CN106998208B - Code word construction method of variable length Polar code - Google Patents

Code word construction method of variable length Polar code Download PDF

Info

Publication number
CN106998208B
CN106998208B CN201710036000.0A CN201710036000A CN106998208B CN 106998208 B CN106998208 B CN 106998208B CN 201710036000 A CN201710036000 A CN 201710036000A CN 106998208 B CN106998208 B CN 106998208B
Authority
CN
China
Prior art keywords
matrix
code
combo
code length
sequence
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201710036000.0A
Other languages
Chinese (zh)
Other versions
CN106998208A (en
Inventor
刘荣科
冯宝平
王闰昕
赵岭
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beihang University
Original Assignee
Beihang University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beihang University filed Critical Beihang University
Priority to CN201710036000.0A priority Critical patent/CN106998208B/en
Publication of CN106998208A publication Critical patent/CN106998208A/en
Application granted granted Critical
Publication of CN106998208B publication Critical patent/CN106998208B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
    • H03M13/13—Linear codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
    • H04L1/0056—Systems characterized by the type of code used
    • H04L1/0057—Block codes

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Error Detection And Correction (AREA)

Abstract

The invention provides a code word construction method of a variable-length Polar code, belonging to the field of communication. The construction of a long code generating matrix is realized by expanding a generating matrix of a short code, and firstly, the code length is expressed as a summation form of powers of 2 based on an integer binary representation; then, taking the value of each item forming the summation form as the size of a sub-matrix forming the new generation matrix; and finally, constructing a new generator matrix through combo-sum combined operation. Compared with the traditional method for constructing the variable-length Polar code, the method does not need to perform puncturing and deleting operation, reduces the encoding complexity and the time delay, and avoids the problem that the traditional method estimates the likelihood information of the unknown bit by using the priori knowledge because the likelihood information of the unknown bit is known at the decoding end, thereby reducing the bit error rate of decoding and improving the system performance.

