0092] Optionally, the bits to be encoded include parity check PC bits.

[0093] The encoding method provided in this embodiment determines the number K of bits to be encoded after receiving input information bits. In addition to online calculation or pre-calculation and storage of a first sequence, the length of which corresponds to the mother code length of the polar code. Multiple second sequences may also be online calculated or stored. The multiple second sequences respectively store sets of information bit position numbers corresponding to bits to be encoded of different lengths K. The second sequence is the entirety or a subset of a third sequence. In this case, the third sequence is the longest set of information bit position numbers under a certain condition, for example, the longest set of information bit position numbers for a specific bit length after rate matching. The sequence order of the polarized channels in the second sequence is consistent with the sequence order of the polarized channels in the third sequence.

[0094] Regardless of whether online calculation or pre-calculation and storage is used, after the positions of the information bits are determined, the remaining positions can be considered as frozen bits or fixed bit positions. Polar encoding is performed on the K bits to be encoded to obtain the Polar-encoded bit sequence.

[0095] The following describes in detail the sequence of polarized channel numbers obtained by sorting the reliability of the i-th polarized channel among N polarized channels. The sequence numbers of the N polarized channels can range from 0 to (N-1) or from 1 to N. In this embodiment of the present application, when determining the reliability of the i-th polarized channel among N polarized channels, the value of i can be 1, 2, ..., N, or 0, 1, ..., N-1.

[0096] It can be understood that the formulas involved in the embodiments of the present application are only examples, and the solutions that can be obtained by those skilled in the art by simply modifying the formulas without affecting the performance of the formulas are all within the scope of protection of the embodiments of the present application.

[0097] The first sequence may be part or all of any of the sequences shown in sequence Q1 or sequence Q2, determined according to different criteria. Optionally, these sequences may be represented by a corresponding table. If the table is in table form, the table items include "reliability or reliability sequence number" and "polarization channel sequence number." The "reliability or reliability sequence number" indicates the natural order of reliability from low to high or from high to low, and the "polarization channel sequence number" indicates the polarization channel sequence number in the corresponding sequence.

[0098] Correspondingly, based on Figure 1 The wireless communication network scenario shown and Figure 2 The communication system framework shown in Figure 5 The embodiment of the present application provides a Polar code decoding method, and the specific process is as follows:

[0099] Step 501: Receive bit information to be decoded, where the bit information to be decoded includes K information bits, and the K information bits are carried on polarized channels corresponding to K sequence numbers of a first sequence. The first sequence includes sequence numbers of N polarized channels, and the first sequence is all or a subsequence of a sequence shown as sequence Q1 or Q2 in the specification. K is a positive integer, and N is the mother code length of the Polar code, where N=2. n , n is a positive integer, K≤N;

[0100] Step 502: Perform Polar code decoding on the bit information to be decoded to obtain the K information bits.

[0101] It is understood that, assuming that the first sequence after excluding punctured or shortened bit positions has M elements, the polarization channel reliabilities corresponding to the selected K sequence numbers are higher than the polarization channel reliabilities corresponding to the remaining (MK) sequence numbers in the sequence. Preferably, the sequence includes the sequence numbers of M polarization channels, which are arranged in the sequence according to their reliabilities, where M is a positive integer. However, it is understood that the reliability ordering in the sequence may be discontinuous due to rate matching, excluding bit positions requiring puncturing or shortening in advance. Furthermore, adjustments to certain positions in the sequence do not affect the reliability of channel transmission in this scenario. For example, interchanging the selected K sequence numbers does not affect the selection of those K sequence numbers; the only requirement is that the polarization channel reliabilities corresponding to the selected K sequence numbers are higher than the polarization channel reliabilities corresponding to the remaining (MK) sequence numbers in the sequence. Optionally, the selected K sequence numbers are the last K sequence numbers in the first sequence, or the selected K sequence numbers are the first K sequence numbers in the first sequence.

[0102] Optionally, the first sequence is pre-stored.

[0103] Optionally, when the mother code length N is 4096, the number of information bits K is: 452, 536, 904, 1048, 1808, 2072, 2712 or 3096; Optionally, K may float based on the above value, for example, increasing or decreasing by 20. Based on 452, the number of information bits K may be an integer between 432 and 472: 433, 434, 435, 436, 437, 438, 439, 440, ..., 470, 471, 472. Similarly, based on 536, the number of information bits K may be an integer between 516 and 556: 516, 517, ..., 555, 556. Based on 3096, the number of information bits K may be an integer between 3076 and 3116: 3076, 3077, ..., 3115, 3116. Other K values ​​are also applicable.

[0104] Alternatively, when the mother code length N is 8192, the number of information bits K is: 235, 470, 940, 1880, 2820, or 3760. Optionally, K may fluctuate based on the above values, for example, by increasing or decreasing by 20. Based on 235, the number of information bits K may be an integer between 215 and 255: 215, 216, ..., 254, 255; based on 470, the number of information bits K may be an integer between 450 and 490: 450, 451, ..., 489, 490; based on 940, the number of information bits K may be an integer between 920 and 960: 920, 921, ..., 959, 960. Other K values ​​are also applicable.

[0105] Optionally, when the mother code length is 4096, the first sequence is sequence Q1 in the specification; or when the mother code length is 8192, the first sequence is sequence Q2 in the specification.

[0106] Optionally, the N polarized channels are numbered from 0 to (N-1) or from 1 to N.

[0107] Optionally, the bits to be encoded include cyclic redundancy check CRC bits.

[0108] Optionally, the bits to be encoded include parity check PC bits.

[0109] based on Figure 4 The same inventive concept of the Polar code encoding method shown in FIG. Figure 6 As shown, the embodiment of the present application further provides a Polar code encoding device 600, which is used to perform Figure 4 Polar code encoding method shown. Figure 4 Part or all of the Polar code encoding method shown can be implemented by hardware or software. When implemented by hardware, the Polar code encoding device 600 includes: an input interface circuit 601 for obtaining bits to be encoded; a logic circuit 602 for executing the above Figure 4 The Polar code encoding method shown is described in detail in the previous method embodiment and will not be repeated here; the output interface circuit 603 is used to output the encoded bit sequence.

[0110] Furthermore, the coded bit sequence output by the encoding device 600 is modulated by the modulator 610 and then output to the transceiver 620. The transceiver 620 performs corresponding processing (including but not limited to digital-to-analog conversion and / or frequency conversion) on the modulated sequence before transmitting it via the antenna 630. It will be readily understood that from a product integration perspective, if certain conditions permit, the modulator 610 and the transceiver 620 can be a single functional implementation module or unit, or the transceiver 620 and the antenna 660 can be a single functional implementation module or unit. Optionally, the system may further include a demodulator 611 for demodulating the coded bit information obtained by the transceiver. (611 is not shown in the figure.) Similarly, the modulator and demodulator may be implemented using a single physical entity. For example, 610 may be a modem, and the encoding device and decoding device may be the same physical entity.

[0111] Optionally, the Polar code encoding device 600 may be a chip or an integrated circuit in a specific implementation.

[0112] Optionally, when part or all of the Polar code encoding method in the above embodiment is implemented by software, such as Figure 7 As shown, the Polar code encoding device 700 includes: a memory 701 for storing a program; a processor 702 for executing the program stored in the memory 701. When the program is executed, the Polar code encoding device 700 can achieve the above Figure 4 The embodiment provides a Polar code encoding method.

[0113] Optionally, the memory 701 may be a physically independent unit or a Figure 7 As shown, the memory 701 and the processor 702 are integrated together.

[0114] Optional, when the above Figure 4 When part or all of the encoding method of the embodiment is implemented via software, the Polar code transmission device 700 may also include only the processor 702. The memory 701 for storing programs is located outside the Polar code encoding device 700. The processor 702 is connected to the memory 701 via circuits / wires to read and execute the programs stored in the memory 701.

[0115] Similarly, based on Figure 5 The same inventive concept of the Polar code decoding method shown in FIG. Figure 8 As shown, the embodiment of the present application also provides a Polar code decoding device 800, which is used to perform Figure 5 The Polar code decoding method shown. Figure 8Part or all of the Polar code decoding method shown can be implemented by hardware or software. When implemented by hardware, the Polar code decoding device 800 includes: an input interface circuit 801 for obtaining bits to be decoded; a logic circuit 802 for executing the above Figure 5 The Polar code decoding method shown is described in detail in the previous method embodiment and will not be repeated here. The output interface circuit 803 is used to output the decoded bit sequence.

[0116] Furthermore, the decoding device 800 is also connected to a demodulator 810 and a transceiver 820, which is further connected to an antenna 830. The antenna receives the encoded bit information, processes it accordingly through the transceiver, and transmits it to the demodulator. The demodulator 810 demodulates the processed encoded bit information and provides it to the decoding device for further processing. It is easy to understand that from the perspective of product integration, if certain conditions permit, the demodulator 810 and transceiver 820 can be a functional implementation module or implementation unit, or the transceiver 820 and antenna 830 can be a functional implementation module or implementation unit.

[0117] Optionally, the Polar code decoding device 800 may be a chip or an integrated circuit in a specific implementation.

[0118] Optionally, when part or all of the Polar code decoding method in the above embodiment is implemented by software, such as Figure 9 As shown, the Polar code decoding device 900 includes: a memory 901 for storing a program; a processor 902 for executing the program stored in the memory 901. When the program is executed, the Polar code decoding device 900 can achieve the above Figure 5 The embodiment provides a Polar code decoding method.

[0119] Optionally, the memory 901 may be a physically independent unit, or the memory 901 and the processor 902 may be integrated together.

[0120] Optional, when the above Figure 5 When part or all of the decoding method of the embodiment is implemented via software, the Polar code transmission device 900 may also include only the processor 902. The memory 901 for storing programs is located outside the Polar code decoding device 900. The processor 902 is connected to the memory 901 via circuits / wires to read and execute the programs stored in the memory 901.

[0121] The processor may be a central processing unit (CPU), a network processor (NP), or a combination of a CPU and an NP. The processor may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The PLD may be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof.

[0122] The memory in the above embodiments may include volatile memory, such as random-access memory (RAM); the memory may also include non-volatile memory, such as flash memory, hard disk drive (HDD) or solid-state drive (SSD); the memory may also include a combination of the above types of memory.

[0123] based on Figure 4 The Polar code encoding method shown in Figure 10 As shown, the embodiment of the present application further provides a Polar code encoding device 1000, which is used to perform Figure 4 The Polar code encoding method shown in FIG. 1 includes a Polar code encoding device 1000 including:

[0124] An acquisition unit 1001 is configured to acquire K bits to be encoded;

[0125] A selecting unit 1002 is configured to select K sequence numbers from a first sequence, where polarized channels corresponding to the K sequence numbers are used to place the bits to be coded;

[0126] The encoding unit 1003 is configured to perform Polar code encoding on the K bits to be encoded to obtain encoded bits.

[0127] The first sequence includes the sequence numbers of N polarized channels. The first sequence is the entire sequence or a subsequence of the sequence Q1 or Q2 in the specification. K is a positive integer, and N is the mother code length of the Polar code, N=2. n , n is a positive integer, K≤N.

[0128] The acquisition unit 1001, the selection unit 1002 and / or the encoding unit 1003 of the Polar code encoding device 1000 are also used to perform Figure 4 For some or all of the methods in the Polar code encoding method shown, the specific functions implemented can refer to the aforementioned Polar code encoding method.

[0129] based on Figure 5 The Polar code decoding method shown in Figure 11 As shown, the embodiment of the present application further provides a Polar code decoding device 1100, which is used to perform Figure 5 The Polar code decoding method shown in FIG. 1 includes a Polar code decoding device 1100 including:

[0130] Receiving unit 1101 is configured to receive bit information to be decoded, where the bit information to be decoded includes K information bits, where the K information bits are carried on polarized channels corresponding to K sequence numbers of a first sequence, where the first sequence includes sequence numbers of N polarized channels, and the first sequence is all or a subsequence of a sequence shown as sequence Q1 or Q2 in the specification, where K is a positive integer, and N is a mother code length of a Polar code, where N=2. n , n is a positive integer, K≤N;

[0131] The decoding unit 1102 is configured to perform Polar code decoding on the bit information to be decoded to obtain the K information bits.

[0132] The acquisition unit 1101 and / or the decoding unit 1102 of the Polar code decoding device 1100 is also used to perform Figure 5 For some or all of the methods in the Polar code decoding method shown, the specific functions implemented can refer to the aforementioned Polar code decoding method.

[0133] The present application also provides a computer storage medium storing a computer program, wherein the computer program includes a computer program for executing Figure 4 Polar code encoding method shown, or perform Figure 5 The Polar code decoding method shown.

[0134] The present application also provides a computer program product comprising instructions, which, when executed on a computer, causes the computer to execute Figure 4 Polar code encoding method shown, or perform Figure 5 The Polar code decoding method shown.

[0135] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0136] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0137] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0138] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0139] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0140] Obviously, those skilled in the art may make various changes and modifications to the embodiments of the present application without departing from the spirit and scope of the embodiments of the present application. Thus, if these modifications and variations of the embodiments of the present application fall within the scope of the claims of the present application and their equivalents, the present application also intends to include such modifications and variations.

[0141] The first sequence Q1 is obtained by equalizing the performance of the codes with the bit length K of 536, 1048, 2072, 3096, 452, 904, 1808, and 2712. The sequence length is 4096, Q1=

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,2895,3724,2001,1022,3629,3467,3413,3386,3305,2981,1947,3672,2791,1785,3359,3292,3024,3197,2929,3730,1996,3635,2549,1901,2970,3255,2875,2808,3846,2495,1959,3684,3522,2781,3427,2924,2002,3630,3496,1907,3414,3849,3306,2982,1527,1976,3659,3469,1786,3388,3279,3011,1949,3198,2930,3745,1759,3417,2550,1902,2985,2903,3732,2795,3637,3475,2972,3313,2877,2782,3904,2687,2553,2017,3524,3259,3429,3850,2004,1963,3688,3470,1909,3375,3308,3040,1950,3661,3746,1855,1788,3418,3013,2986,1531,2932,3719,3638,3504,2959,3857,3314,2878,2797,3667,3477,2554,2018,3287,2907,3736,3430,3641,2527,1991,3261,1910,2993,3852,2803,1965,3662,3528,1775,3433,3014,2008,2919,3748,1913,3420,3491,2988,1533,3858,3777,2798,1971,3696,3478,3017,3383,3316,2936,3723,3669,3642,2556,2020,2909,3262,2994,3615,3481,1966,3291,2967,3434,2805,1995,1914,3407,3968,2751,1534,3873,3778,1887,3683,3493,3018,3860,3303,2923,3752,1973,3670,3536,2543,1783,3441,2910,3725,1023,3644,3482,3387,3320,2996,3673,2806,2024,3293,3025,3436,3731,1997,3874,1916,2971,3494,2809,3847,3780,1974,3685,3523,3020,3442,2925,3726,2003,3631,3497,3415,3864,3307,2983,1977,3674,3484,1787,3389,3294,3026,3199,2931,3760,1998,2551,1903,3000,3733,2810,3876,2973,3686,3552,2783,3905,2926,2032,3525,3498,3444,3851,3784,2005,1978,3689,3471,3390,3309,3041,1951,3676,3747,1789,3419,3028,2987,2933,3734,3639,3505,2974,3315,2879,2812,3906,2555,2019,3526,3737,3431,3880,2006,3690,3500,1911,3853,3310,3042,1980,3663,3529,1790,3448,3015,2009,2934,3749,3421,3506,2989,3859,3792,2799,3697,3479,3032,3317,2937,3738,3908,3643,2557,2021,3263,2995,3854,1967,3692,3530,3435,3044,2010,3750,1915,3422,3969,2990,1535,3888,3779,3698,3508,3019,3861,3318,2938,3753,3671,3537,2558,2022,2911,3740,3645,3483,3321,2997,3912,2807,2025,3532,3437,3970,2012,3875,3808,1917,3495,3048,3862,3781,3754,1975,3700,3538,3021,3443,2940,3727,3646,3512,3865,3322,2998,3675,3485,2026,3295,3027,3438,3761,1999,1918,3001,3972,2811,3877,3782,3687,3553,3022,3920,2927,3756,2033,3540,3499,3445,3866,3785,1979,3704,3486,3391,3324,3056,3677,3762,2028,3029,3002,3735,3878,2975,3554,2813,3907,2034,3527,3976,3446,3881,3786,2007,3691,3501,3868,3311,3043,1981,3678,3544,1791,3449,3030,2935,3764,3507,3004,3793,2814,3936,3033,3556,3739,3909,3882,2036,3502,3855,3788,1982,3693,3531,3450,3045,2011,3751,3423,3984,2991,3889,3794,3699,3509,3034,3319,2939,3768,3910,2559,2023,3741,3884,3694,3560,3913,3046,2040,3533,3452,3971,2013,3890,3809,3510,3049,3863,3796,3755,3701,3539,3036,2941,3742,3647,3513,3323,2999,3914,2027,3534,3439,4000,2014,3810,1919,3973,3050,3892,3783,3702,3568,3023,3921,2942,3757,3541,3514,3867,3800,3705,3487,3325,3057,3916,3763,2029,3003,3974,3879,3812,3555,3052,3922,3758,2035,3542,3977,3447,3896,3787,3706,3516,3869,3326,3058,3679,3545,2030,3031,3765,3005,4032,2815,3937,3557,3978,3924,3883,3816,2037,3503,3870,3789,1983,3708,3546,3451,3060,3766,3985,3006,3795,3938,3035,3558,3769,3911,2038,3980,3885,3790,3695,3561,3928,3047,2041,3548,3453,3986,3891,3824,3511,3064,3797,3770,3940,3037,3743,3886,3562,3915,2042,3535,3454,4001,2015,3811,3988,3051,3893,3798,3703,3569,3038,2943,3772,3515,3801,3944,3564,3917,4002,2044,3975,3894,3813,3570,3053,3923,3759,3543,3992,3897,3802,3707,3517,3327,3059,3918,2031,4004,3814,4033,3054,3952,3572,3979,3925,3898,3817,3518,3871,3804,3709,3547,3061,3767,3007,4034,3939,3559,4008,3926,3818,2039,3981,3900,3791,3710,3576,3929,3062,3549,3987,3825,3065,4036,3771,3941,3982,3887,3820,3563,3930,2043,3550,3455,4016,3826,3989,3066,3799,3942,3039,3773,4040,3945,3565,3932,4003,2045,3990,3895,3828,3571,3068,3774,3993,3803,3946,3566,3919,2046,4005,3815,4048,3055,3953,3573,3994,3899,3832,3519,3805,3948,4006,4035,3954,3574,4009,3927,3819,3996,3901,3806,3711,3577,3063,4064,4037,4010,3956,3983,3902,3821,3578,3931,3551,4017,3827,3067,4038,3943,4012,3822,4041,3960,3580,3933,4018,3991,3829,3069,3775,4042,3947,3567,3934,2047,4020,3830,4049,3070,3995,3833,4044,3949,4007,4050,3955,3575,4024,3834,3997,3807,3950,4065,4052,4011,3957,3998,3903,3836,3579,4066,4039,3958,4013,3823,4056,3961,3581,4019,4068,4014,4043,3962,3582,3935,4021,3831,3071,4072,4045,3964,4022,4051,4025,3835,4046,3951,4080,4053,4026,3999,3837,4067,4054,3959,4028,3838,4057,4069,4015,4058,3963,3583,4070,407 3,4060,3965,4023,4074,4047,3966,4081,4027,4076,4082,4055,4029,3839,4084,4030,4059,4071,4088,4061,4075,4062,3967,4077,4083,4078,4085,4031,4086,4089,4090,4063,4092,4079,4087,4091,4093,4094,4095,].

