KR102334420B1 - Method for encoding and decodong using distributed crc-polar codes and apparatus for performing the same - Google Patents

Abstract

A CRC-polar encoding method is performed in a transmitter using polar coding. The method comprises the following steps of: interleaving at least some bits of information bits and CRC bits for the information bits based on a predetermined order; and polar-encoding the interleaved bits based on a predetermined bit-channel index. According to the present invention, an early error detection effect is excellent and error rate performance increase and delay reduction of a communication system can be realized.

Description

Encoding and decoding method using distributed CRC-polar code, and apparatus for performing the same

The present invention relates to encoding and decoding methods.

The distributed CRC-polar code adjusts each CRC code bit to be located between the information blocks by introducing an interleaver between the CRC encoder and the polar encoder. In this case, a condition for limiting that the index of all information bits constituting each CRC bit is always smaller than the index of the corresponding CRC bit is considered so that successive cancellation (SC) decoding is possible.

The distributed CRC bits are used for tree pruning in the successive cancellation list (SCL) decoding process, and the error rate performance is improved or latency is reduced through early termination of decoding. can be used to make

In this case, in order to maximize the effect of early error detection in successive cancellation-based decoding, a distributed CRC code should be designed so that the index of each CRC bit has the smallest possible value.

D. Hui, M. Breschel, and Y. Blankenship, "Interleaved CRC for polar codes," in Proc. IEEE 87th Veh. Technol. Conf. (VTC Spring), Jun. 2018, p. 1-5. P. Chaki and N. Kamiya, "A novel design of CRC-concatenated polar codes," in Proc. IEEE International Conference on Communications (ICC), 2019.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method for designing a distributed CRC code that has excellent early error detection effect and can achieve improved error rate performance and reduced delay of a communication system.

However, the problem to be solved by the present invention is not limited thereto, and may be variously expanded without departing from the spirit and scope of the present invention.

A cyclic redundancy check (CRC)-polar coding method performed in a transmitter using polar coding according to an embodiment of the present invention for solving the above-described problem is information bits and the information bits based on a predetermined order. and interleaving at least some of the CRC bits for CRC, and polar encoding the interleaved bits based on a predetermined bit-channel index.

According to an aspect, the method includes, before the interleaving of at least some bits, identifying a length K of the information bits when the lengths of the information bits vary, and adding the information bits to the information bits based on a CRC code. The method may further include determining CRC bits for .

According to an aspect, the predetermined order may correspond to a second parity check matrix determined based on a row operation, row permutation, and column permutation of the first parity check matrix of the CRC code.

According to one aspect, the j-th row of the second parity check matrix randomly generates L nonsingular matrices U _j having a size of M×M, where M is the number of CRC bits, L is a natural number -, the L regular matrix U _j Selecting a regular matrix U _j ^* in which the minimum row weight of the non-zero rows of U _j H _{{:,l+1, K+M}} ^{(j- 1)} is the minimum among them - where H ⁽⁰⁾ is The first parity check matrix, H ^(j-1) is The 1st to j-1th rows are the determined second parity check matrices, and H _{{:,l+1, K+M}} ^(j-1) _- is {l+1, l+2, ... , K+M} is a submatrix of H ^(j-1) consisting of column indices, where l is the index of the rightmost nonzero component in the j-1th row of H ^{(j-1) -,} performing row substitution so that the newly found row is located in the j-th row while fixing the first j-1 rows of U _j ^* H ^{(j-1) , and non-zero at the last K+Ml position in the j-th row} It may be determined according to the step of performing thermal substitution so that the components are all located on the left.

According to an aspect, the predetermined order may correspond to a third parity check matrix determined by performing additional column permutation based on bit-channel reliability on the second parity check matrix.

According to one aspect, the method may further include inserting 0 or a predefined value into the information block.

According to an aspect, the L may be determined based on the complexity of the CRC-polar encoding.

According to an aspect, the first parity check matrix may be a standard parity check matrix of the CRC code.