Description

Code word construction method of variable length Polar code
Technical Field
The invention belongs to the field of communication channel coding, and particularly relates to a code word construction method of a variable-length Polar code.
Background
Polar Codes, i.e., polarization code, was 2009 by E.
Figure DEST_PATH_GDA0001328423820000015
A new type of channel coding is proposed. Polarization code is designed based on Channel Polarization (Channel Polarization), the first constructive coding scheme that can prove to reach Channel capacity by strict mathematical methods. However, the Polar code is constructed by Kronecker power, and the construction mode limits the code length of Polar code, thus being inconvenient for the use of Polar code in practical system. The original method can only construct the code length of 2nPolar code of (n ═ 1, 2.). Although Polar codes with other code lengths can be constructed by other polarization cores such as BCH code core, the code length of Polar codes constructed by the method is still limited to the power of the core length, and the decoding structure of Polar codes constructed by the method is complex.
It is well known in the art that in practical communication systems the length of the original information is often uncertain, which requires that the code can be adjusted according to the length of the original information. That is, a coding structure with a series of different code length and code rate is obtained according to the channel condition and the length of the information. Currently, the existing code word structure of the variable length polarization code adopts the method that part of code word bits are deleted from the original code word bits with the length of 2 power to realize the code word structure with the power of non-2. The likelihood information of the deleted code word bits is set to be 0,1 and the like when the receiving end decodes, and then the decoding of the common polarization code is carried out. Although the method realizes the Polar code structure with variable code length, the decoding error probability is also improved, and the performance of the communication system is seriously lost. Therefore, a code word construction method of a Polar code with a variable code length and better performance is needed.
Disclosure of Invention
Based on the requirement, the invention provides a code word construction method of variable-length Polar codes, which combines power Polar code generating matrixes with the original length limited to 2 to realize the construction of generating matrixes of Polar codes with any code length.
The invention provides a code word construction method of a variable length Polar code, which comprises the following steps:
step 1: spreading the code length N binary system to obtain a corresponding binary bit sequence s; wherein N is a positive integer;
step 2: and determining the size of the generating matrix to be selected according to the position of the '1' in the binary bit sequence s obtained in the step 1.
Let q be the number of bit values "1" in the sequence s, where h is the index number in the sequence sdThe bit value of (a) is 1, d represents the d-th 1 occurring from the upper to the lower bits in the sequence s, and d is 1,2, … q. Then select the original generating matrix of q polar codes, which are respectively l in size1,l2,...,lqThe square matrix of (A) is formed,
Figure DEST_PATH_GDA0001328423820000011
hdthe sequence s is indexed from 1 starting from the lower to the upper bits, which is a positive integer.
And step 3: and combining the selected sub-matrixes through Combo-Sum operation to obtain a generator matrix with the code length of N.
Obtaining q generating matrixes according to the step 2
Figure DEST_PATH_GDA0001328423820000012
The generator matrix C with code length N is represented as:
Figure DEST_PATH_GDA0001328423820000013
wherein the content of the first and second substances,
Figure DEST_PATH_GDA0001328423820000014
representing a Combo-Sum operation.
The Combo-Sum operation is: let the matrix involved in the operation be
Figure DEST_PATH_GDA0001328423820000021
And
Figure DEST_PATH_GDA0001328423820000022
the resulting combined matrix is:
Figure DEST_PATH_GDA0001328423820000023
wherein L is1、L2Respectively, the size of the matrix A, B, and the size of the matrix B' is L2×L1Front L in B2Column and matrix B are identical, last L1-L2The columns are all 0 columns.
The invention has the advantages and positive effects that: the code word construction method is realized through Combo-Sum operation, and the Polar code constructed by the method can effectively reduce the decoding error probability and improve the performance of a communication system. The invention realizes the construction of the long code generating matrix by expanding the generating matrix of the short code, and compared with the traditional method, the invention does not need to delete the punching operation, thereby reducing the coding complexity and the time delay. The likelihood information corresponding to the unknown bit at the decoding end is known, so that the problem that the prior knowledge is used for estimating the likelihood information of the unknown bit in the traditional method is solved, the bit error rate of decoding is reduced, and the system performance is improved.
Drawings
FIG. 1 is a flow chart illustrating a codeword construction method according to the present invention;