[0143] The first sequence Q2 is obtained by balancing the performance of codes with the bit length K to be encoded being 235, 470, 940, 1880, 2820, and 3760. The sequence length is 8192 (for the sake of space and practical considerations, the actual sequence length currently displayed by Q2 is 3760. When the mother code length is 8192, the maximum number of information bits in this scenario is 3760, so only the 3760 sequence numbers required out of 8192 are needed). Q2 =

[0144] [6309,5445,6419,5391,6298,6203,5667,5287,6414,5654,6252,5425,5330,5235,6310,6663,5446,5657,6339,5277,3623,6258,5420,4819,6421,5230,6313,6231,5449,3381,3721,6300,4935,6205,5669,5507,5004,5426,5345,4909,4814,3613,3289,5399,5332,5291,6692,5237,5658,6435,5278,3405,5010,5183,4915,6422,6341,6314,3681,6260,3463,6667,5450,4821,3382,3301,4794,3722,6287,4964,3668,3627,6206,5670,3411,4767,6425,3247,2979,5346,4910,3614,6235,3480,5699,5509,4586,3385,3290,5428,2966,5319,4939,5768,3195,5238,6321,5673,4559,7180,5457,4478,5293,3406,5025,6722,3729,6532,5660,4835,6437,6342,5403,2969,5336,5012,3682,6247,3492,6696,5241,2779,4917,4822,3845,6480,3302,2922,6316,4727,4593,3655,7186,3521,6669,5452,5299,3440,4796,2895,6426,3724,6345,4539,3629,6264,3467,5728,5510,3413,4825,3386,3305,5415,2981,5348,4968,1947,3672,6237,5701,2791,6322,5674,4588,3359,3292,6675,5458,4941,5294,3197,5026,2929,3730,6295,5647,5513,3635,6438,2549,1901,5432,2970,5323,4999,6724,3255,2875,5242,4918,4837,3846,6467,5405,2495,1959,4594,3684,7201,3522,6670,5215,2781,6536,4947,5776,3427,4783,2924,6441,6346,5681,2002,4567,7188,5016,3630,6251,3496,1907,5301,3414,4921,4826,3849,6428,3306,5892,2982,1527,4731,1976,4541,3659,6238,3469,5702,6785,5568,1786,4351,3388,3279,6704,5473,3011,4942,1949,3198,2930,3745,6324,5676,1759,5514,3417,6677,5460,2550,1902,5419,2985,5352,5028,2903,3732,6353,5705,2795,4838,3637,6496,3475,5406,2972,5325,5057,7202,3313,2877,5244,2782,6299,4976,5763,6469,2687,6442,2553,5682,2017,4596,7175,3524,5003,6728,3259,4949,5302,3429,4922,4841,3850,6415,6348,5655,2004,5521,1963,4542,3688,6253,3470,1909,6786,5331,4895,4828,3375,3308,6691,5474,3040,4733,1950,4571,3661,7192,3746,6311,1855,1788,5305,3418,6678,5447,3013,6544,5896,2986,1531,4791,2932,6449,3719,6354,5706,5516,3638,6259,3504,5421,2959,5326,5058,3857,3314,2878,5231,2797,6328,4963,5792,3667,6470,3477,6681,5464,2554,2018,4583,7204,3287,5032,2907,3736,6301,4950,5765,3430,4842,3641,6444,2527,5684,1991,5522,7233,5005,6254,3261,1910,5427,2993,5360,4924,4815,3852,6473,5713,2803,4734,1965,4600,3662,7179,3528,6788,5333,4953,1775,5306,3433,6693,5476,3014,6531,5659,2008,4573,2919,6450,3748,6369,1913,5279,3420,5011,6736,3491,5422,2988,1533,4849,3858,6423,3777,6356,5708,2798,6315,1971,3696,6261,3478,6682,5451,3017,5060,3383,3316,4795,2936,3723,6302,4965,5766,3669,3642,6207,2556,5671,2020,5537,7234,5006,2909,3262,5904,2994,5347,4911,4844,3615,6474,3481,5714,5524,1966,4587,7208,3291,5429,2967,5334,4954,5769,3434,6694,5239,2805,6560,5688,1995,4574,7181,6913,6370,1914,4479,5308,3407,5040,6723,3968,6533,5661,2751,1534,4850,3873,6452,3778,6343,1887,6792,5337,5013,3683,6262,3493,6697,5480,3018,4823,3860,6481,3303,2923,3752,6317,4966,1973,3670,7187,3536,6684,5453,2543,1783,5538,3441,4797,2910,6427,3725,6360,5891,5824,1023,3644,6265,3482,5729,5511,7236,5064,3387,3320,5430,2996,5349,4969,5770,3673,6476,5716,2806,6323,5675,2024,4589,7182,3293,6914,5459,3025,4956,5295,3436,5027,6752,3731,6534,5662,1997,5528,3874,6439,6372,1916,5433,2971,5338,5014,6725,3494,6698,5243,2809,4919,4852,3847,6482,3780,7297,6318,1974,4595,3685,7216,3523,6671,5454,3020,6537,5777,3442,4798,2925,6456,3726,6347,5920,2003,7189,5017,3631,6266,3497,5730,5540,3415,4827,3864,6429,3307,5893,2983,5350,4970,1977,3674,6239,3484,5703,6800,5569,1787,4590,3389,3294,6705,5488,3026,4943,5772,3199,2931,3760,6325,5677,1998,5515,7240,6916,5461,2551,1903,5434,3000,5353,5029,6726,3733,6592,5720,2810,4839,3876,6497,7298,5407,2973,5340,5072,3686,7203,3552,6700,5245,2783,6538,4977,5778,3905,6484,2926,6443,6376,5683,2032,4597,7190,3525,5018,6729,3498,5303,3444,4923,4856,3851,6430,3784,6349,5894,2005,1978,4543,3689,6268,3471,5732,6787,5570,4829,3390,3309,6706,5475,3041,4972,1951,3676,7193,3747,6326,5678,1789,5544,3419,6679,5462,3028,6545,5897,2987,5354,5030,2933,3734,6355,5707,5517,3639,6498,3505,5436,2974,5327,5059,3315,2879,5246,2812,6329,4978,5793,3906,6471,7300,6920,5465,2555,2019,4598,7205,3526,5033,6730,3737,6540,4951,5780,3431,4843,3880,6350,5685,2006,5523,7248,5020,3690,6255,3500,1911,6816,5361,4925,4830,3853,6488,3310,5952,3042,4735,1980,4601,3663,7194,3529,6789,5572,1790,5307,3448,6708,5477,3015,6546,5898,2009,2934,3749,6384,5736,5518,3421,3506,5423,2989,5356,5088,3859,3792,2799,5794,3697,6500,3479,5466,3032,5061,3317,5034,2937,3738,4980,3908,7425,3643,2557,2021,5552,5007,3263,5905,2995,5362,4926,4845,3854,7304,1967,4602,3692,3530,5335,4955,5784,3435,3044,2010,4575,6928,3750,1915,5309,3422,5041,3969,5900,2990,1535,4851,3888,3779,5576,3698,3508,3019,5062,3318,2938,4967,7426,3537,2558,2022,7264,5036,2911,3740,4846,3645,3483,5744,3321,2997,4984,3912,2807,2025,4604,3532,6848,3437,3970,2012,3808,1917,3048,7312,1975,3021,6016,2940,7428,3512,2998,2026,6944,1918,3972,3920,3056,7681,6445,6451,6737,6357,5709,6330,6683,7206,6303,5767,6446,5686,7235,6732,6475,5715,5525,7209,6790,6695,5478,6561,5689,7196,6371,6738,6548,6453,6358,5710,6793,6263,6712,5481,3861,3753,6332,5796,3671,6685,5468,5539,6361,5906,5825,6504,5526,7237,5065,7210,5431,5364,5771,6477,5717,6562,5690,7183,6915,4957,5310,5042,6753,6535,5663,5529,3875,6454,6373,6794,5339,5015,6740,3495,6699,5482,4853,3862,6483,3781,3754,6319,3700,7217,3538,6686,5455,6552,3443,4799,6457,3727,6362,5921,5826,3646,6267,5731,5541,7238,5066,3865,3322,5908,5351,4971,5800,3675,6478,3485,5718,6801,5584,4591,7212,3295,5489,3027,4958,5773,3438,6754,3761,6564,5692,1999,5530,7241,6917,6374,5435,3001,5368,5044,6727,6593,5721,2811,4854,3877,6512,3782,7299,6796,5341,5073,3687,7218,3553,6701,5484,3022,6539,5779,6485,2927,6458,3756,6377,5922,2033,7191,3540,5019,6744,3499,5542,3445,4857,3866,6431,3785,6364,5895,5828,1979,3704,6269,3486,5733,6802,5571,5068,3391,3324,6707,5490,4973,5774,3677,7432,3762,6327,5679,2028,5545,7242,6918,5463,3029,5912,3002,5355,5031,6756,3735,6594,5722,5532,3878,6499,7328,5437,2975,5342,5074,3554,6702,5247,2813,6568,4979,5808,3907,6486,7301,6921,6378,2034,4599,7220,3527,5048,6731,3976,6541,5781,3446,4858,3881,6460,3786,6351,5924,2007,7249,5021,3691,6270,3501,5734,6817,5600,4831,3868,6489,3311,5953,3043,4974,1981,3678,7195,3544,6804,5573,1791,5546,3449,6709,5492,3030,6547,5899,5832,2935,3764,6385,5737,5519,7244,6976,3507,5438,3004,5357,5089,7682,3793,6596,5724,2814,6331,5795,3936,6501,7302,6922,5467,3033,5076,7207,3556,5035,6760,3739,6542,4981,5782,3909,7440,3882,6447,6380,5687,2036,5553,7250,5022,6733,3502,6818,5363,4927,4860,3855,6490,3788,7305,5954,1982,4603,3693,7224,3531,6791,5574,5785,3450,6710,5479,3045,6576,5928,2011,7197,6929,3751,6386,5738,5548,3423,6739,3984,6549,5901,2991,5358,5090,3889,3794,6359,5711,6808,5577,3699,6502,3509,6713,5496,3034,5063,7684,3319,2939,3768,6333,4982,5797,3910,7427,7360,6924,5469,2559,2023,5554,7265,5037,6734,3741,6600,5907,5840,4847,3884,6505,7306,5745,5527,7252,5080,3694,7211,3560,6820,5365,4985,5786,3913,6492,5956,3046,6563,5691,2040,4605,7198,3533,6930,6849,5311,3452,5043,6768,3971,6550,5902,2013,3890,6455,3809,6388,5740,6795,5578,6741,3510,6714,5483,3049,5092,3863,3796,7313,3755,6334,5798,3701,7456,3539,6687,5470,3036,6553,6017,7266,5038,2941,3742,6363,5936,5827,7429,3647,6506,3513,5746,5556,7239,5067,7688,3323,5909,2999,5366,4986,5801,3914,6479,7308,5719,7040,5585,2027,4606,7213,3534,6945,6850,4959,5788,3439,6755,4000,6565,5693,2014,5531,7256,6932,3810,6375,1919,6824,5369,5045,6742,3973,6608,5960,3050,4855,3892,6513,3783,7314,6797,5580,3702,7219,3568,6716,5485,3023,6554,6018,3921,2942,6459,3757,6392,5923,5856,7430,3541,6745,3514,5543,7268,5096,3867,3800,6365,5910,5829,5802,3705,6508,3487,5748,6803,5586,5069,7214,3325,6946,5491,3057,4988,5775,3916,7433,3763,6566,5694,2029,5560,7243,6919,6852,5913,3003,5370,5046,6757,3974,6595,5723,5533,3879,6514,3812,7329,6798,5343,5075,7696,3555,6703,5486,3052,6569,5809,3922,6487,7316,6936,3758,6379,2035,7221,3542,5049,6746,3977,6556,6020,3447,4859,3896,6461,3787,6366,5925,5830,7488,3706,6271,3516,5735,6832,5601,5070,3869,3326,5968,3058,4975,5804,3679,7434,3545,6805,5588,2030,5547,7272,6948,5493,3031,5914,5833,6758,3765,6624,5752,5534,7245,6977,7330,5439,3005,5372,5104,7683,4032,6597,5725,2815,6570,5810,3937,6516,7303,6923,6856,5077,7222,3557,5050,6761,3978,6543,5783,3924,7441,3883,6462,3816,6381,5926,2037,7251,5023,6748,3503,6819,5602,4861,3870,6491,3789,7320,5955,1983,3708,7225,3546,6806,5575,6024,3451,6711,5494,3060,6577,5929,5834,7436,3766,6387,5739,5549,7246,6978,3985,5916,3006,5359,5091,7712,3795,6598,5726,6809,5592,3938,6503,7332,6952,5497,3035,5078,7685,3558,6762,3769,6572,4983,5812,3911,7442,7361,6925,6382,2038,5555,7280,5052,6735,3980,6601,5841,4862,3885,6520,3790,7307,5984,7253,5081,3695,7226,3561,6821,5604,5787,3928,6493,5957,3047,6578,5930,2041,7199,3548,6931,6864,5550,3453,6769,3986,6551,5903,5836,3891,3824,6389,5741,6810,5579,6980,3511,6715,5498,3064,5093,7686,3797,7552,3770,6335,5799,3940,7457,7362,6926,5471,3037,6032,7267,5039,6764,3743,6602,5937,5842,7444,3886,6507,7336,5747,5557,7254,5082,7689,3562,6822,5367,4987,5816,3915,6494,7309,5958,7041,2042,4607,7228,3535,6960,6851,5789,3454,6770,4001,6580,5932,2015,7257,6933,3811,6390,5742,6825,5608,6743,3988,6609,5961,3051,5094,3893,3798,7315,6812,5581,3703,7458,3569,6717,5500,3038,6555,6019,7744,2943,3772,6393,5938,5857,7431,7364,6984,3515,5558,7269,5097,7690,3801,6604,5911,5844,5803,3944,6509,7310,5749,7042,5587,5084,7215,3564,6947,6880,4989,5790,3917,7448,4002,6567,5695,2044,5561,7258,6934,6853,6826,5371,5047,6772,3975,6610,5962,3894,6515,3813,7344,6799,5582,7697,3570,6718,5487,3053,6584,6048,3923,7317,6937,3759,6394,5858,7460,3543,6747,3992,6557,6021,7270,5098,3897,3802,6367,5940,5831,7489,3707,6510,3517,5750,6833,5616,5071,7692,3327,5969,3059,4990,5805,3918,7435,7368,7044,5589,2031,5562,7273,6949,6854,5915,5848,6759,4004,6625,5753,5535,7260,6992,3814,7331,6828,5373,5105,7698,4033,6612,5964,3054,6571,5811,3952,6517,7318,6938,6857,7223,3572,5051,6776,3979,6558,6022,3925,3898,6463,3817,6396,5927,5860,7490,6749,3518,6834,5603,5100,3871,3804,7321,5970,5806,3709,7464,3547,6807,5590,6025,7274,6950,5495,3061,5944,5835,7437,3767,6626,5754,5564,7247,6979,7808,5917,3007,5374,5106,7713,4034,6599,5727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7676,8029,8114,8087,7925,7165,7871,8138,8043,7663,8030,6143,8116,7926,8145,7166,8091,7929,8140,8045,8103,8146,8051,7671,8120,7930,8093,7903,8046,8161,8148,8107,8053,8094,7999,7932,7675,8162,8135,8054,8 109,7919,8152,8057,7677,8115,8164,8110,8139,8058,7678,8031,8117,7927,7167,8168,8141,8060,8118,8147,8121,7931,8142,8047,8176,8149,8122,8095,7933,8163,8150,8055,8124,7934,8153,8165,8111,8154,8059,7679,8 166,8169,8156,8061,8119,8170,8143,8062,8177,8123,8172,8178,8151,8125,7935,8180,8126,8155,8167,8184,8157,8171,8158,8063,8173,8179,8174,8181,8127,8182,8185,8186,8159,8188,8175,8183,8187,8189,8190,8191,].

[0145] Shortened position set, S1=

[0146] [15,31,47,63,79,95,111,127,143,159,175,191,207,223,239,255,271,287,303,319,335,351,367,383,399,415,431,447,463,479,495,511,527,543,559,575,591,607,623,639,655,671,687,703,719,735,751,767,783,799,815,831,847,863,879,895,911,927,943,959,975,991,1007,1023,1039,1055,1071,1087,1103,1119,1135,1151,1167,1183,1199,1215,1231,1247,1263,1279,1295,1311,1327,1343,1359,1375,1391,1407,1423,1439,1455,1471,1487,1503,1519,1535,1551,1567,1583,1599,1615,1631,1647,1663,1679,1695,1711,1727,1743,1759,1775,1791,1807,1823,1839,1855,1871,1887,1903,1919,1935,1951,1967,1983,1999,2015,2031,2047,2063,2079,2095,2111,2127,2143,2159,2175,2191,2207,2223,2239,2255,2271,2287,2303,2319,2335,2351,2367,2383,2399,2415,2431,2447,2463,2479,2495,2511,2527,2543,2559,2575,2591,2607,2623,2639,2655,2671,2687,2703,2719,2735,2751,2767,2783,2799,2815,2831,2847,2863,2879,2895,2911,2927,2943,2959,2975,2991,3007,3023,3039,3055,3071,3087,3103,3119,3135,3151,3167,3183,3199,3215,3231,3247,3263,3279,3295,3311,3327,3343,3359,3375,3391,3407,3423,3439,3455,3471,3487,3503,3519,3535,3551,3567,3583,3599,3615,3631,3647,3663,3679,3695,3711,3727,3743,3759,3775,3791,3807,3823,3839,3855,3871,3887,3903,3919,3935,3951,3967,3983,3999,4015,4031,4047,4063,4079,4095].