A transmitter using polar coding according to another embodiment of the present invention for solving the above problems includes a transceiver for transmitting polar coded bits, and at least one processor, wherein the at least one processor is configured in advance Information bits and at least some bits of CRC bits for the information bits are interleaved based on a determined order, and the interleaved bits are polar-encoded based on a predetermined bit-channel index.

A cyclic redundancy check (CRC)-polar decoding method performed in a receiver using polar decoding according to another embodiment of the present invention for solving the above-mentioned problems is a polar decoding method based on values to be used for decoding and a predetermined bit-channel index. decoding, and identifying information bits based on a predetermined order for at least some bits of bits determined by the polar decoding.

According to one aspect, the method includes, before the polar decoding step, receiving a signal corresponding to the information bits from a transmitter, performing demodulation on the received signal, and determining values to be used for the decoding; and identifying the length K of the information bits when the lengths of the information bits are variable.

According to an aspect, the predetermined order may correspond to a second parity check matrix determined based on a row operation, row permutation, and column permutation of the first parity check matrix of the CRC code.

According to one aspect, the j-th row of the second parity check matrix randomly generates L nonsingular matrices U _j having a size of M×M, where M is the number of CRC bits, L is a natural number -, the L regular matrix U _j Selecting a regular matrix U _j ^* in which the minimum row weight of the non-zero rows of U _j H _{{:,l+1, K+M}} ^(j-1) is the minimum among them - where H ⁽⁰⁾ is The first parity check matrix, H ^(j-1) is The 1st to j-1th rows are the determined second parity check matrices, and H _{{:,l+1, K+M}} ^(j-1) _- is {l+1, l+2, ... , K+M} is a submatrix of H ^(j-1) consisting of column indices, where l is the index of the rightmost nonzero component in the j-1th row of H ^{(j-1) -,} performing row substitution so that the newly found row is located in the j-th row while fixing the first j-1 rows of U _j ^* H ^{(j-1) , and non-zero at the last K+Ml position in the j-th row} It may be determined according to the step of performing thermal substitution so that the components are all located on the left.

According to an aspect, the predetermined order may correspond to a third parity check matrix determined by performing additional column permutation based on bit-channel reliability on the second parity check matrix.

According to one aspect, the method may further include inserting 0 or a predefined value into the information block.

According to an aspect, L may be determined based on the complexity of the CRC-polar decoding.

According to an aspect, the L is the CRC-polar and the first parity check matrix may be a standard parity check matrix of the CRC code.

A receiver using polar decoding according to another embodiment of the present invention for solving the above problems includes a transceiver for receiving a signal corresponding to information bits and at least one processor, the at least one processor performs polar decoding based on values to be used for decoding and a predetermined bit-channel index, and identifies the information bits based on a predetermined order for at least some bits of bits determined by the polar decoding.

The disclosed technology may have the following effects. However, this does not mean that a specific embodiment should include all of the following effects or only the following effects, so the scope of the disclosed technology should not be understood as being limited thereby.

According to the CRC-polar encoding and decoding method according to the above-described embodiments of the present invention, and an apparatus for performing the same, an early error detection effect is excellent, and an error rate performance improvement and delay reduction of a communication system can be achieved.

1 is a flowchart of an encoding method using a distributed CRC-polar code according to an embodiment of the present invention.
2 is a flowchart of a method for designing a distributed CRC-polar code according to an embodiment of the present invention.
3 illustrates a parity check matrix of a distributed CRC-polar code according to an embodiment of the present invention.
4 illustrates a configuration of a transmitter using polar coding according to another embodiment of the present invention.
5 shows the configuration of a receiver using polar decoding according to another embodiment of the present invention.
6 illustrates an early error detection capacity (CRC-10) of a distributed CRC-polar code according to an embodiment of the present invention.
7 illustrates an early error detection capacity (CRC-16) of a distributed CRC-polar code according to an embodiment of the present invention.