FIG. 2 is three specific examples of the original generator matrices used in constructing the generator matrices according to the present invention;
FIG. 3 is a diagram illustrating a general correspondence relationship between a new generation matrix and a sub-matrix according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
As shown in FIG. 1, the code word construction method of the variable length Polar code of the present invention realizes the construction of Polar code generating matrix through the following steps 1-3.
Step 1: a binary bit sequence representation is obtained by binary expansion for the code length N. N is a positive integer.
For code length N, using binary expansion to obtain m-bit binary bit sequence s ═ sm,sm-1,...,s2,s1H is an index number from the lower level to the upper level of the binary bit sequence, and h is 1,2, … m, shBit value representing index position h in sequence s, shE {0,1}, m denotes the index position of the highest bit 1 of the binary sequence, sm＝1。
The code length N can be any positive integer, and is not required to be limited to the form of power of 2 like the code length of the original polar code.
For example, when the code length N is 13, the corresponding binary sequence s is {1,1,0,1 }.
Step 2: and determining a generator matrix to be selected by the combination operation according to the position of the '1' in the obtained binary expansion sequence.
And finding out the position of the bit value of 1 in the binary expansion sequence, and setting the number of 1 as q. According to the binary expansion sequence obtained in step 1, N can be expressed as:
Figure DEST_PATH_GDA0001328423820000024
equation (1) shows that N is expressed in power form of 2 according to the position of 1 in the binary bit sequence, where the index number h in the sequence sdThe bit value of (a) is 1, and d represents the d-th 1 occurring from the upper to the lower bits in the sequence s.
Then select the source of q polar codesStarting to generate a matrix, wherein the size of the d-th generating matrix is
Figure DEST_PATH_GDA0001328423820000025
ldIs a natural number and is a power of 2 form.
Selecting q l corresponding to N binary decompositiond×ldThe original generated matrix of Polar code is used as the sub-matrix to be selected in the combination operation, and the selected sub-matrix is expressed as
Figure DEST_PATH_GDA0001328423820000031
Wherein
Figure DEST_PATH_GDA0001328423820000032
Is represented byd×ldSquare matrix, matrix of
Figure DEST_PATH_GDA0001328423820000033
Generating matrices for Polar codes originally, produced by kronecker products, i.e.
Figure DEST_PATH_GDA0001328423820000034
Wherein the matrix
Figure DEST_PATH_GDA0001328423820000035
The parameter n is log2ld，
Figure DEST_PATH_GDA0001328423820000036
Representing kronecker multiplications, which are well known in the art, and primitive generator matrices.
For example: when the code length N is 6, 6 is 22+21＝l1+l2，l1＝4，l22, then selecting a generating matrix G with the code length of the original Polar code of 44×4Generating matrix G with sum code length of 22×2The generator matrix G is a sub-matrix constituting a generator matrix having a code length of 64×4And G2×2The specific values are shown in fig. 2.
When the code length N is 8When 8 is 23＝l1It can be seen that the original Polar code generator matrix structure with the length of 2 is only a special case of the method of the present invention, and the generator matrix G8×8As shown in fig. 2.
And step 3: and combining the selected generator matrixes through Combo-Sum operation so as to construct a generator matrix with the code length of N.
First, the definition of the Combo-Sum operation is proposed. Combo-Sum is a combination operation of two matrices, and the Sum C of Combo-Sum of matrix A and matrix B can be expressed as
Figure DEST_PATH_GDA0001328423820000037
Matrix array
Figure DEST_PATH_GDA0001328423820000038
And
Figure DEST_PATH_GDA0001328423820000039
is a square matrix, L1、L2Respectively, the size of the matrix A, B. To obtain an arbitrary size C, the sizes of A and B need not be the same, where L is taken1≥L2. Wherein the matrix B 'is the same as the matrix B except that all the 0 columns are arranged, and the size of the matrix B' is L2×L1Wherein, the former L of B2Columns are the same as in matrix B, last L1-L2The columns are all 0 columns.
The codeword resulting from the matrix C as the generator matrix may be denoted x ═ uC, and then x and u are further decomposed into two parts, denoted x ═ (x), respectively1,x2) And u ═ u (u)1,u2) X denotes a vector of encoded code words derived from a generator matrix, x1Represents a front L1A number of code words that are each associated with a code word,
Figure DEST_PATH_GDA00013284238200000310
x2after representation of L2A number of code words that are each associated with a code word,
Figure DEST_PATH_GDA00013284238200000311
u1representing the first L of a coded input sequence1One bit of the data is transmitted to the receiver,
Figure DEST_PATH_GDA00013284238200000312
u2post-L representing encoded input sequence2One bit of the data is transmitted to the receiver,
Figure DEST_PATH_GDA00013284238200000313
according to the structure of the matrix C, x1By u1And u2Obtained by the matrixes A and B' together
Figure DEST_PATH_GDA00013284238200000314
x2By u2Obtaining x from the matrix B2＝u2B, so generating codeword x can be expressed as