[0147] It should be noted that the above sequences are only examples. Their application to Polar coding will help improve Polar codec performance. Within any of the example sequences, adjustments or equivalent replacements can be made, including but not limited to the following, without affecting the overall performance:

[0148] 1. Swap the positions of a few elements in a sequence. For example, the position of a sequence number can be adjusted within a set range. For example, if the range is set to 5, the position of the element with sequence number 10 can be adjusted within 5 positions to the left or right.

[0149] 2. Some elements in the sequence are adjusted, but the set of channels selected according to the sequence for transmitting T bits of information is consistent or similar.

[0150] 3. The sequence contains N elements, starting from 0 and ending at N-1. These N elements represent the sequence numbers of the N polarized channels. In practice, the sequence numbers of the N polarized channels can also start from 1 and end at N by incrementing each sequence number by 1. This is also the sequence number format used in the above calculation methods. Of course, other methods can also be used to represent the sequence numbers or identifiers of the polarized channels. This specific representation does not affect the specific position of the polarized channels represented in the sequence.

[0151] 4. The sequence numbers of the N polarized channels in the above sequence are arranged in ascending order of their reliabilities. In this case, selecting K polarized channels in descending order of reliability is equivalent to selecting the polarized channels corresponding to the last K sequence numbers in any of the above sequences. In fact, the sequence numbers of the N polarized channels can also be arranged in descending order of their reliabilities by reversing or reversing the order of the elements in the above sequence. In this case, selecting K polarized channels in descending order of reliability is equivalent to selecting the polarized channels corresponding to the first K sequence numbers.

[0152] 5. The above sequence can also be represented using the normalized reliability of each channel or an equivalent reliability sequence. For example, if channel x is ranked n in the above sequence (the leftmost is 1), the reliability of this channel can be expressed as n or normalized n / N, where N is the length of the sequence.