Since the present invention can have various changes and can have various embodiments, specific embodiments are illustrated in the drawings and described in detail.

However, this is not intended to limit the present invention to specific embodiments, and it should be understood to include all modifications, equivalents and substitutes included in the spirit and scope of the present invention.

Terms such as first, second, etc. may be used to describe various elements, but the elements should not be limited by the terms. The above terms are used only for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, a first component may be referred to as a second component, and similarly, the second component may also be referred to as a first component.

When a component is referred to as being “connected” or “connected” to another component, it may be directly connected or connected to the other component, but it should be understood that other components may exist in between. something to do. On the other hand, when it is said that a certain element is "directly connected" or "directly connected" to another element, it should be understood that the other element does not exist in the middle.

The terms used in the present application are only used to describe specific embodiments, and are not intended to limit the present invention. The singular expression includes the plural expression unless the context clearly dictates otherwise. In the present application, terms such as “comprise” or “have” are intended to designate that a feature, number, step, operation, component, part, or combination thereof described in the specification exists, but one or more other features It should be understood that this does not preclude the existence or addition of numbers, steps, operations, components, parts, or combinations thereof.

Unless defined otherwise, all terms used herein, including technical and scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Terms such as those defined in a commonly used dictionary should be interpreted as having a meaning consistent with the meaning in the context of the related art, and are not interpreted in an ideal or excessively formal meaning unless explicitly defined in the present application. .

Hereinafter, with reference to the accompanying drawings, preferred embodiments of the present invention will be described clearly and in detail so that those of ordinary skill in the art can easily practice the present invention.

The polar code proposed by Arikan is the first error correction code to theoretically prove that the capacity of a binary input discrete memory channel can be achieved through successive cancellation (SC) decoding using the channel polarization phenomenon. am. A polar code of length N = 2 ⁿ (n≥1) has G _N of [Equation 1] as a generating matrix.

이고,

은

의 n차 Kronecker 멱(power) 연산을 의미한다.here

ego,

silver

It means the nth-order Kronecker power operation of .

로 정의된다. 선택되지 않은 나머지 N-K_I개의 비트-채널 인덱스는 동결 집합

{0, 1, … , N-1}＼

를 구성하게 된다. 주어진 입력 벡터 u에 대한 길이 N의 폴라 부호어 c는 [수학식 2]와 같이 계산된다.A general polar code is an information set consisting of _{K I bit-channel indexes with high reliability.}

is defined as _{The remaining NK I} bit-channel indices that are not selected are frozen set

{0, 1, … , N-1}\

will constitute A polar codeword c of length N for a given input vector u is calculated as in [Equation 2].

에 속하는 K_I개의 원소에 대응되는 비트 위치에 정보를 할당하고, 동결 집합

에 속하는 N-K_I개의 비트 위치에는 0의 동결 값을 할당함으로써 구성된다.where u is the set of information

Allocating information to bit positions corresponding to _{K I} elements belonging to the frozen set

It is constructed by assigning a freeze value of 0 to the NK _{I bit positions belonging to .}

로 정의되는 폴라 부호를 직렬 연접함으로써 설계된다. 일반적인 CRC-폴라 부호에서는 CRC 비트들이 정보 블록의 끝부분에 위치한다. CRC-폴라 부호의 복호는 일반적인 SCL 복호를 통해 신뢰도가 높은 L개의 후보 부호어를 생성한 뒤, CRC를 만족하면서 신뢰도가 가장 높은 정보 비트 시퀀스를 선택함으로써 수행된다.Meanwhile, a polar code concatenated with a cyclic redundancy check (CRC) code (hereinafter, referred to as a “CRC-polar code”) has been proposed to improve successive cancellation list (SCL) decoding performance. The CRC-polar codeword is generated by using the CRC codeword as an input of a polar encoder. Specifically, the [N, K] CRC-polar code designed based on the M-bit CRC code is a [K+M, K] CRC code and _{an information set whose size is K I} =K+M.