Figure DEST_PATH_GDA00013284238200000315
Combo-Sum operation defines: two matrixes are given
Figure DEST_PATH_GDA00013284238200000316
Where i denotes the row index of the matrix, j denotes the column index of the matrix, L1,L2Denotes the size of the square matrix, and L1≥L2. Defining two matrixes to carry out Combo-Sum operation to obtain combination
Figure DEST_PATH_GDA00013284238200000317
Figure DEST_PATH_GDA00013284238200000318
Represents a Combo-Sum combinatorial operation, wherein:
Figure DEST_PATH_GDA00013284238200000319
c is represented by formula (2)ijAnd aijAnd bijIs shown in fig. 3. Wherein Γ is {1, 2., L1A subset of L elements of the set, called the difference set2Γ is the set of non-zero columns of matrix B ', the first L of B' must be taken2The order of values is not necessarily in the order of 1,2, …. Let index in set Γ be labeled j0＝1,2,...,L2The index j in the matrix C is the jth of the set Γ0Elements, determining j from Γ according to j0Obtaining cijCorresponding matrix B elements
Figure DEST_PATH_GDA0001328423820000041
When in use
Figure DEST_PATH_GDA0001328423820000042
Combo-Sum and C can be represented as
Figure DEST_PATH_GDA0001328423820000043
The corresponding bit positions represented by equation (3) are shown in fig. 3.
For example
Figure DEST_PATH_GDA0001328423820000044
Combinational operation
Figure DEST_PATH_GDA0001328423820000045
Has the following limitations:
① the A, B matrices participating in the operation may not be permuted.
② the size of the first matrix cannot be smaller than the second matrix, i.e./1≥l2。
③ Combo-Sum operation results are not unique different sets Γ and operation orders will result in different Combo-Sum sums.
For example, the structure of the generator matrix with the code length of 5 may have the following two structures:
the first construction method comprises the following steps:
Figure DEST_PATH_GDA0001328423820000046
the second construction method is as follows:
Figure DEST_PATH_GDA0001328423820000047
Figure DEST_PATH_GDA0001328423820000048
the long code can be decomposed into two or more short codes, and since Combo-Sum operation is not unique, step 3 determines the submatrix participating in Combo-Sum operation according to the binary decomposition order and representation form obtained by step 2 strictly according to the code length N.
For example, for a generator matrix with N-5, this can only be expressed as
Figure DEST_PATH_GDA0001328423820000049
And cannot be represented as
Figure DEST_PATH_GDA00013284238200000410
And
Figure DEST_PATH_GDA00013284238200000411
combined or otherwise represented.
Therefore, the calculation process of step 3 is to generate the matrix for q primitive matrices obtained from step 2
Figure DEST_PATH_GDA0001328423820000051
Performing Combo-Sum combination operation on the data, and selecting two generator matrixes with the maximum code length each time to participate in the Combo-Sum combination operation in the combination operation process, namely obtaining a generator matrix with the code length of N through the Combo-Sum operation according to q original generator matrixes
Figure DEST_PATH_GDA0001328423820000052
For example, the process of generating matrix combination operation with code length N ═ 7 is as follows: obtaining a generator matrix G participating in the combined operation according to the step 24×4,G2×2,G1×1According to the operation criterion: selecting the largest two generations at a timeThe matrix participates in the operation, then
Figure DEST_PATH_GDA0001328423820000053
The matrix combination is represented as:
Figure DEST_PATH_GDA0001328423820000054
Figure DEST_PATH_GDA0001328423820000055
and taking the combined matrix obtained by each Combo-Sum operation as a new sub-matrix, replacing and combining to generate the sub-matrix, and continuing participating in the next Combo-Sum operation until only one sub-matrix is left to obtain a final generated matrix C with the code length of N.
Example 1: and constructing a generating matrix of Polar codes with the code length N-6.
Step 1: a binary bit sequence having a code length N of 6 is represented by s {1,1,0 }.
Step 2: according to the binary bit sequence obtained in the step 1, selecting a combination matrix with a code length N equal to 6:
according to 6-22+21＝l1+l2So that a sub-matrix G having a constituent code length of 6 is obtained4×4,G2×2。
And step 3: the submatrices constituting the generator matrix with the code length N of 6 obtained in step 2 are combined by a Combo-Sum operation.
Figure DEST_PATH_GDA0001328423820000056
The operation process is as follows:
Figure DEST_PATH_GDA0001328423820000057
example 2: and (5) constructing a generating matrix of Polar codes with the code length N being 11.
Step 1: a binary bit sequence with a code length N of 11 is denoted by s {1,0,1,1 }.
Step 2: according to the binary bit sequence obtained in the step 1, selecting a combination matrix with a code length N equal to 11:
according to 11-23+21+20＝l1+l2+l3The size of the submatrix is l1＝8，l2＝2，l 31. So that a sub-matrix G having a constituent code length of 11 is obtained8×8,G2×2,G1×1。
And step 3: the submatrices constituting the generator matrix with the code length N of 11 obtained in step 2 are combined by a Combo-Sum operation.
Figure DEST_PATH_GDA0001328423820000061
The operation process is as follows:
Figure DEST_PATH_GDA0001328423820000062
Figure DEST_PATH_GDA0001328423820000063