Claims

1. A polar code encoding method, characterized in that: include: Obtain K bits to be encoded; K sequence numbers are selected from the first sequence, the bits to be coded are placed on the polarized channels corresponding to the K sequence numbers, and polar codes are performed on the K bits to be coded to obtain coded bits, where: The first sequence includes the sequence numbers of N polarized channels. The first sequence is the entire sequence or a subsequence of the sequence indicated by sequence Q1 or Q2. K is a positive integer, and N is the mother code length of the Polar code, where N=2. n , n is a positive integer, K≤N; in, The sequence Q1= 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,2895,3724,2001,1022,3629,3467,3413,3386,3305,2981,1947,3672,2791,1785,3359,3292,3024,3197,2929,3730,1996,3635,2549,1901,2970,3255,2875,2808,3846,2495,1959,3684,3522,2781,3427,2924,2002,3630,3496,1907,3414,3849,3306,2982,1527,1976,3659,3469,1786,3388,3279,3011,1949,3198,2930,3745,1759,3417,2550,1902,2985,2903,3732,2795,3637,3475,2972,3313,2877,2782,3904,2687,2553,2017,3524,3259,3429,3850,2004,1963,3688,3470,1909,3375,3308,3040,1950,3661,3746,1855,1788,3418,3013,2986,1531,2932,3719,3638,3504,2959,3857,3314,2878,2797,3667,3477,2554,2018,3287,2907,3736,3430,3641,2527,1991,3261,1910,2993,3852,2803,1965,3662,3528,1775,3433,3014,2008,2919,3748,1913,3420,3491,2988,1533,3858,3777,2798,1971,3696,3478,3017,3383,3316,2936,3723,3669,3642,2556,2020,2909,3262,2994,3615,3481,1966,3291,2967,3434,2805,1995,1914,3407,3968,2751,1534,3873,3778,1887,3683,3493,3018,3860,3303,2923,3752,1973,3670,3536,2543,1783,3441,2910,3725,1023,3644,3482,3387,3320,2996,3673,2806,2024,3293,3025,3436,3731,1997,3874,1916,2971,3494,2809,3847,3780,1974,3685,3523,3020,3442,2925,3726,2003,3631,3497,3415,3864,3307,2983,1977,3674,3484,1787,3389,3294,3026,3199,2931,3760,1998,2551,1903,3000,3733,2810,3876,2973,3686,3552,2783,3905,2926,2032,3525,3498,3444,3851,3784,2005,1978,3689,3471,3390,3309,3041,1951,3676,3747,1789,3419,3028,2987,2933,3734,3639,3505,2974,3315,2879,2812,3906,2555,2019,3526,3737,3431,3880,2006,3690,3500,1911,3853,3310,3042,1980,3663,3529,1790,3448,3015,2009,2934,3749,3421,3506,2989,3859,3792,2799,3697,3479,3032,3317,2937,3738,3908,3643,2557,2021,3263,2995,3854,1967,3692,3530,3435,3044,2010,3750,1915,3422,3969,2990,1535,3888,3779,3698,3508,3019,3861,3318,2938,3753,3671,3537,2558,2022,2911,3740,3645,3483,3321,2997,3912,2807,2025,3532,3437,3970,2012,3875,3808,1917,3495,3048,3862,3781,3754,1975,3700,3538,3021,3443,2940,3727,3646,3512,3865,3322,2998,3675,3485,2026,3295,3027,3438,3761,1999,1918,3001,3972,2811,3877,3782,3687,3553,3022,3920,2927,3756,2033,3540,3499,3445,3866,3785,1979,3704,3486,3391,3324,3056,3677,3762,2028,3029,3002,3735,3878,2975,3554,2813,3907,2034,3527,3976,3446,3881,3786,2007,3691,3501,3868,3311,3043,1981,3678,3544,1791,3449,3030,2935,3764,3507,3004,3793,2814,3936,3033,3556,3739,3909,3882,2036,3502,3855,3788,1982,3693,3531,3450,3045,2011,3751,3423,3984,2991,3889,3794,3699,3509,3034,3319,2939,3768,3910,2559,2023,3741,3884,3694,3560,3913,3046,2040,3533,3452,3971,2013,3890,3809,3510,3049,3863,3796,3755,3701,3539,3036,2941,3742,3647,3513,3323,2999,3914,2027,3534,3439,4000,2014,3810,1919,3973,3050,3892,3783,3702,3568,3023,3921,2942,3757,3541,3514,3867,3800,3705,3487,3325,3057,3916,3763,2029,3003,3974,3879,3812,3555,3052,3922,3758,2035,3542,3977,3447,3896,3787,3706,3516,3869,3326,3058,3679,3545,2030,3031,3765,3005,4032,2815,3937,3557,3978,3924,3883,3816,2037,3503,3870,3789,1983,3708,3546,3451,3060,3766,3985,3006,3795,3938,3035,3558,3769,3911,2038,3980,3885,3790,3695,3561,3928,3047,2041,3548,3453,3986,3891,3824,3511,3064,3797,3770,3940,3037,3743,3886,3562,3915,2042,3535,3454,4001,2015,3811,3988,3051,3893,3798,3703,3569,3038,2943,3772,3515,3801,3944,3564,3917,4002,2044,3975,3894,3813,3570,3053,3923,3759,3543,3992,3897,3802,3707,3517,3327,3059,3918,2031,4004,3814,4033,3054,3952,3572,3979,3925,3898,3817,3518,3871,3804,3709,3547,3061,3767,3007,4034,3939,3559,4008,3926,3818,2039,3981,3900,3791,3710,3576,3929,3062,3549,3987,3825,3065,4036,3771,3941,3982,3887,3820,3563,3930,2043,3550,3455,4016,3826,3989,3066,3799,3942,3039,3773,4040,3945,3565,3932,4003,2045,3990,3895,3828,3571,3068,3774,3993,3803,3946,3566,3919,2046,4005,3815,4048,3055,3953,3573,3994,3899,3832,3519,3805,3948,4006,4035,3954,3574,4009,3927,3819,3996,3901,3806,3711,3577,3063,4064,4037,4010,3956,3983,3902,3821,3578,3931,3551,4017,3827,3067,4038,3943,4012,3822,4041,3960,3580,3933,4018,3991,3829,3069,3775,4042,3947,3567,3934,2047,4020,3830,4049,3070,3995,3833,4044,3949,4007,4050,3955,3575,4024,3834,3997,3807,3950,4065,4052,4011,3957,3998,3903,3836,3579,4066,4039,3958,4013,3823,4056,3961,3581,4019,4068,4014,4043,3962,3582,3935,4021,3831,3071,4072,4045,3964,4022,4051,4025,3835,4046,3951,4080,4053,4026,3999,3837,4067,4054,3959,4028,3838,4057,4069,4015,4058,3963,3583,4070,4073,4060,3965,4023,4074,4047,3966,4081,4027,4076,4082,4055,4029,3839,4084,4030,4059,4071,4088,4061,4075,4062,3967,4077,4083,4078,4085,4031,4086,4089,4090,4063,4092,4079,4087,4091,4093,4094,4095,]； The sequence Q2= [6309,5445,6419,5391,6298,6203,5667,5287,6414,5654,6252,5425,5330,5235,6310,6663,5446,5657,6339,5277,3623,6258,5420,4819,6421,5230,6313,6231,5449,3381,3721,6300,4935,6205,5669,5507,5004,5426,5345,4909,4814,3613,3289,5399,5332,5291,6692,5237,5658,6435,5278,3405,5010,5183,4915,6422,6341,6314,3681,6260,3463,6667,5450,4821,3382,3301,4794,3722,6287,4964,3668,3627,6206,5670,3411,4767,6425,3247,2979,5346,4910,3614,6235,3480,5699,5509,4586,3385,3290,5428,2966,5319,4939,5768,3195,5238,6321,5673,4559,7180,5457,4478,5293,3406,5025,6722,3729,6532,5660,4835,6437,6342,5403,2969,5336,5012,3682,6247,3492,6696,5241,2779,4917,4822,3845,6480,3302,2922,6316,4727,4593,3655,7186,3521,6669,5452,5299,3440,4796,2895,6426,3724,6345,4539,3629,6264,3467,5728,5510,3413,4825,3386,3305,5415,2981,5348,4968,1947,3672,6237,5701,2791,6322,5674,4588,3359,3292,6675,5458,4941,5294,3197,5026,2929,3730,6295,5647,5513,3635,6438,2549,1901,5432,2970,5323,4999,6724,3255,2875,5242,4918,4837,3846,6467,5405,2495,1959,4594,3684,7201,3522,6670,5215,2781,6536,4947,5776,3427,4783,2924,6441,6346,5681,2002,4567,7188,5016,3630,6251,3496,1907,5301,3414,4921,4826,3849,6428,3306,5892,2982,1527,4731,1976,4541,3659,6238,3469,5702,6785,5568,1786,4351,3388,3279,6704,5473,3011,4942,1949,3198,2930,3745,6324,5676,1759,5514,3417,6677,5460,2550,1902,5419,2985,5352,5028,2903,3732,6353,5705,2795,4838,3637,6496,3475,5406,2972,5325,5057,7202,3313,2877,5244,2782,6299,4976,5763,6469,2687,6442,2553,5682,2017,4596,7175,3524,5003,6728,3259,4949,5302,3429,4922,4841,3850,6415,6348,5655,2004,5521,1963,4542,3688,6253,3470,1909,6786,5331,4895,4828,3375,3308,6691,5474,3040,4733,1950,4571,3661,7192,3746,6311,1855,1788,5305,3418,6678,5447,3013,6544,5896,2986,1531,4791,2932,6449,3719,6354,5706,5516,3638,6259,3504,5421,2959,5326,5058,3857,3314,2878,5231,2797,6328,4963,5792,3667,6470,3477,6681,5464,2554,2018,4583,7204,3287,5032,2907,3736,6301,4950,5765,3430,4842,3641,6444,2527,5684,1991,5522,7233,5005,6254,3261,1910,5427,2993,5360,4924,4815,3852,6473,5713,2803,4734,1965,4600,3662,7179,3528,6788,5333,4953,1775,5306,3433,6693,5476,3014,6531,5659,2008,4573,2919,6450,3748,6369,1913,5279,3420,5011,6736,3491,5422,2988,1533,4849,3858,6423,3777,6356,5708,2798,6315,1971,3696,6261,3478,6682,5451,3017,5060,3383,3316,4795,2936,3723,6302,4965,5766,3669,3642,6207,2556,5671,2020,5537,7234,5006,2909,3262,5904,2994,5347,4911,4844,3615,6474,3481,5714,5524,1966,4587,7208,3291,5429,2967,5334,4954,5769,3434,6694,5239,2805,6560,5688,1995,4574,7181,6913,6370,1914,4479,5308,3407,5040,6723,3968,6533,5661,2751,1534,4850,3873,6452,3778,6343,1887,6792,5337,5013,3683,6262,3493,6697,5480,3018,4823,3860,6481,3303,2923,3752,6317,4966,1973,3670,7187,3536,6684,5453,2543,1783,5538,3441,4797,2910,6427,3725,6360,5891,5824,1023,3644,6265,3482,5729,5511,7236,5064,3387,3320,5430,2996,5349,4969,5770,3673,6476,5716,2806,6323,5675,2024,4589,7182,3293,6914,5459,3025,4956,5295,3436,5027,6752,3731,6534,5662,1997,5528,3874,6439,6372,1916,5433,2971,5338,5014,6725,3494,6698,5243,2809,4919,4852,3847,6482,3780,7297,6318,1974,4595,3685,7216,3523,6671,5454,3020,6537,5777,3442,4798,2925,6456,3726,6347,5920,2003,7189,5017,3631,6266,3497,5730,5540,3415,4827,3864,6429,3307,5893, 2983,5350,4970,1977,3674,6239,3484,5703,6800,5569,1787,4590,3389,3294,6705,5488,3026,4943,5772,3199, 2931,3760,6325,5677,1998,5515,7240,6916,5461,2551,1903,5434,3000,5353,5029,6726,3733,6592,5720,2810, 4839,3876,6497,7298,5407,2973,5340,5072,3686,7203,3552,6700,5245,2783,6538,4977,5778,3905,6484,2926, 6443,6376,5683,2032,4597,7190,3525,5018,6729,3498,5303,3444,4923,4856,3851,6430,3784,6349,5894,2005, 1978,4543,3689,6268,3471,5732,6787,5570,4829,3390,3309,6706,5475,3041,4972,1951,3676,7193,3747,6326, 5678,1789,5544,3419,6679,5462,3028,6545,5897,2987,5354,5030,2933,3734,6355,5707,5517,3639,6498,3505, 5436,2974,5327,5059,3315,2879,5246,2812,6329,4978,5793,3906,6471,7300,6920,5465,2555,2019,4598,7205, 3526,5033,6730,3737,6540,4951,5780,3431,4843,3880,6350,5685,2006,5523,7248,5020,3690,6255,3500,1911, 6816,5361,4925,4830,3853,6488,3310,5952,3042,4735,1980,4601,3663,7194,3529,6789,5572,1790,5307,3448, 6708,5477,3015,6546,5898,2009,2934,3749,6384,5736,5518,3421,3506,5423,2989,5356,5088,3859,3792,2799, 5794,3697,6500,3479,5466,3032,5061,3317,5034,2937,3738,4980,3908,7425,3643,2557,2021,5552,5007,3263, 5905,2995,5362,4926,4845,3854,7304,1967,4602,3692,3530,5335,4955,5784,3435,3044,2010,4575,6928,3750, 1915,5309,3422,5041,3969,5900,2990,1535,4851,3888,3779,5576,3698,3508,3019,5062,3318,2938,4967,7426, 3537,2558,2022,7264,5036,2911,3740,4846,3645,3483,5744,3321,2997,4984,3912,2807,2025,4604,3532,6848, 3437,3970,2012,3808,1917,3048,7312,1975,3021,6016,2940,7428,3512,2998,2026,6944,1918,3972,3920,3056, 7681,6445,6451,6737,6357,5709,6330,6683,7206,6303,5767,6446,5686,7235,6732,6475,5715,5525,7209,6790, 6695,5478,6561,5689,7196,6371,6738,6548,6453,6358,5710,6793,6263,6712,5481,3861,3753,6332,5796,3671, 6685,5468,5539,6361,5906,5825,6504,5526,7237,5065,7210,5431,5364,5771,6477,5717,6562,5690,7183,6915, 4957,5310,5042,6753,6535,5663,5529,3875,6454,6373,6794,5339,5015,6740,3495,6699,5482,4853,3862,6483, 3781,3754,6319,3700,7217,3538,6686,5455,6552,3443,4799,6457,3727,6362,5921,5826,3646,6267,5731,5541, 7238,5066,3865,3322,5908,5351,4971,5800,3675,6478,3485,5718,6801,5584,4591,7212,3295,5489,3027,4958, 5773,3438,6754,3761,6564,5692,1999,5530,7241,6917,6374,5435,3001,5368,5044,6727,6593,5721,2811,4854, 3877,6512,3782,7299,6796,5341,5073,3687,7218,3553,6701,5484,3022,6539,5779,6485,2927,6458,3756,6377, 5922,2033,7191,3540,5019,6744,3499,5542,3445,4857,3866,6431,3785,6364,5895,5828,1979,3704,6269,3486, 5733,6802,5571,5068,3391,3324,6707,5490,4973,5774,3677,7432,3762,6327,5679,2028,5545,7242,6918,5463, 3029,5912,3002,5355,5031,6756,3735,6594,5722,5532,3878,6499,7328,5437,2975,5342,5074,3554,6702,5247, 2813,6568,4979,5808,3907,6486,7301,6921,6378,2034,4599,7220,3527,5048,6731,3976,6541,5781,3446,4858, 3881,6460,3786,6351,5924,2007,7249,5021,3691,6270,3501,5734,6817,5600,4831,3868,6489,3311,5953,3043, 4974,1981,3678,7195,3544,6804,5573,1791,5546,3449,6709,5492,3030,6547,5899,5832,2935,3764,6385,5737, 5519,7244,6976,3507,5438,3004,5357,5089,7682,3793,6596,5724,2814,6331,5795,3936,6501,7302,6922,5467, 3033,5076,7207,3556,5035,6760,3739,6542,4981,5782,3909,7440,3882,6447,6380,5687,2036,5553,7250,5022, 6733,3502,6818,5363,4927,4860,3855,6490,3788,7305,5954,1982,4603,3693,7224,3531,6791,5574,5785,3450, 6710,5479,3045,6576,5928,2011,7197,6929,3751,6386,5738,5548,3423,6739,3984,6549,5901,2991,5358,5090, 3889,3794,6359,5711,6808,5577,3699,6502,3509,6713,5496,3034,5063,7684,3319,2939,3768,6333,4982,5797, 3910,7427,7360,6924,5469,2559,2023,5554,7265,5037,6734,3741,6600,5907,5840,4847,3884,6505,7306,5745, 5527,7252,5080,3694,7211,3560,6820,5365,4985,5786,3913,6492,5956,3046,6563,5691,2040,4605,7198,3533, 6930,6849,5311,3452,5043,6768,3971,6550,5902,2013,3890,6455,3809,6388,5740,6795,5578,6741,3510,6714, 5483,3049,5092,3863,3796,7313,3755,6334,5798,3701,7456,3539,6687,5470,3036,6553,6017,7266,5038,2941, 3742,6363,5936,5827,7429,3647,6506,3513,5746,5556,7239,5067,7688,3323,5909,2999,5366,4986,5801,3914, 6479,7308,5719,7040,5585,2027,4606,7213,3534,6945,6850,4959,5788,3439,6755,4000,6565,5693,2014,5531, 7256,6932,3810,6375,1919,6824,5369,5045,6742,3973,6608,5960,3050,4855,3892,6513,3783,7314,6797,5580, 3702,7219,3568,6716,5485,3023,6554,6018,3921,2942,6459,3757,6392,5923,5856,7430,3541,6745,3514,5543, 7268,5096,3867,3800,6365,5910,5829,5802,3705,6508,3487,5748,6803,5586,5069,7214,3325,6946,5491,3057, 4988,5775,3916,7433,3763,6566,5694,2029,5560,7243,6919,6852,5913,3003,5370,5046,6757,3974,6595,5723, 5533,3879,6514,3812,7329,6798,5343,5075,7696,3555,6703,5486,3052,6569,5809,3922,6487,7316,6936,3758, 6379,2035,7221,3542,5049,6746,3977,6556,6020,3447,4859,3896,6461,3787,6366,5925,5830,7488,3706,6271, 3516,5735,6832,5601,5070,3869,3326,5968,3058,4975,5804,3679,7434,3545,6805,5588,2030,5547,7272,6948, 5493,3031,5914,5833,6758,3765,6624,5752,5534,7245,6977,7330,5439,3005,5372,5104,7683,4032,6597,5725, 2815,6570,5810,3937,6516,7303,6923,6856,5077,7222,3557,5050,6761,3978,6543,5783,3924,7441,3883,6462, 3816,6381,5926,2037,7251,5023,6748,3503,6819,5602,4861,3870,6491,3789,7320,5955,1983,3708,7225,3546, 6806,5575,6024,3451,6711,5494,3060,6577,5929,5834,7436,3766,6387,5739,5549,7246,6978,3985,5916,3006, 5359,5091,7712,3795,6598,5726,6809,5592,3938,6503,7332,6952,5497,3035,5078,7685,3558,6762,3769,6572, 4983,5812,3911,7442,7361,6925,6382,2038,5555,7280,5052,6735,3980,6601,5841,4862,3885,6520,3790,7307, 5984,7253,5081,3695,7226,3561,6821,5604,5787,3928,6493,5957,3047,6578,5930,2041,7199,3548,6931,6864, 5550,3453,6769,3986,6551,5903,5836,3891,3824,6389,5741,6810,5579,6980,3511,6715,5498,3064,5093,7686, 3797,7552,3770,6335,5799,3940,7457,7362,6926,5471,3037,6032,7267,5039,6764,3743,6602,5937,5842,7444, 3886,6507,7336,5747,5557,7254,5082,7689,3562,6822,5367,4987,5816,3915,6494,7309,5958,7041,2042,4607, 7228,3535,6960,6851,5789,3454,6770,4001,6580,5932,2015,7257,6933,3811,6390,5742,6825,5608,6743,3988, 6609,5961,3051,5094,3893,3798,7315,6812,5581,3703,7458,3569,6717,5500,3038,6555,6019,7744,2943,3772, 6393,5938,5857,7431,7364,6984,3515,5558,7269,5097,7690,3801,6604,5911,5844,5803,3944,6509,7310,5749, 7042,5587,5084,7215,3564,6947,6880,4989,5790,3917,7448,4002,6567,5695,2044,5561,7258,6934,6853,6826, 5371,5047,6772,3975,6610,5962,3894,6515,3813,7344,6799,5582,7697,3570,6718,5487,3053,6584,6048,3923, 7317,6937,3759,6394,5858,7460,3543,6747,3992,6557,6021,7270,5098,3897,3802,6367,5940,5831,7489,3707, 6510,3517,5750,6833,5616,5071,7692,3327,5969,3059,4990,5805,3918,7435,7368,7044,5589,2031,5562,7273, 6949,6854,5915,5848,6759,4004,6625,5753,5535,7260,6992,3814,7331,6828,5373,5105,7698,4033,6612,5964, 3054,6571,5811,3952,6517,7318,6938,6857,7223,3572,5051,6776,3979,6558,6022,3925,3898,6463,3817,6396, 5927,5860,7490,6749,3518,6834,5603,5100,3871,3804,7321,5970,5806,3709,7464,3547,6807,5590,6025,7274, 6950,5495,3061,5944,5835,7437,3767,6626,5754,5564,7247,6979,7808,5917,3007,5374,5106,7713,4034,6599, 5727,7048,5593,3939,6518,7333,6953,6858,5079,7700,3559,6763,4008,6573,5813,3926,7443,7376,6940,3818, 6383,2039,7281,5053,6750,3981,6616,6080,4863,3900,6521,3791,7322,5985,7492,3710,7227,3576,6836,5605, 6026,3929,5972,3062,6579,5931,5864,7438,3549,6865,5551,7276,7008,3987,5918,5837,7714,3825,6628,5756, 6811,5594,6981,7334,6954,5499,3065,5108,7687,4036,7553,3771,6574,5814,3941,7472,7363,6927,6860,6033, 7282,5054,6765,3982,6603,5843,7445,3887,6522,3820,7337,5986,7255,5083,7704,3563,6823,5606,5817,3930, 6495,7324,5959,7056,2043,7229,3550,6961,6866,6028,3455,6771,4016,6581,5933,5838,7496,3826,6391,5743, 6840,5609,6982,3989,5976,3066,5095,7716,3799,7554,6813,5596,3942,7459,7392,6956,5501,3039,6034,7745, 6766,3773,6632,5939,5872,7446,7365,6985,7338,5559,7284,5112,7691,4040,6605,5845,5818,3945,6524,7311, 5988,7043,5085,7230,3565,6962,6881,5791,3932,7449,4003,6582,5934,2045,7259,6935,6868,6827,5610,6773, 3990,6611,5963,3895,3828,7345,6814,5583,7936,3571,6719,5502,3068,6585,6049,7746,7556,3774,6395,5859, 7461,7366,6986,3993,6036,7271,5099,7720,3803,6606,5941,5846,7504,3946,6511,7340,5751,7072,5617,5086, 7693,3566,6882,4991,5820,3919,7450,7369,7045,2046,5563,7288,6964,6855,5849,6774,4005,6640,5992,7261, 6993,3815,7346,6829,5612,7699,4048,6613,5965,3055,6586,6050,3953,7319,6939,6872,7462,3573,6777,3994, 6559,6023,7748,3899,3832,6397,5942,5861,7491,6988,3519,6835,5618,5101,7694,3805,7560,5971,5807,3948, 7465,7370,7046,5591,6040,7275,6951,6884,5945,5850,7452,4006,6627,5755,5565,7262,6994,7809,6830,5375, 5107,7728,4035,6614,5966,7049,3954,6519,7348,6968,6859,7701,3574,6778,4009,6588,6052,3927,7377,6941, 3819,6398,5862,7520,6751,3996,6617,6081,5102,3901,3806,7323,6000,7493,3711,7466,3577,6837,5620,6027, 7752,5973,3063,5946,5865,7439,7372,7104,5566,7277,7009,7810,5919,5852,7715,4064,6629,5757,7050,5595, 6996,7335,6955,6888,5109,7702,4037,7568,4010,6575,5815,3956,7473,7378,6942,6861,7283,5055,6780,3983, 6618,6082,3902,6523,3821,7352,5987,7494,7705,3578,6838,5607,6056,3931,7325,5974,7057,5866,7468,3551, 6867,6029,7278,7010,4017,5948,5839,7497,3827,6630,5758,6841,5624,6983,7812,5977,3067,5110,7717,4038, 7555,7052,5597,3943,7474,7393,6957,6862,6035,7760,6767,4012,6633,5873,7447,7380,7000,3822,7339,7285, 5113,7706,4041,6620,6084,5819,3960,6525,7326,5989,7058,7231,3580,6963,6896,6030,3933,4018,6583,5935, 5868,7498,6869,6842,5611,7012,3991,5978,7718,3829,7584,6815,5598,7937,7394,6958,5503,3069,6064,7747, 7557,3775,6634,5874,7476,7367,6987,7816,6037,7286,5114,7721,4042,6607,5847,7505,3947,6526,7341,5990, 7073,5087,7708,3567,6883,5821,3934,7451,7384,7060,2047,7289,6965,6870,6088,6775,4020,6641,5993,7500, 3830,7347,6844,5613,7938,4049,5980,3070,6587,6051,7776,7558,6873,7463,7396,7016,3995,6038,7749,7722, 3833,6636,5943,5876,7506,6989,7342,7074,5619,5116,7695,4044,7561,5822,3949,7480,7371,7047,6041,7290, 6966,6885,5851,7453,4007,6642,5994,7263,6995,7824,6831,5614,7729,4050,6615,5967,7064,3955,7349,6969, 6874,7940,3575,6779,4024,6589,6053,7750,7616,3834,6399,5863,7521,6990,3997,6096,5103,7724,3807,7562, 6001,7508,3950,7467,7400,7076,5621,6042,7753,6886,5947,5880,7454,7373,7105,5567,7292,7024,7811,5853, 7730,4065,6644,5996,7051,6997,7350,6970,6889,7703,4052,7569,4011,6590,6054,3957,7379,6943,6876,7522, 6781,3998,6619,6083,3903,3836,7353,6002,7495,7944,3579,6839,5622,6057,7754,7564,5975,5867,7469,7374, 7106,6044,7279,7011,7840,5949,5854,7512,4066,6631,5759,7080,5625,6998,7813,6890,5111,7732,4039,7570, 7053,3958,7475,7408,6972,6863,7761,6782,4013,6648,6112,7381,7001,3823,7354,7524,7707,4056,6621,6085, 6058,3961,7327,6004,7059,7470,3581,6897,6031,7756,4019,5950,5869,7499,7108,6843,5626,7013,7814,5979, 7719,4068,7585,7054,5599,7952,7395,6959,6892,6065,7762,7572,4014,6635,5875,7477,7382,7002,7817,7287, 5115,7736,4043,6622,6086,3962,6527,7356,5991,7088,7709,3582,6898,6060,3935,7385,7061,5870,7528,6871, 6089,7014,4021,6008,7501,3831,7586,6845,5628,7939,7872,5981,3071,6066,7777,7559,7112,7478,7397,7017, 7818,6039,7764,7723,4072,6637,5877,7507,7004,7343,7075,5117,7710,4045,7576,5823,3964,7481,7386,7062, 7291,6967,6900,6090,4022,6643,5995,7502,7825,6846,5615,7968,4051,5982,7065,7778,7588,6875,7941,7398, 7018,4025,6068,7751,7617,3835,6638,5878,7536,6991,7820,6097,5118,7725,4046,7563,7509,3951,7482,7401, 7077,6043,7768,6887,5881,7455,7388,7120,7293,7025,7826,6092,7731,4080,6645,5997,7066,7351,6971,6904, 7942,4053,4026,6591,6055,7780,7618,6877,7523,7020,3999,6098,7726,3837,7592,6003,7510,7945,7402,7078, 5623,6072,7755,7565,5882,7484,7375,7107,6045,7294,7026,7841,5855,7513,4067,6646,5998,7081,6999,7828, 6891,7733,4054,7571,7068,3959,7409,6973,6878,8000,6783,4028,6649,6113,7620,3838,7355,7525,7946,4057, 6100,6059,7784,7566,6005,7471,7404,7136,6046,7757,7842,5951,5884,7514,7109,7082,5627,7028,7815,7734, 4069,7600,7055,7953,7410,6974,6893,7763,7573,4015,6650,6114,7383,7003,7832,7526,7737,4058,6623,6087, 3963,7357,6006,7089,7948,3583,6899,6061,7758,7624,5871,7529,7110,6104,7015,7844,6009,7516,4070,7587, 7084,5629,7954,7873,6894,6067,7792,7574,7113,7479,7412,7032,7819,7765,7738,4073,6652,6116,7005,7358, 7090,7711,4060,7577,6062,3965,7387,7063,7530,6901,6091,4023,6010,7503,8064,6847,5630,7969,7874,5983, 7779,7589,7114,7956,7399,7019,7848,6069,7766,7632,4074,6639,5879,7537,7006,7821,5119,7740,4047,7578, 3966,7483,7416,7092,7769,6902,6120,7389,7121,7532,7827,6093,7970,4081,6012,7067,7590,6905,7943,7876, 4027,6070,7781,7619,7116,7538,7021,7822,6099,7727,4076,7593,7511,7960,7403,7079,6073,7770,7580,5883, 7485,7390,7122,7295,7027,7856,6094,4082,6647,5999,7096,7829,6906,7972,4055,7069,7782,7648,6879,8001, 7022,4029,6128,7621,3839,7594,7540,7947,7880,6101,6074,7785,7567,7486,7405,7137,6047,7772,7843,5885, 7515,7124,7083,7029,7830,7735,4084,7601,7070,7411,6975,6908,8002,4030,6651,6115,7622,7833,7527,7976, 4059,6102,7786,7596,6007,7949,7406,7138,6076,7759,7625,5886,7544,7111,6105,7030,7845,7517,4071,7602, 7085,7955,7888,6895,7793,7575,7128,7413,7033,7834,8004,7739,4088,6653,6117,7359,7091,7950,4061,6063, 7788,7626,7531,7140,6106,7846,6011,7518,8065,7086,5631,7984,7875,7794,7604,7115,7957,7414,7034,7849, 7767,7633,4075,6654,6118,7007,7836,7741,4062,7579,3967,7417,7093,8008,6903,6121,7628,7533,8066,6108, 7971,7904,6013,7591,7144,7958,7877,7850,6071,7796,7634,7117,7539,7036,7823,7742,4077,7608,7961,7418, 7094,7771,7581,6122,7391,7123,7534,7857,6095,4083,6014,7097,8068,6907,7973,7878,7783,7649,7118,8016, 7023,7852,6129,7636,4078,7595,7541,7962,7881,6075,7800,7582,7487,7420,7152,7773,7858,6124,7125,7098, 7831,7974,4085,7071,7650,6909,8003,4031,6130,7623,8072,7542,7977,7882,6103,7787,7597,7964,7407,7139, 6077,7774,7640,5887,7545,7126,7031,7860,4086,7603,7100,7889,6910,8032,7129,7652,7835,8005,7978,4089, 6132,7598,7951,7884,6078,7789,7627,7546,7141,6107,7847,7519,8080,7087,7985,7890,7795,7605,7130,7415, 7035,7864,8006,4090,6655,6119,7837,7980,4063,7790,7656,8009,7142,6136,7629,7548,8067,6109,7986,7905, 7606,7145,7959,7892,7851,7797,7635,7132,7037,7838,7743,4092,7609,7419,7095,8010,6123,7630,7535,8096, 6110,7906,6015,8069,7146,7988,7879,7798,7664,7119,8017,7038,7853,7637,4079,7610,7963,7896,7801,7583, 7421,7153,8012,7859,6125,7099,8070,7975,7908,7651,7148,8018,7854,6131,7638,8073,7543,7992,7883,7802, 7612,7965,7422,7154,7775,7641,6126,7127,7861,4087,7101,8128,6911,8033,7653,8074,8020,7979,7912,6133, 7599,7966,7885,6079,7804,7642,7547,7156,7862,8081,7102,7891,8034,7131,7654,7865,8007,4091,6134,8076, 7981,7886,7791,7657,8024,7143,6137,7644,7549,8082,7987,7920,7607,7160,7893,7866,8036,7133,7839,7982, 4093,7658,8011,6138,7631,7550,8097,6111,7907,8084,7147,7989,7894,7799,7665,7134,7039,7868,4094,7611, 7897,8040,7660,8013,8098,6140,8071,7990,7909,7666,7149,8019,7855,7639,8088,7993,7898,7803,7613,7423, 7155,8014,6127,8100,7910,8129,7150,8048,7668,8075,8021,7994,7913,7614,7967,7900,7805,7643,7157,7863, 7103,8130,8035,7655,8104,8022,7914,6135,8077,7996,7887,7806,7672,8025,7158,7645,8083,7921,7161,8132, 7867,8037,8078,7983,7916,7659,8026,6139,7646,7551,8112,7922,8085,7162,7895,8038,7135,7869,4095,8136, 8041,7661,8028,8099,6141,8086,7991,7924,7667,7164,7870,8089,7899,8042,7662,8015,6142,8101,7911,8144, 7151,8049,7669,8090,7995,7928,7615,7901,8044,8102,8131,8050,7670,8105,8023,7915,8092,7997,7902,7807, 7673,7159,8160,8133,8106,8052,8079,7998,7917,7674,8027,7647,8113,7923,7163,8134,8039,8108,7918,8137, 8056,7676,8029,8114,8087,7925,7165,7871,8138,8043,7663,8030,6143,8116,7926,8145,7166,8091,7929,8140, 8045,8103,8146,8051,7671,8120,7930,8093,7903,8046,8161,8148,8107,8053,8094,7999,7932,7675,8162,8135, 8054,8109,7919,8152,8057,7677,8115,8164,8110,8139,8058,7678,8031,8117,7927,7167,8168,8141,8060,8118, 8147,8121,7931,8142,8047,8176,8149,8122,8095,7933,8163,8150,8055,8124,7934,8153,8165,8111,8154,8059, 7679,8166,8169,8156,8061,8119,8170,8143,8062,8177,8123,8172,8178,8151,8125,7935,8180,8126,8155,8167, 8184,8157,8171,8158,8063,8173,8179,8174,8181,8127,8182,8185,8186,8159,8188,8175,8183,8187,8189,8190,8191,]； When the mother code length is 4096, the first sequence is the sequence Q1, the number of bits to be encoded K=L+M, and L is 452, 536, 904, 1048, 1808, 2072, 2712, or 3096; or when the mother code length is 8192, the first sequence is the sequence Q2, the number of bits to be encoded K=L+M, and the number of bits to be encoded L is 235, 470, 940, 1880, 2820, or 3760; and M is any integer greater than or equal to -20 and less than or equal to 20.

2. The method according to claim 1, characterized in that The method further comprises: Rate matching is performed on the bits encoded by the Polar code to obtain rate-matched bits.

3. The method according to claim 1 or 2, characterized in that The first sequence is pre-stored.

4. The method according to claim 1 or 2, characterized in that The N polarized channels are numbered from 0 to (N-1) or from 1 to N.

5. The method according to claim 1 or 2, characterized in that The bits to be encoded include cyclic redundancy check (CRC) bits.

6. The method according to claim 1 or 2, characterized in that The bits to be encoded include parity check PC bits.

7. A polar code decoding method, characterized in that: include: Receive bit information to be decoded, where the bit information to be decoded includes K information bits, where the K information bits are carried on polarized channels corresponding to K sequence numbers of a first sequence, where the first sequence includes sequence numbers of N polarized channels, and the first sequence is all or a subsequence of a sequence represented by sequence Q1 or Q2, where K is a positive integer, and N is a mother code length of a Polar code, where N=2. n , n is a positive integer, K≤N; Performing Polar code decoding on the bit information to be decoded to obtain the K information bits; in, The sequence Q1= 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,2895,3724,2001,1022,3629,3467,3413,3386,3305,2981,1947,3672,2791,1785,3359,3292,3024,3197,2929,3730,1996,3635,2549,1901,2970,3255,2875,2808,3846,2495,1959,3684,3522,2781,3427,2924,2002,3630,3496,1907,3414,3849,3306,2982,1527,1976,3659,3469,1786,3388,3279,3011,1949,3198,2930,3745,1759,3417,2550,1902,2985,2903,3732,2795,3637,3475,2972,3313,2877,2782,3904,2687,2553,2017,3524,3259,3429,3850,2004,1963,3688,3470,1909,3375,3308,3040,1950,3661,3746,1855,1788,3418,3013,2986,1531,2932,3719,3638,3504,2959,3857,3314,2878,2797,3667,3477,2554,2018,3287,2907,3736,3430,3641,2527,1991,3261,1910,2993,3852,2803,1965,3662,3528,1775,3433,3014,2008,2919,3748,1913,3420,3491,2988,1533,3858,3777,2798,1971,3696,3478,3017,3383,3316,2936,3723,3669,3642,2556,2020,2909,3262,2994,3615,3481,1966,3291,2967,3434,2805,1995,1914,3407,3968,2751,1534,3873,3778,1887,3683,3493,3018,3860,3303,2923,3752,1973,3670,3536,2543,1783,3441,2910,3725,1023,3644,3482,3387,3320,2996,3673,2806,2024,3293,3025,3436,3731,1997,3874,1916,2971,3494,2809,3847,3780,1974,3685,3523,3020,3442,2925,3726,2003,3631,3497,3415,3864,3307,2983,1977,3674,3484,1787,3389,3294,3026,3199,2931,3760,1998,2551,1903,3000,3733,2810,3876,2973,3686,3552,2783,3905,2926,2032,3525,3498,3444,3851,3784,2005,1978,3689,3471,3390,3309,3041,1951,3676,3747,1789,3419,3028,2987,2933,3734,3639,3505,2974,3315,2879,2812,3906,2555,2019,3526,3737,3431,3880,2006,3690,3500,1911,3853,3310,3042,1980,3663,3529,1790,3448,3015,2009,2934,3749,3421,3506,2989,3859,3792,2799,3697,3479,3032,3317,2937,3738,3908,3643,2557,2021,3263,2995,3854,1967,3692,3530,3435,3044,2010,3750,1915,3422,3969,2990,1535,3888,3779,3698,3508,3019,3861,3318,2938,3753,3671,3537,2558,2022,2911,3740,3645,3483,3321,2997,3912,2807,2025,3532,3437,3970,2012,3875,3808,1917,3495,3048,3862,3781,3754,1975,3700,3538,3021,3443,2940,3727,3646,3512,3865,3322,2998,3675,3485,2026,3295,3027,3438,3761,1999,1918,3001,3972,2811,3877,3782,3687,3553,3022,3920,2927,3756,2033,3540,3499,3445,3866,3785,1979,3704,3486,3391,3324,3056,3677,3762,2028,3029,3002,3735,3878,2975,3554,2813,3907,2034,3527,3976,3446,3881,3786,2007,3691,3501,3868,3311,3043,1981,3678,3544,1791,3449,3030,2935,3764,3507,3004,3793,2814,3936,3033,3556,3739,3909,3882,2036,3502,3855,3788,1982,3693,3531,3450,3045,2011,3751,3423,3984,2991,3889,3794,3699,3509,3034,3319,2939,3768,3910,2559,2023,3741,3884,3694,3560,3913,3046,2040,3533,3452,3971,2013,3890,3809,3510,3049,3863,3796,3755,3701,3539,3036,2941,3742,3647,3513,3323,2999,3914,2027,3534,3439,4000,2014,3810,1919,3973,3050,3892,3783,3702,3568,3023,3921,2942,3757,3541,3514,3867,3800,3705,3487,3325,3057,3916,3763,2029,3003,3974,3879,3812,3555,3052,3922,3758,2035,3542,3977,3447,3896,3787,3706,3516,3869,3326,3058,3679,3545,2030,3031,3765,3005,4032,2815,3937,3557,3978,3924,3883,3816,2037,3503,3870,3789,1983,3708,3546,3451,3060,3766,3985,3006,3795,3938,3035,3558,3769,3911,2038,3980,3885,3790,3695,3561,3928,3047,2041,3548,3453,3986,3891,3824,3511,3064,3797,3770,3940,3037,3743,3886,3562,3915,2042,3535,3454,4001,2015,3811,3988,3051,3893,3798,3703,3569,3038,2943,3772,3515,3801,3944,3564,3917,4002,2044,3975,3894,3813,3570,3053,3923,3759,3543,3992,3897,3802,3707,3517,3327,3059,3918,2031,4004,3814,4033,3054,3952,3572,3979,3925,3898,3817,3518,3871,3804,3709,3547,3061,3767,3007,4034,3939,3559,4008,3926,3818,2039,3981,3900,3791,3710,3576,3929,3062,3549,3987,3825,3065,4036,3771,3941,3982,3887,3820,3563,3930,2043,3550,3455,4016,3826,3989,3066,3799,3942,3039,3773,4040,3945,3565,3932,4003,2045,3990,3895,3828,3571,3068,3774,3993,3803,3946,3566,3919,2046,4005,3815,4048,3055,3953,3573,3994,3899,3832,3519,3805,3948,4006,4035,3954,3574,4009,3927,3819,3996,3901,3806,3711,3577,3063,4064,4037,4010,3956,3983,3902,3821,3578,3931,3551,4017,3827,3067,4038,3943,4012,3822,4041,3960,3580,3933,4018,3991,3829,3069,3775,4042,3947,3567,3934,2047,4020,3830,4049,3070,3995,3833,4044,3949,4007,4050,3955,3575,4024,3834,3997,3807,3950,4065,4052,4011,3957,3998,3903,3836,3579,4066,4039,3958,4013,3823,4056,3961,3581,4019,4068,4014,4043,3962,3582,3935,4021,3831,3071,4072,4045,3964,4022,4051,4025,3835,4046,3951,4080,4053,4026,3999,3837,4067,4054,3959,4028,3838,4057,4069,4015,4058,3963,3583,4070,4073,4060,3965,4023,4074,4047,3966,4081,4027,4076,4082,4055,4029,3839,4084,4030,4059,4071,4088,4061,4075,4062,3967,4077,4083,4078,4085,4031,4086,4089,4090,4063,4092,4079,4087,4091,4093,4094,4095,]； The sequence Q2= [6309,5445,6419,5391,6298,6203,5667,5287,6414,5654,6252,5425,5330,5235,6310,6663,5446,5657,6339,5277,3623,6258,5420,4819,6421,5230,6313,6231,5449,3381,3721,6300,4935,6205,5669,5507,5004,5426,5345,4909,4814,3613,3289,5399,5332,5291,6692,5237,5658,6435,5278,3405,5010,5183,4915,6422,6341,6314,3681,6260,3463,6667,5450,4821,3382,3301,4794,3722,6287,4964,3668,3627,6206,5670,3411,4767,6425,3247,2979,5346,4910,3614,6235,3480,5699,5509,4586,3385,3290,5428,2966,5319,4939,5768,3195,5238,6321,5673,4559,7180,5457,4478,5293,3406,5025,6722,3729,6532,5660,4835,6437,6342,5403,2969,5336,5012,3682,6247,3492,6696,5241,2779,4917,4822,3845,6480,3302,2922,6316,4727,4593,3655,7186,3521,6669,5452,5299,3440,4796,2895,6426,3724,6345,4539,3629,6264,3467,5728,5510,3413,4825,3386,3305,5415,2981,5348,4968,1947,3672,6237,5701,2791,6322,5674,4588,3359,3292,6675,5458,4941,5294,3197,5026,2929,3730,6295,5647,5513,3635,6438,2549,1901,5432,2970,5323,4999,6724,3255,2875,5242,4918,4837,3846,6467,5405,2495,1959,4594,3684,7201,3522,6670,5215,2781,6536,4947,5776,3427,4783,2924,6441,6346,5681,2002,4567,7188,5016,3630,6251,3496,1907,5301,3414,4921,4826,3849,6428,3306,5892,2982,1527,4731,1976,4541,3659,6238,3469,5702,6785,5568,1786,4351,3388,3279,6704,5473,3011,4942,1949,3198,2930,3745,6324,5676,1759,5514,3417,6677,5460,2550,1902,5419,2985,5352,5028,2903,3732,6353,5705,2795,4838,3637,6496,3475,5406,2972,5325,5057,7202,3313,2877,5244,2782,6299,4976,5763,6469,2687,6442,2553,5682,2017,4596,7175,3524,5003,6728,3259,4949,5302,3429,4922,4841,3850,6415,6348,5655,2004,5521,1963,4542,3688,6253,3470,1909,6786,5331,4895,4828,3375,3308,6691,5474,3040,4733,1950,4571,3661,7192,3746,6311,1855,1788,5305,3418,6678,5447,3013,6544,5896,2986,1531,4791,2932,6449,3719,6354,5706,5516,3638,6259,3504,5421,2959,5326,5058,3857,3314,2878, 5231,2797,6328,4963,5792,3667,6470,3477,6681,5464,2554,2018,4583,7204,3287,5032,2907,3736,6301,4950, 5765,3430,4842,3641,6444,2527,5684,1991,5522,7233,5005,6254,3261,1910,5427,2993,5360,4924,4815,3852, 6473,5713,2803,4734,1965,4600,3662,7179,3528,6788,5333,4953,1775,5306,3433,6693,5476,3014,6531,5659, 2008,4573,2919,6450,3748,6369,1913,5279,3420,5011,6736,3491,5422,2988,1533,4849,3858,6423,3777,6356, 5708,2798,6315,1971,3696,6261,3478,6682,5451,3017,5060,3383,3316,4795,2936,3723,6302,4965,5766,3669, 3642,6207,2556,5671,2020,5537,7234,5006,2909,3262,5904,2994,5347,4911,4844,3615,6474,3481,5714,5524, 1966,4587,7208,3291,5429,2967,5334,4954,5769,3434,6694,5239,2805,6560,5688,1995,4574,7181,6913,6370, 1914,4479,5308,3407,5040,6723,3968,6533,5661,2751,1534,4850,3873,6452,3778,6343,1887,6792,5337,5013, 3683,6262,3493,6697,5480,3018,4823,3860,6481,3303,2923,3752,6317,4966,1973,3670,7187,3536,6684,5453, 2543,1783,5538,3441,4797,2910,6427,3725,6360,5891,5824,1023,3644,6265,3482,5729,5511,7236,5064,3387, 3320,5430,2996,5349,4969,5770,3673,6476,5716,2806,6323,5675,2024,4589,7182,3293,6914,5459,3025,4956, 5295,3436,5027,6752,3731,6534,5662,1997,5528,3874,6439,6372,1916,5433,2971,5338,5014,6725,3494,6698, 5243,2809,4919,4852,3847,6482,3780,7297,6318,1974,4595,3685,7216,3523,6671,5454,3020,6537,5777,3442, 4798,2925,6456,3726,6347,5920,2003,7189,5017,3631,6266,3497,5730,5540,3415,4827,3864,6429,3307,5893, 2983,5350,4970,1977,3674,6239,3484,5703,6800,5569,1787,4590,3389,3294,6705,5488,3026,4943,5772,3199, 2931,3760,6325,5677,1998,5515,7240,6916,5461,2551,1903,5434,3000,5353,5029,6726,3733,6592,5720,2810, 4839,3876,6497,7298,5407,2973,5340,5072,3686,7203,3552,6700,5245,2783,6538,4977,5778,3905,6484,2926, 6443,6376,5683,2032,4597,7190,3525,5018,6729,3498,5303,3444,4923,4856,3851,6430,3784,6349,5894,2005, 1978,4543,3689,6268,3471,5732,6787,5570,4829,3390,3309,6706,5475,3041,4972,1951,3676,7193,3747,6326, 5678,1789,5544,3419,6679,5462,3028,6545,5897,2987,5354,5030,2933,3734,6355,5707,5517,3639,6498,3505, 5436,2974,5327,5059,3315,2879,5246,2812,6329,4978,5793,3906,6471,7300,6920,5465,2555,2019,4598,7205, 3526,5033,6730,3737,6540,4951,5780,3431,4843,3880,6350,5685,2006,5523,7248,5020,3690,6255,3500,1911, 6816,5361,4925,4830,3853,6488,3310,5952,3042,4735,1980,4601,3663,7194,3529,6789,5572,1790,5307,3448, 6708,5477,3015,6546,5898,2009,2934,3749,6384,5736,5518,3421,3506,5423,2989,5356,5088,3859,3792,2799, 5794,3697,6500,3479,5466,3032,5061,3317,5034,2937,3738,4980,3908,7425,3643,2557,2021,5552,5007,3263, 5905,2995,5362,4926,4845,3854,7304,1967,4602,3692,3530,5335,4955,5784,3435,3044,2010,4575,6928,3750, 1915,5309,3422,5041,3969,5900,2990,1535,4851,3888,3779,5576,3698,3508,3019,5062,3318,2938,4967,7426, 3537,2558,2022,7264,5036,2911,3740,4846,3645,3483,5744,3321,2997,4984,3912,2807,2025,4604,3532,6848, 3437,3970,2012,3808,1917,3048,7312,1975,3021,6016,2940,7428,3512,2998,2026,6944,1918,3972,3920,3056, 7681,6445,6451,6737,6357,5709,6330,6683,7206,6303,5767,6446,5686,7235,6732,6475,5715,5525,7209,6790, 6695,5478,6561,5689,7196,6371,6738,6548,6453,6358,5710,6793,6263,6712,5481,3861,3753,6332,5796,3671, 6685,5468,5539,6361,5906,5825,6504,5526,7237,5065,7210,5431,5364,5771,6477,5717,6562,5690,7183,6915, 4957,5310,5042,6753,6535,5663,5529,3875,6454,6373,6794,5339,5015,6740,3495,6699,5482,4853,3862,6483, 3781,3754,6319,3700,7217,3538,6686,5455,6552,3443,4799,6457,3727,6362,5921,5826,3646,6267,5731,5541, 7238,5066,3865,3322,5908,5351,4971,5800,3675,6478,3485,5718,6801,5584,4591,7212,3295,5489,3027,4958, 5773,3438,6754,3761,6564,5692,1999,5530,7241,6917,6374,5435,3001,5368,5044,6727,6593,5721,2811,4854, 3877,6512,3782,7299,6796,5341,5073,3687,7218,3553,6701,5484,3022,6539,5779,6485,2927,6458,3756,6377, 5922,2033,7191,3540,5019,6744,3499,5542,3445,4857,3866,6431,3785,6364,5895,5828,1979,3704,6269,3486, 5733,6802,5571,5068,3391,3324,6707,5490,4973,5774,3677,7432,3762,6327,5679,2028,5545,7242,6918,5463, 3029,5912,3002,5355,5031,6756,3735,6594,5722,5532,3878,6499,7328,5437,2975,5342,5074,3554,6702,5247, 2813,6568,4979,5808,3907,6486,7301,6921,6378,2034,4599,7220,3527,5048,6731,3976,6541,5781,3446,4858, 3881,6460,3786,6351,5924,2007,7249,5021,3691,6270,3501,5734,6817,5600,4831,3868,6489,3311,5953,3043, 4974,1981,3678,7195,3544,6804,5573,1791,5546,3449,6709,5492,3030,6547,5899,5832,2935,3764,6385,5737, 5519,7244,6976,3507,5438,3004,5357,5089,7682,3793,6596,5724,2814,6331,5795,3936,6501,7302,6922,5467, 3033,5076,7207,3556,5035,6760,3739,6542,4981,5782,3909,7440,3882,6447,6380,5687,2036,5553,7250,5022, 6733,3502,6818,5363,4927,4860,3855,6490,3788,7305,5954,1982,4603,3693,7224,3531,6791,5574,5785,3450, 6710,5479,3045,6576,5928,2011,7197,6929,3751,6386,5738,5548,3423,6739,3984,6549,5901,2991,5358,5090, 3889,3794,6359,5711,6808,5577,3699,6502,3509,6713,5496,3034,5063,7684,3319,2939,3768,6333,4982,5797, 3910,7427,7360,6924,5469,2559,2023,5554,7265,5037,6734,3741,6600,5907,5840,4847,3884,6505,7306,5745, 5527,7252,5080,3694,7211,3560,6820,5365,4985,5786,3913,6492,5956,3046,6563,5691,2040,4605,7198,3533, 6930,6849,5311,3452,5043,6768,3971,6550,5902,2013,3890,6455,3809,6388,5740,6795,5578,6741,3510,6714, 