It is designed by concatenating the polar codes defined by . In the general CRC-polar code, CRC bits are located at the end of the information block. The decoding of the CRC-polar code is performed by generating L candidate codewords with high reliability through general SCL decoding, and then selecting an information bit sequence with the highest reliability while satisfying the CRC.

In the distributed CRC-polar code, unlike the conventional CRC-polar code, by introducing an interleaver between the CRC encoder and the polar encoder, each CRC code bit is adjusted so that it is located between the information blocks. In this case, a condition for limiting that the index of all information bits constituting each CRC bit is always smaller than the index of the corresponding CRC bit is considered so that SC decoding is possible. Since the distributed CRC code is equivalent to the original CRC code, it has the same error-detection-capability. Distributed CRC bits can be used for tree pruning like dynamic freeze bits in the SCL decoding process to improve error rate performance or to reduce complexity and latency through early termination of decoding. have.

In order to maximize the effect of early error detection in SC or SCL decoding, a distributed CRC code should be designed so that the index of each CRC bit has the smallest possible value. In particular, the first few CRC bits play a more important role in the effectiveness of early error detection. Conventionally, in order to adjust the position of the CRC bit to have a low index, a method of permuting rows and columns of a generation matrix for a CRC code or permutation of rows and columns of a parity check matrix has been considered.

1 is a flowchart of an encoding method using a distributed CRC-polar code according to an embodiment of the present invention. The coding method using the distributed CRC-polar code may be performed by a transmitter or a receiver of a communication system or a broadcasting system.

When performed by the transmitter, the length (K) of information bits to be transmitted is first identified (S110). If the length of the information bits is always fixed, this step may be omitted.

Next, CRC bits for the information bits are determined based on the CRC code (S130). For example, the CRC bits may be determined by performing encoding on the information bits based on the CRC code. Here, the CRC bit may be a CRC parity bit.

Next, at least some of the information bits and the CRC bits are interleaved based on a predetermined order (S150). Here, the predetermined order may correspond to a parity check matrix determined based on a row operation, a row permutation, and a column permutation with respect to the parity check matrix of the CRC code, and the row operation may correspond to at least one of the rows constituting the parity check matrix. It may mean a linear operation for some. Also, according to an embodiment, a parity check matrix may be generated based on additional column permutation in consideration of bit-channel reliability, and zero padding may be performed to support various code lengths. This step will be described later with reference to FIG. 2 .

Next, the interleaved bits are polar-encoded based on a predetermined bit-channel index (S170). Thereafter, when encoding is completed, bits to be transmitted are determined, and puncturing or rate-matching may be applied to at least a portion of bits to be transmitted according to a given transmission resource according to a system and then transmitted.

Meanwhile, in the case of being performed by the receiver, a signal corresponding to information bits transmitted from the transmitter is first received, and values to be used for decoding are determined by performing demodulation on the received signal. For example, a value to be used for decoding may be a log-likelihood ratio (LLR) value.

It also identifies the length of the information bits based on the received signal. As in the case performed in the transmitter, this step may be omitted if the length of the information bits is always fixed.

Next, polar decoding is performed based on the determined value and the bit-channel index of the predetermined polar code. Depending on the system, when punctured or rate-matched bits exist according to a given transmission resource in the transmitter, an operation of inserting appropriate values into the corresponding bits may be additionally performed. In general, when an LLR value is used for decoding, a value of 0 is inserted into punctured bits, but the present invention is not limited thereto.

Next, information bits are identified based on a predetermined order for at least some of the bits determined by performing polar decoding. Here, the predetermined order may correspond to a parity check matrix determined based on a row operation, a row permutation, and a column permutation with respect to the parity check matrix of the CRC code, and the row operation is performed on at least a portion of a row constituting the parity check matrix. It may mean a linear operation for . Also, according to an embodiment, a parity check matrix may be generated based on additional column permutation in consideration of bit-channel reliability, and zero padding may be performed to support various code lengths.

2 is a flowchart of a method for designing a distributed CRC-polar code according to an embodiment of the present invention.

Given the CRC generation polynomial g(x), the generation matrix G of size K×(K+M) and the standard parity check matrix H of size M×(K+M) are respectively [Equation 3] and [Equation 4] ] is the same as

Here, I _K and I _M are identity matrices of K×K and M×M, respectively, and P is a matrix of K×M determined by g(x). Non-zero components of I _M in H correspond to CRC bits, and non-zero components of each row of P ^T correspond to information bits participating in the parity check expression of each CRC bit. In this specification, for convenience of explanation, a method of designing a new parity check matrix H _new defining an equivalent CRC code using a standard parity check matrix H is described, but the present invention is not limited thereto. It can be carried out using

Referring to FIG. 2 , first, a linear combination of rows of H is randomly generated to determine the first row of H _new ( S201 , S203 , and S205 ). Specifically, L nonsingular matrices U ₁ having a size of M×M are randomly generated and multiplied by H .

Next, a regular matrix U ₁ ^* having the minimum minimum row weight of U ₁ H among the L regular matrices is selected (S207, S209, S211, S213, S215, S217, S219).

Next, row substitution is performed so that the row with the minimum weight of U ₁ ^* H is positioned in the first row, and then column substitution is performed so that all non-zero components of the first row are positioned on the left (S223). The matrix obtained here will be referred to as H ^(1).

Thereafter, H ^(M) is obtained by repeating the same process , and H _new can be obtained through this (S225, S227, S229).

Looking specifically, when H ^(j-1) is fixed that is, when the first j-1 of the row of H _new determined and determines the j-th row of H _new by the next iteration. If ^{the index of the rightmost non-zero component in the j-1th row of H (j-1)} is l, similarly to the previous process, it has a size of M×M defined as in [Equation 5]. Randomly generate L regular matrices U _{j .}

Here, V is a regular matrix of size (M-j+1)×(M-j+1).

Next, a regular matrix U _j ^* in which the minimum row weight of non-zero rows of U _j H _{:.l+1,K+M} ^(j-1) is the minimum among the L regular matrices is selected. In this case, H _{{:.l+ 1,K +M}} ^{(j- 1)} is {l+1, l+2, … , K+M} is a submatrix of H ^(j-1) composed of column indices belonging to , and has a size of M×(K+Ml).

Next, while fixing the first j-1 rows of U _j ^* H ^(j-1) , row substitution is performed so that the newly found row is located in the j-th row.

Next, column substitution is performed so that all non-zero components are located on the left at the last K+Ml position in the j-th row. Here, the obtained matrix will be referred to as H ^(j). This process is repeated until j = M, and through this, H _new is obtained.

To get the optimal matrix H _new based on the full search, ^{(2 M} -1)(2 ^M -2)… (2 ^M -2 ^M-1 ) iterations are required, which increases rapidly as M increases. On the other hand, according to the coding method using a distributed CRC-polar code according to an embodiment of the present invention, complexity can be controlled by appropriately selecting the number L of randomly generated regular matrices.

With respect to the parity check matrix H _new obtained by the above-described method, the index of the j-th (1≤j≤M) CRC bit is as in [Equation 6].

Here, the parity check matrix H _new has a rightmost nonzero element in each row at a different column index. That is, r ₁ , r ₂ , ... , r _M have different values.

Meanwhile, the distributed CRC code may be designed based on bit-channel reliability. Specifically, K _I = K + M bit-channel reliability sequences R(1), R(2), ... , R(K _I ), the reliability of the bit-channel to which the CRC bit is allocated is R(r ₁ ), R(r ₂ ), ... , R(r _M ). When the r ₁ th column and the k (r ₁ <k <r _{2 ) th column are substituted for the parity check matrix H new} designed according to the embodiment of the present invention, the index of the first CRC bit is changed from _{r 1 to k,} Accordingly, the reliability of the bit-channel to which the first CRC bit is allocated _{is changed from R(r 1} ) to R(k). A new parity check matrix can be designed by repeating this process for another j (1<j<M)-th CRC bit.

In addition, the distributed CRC code may perform zero padding to support various code lengths. Let _{K max be} the maximum information length of the designed distributed CRC code. First, according to an embodiment of the present invention, a [K _max +M, K _max ] distributed CRC code defined by a parity check matrix H _{new having a size of M×(K max +M) is designed. K max} -K' 0 or predefined values are inserted into the K' bit information block to generate the codeword of the [K'+M, K'] distributed CRC code with an information length of K'≤K _max. (padding) In this case, the inserted zeros may be located at both ends or may be distributed in consideration of the reliability of the bit-channel. In addition, a codeword of length K'+M can be generated by performing CRC encoding on an information block of _{length K max and then removing the inserted 0 again.}

3 illustrates a parity check matrix of a distributed CRC-polar code according to an embodiment of the present invention.

As an example, FIG. 3 considers a [30+10, 30] CRC code having a ^{generative polynomial g(x)=x 10} +x ⁹ +x ⁵ +x ^{4 +x+1.} 3 (a) is a standard parity check matrix, (b) is a parity check matrix obtained through row permutation and column permutation, (c) is a diagram of a parity check matrix ( H _new ) according to an embodiment of the present invention did it In FIG. 3 , a black rectangle indicates distributed CRC bits, and it can be seen that the parity check matrix according to an embodiment of the present invention has distributed CRC bits of the lowest index.

4 illustrates a configuration of a transmitter using polar coding according to another embodiment of the present invention.

Referring to FIG. 4 , a transmitter 400 using polar coding according to another embodiment of the present invention includes a transceiver 420 for transmitting polar coded bits and at least the above-described CRC-polar coding method. One processor 440 is included.

Specifically, the at least one processor 440 identifies the length K of the information bits when the length of the information bits varies, determines the CRC bits for the information bits based on the CRC code, and determines a predetermined At least some of the information bits and the CRC bits are interleaved based on an order, and the interleaved bits are polar-coded based on a predetermined bit-channel index.

Here, the predetermined order may correspond to a parity check matrix determined based on a row operation, a row permutation, and a column permutation with respect to the parity check matrix of the CRC code, and the row operation may correspond to at least one of the rows constituting the parity check matrix. It may mean a linear operation for some. Also, according to an embodiment, a parity check matrix may be generated based on additional column permutation in consideration of bit-channel reliability, and zero padding may be performed to support various code lengths.

5 shows the configuration of a receiver using polar decoding according to another embodiment of the present invention.

5, a receiver 500 using polar decoding according to another embodiment of the present invention includes a transceiver 520 for receiving a signal corresponding to information bits and the above-described CRC-polar decoding method. It includes at least one processor 540 to perform.

Specifically, the at least one processor 540 performs demodulation on the received signal to determine values to be used for decoding, identifies the length (K) of the information bits when the length of the information bits is variable, and the determined polar decoding based on the values and a predetermined bit-channel index, and identifying the information bits based on a predetermined order for at least some bits of bits determined by the polar decoding.

Here, the predetermined order may correspond to a parity check matrix determined based on a row operation, a row permutation, and a column permutation with respect to the parity check matrix of the CRC code, and the row operation may correspond to at least one of the rows constituting the parity check matrix. It may mean a linear operation for some. Also, according to an embodiment, a parity check matrix may be generated based on additional column permutation in consideration of bit-channel reliability, and zero padding may be performed to support various code lengths.

6 is a diagram illustrating an early error detection capacity (CRC-10) of a distributed CRC-polar code according to embodiments of the present invention, and FIG. 7 is a diagram of a distributed CRC-polar code according to embodiments of the present invention. The early error detection capacity (CRC-16) is shown.

6 and 7, the early error detection capability for the first three CRC bits in the distributed CRC code is compared with the method according to an embodiment of the present invention and the method according to [1] and [2] below. shown. Here, the CRC generation polynomial is considered g ₁ (x)=x ¹⁰ +x ⁹ +x ⁵ +x ⁴ +x+ 1 and g ₂ (x)=x ¹⁶ +x ¹² +x ⁵ +1. The x-axis represents the information length of the CRC code, and the y-axis represents the ratio of the number of information bits appearing before each CRC bit to the information length. It can be seen that a distributed CRC code having a larger early error detection capacity of the method according to an embodiment of the present invention can be designed than other methods.

[1] D. Hui, M. Breschel, and Y. Blankenship, "Interleaved CRC for polar codes," in Proc . IEEE 87th Veh . Technol . Conf . ( VTC Spring) , Jun. 2018, p. 1-5.

[2] P. Chaki and N. Kamiya, "A novel design of CRC-concatenated polar codes," in Proc . IEEE International Conference on Communications (ICC) , 2019.

Although described above with reference to the drawings and embodiments, it does not mean that the protection scope of the present invention is limited by the drawings or embodiments, and those skilled in the art will appreciate the spirit and scope of the present invention described in the claims below. It will be understood that various modifications and variations of the present invention can be made without departing from the scope thereof.

400: transmitter
500: receiver

Claims (18)

In a cyclic redundancy check (CRC)-polar coding method performed in a transmitter using polar coding,
based on a predetermined order, interleaving at least some bits of information bits and CRC bits for the information bits determined based on a CRC code; and
polar encoding the interleaved bits based on a predetermined bit-channel index,
The predetermined order corresponds to a second parity check matrix determined based on a first parity check matrix for the CRC code,
The j-th row of the second parity check matrix is
randomly generating L nonsingular matrices U _j having a size of M×M, where M is the number of CRC bits and L is a natural number;
The L nonsingular matrix U _j in _{U j H {:, l +} 1, K + M} (j-1) 0 selecting a nonsingular matrix U _j ^* is the minimum line weight of the line is minimum non-of- Here, H ⁽⁰⁾ is the first parity check matrix, and H ^(j-1) is The 1st to j-1th rows are the determined second parity check matrices, and H _{{:,l+1, K+M}} ^(j-1) _- is {l+1, l+2, ... , K+M} is a submatrix of H ^(j-1) consisting of column indices, and l is the index of the rightmost nonzero component in the j-1th row of H ^{(j-1) -;}
performing row substitution so that the newly found row is located in the j-th row while fixing the first j-1 rows of U _j ^* H ^(j-1); and
The CRC-polar encoding method, which is determined according to the step of performing column permutation so that all non-zero components are located to the left at the last K+Ml position in the j-th row. delete delete delete According to claim 1,
and the predetermined order corresponds to a third parity check matrix determined by performing additional column permutation based on bit-channel reliability on the second parity check matrix. delete According to claim 1,
The L is determined based on the complexity of the CRC-polar encoding. According to claim 1,
The first parity check matrix is expressed by the following equation

The standard parity check matrix is determined by - P where ^T is the transpose of matrix P of K × M, which is determined by the CRC generator polynomial g (x), I _M is M × M identity matrix being a -, CRC- Polar encoding method. a transceiver that transmits polar coded bits; and
at least one processor;
the at least one processor
Interleaving at least some bits of information bits based on a predetermined order and CRC bits for the information bits determined based on a CRC code, and
Polar encoding the interleaved bits based on a predetermined bit-channel index,
The predetermined order corresponds to a second parity check matrix determined based on a first parity check matrix for the CRC code,
The j-th row of the second parity check matrix is
randomly generating L nonsingular matrices U _j having a size of M×M, where M is the number of CRC bits and L is a natural number;
The L nonsingular matrix U _j in _{U j H {:, l +} 1, K + M} (j-1) 0 selecting a nonsingular matrix U _j ^* is the minimum line weight of the line is minimum non-of- Here, H ⁽⁰⁾ is the first parity check matrix, and H ^(j-1) is The 1st to j-1th rows are the determined second parity check matrices, and H _{{:,l+1, K+M}} ^(j-1) _- is {l+1, l+2, ... , K+M} is a submatrix of H ^(j-1) consisting of column indices, and l is the index of the rightmost nonzero component in the j-1th row of H ^{(j-1) -;}
performing row substitution so that the newly found row is located in the j-th row while fixing the first j-1 rows of U _j ^* H ^(j-1); and
Transmitter using polar coding, determined according to the step of performing column permutation so that all non-zero components in the last K+Ml position in the j-th row are located to the left. In a cyclic redundancy check (CRC)-polar decoding method performed in a receiver using polar decoding,
performing polar decoding based on values to be used for decoding and a predetermined bit-channel index; and
identifying information bits based on a predetermined order for at least some bits of bits determined by the polar decoding;
The predetermined order corresponds to a second parity check matrix determined based on the first parity check matrix for the CRC code,
The j-th row of the second parity check matrix is
randomly generating L nonsingular matrices U _j having a size of M×M, where M is the number of CRC bits and L is a natural number;
The L nonsingular matrix U _j in _{U j H {:, l +} 1, K + M} (j-1) 0 selecting a nonsingular matrix U _j ^* is the minimum line weight of the line is minimum non-of- Here, H ⁽⁰⁾ is the first parity check matrix, and H ^(j-1) is The 1st to j-1th rows are the determined second parity check matrices, and H _{{:,l+1, K+M}} ^(j-1) _- is {l+1, l+2, ... , K+M} is a submatrix of H ^(j-1) consisting of column indices, and l is the index of the rightmost nonzero component in the j-1th row of H ^{(j-1) -;}
performing row substitution so that the newly found row is located in the j-th row while fixing the first j-1 rows of U _j ^* H ^(j-1); and
The CRC-polar decoding method, which is determined according to the step of performing column substitution so that all non-zero components are located on the left at the last K+Ml position in the j-th row. delete delete delete 11. The method of claim 10,
The predetermined order corresponds to a third parity check matrix determined by performing additional column permutation based on bit-channel reliability on the second parity check matrix. delete 11. The method of claim 10,
The L is determined based on the complexity of the CRC-polar decoding. 11. The method of claim 10,
The first parity check matrix is expressed by the following equation

The standard parity check matrix is determined by - P where ^T is the transpose of matrix P of K × M, which is determined by the CRC generator polynomial g (x), I _M is M × M identity matrix being a -, CRC- Polar decryption method. a transceiver for receiving a signal corresponding to the information bits; and
at least one processor;
the at least one processor
Polar decoding based on values to be used for decoding and a predetermined bit-channel index, and
Identifying the information bits based on a predetermined order for at least some bits of the bits determined by the polar decoding,
The predetermined order corresponds to a second parity check matrix determined based on the first parity check matrix for the CRC code,
The j-th row of the second parity check matrix is
randomly generating L nonsingular matrices U _j having a size of M×M, where M is the number of CRC bits and L is a natural number;
The L nonsingular matrix U _j in _{U j H {:, l +} 1, K + M} (j-1) 0 selecting a nonsingular matrix U _j ^* is the minimum line weight of the line is minimum non-of- Here, H ⁽⁰⁾ is the first parity check matrix, and H ^(j-1) is The 1st to j-1th rows are the determined second parity check matrices, and H _{{:,l+1, K+M}} ^(j-1) _- is {l+1, l+2, ... , K+M} is a submatrix of H ^(j-1) consisting of column indices, and l is the index of the rightmost nonzero component in the j-1th row of H ^{(j-1) -;}
performing row substitution so that the newly found row is located in the j-th row while fixing the first j-1 rows of U _j ^* H ^(j-1); and
A receiver using polar decoding, determined according to the step of performing column permutation so that all non-zero components in the last K+Ml position in the j-th row are located to the left.

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