Claims (3)

1. a code word construction method of Polar codes with variable code length is characterized by comprising the following steps:
step 1: spreading the code length N binary system to obtain a corresponding binary bit sequence s; wherein N is a positive integer;
step 2: determining the size of a generating matrix to be selected according to the position of '1' in the obtained binary bit sequence s;
let q be the number of bit values "1" in the sequence s, where h is the index number in the sequence sdD represents the d-th 1 occurring from the upper to the lower in the sequence s, and d is 1,2, … q; then, the generator matrices of q polar codes are selected, and the size is l1,l2,...,lqThe square matrix of (A) is formed,
Figure FDA0002353576750000011
hdis a positive integer(ii) a The sequence s is indexed from 1 from the low order to the high order;
and step 3: combining the selected generator matrixes through Combo-Sum operation to obtain a generator matrix with the code length of N;
obtaining q generating matrixes according to the step 2
Figure FDA0002353576750000012
The generator matrix with code length N is represented as:
Figure FDA0002353576750000013
wherein the content of the first and second substances,
Figure FDA0002353576750000014
represents Combo-Sum operation;
the Combo-Sum operation is: let the matrix involved in the operation be
Figure FDA0002353576750000015
And
Figure FDA0002353576750000016
the resulting combined matrix C is:
Figure FDA0002353576750000017
wherein L is1、L2Respectively, the size of the matrix A, B, and the size of the matrix B' is L2×L1Front L in B2Column and matrix B are identical, last L1-L2The columns are all 0 columns.
2. The method for constructing Polar code words with variable code length according to claim 1, wherein in the step 3, the Combo-Sum operation is implemented by: let two matrices participate in Combo-Sum operation as
Figure FDA0002353576750000018
And
Figure FDA0002353576750000019
the Combo-Sum operation result of the two matrices is
Figure FDA00023535767500000110
Wherein the elements
Figure FDA00023535767500000111
Wherein Γ is {1, 2., L1A subset of the set, called the difference set, with L elements of the set Γ2Index in the set Γ is marked j0＝1,2,...,l2J-th of the set Γ0The value of each element is an index j in C.
3. The method as claimed in claim 2, wherein in the Combo-Sum operation, the matrices a and B involved in the operation cannot exchange orders, and the size of the first matrix a cannot be smaller than that of the second matrix B.
CN201710036000.0A 2017-01-17 2017-01-17 Code word construction method of variable length Polar code Active CN106998208B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710036000.0A CN106998208B (en) 2017-01-17 2017-01-17 Code word construction method of variable length Polar code

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710036000.0A CN106998208B (en) 2017-01-17 2017-01-17 Code word construction method of variable length Polar code

Publications (2)

Publication Number Publication Date
CN106998208A CN106998208A (en) 2017-08-01
CN106998208B true CN106998208B (en) 2020-04-28

Family

ID=59431470

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710036000.0A Active CN106998208B (en) 2017-01-17 2017-01-17 Code word construction method of variable length Polar code

Country Status (1)

Country Link
CN (1) CN106998208B (en)