5483,3049,5092,3863,3796,7313,3755,6334,5798,3701,7456,3539,6687,5470,3036,6553,6017,7266,5038,2941, 3742,6363,5936,5827,7429,3647,6506,3513,5746,5556,7239,5067,7688,3323,5909,2999,5366,4986,5801,3914, 6479,7308,5719,7040,5585,2027,4606,7213,3534,6945,6850,4959,5788,3439,6755,4000,6565,5693,2014,5531, 7256,6932,3810,6375,1919,6824,5369,5045,6742,3973,6608,5960,3050,4855,3892,6513,3783,7314,6797,5580, 3702,7219,3568,6716,5485,3023,6554,6018,3921,2942,6459,3757,6392,5923,5856,7430,3541,6745,3514,5543, 7268,5096,3867,3800,6365,5910,5829,5802,3705,6508,3487,5748,6803,5586,5069,7214,3325,6946,5491,3057, 4988,5775,3916,7433,3763,6566,5694,2029,5560,7243,6919,6852,5913,3003,5370,5046,6757,3974,6595,5723, 5533,3879,6514,3812,7329,6798,5343,5075,7696,3555,6703,5486,3052,6569,5809,3922,6487,7316,6936,3758, 6379,2035,7221,3542,5049,6746,3977,6556,6020,3447,4859,3896,6461,3787,6366,5925,5830,7488,3706,6271, 3516,5735,6832,5601,5070,3869,3326,5968,3058,4975,5804,3679,7434,3545,6805,5588,2030,5547,7272,6948, 5493,3031,5914,5833,6758,3765,6624,5752,5534,7245,6977,7330,5439,3005,5372,5104,7683,4032,6597,5725, 2815,6570,5810,3937,6516,7303,6923,6856,5077,7222,3557,5050,6761,3978,6543,5783,3924,7441,3883,6462, 3816,6381,5926,2037,7251,5023,6748,3503,6819,5602,4861,3870,6491,3789,7320,5955,1983,3708,7225,3546, 6806,5575,6024,3451,6711,5494,3060,6577,5929,5834,7436,3766,6387,5739,5549,7246,6978,3985,5916,3006, 5359,5091,7712,3795,6598,5726,6809,5592,3938,6503,7332,6952,5497,3035,5078,7685,3558,6762,3769,6572, 4983,5812,3911,7442,7361,6925,6382,2038,5555,7280,5052,6735,3980,6601,5841,4862,3885,6520,3790,7307, 5984,7253,5081,3695,7226,3561,6821,5604,5787,3928,6493,5957,3047,6578,5930,2041,7199,3548,6931,6864, 5550,3453,6769,3986,6551,5903,5836,3891,3824,6389,5741,6810,5579,6980,3511,6715,5498,3064,5093,7686, 3797,7552,3770,6335,5799,3940,7457,7362,6926,5471,3037,6032,7267,5039,6764,3743,6602,5937,5842,7444, 3886,6507,7336,5747,5557,7254,5082,7689,3562,6822,5367,4987,5816,3915,6494,7309,5958,7041,2042,4607, 7228,3535,6960,6851,5789,3454,6770,4001,6580,5932,2015,7257,6933,3811,6390,5742,6825,5608,6743,3988, 6609,5961,3051,5094,3893,3798,7315,6812,5581,3703,7458,3569,6717,5500,3038,6555,6019,7744,2943,3772, 6393,5938,5857,7431,7364,6984,3515,5558,7269,5097,7690,3801,6604,5911,5844,5803,3944,6509,7310,5749, 7042,5587,5084,7215,3564,6947,6880,4989,5790,3917,7448,4002,6567,5695,2044,5561,7258,6934,6853,6826, 5371,5047,6772,3975,6610,5962,3894,6515,3813,7344,6799,5582,7697,3570,6718,5487,3053,6584,6048,3923, 7317,6937,3759,6394,5858,7460,3543,6747,3992,6557,6021,7270,5098,3897,3802,6367,5940,5831,7489,3707, 6510,3517,5750,6833,5616,5071,7692,3327,5969,3059,4990,5805,3918,7435,7368,7044,5589,2031,5562,7273, 6949,6854,5915,5848,6759,4004,6625,5753,5535,7260,6992,3814,7331,6828,5373,5105,7698,4033,6612,5964, 3054,6571,5811,3952,6517,7318,6938,6857,7223,3572,5051,6776,3979,6558,6022,3925,3898,6463,3817,6396, 5927,5860,7490,6749,3518,6834,5603,5100,3871,3804,7321,5970,5806,3709,7464,3547,6807,5590,6025,7274, 6950,5495,3061,5944,5835,7437,3767,6626,5754,5564,7247,6979,7808,5917,3007,5374,5106,7713,4034,6599, 5727,7048,5593,3939,6518,7333,6953,6858,5079,7700,3559,6763,4008,6573,5813,3926,7443,7376,6940,3818, 6383,2039,7281,5053,6750,3981,6616,6080,4863,3900,6521,3791,7322,5985,7492,3710,7227,3576,6836,5605, 6026,3929,5972,3062,6579,5931,5864,7438,3549,6865,5551,7276,7008,3987,5918,5837,7714,3825,6628,5756, 6811,5594,6981,7334,6954,5499,3065,5108,7687,4036,7553,3771,6574,5814,3941,7472,7363,6927,6860,6033, 7282,5054,6765,3982,6603,5843,7445,3887,6522,3820,7337,5986,7255,5083,7704,3563,6823,5606,5817,3930, 6495,7324,5959,7056,2043,7229,3550,6961,6866,6028,3455,6771,4016,6581,5933,5838,7496,3826,6391,5743, 6840,5609,6982,3989,5976,3066,5095,7716,3799,7554,6813,5596,3942,7459,7392,6956,5501,3039,6034,7745, 6766,3773,6632,5939,5872,7446,7365,6985,7338,5559,7284,5112,7691,4040,6605,5845,5818,3945,6524,7311, 5988,7043,5085,7230,3565,6962,6881,5791,3932,7449,4003,6582,5934,2045,7259,6935,6868,6827,5610,6773, 3990,6611,5963,3895,3828,7345,6814,5583,7936,3571,6719,5502,3068,6585,6049,7746,7556,3774,6395,5859, 7461,7366,6986,3993,6036,7271,5099,7720,3803,6606,5941,5846,7504,3946,6511,7340,5751,7072,5617,5086, 7693,3566,6882,4991,5820,3919,7450,7369,7045,2046,5563,7288,6964,6855,5849,6774,4005,6640,5992,7261, 6993,3815,7346,6829,5612,7699,4048,6613,5965,3055,6586,6050,3953,7319,6939,6872,7462,3573,6777,3994, 6559,6023,7748,3899,3832,6397,5942,5861,7491,6988,3519,6835,5618,5101,7694,3805,7560,5971,5807,3948, 7465,7370,7046,5591,6040,7275,6951,6884,5945,5850,7452,4006,6627,5755,5565,7262,6994,7809,6830,5375, 5107,7728,4035,6614,5966,7049,3954,6519,7348,6968,6859,7701,3574,6778,4009,6588,6052,3927,7377,6941, 3819,6398,5862,7520,6751,3996,6617,6081,5102,3901,3806,7323,6000,7493,3711,7466,3577,6837,5620,6027, 7752,5973,3063,5946,5865,7439,7372,7104,5566,7277,7009,7810,5919,5852,7715,4064,6629,5757,7050,5595, 6996,7335,6955,6888,5109,7702,4037,7568,4010,6575,5815,3956,7473,7378,6942,6861,7283,5055,6780,3983, 6618,6082,3902,6523,3821,7352,5987,7494,7705,3578,6838,5607,6056,3931,7325,5974,7057,5866,7468,3551, 6867,6029,7278,7010,4017,5948,5839,7497,3827,6630,5758,6841,5624,6983,7812,5977,3067,5110,7717,4038, 7555,7052,5597,3943,7474,7393,6957,6862,6035,7760,6767,4012,6633,5873,7447,7380,7000,3822,7339,7285, 5113,7706,4041,6620,6084,5819,3960,6525,7326,5989,7058,7231,3580,6963,6896,6030,3933,4018,6583,5935, 5868,7498,6869,6842,5611,7012,3991,5978,7718,3829,7584,6815,5598,7937,7394,6958,5503,3069,6064,7747, 7557,3775,6634,5874,7476,7367,6987,7816,6037,7286,5114,7721,4042,6607,5847,7505,3947,6526,7341,5990, 7073,5087,7708,3567,6883,5821,3934,7451,7384,7060,2047,7289,6965,6870,6088,6775,4020,6641,5993,7500, 3830,7347,6844,5613,7938,4049,5980,3070,6587,6051,7776,7558,6873,7463,7396,7016,3995,6038,7749,7722, 3833,6636,5943,5876,7506,6989,7342,7074,5619,5116,7695,4044,7561,5822,3949,7480,7371,7047,6041,7290, 6966,6885,5851,7453,4007,6642,5994,7263,6995,7824,6831,5614,7729,4050,6615,5967,7064,3955,7349,6969, 6874,7940,3575,6779,4024,6589,6053,7750,7616,3834,6399,5863,7521,6990,3997,6096,5103,7724,3807,7562, 6001,7508,3950,7467,7400,7076,5621,6042,7753,6886,5947,5880,7454,7373,7105,5567,7292,7024,7811,5853, 7730,4065,6644,5996,7051,6997,7350,6970,6889,7703,4052,7569,4011,6590,6054,3957,7379,6943,6876,7522, 6781,3998,6619,6083,3903,3836,7353,6002,7495,7944,3579,6839,5622,6057,7754,7564,5975,5867,7469,7374, 7106,6044,7279,7011,7840,5949,5854,7512,4066,6631,5759,7080,5625,6998,7813,6890,5111,7732,4039,7570, 7053,3958,7475,7408,6972,6863,7761,6782,4013,6648,6112,7381,7001,3823,7354,7524,7707,4056,6621,6085, 6058,3961,7327,6004,7059,7470,3581,6897,6031,7756,4019,5950,5869,7499,7108,6843,5626,7013,7814,5979, 7719,4068,7585,7054,5599,7952,7395,6959,6892,6065,7762,7572,4014,6635,5875,7477,7382,7002,7817,7287, 5115,7736,4043,6622,6086,3962,6527,7356,5991,7088,7709,3582,6898,6060,3935,7385,7061,5870,7528,6871, 6089,7014,4021,6008,7501,3831,7586,6845,5628,7939,7872,5981,3071,6066,7777,7559,7112,7478,7397,7017, 7818,6039,7764,7723,4072,6637,5877,7507,7004,7343,7075,5117,7710,4045,7576,5823,3964,7481,7386,7062, 7291,6967,6900,6090,4022,6643,5995,7502,7825,6846,5615,7968,4051,5982,7065,7778,7588,6875,7941,7398, 7018,4025,6068,7751,7617,3835,6638,5878,7536,6991,7820,6097,5118,7725,4046,7563,7509,3951,7482,7401, 7077,6043,7768,6887,5881,7455,7388,7120,7293,7025,7826,6092,7731,4080,6645,5997,7066,7351,6971,6904, 7942,4053,4026,6591,6055,7780,7618,6877,7523,7020,3999,6098,7726,3837,7592,6003,7510,7945,7402,7078, 5623,6072,7755,7565,5882,7484,7375,7107,6045,7294,7026,7841,5855,7513,4067,6646,5998,7081,6999,7828, 6891,7733,4054,7571,7068,3959,7409,6973,6878,8000,6783,4028,6649,6113,7620,3838,7355,7525,7946,4057, 6100,6059,7784,7566,6005,7471,7404,7136,6046,7757,7842,5951,5884,7514,7109,7082,5627,7028,7815,7734, 4069,7600,7055,7953,7410,6974,6893,7763,7573,4015,6650,6114,7383,7003,7832,7526,7737,4058,6623,6087, 3963,7357,6006,7089,7948,3583,6899,6061,7758,7624,5871,7529,7110,6104,7015,7844,6009,7516,4070,7587, 7084,5629,7954,7873,6894,6067,7792,7574,7113,7479,7412,7032,7819,7765,7738,4073,6652,6116,7005,7358, 7090,7711,4060,7577,6062,3965,7387,7063,7530,6901,6091,4023,6010,7503,8064,6847,5630,7969,7874,5983, 7779,7589,7114,7956,7399,7019,7848,6069,7766,7632,4074,6639,5879,7537,7006,7821,5119,7740,4047,7578, 3966,7483,7416,7092,7769,6902,6120,7389,7121,7532,7827,6093,7970,4081,6012,7067,7590,6905,7943,7876, 4027,6070,7781,7619,7116,7538,7021,7822,6099,7727,4076,7593,7511,7960,7403,7079,6073,7770,7580,5883, 7485,7390,7122,7295,7027,7856,6094,4082,6647,5999,7096,7829,6906,7972,4055,7069,7782,7648,6879,8001, 7022,4029,6128,7621,3839,7594,7540,7947,7880,6101,6074,7785,7567,7486,7405,7137,6047,7772,7843,5885, 7515,7124,7083,7029,7830,7735,4084,7601,7070,7411,6975,6908,8002,4030,6651,6115,7622,7833,7527,7976, 4059,6102,7786,7596,6007,7949,7406,7138,6076,7759,7625,5886,7544,7111,6105,7030,7845,7517,4071,7602, 7085,7955,7888,6895,7793,7575,7128,7413,7033,7834,8004,7739,4088,6653,6117,7359,7091,7950,4061,6063, 7788,7626,7531,7140,6106,7846,6011,7518,8065,7086,5631,7984,7875,7794,7604,7115,7957,7414,7034,7849, 7767,7633,4075,6654,6118,7007,7836,7741,4062,7579,3967,7417,7093,8008,6903,6121,7628,7533,8066,6108, 7971,7904,6013,7591,7144,7958,7877,7850,6071,7796,7634,7117,7539,7036,7823,7742,4077,7608,7961,7418, 7094,7771,7581,6122,7391,7123,7534,7857,6095,4083,6014,7097,8068,6907,7973,7878,7783,7649,7118,8016, 7023,7852,6129,7636,4078,7595,7541,7962,7881,6075,7800,7582,7487,7420,7152,7773,7858,6124,7125,7098, 7831,7974,4085,7071,7650,6909,8003,4031,6130,7623,8072,7542,7977,7882,6103,7787,7597,7964,7407,7139, 6077,7774,7640,5887,7545,7126,7031,7860,4086,7603,7100,7889,6910,8032,7129,7652,7835,8005,7978,4089, 6132,7598,7951,7884,6078,7789,7627,7546,7141,6107,7847,7519,8080,7087,7985,7890,7795,7605,7130,7415, 7035,7864,8006,4090,6655,6119,7837,7980,4063,7790,7656,8009,7142,6136,7629,7548,8067,6109,7986,7905, 7606,7145,7959,7892,7851,7797,7635,7132,7037,7838,7743,4092,7609,7419,7095,8010,6123,7630,7535,8096, 6110,7906,6015,8069,7146,7988,7879,7798,7664,7119,8017,7038,7853,7637,4079,7610,7963,7896,7801,7583, 7421,7153,8012,7859,6125,7099,8070,7975,7908,7651,7148,8018,7854,6131,7638,8073,7543,7992,7883,7802, 7612,7965,7422,7154,7775,7641,6126,7127,7861,4087,7101,8128,6911,8033,7653,8074,8020,7979,7912,6133, 7599,7966,7885,6079,7804,7642,7547,7156,7862,8081,7102,7891,8034,7131,7654,7865,8007,4091,6134,8076, 7981,7886,7791,7657,8024,7143,6137,7644,7549,8082,7987,7920,7607,7160,7893,7866,8036,7133,7839,7982,4093,7658,8011,6138,7631,7550,8097,6111,7907,8084,7147,7989,7894,7799,7665,7134,7039,7868,4094,7611,7897,8040,7660,8013,8098,6140,8071,7990,7909,7666,7149,8019,7855,7639,8088,7993,7898,7803,7613,7423,7155,8014,6127,8100,7910,8129,7150,8048,7668,8075,8021,7994,7913,7614,7967,7900,7805,7643,7157,7863,7103,8130,8035,7655,8104,8022,7914,6135,8077,7996,7887,7806,7672,8025,7158,7645,8083,7921,7161,8132,7867,8037,8078,7983,7916,7659,8026,6139,7646,7551,8112,7922,8085,7162,7895,8038,7135,7869,4095,8136,8041,7661,8028,8099,6141,8086,7991,7924,7667,7164,7870,8089,7899,8042,7662,8015,6142,8101,7911,8144,7151,8049,7669,8090,7995,7928,7615,7901,8044,8102,8131,8050,7670,8105,8023,7915,8092,7997,7902,7807,7673,7159,8160,8133,8106,8052,8079,7998,7917,7674,8027,7647,8113,7923,7163,8134,8039,8108,7918,8137,8056,7676,8029,8114,8087,7925,7165,7871,8138,8043,7663,8030,6143,8116,7926,8145,7166,8091,7929,8140,8045,8103,8146,8051,7671,8120,7930,8093,7903,8046,8161,8148,8107,8053,8094,7999,7932,7675,8162,8135,8054,8109,7919,8152,8057,7677,8115,8164,8110,8139,8058,7678,8031,8117,7927,7167,8168,8141,8060,8118,8147,8121,7931,8142,8047,8176,8149,8122,8095,7933,8163,8150,8055,8124,7934,8153,8165,8111,8154,8059,7679,8166,8169,8156,8061,8119,8170,8143,8062,8177,8123,8172,8178,8151,8125,7935,8180,8126,8155,8167,8184,8157,8171,8158,8063,8173,8179,8174,8181,8127,8182,8185,8186,8159,8188,8175,8183,8187,8189,8190,8191,]； When the mother code length is 4096, the first sequence is the sequence Q1, the number of information bits K=L+M, and the number of information bits L is: 452, 536, 904, 1048, 1808, 2072, 2712, or 3096; or when the mother code length is 8192, the first sequence is the sequence Q2, the number of information bits K=L+M, and the number of information bits L is: 235, 470, 940, 1880, 2820, or 3760; M is any integer greater than or equal to -20 and less than or equal to 20.

8. The method according to claim 7, characterized in that The polarized channel reliabilities corresponding to the selected K sequence numbers are higher than the polarized channel reliabilities corresponding to the remaining (NK) sequence numbers in the first sequence.

9. The method according to claim 7 or 8, characterized in that The first sequence is pre-stored.

10. The method according to claim 7 or 8, characterized in that The N polarized channels are numbered from 0 to (N-1) or from 1 to N.

11. The method according to claim 7 or 8, characterized in that The information bits include cyclic redundancy check (CRC) bits.

12. The method according to claim 7 or 8, characterized in that The information bits include parity check PC bits.

13. A polar code encoding device, characterized in that: include: An acquisition unit, configured to acquire K bits to be encoded; a selecting unit, configured to select K sequence numbers from a first sequence, where polarized channels corresponding to the K sequence numbers place the bits to be coded; an encoding unit, configured to perform Polar code encoding on the K bits to be encoded to obtain encoded bits; in, The first sequence includes the sequence numbers of N polarized channels. The first sequence is the entire sequence or a subsequence of the sequence indicated by sequence Q1 or Q2. K is a positive integer, and N is the mother code length of the Polar code, where N=2. n , n is a positive integer, K≤N; in, The sequence Q1= 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,2895,3724,2001,1022,3629,3467,3413,3386,3305,2981,1947,3672,2791,1785,3359,3292,3024,3197,2929,3730,1996,3635,2549,1901,2970,3255,2875,2808,3846,2495,1959,3684,3522,2781,3427,2924,2002,3630,3496,1907,3414,3849,3306,2982,1527,1976,3659,3469,1786,3388,3279,3011,1949,3198,2930,3745,1759,3417,2550,1902,2985,2903,3732,2795,3637,3475,2972,3313,2877,2782,3904,2687,2553,2017,3524,3259,3429,3850,2004,1963,3688,3470,1909,3375,3308,3040,1950,3661,3746,1855,1788,3418,3013,2986,1531,2932,3719,3638,3504,2959,3857,3314,2878,2797,3667,3477,2554,2018,3287,2907,3736,3430,3641,2527,1991,3261,1910,2993,3852,2803,1965,3662,3528,1775,3433,3014,2008,2919,3748,1913,3420,3491,2988,1533,3858,3777,2798,1971,3696,3478,3017,3383,3316,2936,3723,3669,3642,2556,2020,2909,3262,2994,3615,3481,1966,3291,2967,3434,2805,1995,1914,3407,3968,2751,1534,3873,3778,1887,3683,3493,3018,3860,3303,2923,3752,1973,3670,3536,2543,1783,3441,2910,3725,1023,3644,3482,3387,3320,2996,3673,2806,2024,3293,3025,3436,3731,1997,3874,1916,2971,3494,2809,3847,3780,1974,3685,3523,3020,3442,2925,3726,2003,3631,3497,3415,3864,3307,2983,1977,3674,3484,1787,3389,3294,3026,3199,2931,3760,1998,2551,1903,3000,3733,2810,3876,2973,3686,3552,2783,3905,2926,2032,3525,3498,3444,3851,3784,2005,1978,3689,3471,3390,3309,3041,1951,3676,3747,1789,3419,3028,2987,2933,3734,3639,3505,2974,3315,2879,2812,3906,2555,2019,3526,3737,3431,3880,2006,3690,3500,1911,3853,3310,3042,1980,3663,3529,1790,3448,3015,2009,2934,3749,3421,3506,2989,3859,3792,2799,3697,3479,3032,3317,2937,3738,3908,3643,2557,2021,3263,2995,3854,1967,3692,3530,3435,3044,2010,3750,1915,3422,3969,2990,1535,3888,3779,3698,3508,3019,3861,3318,2938,3753,3671,3537,2558,2022,2911,3740,3645,3483,3321,2997,3912,2807,2025,3532,3437,3970,2012,3875,3808,1917,3495,3048,3862,3781,3754,1975,3700,3538,3021,3443,2940,3727,3646,3512,3865,3322,2998,3675,3485,2026,3295,3027,3438,3761,1999,1918,3001,3972,2811,3877,3782,3687,3553,3022,3920,2927,3756,2033,3540,3499,3445,3866,3785,1979,3704,3486,3391,3324,3056,3677,3762,2028,3029,3002,3735,3878,2975,3554,2813,3907,2034,3527,3976,3446,3881,3786,2007,3691,3501,3868,3311,3043,1981,3678,3544,1791,3449,3030,2935,3764,3507,3004,3793,2814,3936,3033,3556,3739,3909,3882,2036,3502,3855,3788,1982,3693,3531,3450,3045,2011,3751,3423,3984,2991,3889,3794,3699,3509,3034,3319,2939,3768,3910,2559,2023,3741,3884,3694,3560,3913,3046,2040,3533,3452,3971,2013,3890,3809,3510,3049,3863,3796,3755,3701,3539,3036,2941,3742,3647,3513,3323,2999,3914,2027,3534,3439,4000,2014,3810,1919,3973,3050,3892,3783,3702,3568,3023,3921,2942,3757,3541,3514,3867,3800,3705,3487,3325,3057,3916,3763,2029,3003,3974,3879,3812,3555,3052,3922,3758,2035,3542,3977,3447,3896,3787,3706,3516,3869,3326,3058,3679,3545,2030,3031,3765,3005,4032,2815,3937,3557,3978,3924,3883,3816,2037,3503,3870,3789,1983,3708,3546,3451,3060,3766,3985,3006,3795,3938,3035,3558,3769,3911,2038,3980,3885,3790,3695,3561,3928,3047,2041,3548,3453,3986,3891,3824,3511,3064,3797,3770,3940,3037,3743,3886,3562,3915,2042,3535,3454,4001,2015,3811,3988,3051,3893,3798,3703,3569,3038,2943,3772,3515,3801,3944,3564,3917,4002,2044,3975,3894,3813,3570,3053,3923,3759,3543,3992,3897,3802,3707,3517,3327,3059,3918,2031,4004,3814,4033,3054,3952,3572,3979,3925,3898,3817,3518,3871,3804,3709,3547,3061,3767,3007,4034,3939,3559,4008,3926,3818,2039,3981,3900,3791,3710,3576,3929,3062,3549,3987,3825,3065,4036,3771,3941,3982,3887,3820,3563,3930,2043,3550,3455,4016,3826,3989,3066,3799,3942,3039,3773,4040,3945,3565,3932,4003,2045,3990,3895,3828,3571,3068,3774,3993,3803,3946,3566,3919,2046,4005,3815,4048,3055,3953,3573,3994,3899,3832,3519,3805,3948,4006,4035,3954,3574,4009,3927,3819,3996,3901,3806,3711,3577,3063,4064,4037,4010,3956,3983,3902,3821,3578,3931,3551,4017,3827,3067,4038,3943,4012,3822,4041,3960,3580,3933,4018,3991,3829,3069,3775,4042,3947,3567,3934,2047,4020,3830,4049,3070,3995,3833,4044,3949,4007,4050,3955,3575,4024,3834,3997,3807,3950,4065,4052,4011,3957,3998,3903,3836,3579,4066,4039,3958,4013,3823,4056,3961,3581,4019,4068,4014,4043,3962,3582,3935,4021,3831,3071,4072,4045,3964,4022,4051,4025,3835,4046,3951,4080,4053,4026,3999,3837,4067,4054,3959,4028,3838,4057,4069,4015,4058,3963,3583,4070,4073,4060,3965,4023,4074,4047,3966,4081,4027,4076,4082,4055,4029,3839,4084,4030,4059,4071,4088,4061,4075,4062,3967,4077,4083,4078,4085,4031,4086,4089,4090,4063,4092,4079,4087,4091,4093,4094,4095,]； The sequence Q2= [6309,5445,6419,5391,6298,6203,5667,5287,6414,5654,6252,5425,5330,5235,6310,6663,5446,5657,6339, 5277,3623,6258,5420,4819,6421,5230,6313,6231,5449,3381,3721,6300,4935,6205,5669,5507,5004,5426,5345, 4909,4814,3613,3289,5399,5332,5291,6692,5237,5658,6435,5278,3405,5010,5183,4915,6422,6341,6314,3681, 6260,3463,6667,5450,4821,3382,3301,4794,3722,6287,4964,3668,3627,6206,5670,3411,4767,6425,3247,2979, 5346,4910,3614,6235,3480,5699,5509,4586,3385,3290,5428,2966,5319,4939,5768,3195,5238,6321,5673,4559, 7180,5457,4478,5293,3406,5025,6722,3729,6532,5660,4835,6437,6342,5403,2969,5336,5012,3682,6247,3492, 6696,5241,2779,4917,4822,3845,6480,3302,2922,6316,4727,4593,3655,7186,3521,6669,5452,5299,3440,4796, 2895,6426,3724,6345,4539,3629,6264,3467,5728,5510,3413,4825,3386,3305,5415,2981,5348,4968,1947,3672, 6237,5701,2791,6322,5674,4588,3359,3292,6675,5458,4941,5294,3197,5026,2929,3730,6295,5647,5513,3635, 6438,2549,1901,5432,2970,5323,4999,6724,3255,2875,5242,4918,4837,3846,6467,5405,2495,1959,4594,3684, 7201,3522,6670,5215,2781,6536,4947,5776,3427,4783,2924,6441,6346,5681,2002,4567,7188,5016,3630,6251, 3496,1907,5301,3414,4921,4826,3849,6428,3306,5892,2982,1527,4731,1976,4541,3659,6238,3469,5702,6785, 5568,1786,4351,3388,3279,6704,5473,3011,4942,1949,3198,2930,3745,6324,5676,1759,5514,3417,6677,5460, 2550,1902,5419,2985,5352,5028,2903,3732,6353,5705,2795,4838,3637,6496,3475,5406,2972,5325,5057,7202, 3313,2877,5244,2782,6299,4976,5763,6469,2687,6442,2553,5682,2017,4596,7175,3524,5003,6728,3259,4949, 5302,3429,4922,4841,3850,6415,6348,5655,2004,5521,1963,4542,3688,6253,3470,1909,6786,5331,4895,4828, 3375,3308,6691,5474,3040,4733,1950,4571,3661,7192,3746,6311,1855,1788,5305,3418,6678,5447,3013,6544, 5896,2986,1531,4791,2932,6449,3719,6354,5706,5516,3638,6259,3504,5421,2959,5326,5058,3857,3314,2878, 5231,2797,6328,4963,5792,3667,6470,3477,6681,5464,2554,2018,4583,7204,3287,5032,2907,3736,6301,4950, 5765,3430,4842,3641,6444,2527,5684,1991,5522,7233,5005,6254,3261,1910,5427,2993,5360,4924,4815,3852, 6473,5713,2803,4734,1965,4600,3662,7179,3528,6788,5333,4953,1775,5306,3433,6693,5476,3014,6531,5659, 2008,4573,2919,6450,3748,6369,1913,5279,3420,5011,6736,3491,5422,2988,1533,4849,3858,6423,3777,6356, 5708,2798,6315,1971,3696,6261,3478,6682,5451,3017,5060,3383,3316,4795,2936,3723,6302,4965,5766,3669, 3642,6207,2556,5671,2020,5537,7234,5006,2909,3262,5904,2994,5347,4911,4844,3615,6474,3481,5714,5524, 1966,4587,7208,3291,5429,2967,5334,4954,5769,3434,6694,5239,2805,6560,5688,1995,4574,7181,6913,6370, 1914,4479,5308,3407,5040,6723,3968,6533,5661,2751,1534,4850,3873,6452,3778,6343,1887,6792,5337,5013, 3683,6262,3493,6697,5480,3018,4823,3860,6481,3303,2923,3752,6317,4966,1973,3670,7187,3536,6684,5453, 2543,1783,5538,3441,4797,2910,6427,3725,6360,5891,5824,1023,3644,6265,3482,5729,5511,7236,5064,3387, 3320,5430,2996,5349,4969,5770,3673,6476,5716,2806,6323,5675,2024,4589,7182,3293,6914,5459,3025,4956, 5295,3436,5027,6752,3731,6534,5662,1997,5528,3874,6439,6372,1916,5433,2971,5338,5014,6725,3494,6698, 5243,2809,4919,4852,3847,6482,3780,7297,6318,1974,4595,3685,7216,3523,6671,5454,3020,6537,5777,3442, 4798,2925,6456,3726,6347,5920,2003,7189,5017,3631,6266,3497,5730,5540,3415,4827,3864,6429,3307,5893, 2983,5350,4970,1977,3674,6239,3484,5703,6800,5569,1787,4590,3389,3294,6705,5488,3026,4943,5772,3199, 2931,3760,6325,5677,1998,5515,7240,6916,5461,2551,1903,5434,3000,5353,5029,6726,3733,6592,5720,2810, 4839,3876,6497,7298,5407,2973,5340,5072,3686,7203,3552,6700,5245,2783,6538,4977,5778,3905,6484,2926, 6443,6376,5683,2032,4597,7190,3525,5018,6729,3498,5303,3444,4923,4856,3851,6430,3784,6349,5894,2005, 1978,4543,3689,6268,3471,5732,6787,5570,4829,3390,3309,6706,5475,3041,4972,1951,3676,7193,3747,6326, 5678,1789,5544,3419,6679,5462,3028,6545,5897,2987,5354,5030,2933,3734,6355,5707,5517,3639,6498,3505, 5436,2974,5327,5059,3315,2879,5246,2812,6329,4978,5793,3906,6471,7300,6920,5465,2555,2019,4598,7205, 3526,5033,6730,3737,6540,4951,5780,3431,4843,3880,6350,5685,2006,5523,7248,5020,3690,6255,3500,1911, 6816,5361,4925,4830,3853,6488,3310,5952,3042,4735,1980,4601,3663,7194,3529,6789,5572,1790,5307,3448, 6708,5477,3015,6546,5898,2009,2934,3749,6384,5736,5518,3421,3506,5423,2989,5356,5088,3859,3792,2799, 5794,3697,6500,3479,5466,3032,5061,3317,5034,2937,3738,4980,3908,7425,3643,2557,2021,5552,5007,3263, 5905,2995,5362,4926,4845,3854,7304,1967,4602,3692,3530,5335,4955,5784,3435,3044,2010,4575,6928,3750, 1915,5309,3422,5041,3969,5900,2990,1535,4851,3888,3779,5576,3698,3508,3019,5062,3318,2938,4967,7426, 3537,2558,2022,7264,5036,2911,3740,4846,3645,3483,5744,3321,2997,4984,3912,2807,2025,4604,3532,6848, 3437,3970,2012,3808,1917,3048,7312,1975,3021,6016,2940,7428,3512,2998,2026,6944,1918,3972,3920,3056, 7681,6445,6451,6737,6357,5709,6330,6683,7206,6303,5767,6446,5686,7235,6732,6475,5715,5525,7209,6790, 6695,5478,6561,5689,7196,6371,6738,6548,6453,6358,5710,6793,6263,6712,5481,3861,3753,6332,5796,3671, 6685,5468,5539,6361,5906,5825,6504,5526,7237,5065,7210,5431,5364,5771,6477,5717,6562,5690,7183,6915, 4957,5310,5042,6753,6535,5663,5529,3875,6454,6373,6794,5339,5015,6740,3495,6699,5482,4853,3862,6483, 3781,3754,6319,3700,7217,3538,6686,5455,6552,3443,4799,6457,3727,6362,5921,5826,3646,6267,5731,5541, 7238,5066,3865,3322,5908,5351,4971,5800,3675,6478,3485,5718,6801,5584,4591,7212,3295,5489,3027,4958, 5773,3438,6754,3761,6564,5692,1999,5530,7241,6917,6374,5435,3001,5368,5044,6727,6593,5721,2811,4854, 3877,6512,3782,7299,6796,5341,5073,3687,7218,3553,6701,5484,3022,6539,5779,6485,2927,6458,3756,6377, 5922,2033,7191,3540,5019,6744,3499,5542,3445,4857,3866,6431,3785,6364,5895,5828,1979,3704,6269,3486, 5733,6802,5571,5068,3391,3324,6707,5490,4973,5774,3677,7432,3762,6327,5679,2028,5545,7242,6918,5463, 3029,5912,3002,5355,5031,6756,3735,6594,5722,5532,3878,6499,7328,5437,2975,5342,5074,3554,6702,5247, 2813,6568,4979,5808,3907,6486,7301,6921,6378,2034,4599,7220,3527,5048,6731,3976,6541,5781,3446,4858, 3881,6460,3786,6351,5924,2007,7249,5021,3691,6270,3501,5734,6817,5600,4831,3868,6489,3311,5953,3043, 4974,1981,3678,7195,3544,6804,5573,1791,5546,3449,6709,5492,3030,6547,5899,5832,2935,3764,6385,5737, 5519,7244,6976,3507,5438,3004,5357,5089,7682,3793,6596,5724,2814,6331,5795,3936,6501,7302,6922,5467, 3033,5076,7207,3556,5035,6760,3739,6542,4981,5782,3909,7440,3882,6447,6380,5687,2036,5553,7250,5022, 6733,3502,6818,5363,4927,4860,3855,6490,3788,7305,5954,1982,4603,3693,7224,3531,6791,5574,5785,3450, 6710,5479,3045,6576,5928,2011,7197,6929,3751,6386,5738,5548,3423,6739,3984,6549,5901,2991,5358,5090, 3889,3794,6359,5711,6808,5577,3699,6502,3509,6713,5496,3034,5063,7684,3319,2939,3768,6333,4982,5797, 3910,7427,7360,6924,5469,2559,2023,5554,7265,5037,6734,3741,6600,5907,5840,4847,3884,6505,7306,5745, 5527,7252,5080,3694,7211,3560,6820,5365,4985,5786,3913,6492,5956,3046,6563,5691,2040,4605,7198,3533, 6930,6849,5311,3452,5043,6768,3971,6550,5902,2013,3890,6455,3809,6388,5740,6795,5578,6741,3510,6714, 5483,3049,5092,3863,3796,7313,3755,6334,5798,3701,7456,3539,6687,5470,3036,6553,6017,7266,5038,2941, 3742,6363,5936,5827,7429,3647,6506,3513,5746,5556,7239,5067,7688,3323,5909,2999,5366,4986,5801,3914, 6479,7308,5719,7040,5585,2027,4606,7213,3534,6945,6850,4959,5788,3439,6755,4000,6565,5693,2014,5531, 7256,6932,3810,6375,1919,6824,5369,5045,6742,3973,6608,5960,3050,4855,3892,6513,3783,7314,6797,5580, 3702,7219,3568,6716,5485,3023,6554,6018,3921,2942,6459,3757,6392,5923,5856,7430,3541,6745,3514,5543, 7268,5096,3867,3800,6365,5910,5829,5802,3705,6508,3487,5748,6803,5586,5069,7214,3325,6946,5491,3057, 4988,5775,3916,7433,3763,6566,5694,2029,5560,7243,6919,6852,5913,3003,5370,5046,6757,3974,6595,5723, 5533,3879,6514,3812,7329,6798,5343,5075,7696,3555,6703,5486,3052,6569,5809,3922,6487,7316,6936,3758, 6379,2035,7221,3542,5049,6746,3977,6556,6020,3447,4859,3896,6461,3787,6366,5925,5830,7488,3706,6271, 3516,5735,6832,5601,5070,3869,3326,5968,3058,4975,5804,3679,7434,3545,6805,5588,2030,5547,7272,6948, 5493,3031,5914,5833,6758,3765,6624,5752,5534,7245,6977,7330,5439,3005,5372,5104,7683,4032,6597,5725, 2815,6570,5810,3937,6516,7303,6923,6856,5077,7222,3557,5050,6761,3978,6543,5783,3924,7441,3883,6462, 3816,6381,5926,2037,7251,5023,6748,3503,6819,5602,4861,3870,6491,3789,7320,5955,1983,3708,7225,3546, 6806,5575,6024,3451,6711,5494,3060,6577,5929,5834,7436,3766,6387,5739,5549,7246,6978,3985,5916,3006, 5359,5091,7712,3795,6598,5726,6809,5592,3938,6503,7332,6952,5497,3035,5078,7685,3558,6762,3769,6572, 4983,5812,3911,7442,7361,6925,6382,2038,5555,7280,5052,6735,3980,6601,5841,4862,3885,6520,3790,7307, 5984,7253,5081,3695,7226,3561,6821,5604,5787,3928,6493,5957,3047,6578,5930,2041,7199,3548,6931,6864, 5550,3453,6769,3986,6551,5903,5836,3891,3824,6389,5741,6810,5579,6980,3511,6715,5498,3064,5093,7686, 3797,7552,3770,6335,5799,3940,7457,7362,6926,5471,3037,6032,7267,5039,6764,3743,6602,5937,5842,7444, 3886,6507,7336,5747,5557,7254,5082,7689,3562,6822,5367,4987,5816,3915,6494,7309,5958,7041,2042,4607, 7228,3535,6960,6851,5789,3454,6770,4001,6580,5932,2015,7257,6933,3811,6390,5742,6825,5608,6743,3988, 6609,5961,3051,5094,3893,3798,7315,6812,5581,3703,7458,3569,6717,5500,3038,6555,6019,7744,2943,3772, 6393,5938,5857,7431,7364,6984,3515,5558,7269,5097,7690,3801,6604,5911,5844,5803,3944,6509,7310,5749, 7042,5587,5084,7215,3564,6947,6880,4989,5790,3917,7448,4002,6567,5695,2044,5561,7258,6934,6853,6826, 5371,5047,6772,3975,6610,5962,3894,6515,3813,7344,6799,5582,7697,3570,6718,5487,3053,6584,6048,3923, 7317,6937,3759,6394,5858,7460,3543,6747,3992,6557,6021,7270,5098,3897,3802,6367,5940,5831,7489,3707, 6510,3517,5750,6833,5616,5071,7692,3327,5969,3059,4990,5805,3918,7435,7368,7044,5589,2031,5562,7273, 6949,6854,5915,5848,6759,4004,6625,5753,5535,7260,6992,3814,7331,6828,5373,5105,7698,4033,6612,5964, 3054,6571,5811,3952,6517,7318,6938,6857,7223,3572,5051,6776,3979,6558,6022,3925,3898,6463,3817,6396, 5927,5860,7490,6749,3518,6834,5603,5100,3871,3804,7321,5970,5806,3709,7464,3547,6807,5590,6025,7274, 6950,5495,3061,5944,5835,7437,3767,6626,5754,5564,7247,6979,7808,5917,3007,5374,5106,7713,4034,6599, 5727,7048,5593,3939,6518,7333,6953,6858,5079,7700,3559,6763,4008,6573,5813,3926,7443,7376,6940,3818, 6383,2039,7281,5053,6750,3981,6616,6080,4863,3900,6521,3791,7322,5985,7492,3710,7227,3576,6836,5605, 6026,3929,5972,3062,6579,5931,5864,7438,3549,6865,5551,7276,7008,3987,5918,5837,7714,3825,6628,5756, 6811,5594,6981,7334,6954,5499,3065,5108,7687,4036,7553,3771,6574,5814,3941,7472,7363,6927,6860,6033, 7282,5054,6765,3982,6603,5843,7445,3887,6522,3820,7337,5986,7255,5083,7704,3563,6823,5606,5817,3930, 6495,7324,5959,7056,2043,7229,3550,6961,6866,6028,3455,6771,4016,6581,5933,5838,7496,3826,6391,5743, 6840,5609,6982,3989,5976,3066,5095,7716,3799,7554,6813,5596,3942,7459,7392,6956,5501,3039,6034,7745, 6766,3773,6632,5939,5872,7446,7365,6985,7338,5559,7284,5112,7691,4040,6605,5845,5818,3945,6524,7311, 5988,7043,5085,7230,3565,6962,6881,5791,3932,7449,4003,6582,5934,2045,7259,6935,6868,6827,5610,6773, 3990,6611,5963,3895,3828,7345,6814,5583,7936,3571,6719,5502,3068,6585,6049,7746,7556,3774,6395,5859, 7461,7366,6986,3993,6036,7271,5099,7720,3803,6606,5941,5846,7504,3946,6511,7340,5751,7072,5617,5086, 7693,3566,6882,4991,5820,3919,7450,7369,7045,2046,5563,7288,6964,6855,5849,6774,4005,6640,5992,7261, 6993,3815,7346,6829,5612,7699,4048,6613,5965,3055,6586,6050,3953,7319,6939,6872,7462,3573,6777,3994, 6559,6023,7748,3899,3832,6397,5942,5861,7491,6988,3519,6835,5618,5101,7694,3805,7560,5971,5807,3948, 7465,7370,7046,5591,6040,7275,6951,6884,5945,5850,7452,4006,6627,5755,5565,7262,6994,7809,6830,5375, 5107,7728,4035,6614,5966,7049,3954,6519,7348,6968,6859,7701,3574,6778,4009,6588,6052,3927,7377,6941, 3819,6398,5862,7520,6751,3996,6617,6081,5102,3901,3806,7323,6000,7493,3711,7466,3577,6837,5620,6027, 7752,5973,3063,5946,5865,7439,7372,7104,5566,7277,7009,7810,5919,5852,7715,4064,6629,5757,7050,5595, 6996,7335,6955,6888,5109,7702,4037,7568,4010,6575,5815,3956,7473,7378,6942,6861,7283,5055,6780,3983, 6618,6082,3902,6523,3821,7352,5987,7494,7705,3578,6838,5607,6056,3931,7325,5974,7057,5866,7468,3551, 6867,6029,7278,7010,4017,5948,5839,7497,3827,6630,5758,6841,5624,6983,7812,5977,3067,5110,7717,4038, 7555,7052,5597,3943,7474,7393,6957,6862,6035,7760,6767,4012,6633,5873,7447,7380,7000,3822,7339,7285, 5113,7706,4041,6620,6084,5819,3960,6525,7326,5989,7058,7231,3580,6963,6896,6030,3933,4018,6583,5935, 5868,7498,6869,6842,5611,7012,3991,5978,7718,3829,7584,6815,5598,7937,7394,6958,5503,3069,6064,7747, 7557,3775,6634,5874,7476,7367,6987,7816,6037,7286,5114,7721,4042,6607,5847,7505,3947,6526,7341,5990, 7073,5087,7708,3567,6883,5821,3934,7451,7384,7060,2047,7289,6965,6870,6088,6775,4020,6641,5993,7500, 3830,7347,6844,5613,7938,4049,5980,3070,6587,6051,7776,7558,6873,7463,7396,7016,3995,6038,7749,7722, 3833,6636,5943,5876,7506,6989,7342,7074,5619,5116,7695,4044,7561,5822,3949,7480,7371,7047,6041,7290, 6966,6885,5851,7453,4007,6642,5994,7263,6995,7824,6831,5614,7729,4050,6615,5967,7064,3955,7349,6969, 6874,7940,3575,6779,4024,6589,6053,7750,7616,3834,6399,5863,7521,6990,3997,6096,5103,7724,3807,7562, 6001,7508,3950,7467,7400,7076,5621,6042,7753,6886,5947,5880,7454,7373,7105,5567,7292,7024,7811,5853, 7730,4065,6644,5996,7051,6997,7350,6970,6889,7703,4052,7569,4011,6590,6054,3957,7379,6943,6876,7522, 6781,3998,6619,6083,3903,3836,7353,6002,7495,7944,3579,6839,5622,6057,7754,7564,5975,5867,7469,7374, 7106,6044,7279,7011,7840,5949,5854,7512,4066,6631,5759,7080,5625,6998,7813,6890,5111,7732,4039,7570, 7053,3958,7475,7408,6972,6863,7761,6782,4013,6648,6112,7381,7001,3823,7354,7524,7707,4056,6621,6085, 6058,3961,7327,6004,7059,7470,3581,6897,6031,7756,4019,5950,5869,7499,7108,6843,5626,7013,7814,5979, 7719,4068,7585,7054,5599,7952,7395,6959,6892,6065,7762,7572,4014,6635,5875,7477,7382,7002,7817,7287, 5115,7736,4043,6622,6086,3962,6527,7356,5991,7088,7709,3582,6898,6060,3935,7385,7061,5870,7528,6871, 6089,7014,4021,6008,7501,3831,7586,6845,5628,7939,7872,5981,3071,6066,7777,7559,7112,7478,7397,7017, 7818,6039,7764,7723,4072,6637,5877,7507,7004,7343,7075,5117,7710,4045,7576,5823,3964,7481,7386,7062, 7291,6967,6900,6090,4022,6643,5995,7502,7825,6846,5615,7968,4051,5982,7065,7778,7588,6875,7941,7398, 7018,4025,6068,7751,7617,3835,6638,5878,7536,6991,7820,6097,5118,7725,4046,7563,7509,3951,7482,7401, 7077,6043,7768,6887,5881,7455,7388,7120,7293,7025,7826,6092,7731,4080,6645,5997,7066,7351,6971,6904, 7942,4053,4026,6591,6055,7780,7618,6877,7523,7020,3999,6098,7726,3837,7592,6003,7510,7945,7402,7078, 5623,6072,7755,7565,5882,7484,7375,7107,6045,7294,7026,7841,5855,7513,4067,6646,5998,7081,6999,7828, 6891,7733,4054,7571,7068,3959,7409,6973,6878,8000,6783,4028,6649,6113,7620,3838,7355,7525,7946,4057, 6100,6059,7784,7566,6005,7471,7404,7136,6046,7757,7842,5951,5884,7514,7109,7082,5627,7028,7815,7734, 4069,7600,7055,7953,7410,6974,6893,7763,7573,4015,6650,6114,7383,7003,7832,7526,7737,4058,6623,6087, 3963,7357,6006,7089,7948,3583,6899,6061,7758,7624,5871,7529,7110,6104,7015,7844,6009,7516,4070,7587, 7084,5629,7954,7873,6894,6067,7792,7574,7113,7479,7412,7032,7819,7765,7738,4073,6652,6116,7005,7358, 7090,7711,4060,7577,6062,3965,7387,7063,7530,6901,6091,4023,6010,7503,8064,6847,5630,7969,7874,5983, 7779,7589,7114,7956,7399,7019,7848,6069,7766,7632,4074,6639,5879,7537,7006,7821,5119,7740,4047,7578, 3966,7483,7416,7092,7769,6902,6120,7389,7121,7532,7827,6093,7970,4081,6012,7067,7590,6905,7943,7876, 4027,6070,7781,7619,7116,7538,7021,7822,6099,7727,4076,7593,7511,7960,7403,7079,6073,7770,7580,5883, 7485,7390,7122,7295,7027,7856,6094,4082,6647,5999,7096,7829,6906,7972,4055,7069,7782,7648,6879,8001, 7022,4029,6128,7621,3839,7594,7540,7947,7880,6101,6074,7785,7567,7486,7405,7137,6047,7772,7843,5885, 7515,7124,7083,7029,7830,7735,4084,7601,7070,7411,6975,6908,8002,4030,6651,6115,7622,7833,7527,7976,4059,6102,7786,7596,6007,7949,7406,7138,6076,7759,7625,5886,7544,7111,6105,7030,7845,7517,4071,7602,7085,7955,7888,6895,7793,7575,7128,7413,7033,7834,8004,7739,4088,6653,6117,7359,7091,7950,4061,6063,7788,7626,7531,7140,6106,7846,6011,7518,8065,7086,5631,7984,7875,7794,7604,7115,7957,7414,7034,7849,7767,7633,4075,6654,6118,7007,7836,7741,4062,7579,3967,7417,7093,8008,6903,6121,7628,7533,8066,6108,7971,7904,6013,7591,7144,7958,7877,7850,6071,7796,7634,7117,7539,7036,7823,7742,4077,7608,7961,7418,7094,7771,7581,6122,7391,7123,7534,7857,6095,4083,6014,7097,8068,6907,7973,7878,7783,7649,7118,8016,7023,7852,6129,7636,4078,7595,7541,7962,7881,6075,7800,7582,7487,7420,7152,7773,7858,6124,7125,7098,7831,7974,4085,7071,7650,6909,8003,4031,6130,7623,8072,7542,7977,7882,6103,7787,7597,7964,7407,7139,6077,7774,7640,5887,7545,7126,7031,7860,4086,7603,7100,7889,6910,8032,7129,7652,7835,8005,7978,4089,6132,7598,7951,7884,6078,7789,7627,7546,7141,6107,7847,7519,8080,7087,7985,7890,7795,7605,7130,7415,7035,7864,8006,4090,6655,6119,7837,7980,4063,7790,7656,8009,7142,6136,7629,7548,8067,6109,7986,7905,7606,7145,7959,7892,7851,7797,7635,7132,7037,7838,7743,4092,7609,7419,7095,8010,6123,7630,7535,8096,6110,7906,6015,8069,7146,7988,7879,7798,7664,7119,8017,7038,7853,7637,4079,7610,7963,7896,7801,7583,7421,7153,8012,7859,6125,7099,8070,7975,7908,7651,7148,8018,7854,6131,7638,8073,7543,7992,7883,7802,7612,7965,7422,7154,7775,7641,6126,7127,7861,4087,7101,8128,6911,8033,7653,8074,8020,7979,7912,6133,7599,7966,7885,6079,7804,7642,7547,7156,7862,8081,7102,7891,8034,7131,7654,7865,8007,4091,6134,8076,7981,7886,7791,7657,8024,7143,6137,7644,7549,8082,7987,7920,7607,7160,7893,7866,8036,7133,7839,7982,4093,7658,8011,6138,7631,7550,8097,6111,7907,8084,7147,7989,7894,7799,7665,7134,7039,7868,4094,7611,7897,8040,7660,8013,8098,6140,8071,7990,7909,7666,7149,8019,7855,7639,8088,7993,7898,7803,7613,7423,7155,8014,6127,8100,7910,8129,7150,8048,7668,8075,8021,7994,7913,7614,7967,7900,7805,7643,7157,7863,7103,8130,8035,7655,8104,8022,7914,6135,8077,7996,7887,7806,7672,8025,7158,7645,8083,7921,7161,8132,7867,8037,8078,7983,7916,7659,8026,6139,7646,7551,8112,7922,8085,7162,7895,8038,7135,7869,4095,8136,8041,7661,8028,8099,6141,8086,7991,7924,7667,7164,7870,8089,7899,8042,7662,8015,6142,8101,7911,8144,7151,8049,7669,8090,7995,7928,7615,7901,8044,8102,8131,8050,7670,8105,8023,7915,8092,7997,7902,7807,7673,7159,8160,8133,8106,8052,8079,7998,7917,7674,8027,7647,8113,7923,7163,8134,8039,8108,7918,8137,8056,7676,8029,8114,8087,7925,7165,7871,8138,8043,7663,8030,6143,8116,7926,8145,7166,8091,7929,8140,8045,8103,8146,8051,7671,8120,7930,8093,7903,8046,8161,8148,8107,8053,8094,7999,7932,7675,8162,8135,8054,8109,7919,8152,8057,7677,8115,8164,8110,8139,8058,7678,8031,8117,7927,7167,8168,8141,8060,8118,8147,8121,7931,8142,8047,8176,8149,8122,8095,7933,8163,8150,8055,8124,7934,8153,8165,8111,8154,8059,7679,8166,8169,8156,8061,8119,8170,8143,8062,8177,8123,8172,8178,8151,8125,7935,8180,8126,8155,8167,8184,8157,8171,8158,8063,8173,8179,8174,8181,8127,8182,8185,8186,8159,8188,8175,8183,8187,8189,8190,8191,]； When the mother code length is 4096, the first sequence is the sequence Q1, the number of bits to be encoded K=L+M, and L is 452, 536, 904, 1048, 1808, 2072, 2712, or 3096; or when the mother code length is 8192, the first sequence is the sequence Q2, the number of bits to be encoded K=L+M, and the number of bits to be encoded L is 235, 470, 940, 1880, 2820, or 3760; and M is any integer greater than or equal to -20 and less than or equal to 20.

14. The device according to claim 13, characterized in that The apparatus further includes: a rate matching unit configured to perform rate matching on the bits encoded by the Polar code to obtain rate-matched bits.

15. The device according to claim 13 or 14, characterized in that The first sequence is pre-stored.

16. The device according to claim 13 or 14, characterized in that The N polarized channels are numbered from 0 to (N-1) or from 1 to N.

17. The device according to claim 13 or 14, characterized in that The bits to be encoded include cyclic redundancy check (CRC) bits.

18. The device according to claim 13 or 14, characterized in that The bits to be encoded include parity check PC bits.

19. A polar code processing device, characterized in that: include: Memory, used to store programs; A processor, configured to execute the program stored in the memory; when the program is executed, the processor is configured to execute the method according to any one of claims 1 to 6, or execute the method according to any one of claims 7 to 12.

20. The device according to claim 19, characterized in that The Polar code processing device is a chip or an integrated circuit.

21. A computer storage medium, characterized in that A computer program is stored, and when the computer program is executed on a computer, the method according to any one of claims 1 to 12 is executed.

22. A computer program product comprising instructions, characterized in that When the method is run on a computer, the method according to any one of claims 1 to 12 is executed.

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