Families Citing this family (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111034057B (en) * 2017-08-23 2022-04-22 华为技术有限公司 Equipment and method for generating multi-core polarization code
WO2019095267A1 (en) * 2017-11-17 2019-05-23 Qualcomm Incorporated Polar coding techniques for blind detection of different payload sizes
CN108494523B (en) * 2018-01-31 2020-02-14 北京航空航天大学 Multi-CRC coding method of Polar code
US11057053B2 (en) 2018-09-28 2021-07-06 Huawei Technologies Co., Ltd. Method and apparatus for wirelessly communicating over a noisy channel with a variable codeword length polar code to improve transmission capacity
CN109787640A (en) * 2019-01-25 2019-05-21 北京航空航天大学 A kind of two stage low complex degree polarization code constructing method
CN112235075B (en) * 2020-09-16 2022-09-27 西安空间无线电技术研究所 Polar coding method and device for satellite communication channel
CN114513212A (en) * 2020-11-16 2022-05-17 华为技术有限公司 Polarization coding method and device

Family Cites Families (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8347186B1 (en) * 2012-04-19 2013-01-01 Polaran Yazilim Bilisim Danismanlik Ithalat Ihracat Sanayi Ticaret Limited Sirketi Method and system for error correction in transmitting data using low complexity systematic encoder
CN102694765B (en) * 2012-05-15 2014-11-12 北京航空航天大学 Design method of non-2 integer power order QAM (quadrature amplitude modulation)
CN103516476B (en) * 2012-06-29 2016-12-21 华为技术有限公司 Coded method and equipment
CN103023618B (en) * 2013-01-11 2015-04-22 北京邮电大学 Random code length polar encoding method
RU2571587C2 (en) * 2014-04-10 2015-12-20 Самсунг Электроникс Ко., Лтд. Method and device for encoding and decoding data in convoluted polar code
US9628114B2 (en) * 2015-03-31 2017-04-18 Macronix International Co., Ltd. Length-compatible extended polar codes
CN106100795B (en) * 2016-06-17 2020-04-21 哈尔滨工业大学深圳研究生院 Polar code coding cooperation method based on Plotkin construction and information bit re-dormancy

Also Published As

Publication number Publication date
CN106998208A (en) 2017-08-01

Similar Documents

Publication Publication Date Title
CN106998208B (en) Code word construction method of variable length Polar code
CN106685586B (en) Method and apparatus for generating low density parity check code for transmission in a channel
CN109586732B (en) System and method for encoding and decoding LDPC codes with medium and short codes
CN107124251B (en) Polarization code encoding method based on any kernel
CN107666324B (en) Polar code and arithmetic coding combined information source lossy compression coding method
CN109075805B (en) Apparatus and method for implementing polarization code
CN110233628B (en) Self-adaptive belief propagation list decoding method for polarization code
CN107332570B (en) Polarization code coding method of segmented cascade Hash sequence
KR20130001494A (en) Decoding method using polar code sequence
CN109983705B (en) Apparatus and method for generating polarization code
CN105763203A (en) Multi-element LDPC code decoding method based on hard reliability information
CN106877885B (en) Method and system for constructing polarization code by using Bahatta-cut sub-parameters
CN100508442C (en) Coding-decoding method and device
JP6817414B2 (en) Coding and decoding of polar codes extended to non-powers of 2
CN106067824A (en) A kind of sequencing data compression method based on bigeminy codon
CN109067408A (en) A kind of design method of protograph LDPC code
CN112332857B (en) Cyclic shift network system and cyclic shift method for LDPC code
CN105871385B (en) A kind of LDPC convolutional-code building method
Hernandez et al. The three/two Gaussian parametric LDLC lattice decoding algorithm and its analysis
CN109639290B (en) Semi-random grouping superposition coding and decoding method
CN116192157A (en) Implementation method for reducing QC-LDPC code generation matrix density
CN115642918A (en) Encoding optimization method, device and equipment of double-prototype-graph LDPC code and storage medium
CN113422611B (en) Highly parallel encoding method of QC-LDPC encoder
CN106130565B (en) Method for obtaining RC-LDPC convolutional code by RC-LDPC block code
CN112104379B (en) Polarization code confidence propagation dynamic overturning decoding method based on key set

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant