CN111988044B - Code word construction method of punctured Polar code - Google Patents

Code word construction method of punctured Polar code Download PDF

Info

Publication number
CN111988044B
CN111988044B CN201910584639.1A CN201910584639A CN111988044B CN 111988044 B CN111988044 B CN 111988044B CN 201910584639 A CN201910584639 A CN 201910584639A CN 111988044 B CN111988044 B CN 111988044B
Authority
CN
China
Prior art keywords
polarization
length
code
matrix
channels
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
CN201910584639.1A
Other languages
Chinese (zh)
Other versions
CN111988044A (en
Inventor
邓宏贵
熊儒菁
封雨鑫
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.)
Central South University
Original Assignee
Central South 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 Central South University filed Critical Central South University
Priority to CN201910584639.1A priority Critical patent/CN111988044B/en
Publication of CN111988044A publication Critical patent/CN111988044A/en
Application granted granted Critical
Publication of CN111988044B publication Critical patent/CN111988044B/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

Abstract

The invention discloses a code word construction method of a punctured Polar code, which comprises the following steps: determining encoding parameters and setting a polarization kernel; sequencing all the split sub-channels according to the channel capacity of the split sub-channels, and constructing an information sequence according to a fixed coding length; calculating a polarization generating matrix according to the fixed coding length and the polarization kernel; calculating an initial coding sequence according to the information sequence and the polarization generating matrix; sequentially selecting a columns in the column weight of each column of the polarization generating matrix, and constructing a code word deleting matrix according to the index number of the column weight; and according to the code word deletion matrix, respectively indexing the elements at the corresponding positions in the initial coding sequence and deleting the elements to obtain the final coding sequence. The invention deletes the code words according to the correlation degree of the code mapping, not only realizes low complexity and high application flexibility of Polar codes, but also has better decoding performance, ensures the stability of a communication system and has wide application prospect.

Description

Code word construction method of punctured Polar code
Technical Field
The invention belongs to the field of digital communication channel coding, and particularly relates to a code word construction method of a punctured Polar code.
Background
Polar code is a coding scheme for communication proposed in 2009 by e.arikan, and theoretically it is a coding mode that can reach shannon limit proved by strict mathematical reasoning. At the transmitting end, the N independent channels are polarized with each other, the channel capacity of the split sub-channel tends to 0 or 1, and the channel polarization process includes two processes of channel combination and channel splitting as shown in fig. 1. When the code length tends to infinity, a part of the channels becomes pure noise channels and another part of the channels becomes noise-free channels. The proportion of the split sub-channels with channel capacity of 0 or 1 after polarization to the total channel varies with the code length as shown in fig. 2, and the distribution diagram of the channel capacity when the code length N is 512 is also shown in fig. 3. At the receiving end, the special structure of the polarization code enables the polarization code to adopt a serial cancellation algorithm, and the performance similar to the maximum likelihood decoding is obtained with lower complexity. The excellent performance makes it an important encoding method for 5G communication.
Because the traditional polar code is constructed based on the Crohn's power of Arikan kernel, the code length of the polar code is limited to 2n(n is a positive integer), and in an actual communication system, it is known that the length of original information is often uncertain, so that the encoding can be adjusted according to the length of the original information, that is, a problem that we must consider is that although the purpose of constructing other code lengths can be achieved by using other polarization kernels, such as BCH code kernels, the code length is limited to the power of the kernel length, and the decoding structure of the Polar code constructed by the method is complex; although some existing partial code word deleting algorithms can construct Polar codes with any length, the consideration factor is not sufficient when deleting code words, the constructed Polar codes have poor performance, and the performance of a communication system is damaged. Therefore, it is urgently needed to develop a code word construction method of a punctured Polar code with better performance to meet the communication requirement.
Disclosure of Invention
The invention provides a method for constructing a punctured Polar code word with convenient use and excellent decoding performance, and aims to construct Polar codes with any code length and improve the application flexibility and the error rate performance of the Polar codes in a communication system.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a code word construction method of a punctured Polar code comprises the following steps:
step 1, determining an encoding information bit length K, a fixed encoding length N and a final encoding length M, and setting a polarization core of polarization encoding;
step 2, sequencing all N split sub-channels after channel polarization under a specific signal-to-noise ratio according to the channel capacity of the split sub-channels, and constructing an information sequence with the length of N according to a sequenced channel capacity matrix and a fixed coding length K;
step 3, calculating a polarization generating matrix according to the fixed coding length N and the polarization kernel;
step 4, obtaining an initial coding sequence with the length of N according to the information sequence obtained in the step 2 and the polarization generation matrix obtained in the step 3;
step 5, calculating the column weight of each column of the polarization generating matrix, sequentially selecting a columns according to the column weight in the order of magnitude, and constructing a code word deleting matrix with the length of a according to the index number of the a columns in the polarization generating matrix;
the number of the code words which are deleted according to the requirement a is: a is N-M;
and 6, respectively indexing elements at corresponding positions in the initial coding sequence according to a element values in the codeword deletion matrix and deleting the elements to obtain a final coding sequence with the length of M.
Further, in step 5, when the a-th column is selected, if several columns with the same column weight are present, the odd-numbered column with the larger index number is preferentially selected.
Further, polarization generating matrix GNThe calculation formula of (2) is as follows:
Figure BDA0002114126320000021
wherein, F represents a polarization nucleus,
Figure BDA0002114126320000022
denotes n Kronecker power calculations on the polarization nucleus F, BNIs shown to be obtained
Figure BDA0002114126320000023
Carrying out a reverse rearrangement in which N is 2n。
Further, the specific process of step 2 is as follows: first all the polarized split sub-channels are marked as W1,W2,...,WNSorting the channel capacities of the N split sub-channels under a specific signal-to-noise ratio by adopting a density evolution method; then K split sub-channels with large channel capacity are used for setting information bits, and the rest N-K split sub-channelsSetting freezing bit or fixed bit to obtain N length information sequence
Figure BDA0002114126320000024
Further, the calculation formula of the initial coding sequence in step 4 is as follows:
Figure BDA0002114126320000025
in the formula (I), the compound is shown in the specification,
Figure BDA0002114126320000026
represents an initial coding sequence including a 1 for a flag information bit and a 0 for a flag freeze bit or a fixed bit;
Figure BDA0002114126320000027
representing an information sequence, GNRepresenting a polarization generating matrix.
Advantageous effects
The code word construction method of the punctured Polar code provided by the invention has the advantages that: the calculation and operation method is simple and easy to implement, the calculation complexity is low, the encoder and the decoder know the deletion position when the initial coding sequence is deleted, Polar codes with any code length can be constructed, and the application limit of the traditional Polar codes is overcome. And simultaneously, the invention deletes the code words according to the correlation degree of the coding mapping, constructs the Polar codes with any code length by deleting the code word sequences output by the coder as far as possible without damage, ensures the effective transmission of information, greatly reduces the decoding error rate while improving the application flexibility by constructing the Polar codes with any code length, namely improves the decoding performance of the Polar codes with any code length, ensures the stability of a communication system, and has wide application prospect in the current and future communication.
Drawings
FIG. 1 is a diagram illustrating a polarization process of a channel polarization phenomenon;
FIG. 2 is a diagram illustrating the relationship between the code length N and the occupied ratio of the split sub-channel with channel capacity of 0 or 1;
FIG. 3 is a diagram of a channel capacity distribution with a code length N of 512;
FIG. 4 is a simplified diagram of a polar coding map;
FIG. 5 is a diagram illustrating the encoding mapping categories defined in the present invention;
FIG. 6 is a schematic flow diagram of the method of the present invention;
FIG. 7 is a graph comparing the performance advantages of the method of the present invention with the prior art when the values N32, M28 and K16 are taken;
fig. 8 is a graph comparing the performance advantages of the method of the present invention with those of the prior art when the values N128, M110 and K64 are taken.
Detailed Description
The following describes embodiments of the present invention in detail, which are developed based on the technical solutions of the present invention, and give detailed implementation manners and specific operation procedures to further explain the technical solutions of the present invention.
The invention provides a method for constructing a punctured Polar code word with convenient use and excellent decoding performance, which aims to construct Polar codes (Polar codes, namely Polar codes) with any code length and improve the application flexibility and the bit error rate performance of the Polar codes in a communication system, and as shown in fig. 6, the method specifically comprises the following steps:
step 1, determining coding parameters and setting a polarization core required by polarization coding.
The encoding parameters specifically include an encoding information bit length K, a fixed encoding length N, and a final encoding length M. The final code length M is the length of any constructed code length Polar code, and the final code length M satisfies the relation: k is<M<N，N＝2nAnd n is a positive integer; setting the polarization nucleus to
Figure BDA0002114126320000031
Step 2, sequencing all N split sub-channels after channel polarization under a specific signal-to-noise ratio according to the channel capacity thereof, and constructing an information sequence with the length of N according to the sequenced channel capacity matrix and the fixed coding length K, wherein the specific process comprises the following steps:
step 2.1, all polarized split sub-channels are marked as W1,W2,...,WNSorting the channel capacities of the N split sub-channels under a specific signal-to-noise ratio by adopting a density evolution method;
step 2.2, using K split sub-channels with large channel capacity to set information bits, setting freezing bits or fixed bits for the rest N-K split sub-channels, and constructing to obtain an information sequence with the length of N
Figure BDA0002114126320000032
Step 3, calculating a polarization generating matrix G according to the fixed coding length N and the polarization kernel FNThe calculation formula is as follows:
Figure BDA0002114126320000041
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002114126320000042
denotes n Kronecker power calculations on the polarization nucleus F, BNIndicating that the reverse rearrangement calculation is performed.
Step 4, according to the information sequence obtained in step 2
Figure BDA0002114126320000043
And the polarization generation matrix G obtained in step 3NObtaining the initial coding sequence with the length of N
Figure BDA0002114126320000044
The calculation formula is as follows:
Figure BDA0002114126320000045
wherein
Figure BDA0002114126320000046
Represents the information sequence (u) obtained according to step 21,u2,u3,…,uN) Containing K information bits and N-K frozen bits;
Figure BDA0002114126320000047
represents the initial coding sequence (x) obtained by calculation1,x2,x3,…,xN)。
Step 5, generating a matrix G according to the polarization obtained in the step 3NAnd the number a of the code words needing to be deleted, and calculating to obtain a code word deletion matrix, specifically adopting the following steps to calculate to obtain the code word deletion matrix:
step 5.1, setting a product factor; polarization is generated into matrix GNAll elements of each column and the product factor are subjected to product accumulation calculation to obtain a polarization generation matrix GNA column weight of the respective column;
step 5.2, selecting 1-a rows once according to the row weight, and marking the indexes of the rows as a code word deleting matrix z; when the same weight occurs when the a-th column is selected, the odd-numbered column with the larger index number is preferably selected.
The number a of the code words to be deleted takes the following values: a is N-M.
In the code mapping of the polar code, as shown in FIG. 4, the information sequence
Figure BDA0002114126320000048
Initial coding sequence obtained by polarization coding
Figure BDA0002114126320000049
They are not in a one-to-one relationship, e.g. u1After polarization encoding, it is not x1. Research shows that a correlation degree exists between the code words, and when the code word bit with the maximum correlation degree with the frozen bit in the information sequence is deleted at the code word end, the performance of the obtained punctured polarization code (namely, the polarization code with any code length, namely, the final coding sequence in the invention) is optimal. U in the information sequence1X in the initial code sequence when the position is frozen1Not necessarily with the freezing point u1The most relevant bits due to the polarization generating matrix GNThe function of (1). It has been found through research that there is a difference in the classification of code mappings in polarization coding, which is defined by the present invention as a class of mappings andtwo types of mapping, as shown in fig. 5. The greater the number of one type of mapping in the code mapping, the greater the degree of association between the information sequence and the bits of the initial code sequence, which is reflected in the generator matrix GNThe method selects the column index number with the maximum column weight as an element of a code word deletion matrix, so as to index the information of the corresponding position of the initial coding sequence and delete the information to obtain a final coding sequence, namely the polarization code with any code length. When there are columns with the same column weight, an odd column index with a larger value is preferably selected.
Step 6, deleting a element values in the matrix according to the code words, wherein the element values are the polarization generation matrix GNThe column index number with the maximum middle column weight is respectively indexed to the elements at the corresponding positions in the initial coding sequence and deleted to obtain the final coding sequence with the length of M, namely the code word with any code length of M
Figure BDA0002114126320000051
Generating a matrix G due to polarizationNThe column weight of each column in each column reflects the correlation degree of the coding mapping between the information sequence and the initial coding sequence, so the correlation degree is used as the core idea of designing the puncturing polar code, namely, the column weight of each column in the polarization generating matrix is used for constructing a code word deleting matrix, and then the code word deleting matrix is used for indexing, and the code word with the maximum correlation degree with the frozen bit or the fixed bit in the initial coding sequence is deleted, so the performance of the polar code is influenced as little as possible, and finally the polar code with any code length and better performance can be obtained.
The process of the invention is further illustrated below with reference to a specific example:
in the structure, the length of any code is not 2nWhen the Polar code is used, the code mapping association degree is used as a main reference element and is mainly embodied in the calculation of the generated matrix array weight, the index number of the code word sequence with the greater association degree with the frozen bit is used as the element of the code word deletion matrix for storage, and the bit deletion is carried out on the initial coding sequence according to the matrix, so that the random code length is realizedPolar coding.
Firstly, determining the length K of an encoding information bit to be 4, the length N of a fixed encoding to be 8 and the length M of a final encoding to be 5, wherein M is the length of a structured arbitrary code length Polar code, and Arikan core is adopted as a polarization core
Figure BDA0002114126320000052
Labeling all polarized split sub-channels as W1,W2,W3,W4,W5,W6,W7,W8Sorting the channel capacity of 8 split sub-channels under a specific signal-to-noise ratio by adopting a density evolution method, and marking the sorted channel index sequence as a matrix j ═ W4W7W6W8W1W3W2W5]According to the channel capacity and coding parameter information bit K being 4, 4 split sub-channels (namely W) with larger channel capacity are selected4,W7,W6,W8) For transmitting information bits to obtain an information sequence
Figure BDA0002114126320000053
Setting polarization nuclei
Figure BDA0002114126320000054
N Kronecker powers of F
Figure BDA0002114126320000055
And calculating to obtain a polarization matrix G:
Figure BDA0002114126320000056
carrying out reverse-order rearrangement on the polarization matrix G to obtain a polarization generation matrix G8：
Figure BDA0002114126320000061
The number a of deleted codewords N-M-8-5-3;
information sequence
Figure BDA0002114126320000062
Is an initial coding sequence; the calculation of the first type of mapping number, i.e. refraction into the generator matrix, is represented by calculating the column weight size. If the product factor is 1, G8The column weight of the middle 1 st column is 8, which is the maximum of all columns, the column weights of the 2 nd, 3 rd and 5 th columns are all 4, three columns are selected for deleting, the 1 st, 3 rd and 5 th columns are selected for deleting according to the large number criterion of odd columns, and the codeword deletion matrix z is [ 135 ]]；
Deleting elements in matrix z according to code words, and aligning initial coding sequence
Figure BDA0002114126320000063
Deleting the corresponding position index to obtain the final code sequence
Figure BDA0002114126320000064
Fig. 7 and 8 are graphs of performance simulation results of the present invention, wherein BER in the graphs refers to bit error rate, FER refers to frame error rate, and both are key indicators for checking decoding correctness. It can be seen from the figure that when Polar codes with any code length are constructed, the performance of the method used in the present invention is improved significantly compared with the method proposed in the prior paper.
The reference numerals of the steps do not represent the sequence of executing the steps, and those skilled in the art can change the execution sequence of the steps (for example, the execution sequence of step 2 and step 3, the execution sequence of step 4 and step 5 can be arbitrarily exchanged, and the execution of the subsequent steps does not conflict), and all of the steps belong to the protection scope of the present invention.
The above embodiments are preferred embodiments of the present application, and those skilled in the art can make various changes or modifications without departing from the general concept of the present application, and such changes or modifications should fall within the scope of the claims of the present application.

Claims (4)

1. A code word construction method of a punctured Polar code is characterized by comprising the following steps:
step 1, determining an encoding information bit length K, a fixed encoding length N and a final encoding length M, and setting a polarization core of polarization encoding;
step 2, sequencing all N split sub-channels after channel polarization under a specific signal-to-noise ratio according to the channel capacity of the split sub-channels, and constructing an information sequence with the length of N according to a sequenced channel capacity matrix and a fixed coding length K;
step 3, calculating a polarization generating matrix according to the fixed coding length N and the polarization kernel;
step 4, obtaining an initial coding sequence with the length of N according to the information sequence obtained in the step 2 and the polarization generation matrix obtained in the step 3;
step 5, calculating the column weight of each column of the polarization generating matrix, sequentially selecting a columns according to the column weight in the order of magnitude, and constructing a code word deleting matrix with the length of a according to the index number of the a columns in the polarization generating matrix;
the number of the code words which are deleted according to the requirement a is: a is N-M;
when the a-th column is selected, if a plurality of columns with the same column weight exist, selecting an odd-numbered column with a larger index number;
and 6, respectively indexing elements at corresponding positions in the initial coding sequence according to a element values in the codeword deletion matrix, and deleting the elements to obtain a final coding sequence with the length of M.
2. The method of claim 1, wherein the polarization generating matrix GNThe calculation formula of (c) is:
Figure FDA0003571163490000011
wherein, F represents a polarization nucleus,
Figure FDA0003571163490000012
denotes n Kronecker power calculations on the polarization nucleus F, BNIs shown to be obtained
Figure FDA0003571163490000013
Carrying out reverse rearrangement, wherein N is 2n。
3. The method according to claim 1, wherein the specific process of step 2 is as follows: first all polarized split sub-channels are marked as W1,W2,...,WNSorting the channel capacities of the N split sub-channels under a specific signal-to-noise ratio by adopting a density evolution method; then K split sub-channels with large channel capacity are used for setting information bits, and the rest N-K split sub-channels are set with freezing bits or fixed bits to construct and obtain an information sequence with the length of N
Figure FDA0003571163490000014
4. The method of claim 1, wherein the initial coding sequence in step 4 is calculated by the formula:
Figure FDA0003571163490000015
in the formula (I), the compound is shown in the specification,
Figure FDA0003571163490000016
represents an initial coding sequence including a 1 for a flag information bit and a 0 for a flag freeze bit or a fixed bit;
Figure FDA0003571163490000017
representing an information sequence, GNRepresenting a polarization generating matrix.
CN201910584639.1A 2019-07-01 2019-07-01 Code word construction method of punctured Polar code Active CN111988044B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910584639.1A CN111988044B (en) 2019-07-01 2019-07-01 Code word construction method of punctured Polar code

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910584639.1A CN111988044B (en) 2019-07-01 2019-07-01 Code word construction method of punctured Polar code

Publications (2)

Publication Number Publication Date
CN111988044A CN111988044A (en) 2020-11-24
CN111988044B true CN111988044B (en) 2022-07-19

Family

ID=73437261

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910584639.1A Active CN111988044B (en) 2019-07-01 2019-07-01 Code word construction method of punctured Polar code

Country Status (1)

Country Link
CN (1) CN111988044B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115208514B (en) * 2022-06-24 2023-09-05 中国人民解放军海军航空大学 Dual space-based polarization code parameter identification method and device and computer equipment

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101119178A (en) * 2006-08-01 2008-02-06 华为技术有限公司 Signal transmitting, receiving method and signal transmitting device
CN101218773A (en) * 2005-05-04 2008-07-09 松下电器产业株式会社 Signal space expansion for 16 QAM scheme
CN103023618A (en) * 2013-01-11 2013-04-03 北京邮电大学 Random code length polar encoding method
CN107370488A (en) * 2016-05-13 2017-11-21 中兴通讯股份有限公司 Error correction/encoding method and device
US10075197B1 (en) * 2017-03-07 2018-09-11 Lg Electronics Inc. Method and apparatus for transmitting hamming weight and codeword
WO2019090468A1 (en) * 2017-11-07 2019-05-16 Qualcomm Incorporated Methods and apparatus for crc concatenated polar encoding

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR100984289B1 (en) * 2005-12-07 2010-09-30 포항공과대학교 산학협력단 Signal transmitting/receiving apparatus for supporting variable coding rate in a communication system and method thereof

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101218773A (en) * 2005-05-04 2008-07-09 松下电器产业株式会社 Signal space expansion for 16 QAM scheme
CN101119178A (en) * 2006-08-01 2008-02-06 华为技术有限公司 Signal transmitting, receiving method and signal transmitting device
CN103023618A (en) * 2013-01-11 2013-04-03 北京邮电大学 Random code length polar encoding method
CN107370488A (en) * 2016-05-13 2017-11-21 中兴通讯股份有限公司 Error correction/encoding method and device
US10075197B1 (en) * 2017-03-07 2018-09-11 Lg Electronics Inc. Method and apparatus for transmitting hamming weight and codeword
WO2019090468A1 (en) * 2017-11-07 2019-05-16 Qualcomm Incorporated Methods and apparatus for crc concatenated polar encoding

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Odd-even effects of the polar anchoring strength for nematic liquid crystal on polyimide Langmuir-Blodgett surfaces with alkyl chain lengths;Dae-Shik Seo等;《Proceedings of 5th International Conference on Properties and Applications of Dielectric Materials》;20020806;第2卷;603-605 *
RS+交织+卷积码级联纠错的FPGA实现;邓宏贵等;《信息与控制》;20071215;第36卷(第06期);118-122 *
基于蝶形流程图的分组码最大后验概率软判决译码方法;李琪等;《清华大学学报(自然科学版)》;20141220(第12期);90-95 *

Also Published As

Publication number Publication date
CN111988044A (en) 2020-11-24

Similar Documents

Publication Publication Date Title
KR102621627B1 (en) Apparatus and method for encoding with cyclic redundancy check and polar code
CN102412842B (en) The coded method of a kind of low density parity check code and device
CN106452460B (en) A kind of polarization code and the error correction/encoding method of duplication code cascade
EP2239854B9 (en) Shortening and puncturing of low-density parity-check (LDPC) codes for channel decoding
RU2610251C2 (en) Method and device for hybrid polar code generating
KR100984289B1 (en) Signal transmitting/receiving apparatus for supporting variable coding rate in a communication system and method thereof
RU2450442C2 (en) Method and apparatus for channel encoding and decoding in communication system using low-density parity-check codes
CN101904101B (en) Encoder, decoder, encoding method, and decoding method
US7831884B2 (en) Method of correcting message errors using cyclic redundancy checks
WO2017107761A1 (en) Error correction coding method based on cascading of polar codes and repetition codes or multi-bit parity check codes
CN101656541B (en) Coding method and device of RS codes
CN106685656A (en) Method for correcting data errors in continuously variable quantum key distribution system based on polarization code
CN106685434B (en) A kind of building method of the polar code of partial polarization
CN110048727B (en) Polar code coding method with any code length
CN109347487A (en) Freeze the polarization code SCL interpretation method of auxiliary based on bit
CN109075805A (en) Realize the device and method of polarization code
CN109067408A (en) A kind of design method of protograph LDPC code
CN109768846B (en) Hole drilling method, system, device and medium based on two-core three-core mixed polarization code
CN111988044B (en) Code word construction method of punctured Polar code
CN110233698A (en) Coding and interpretation method, sending device, receiving device, the medium of polarization code
CN111988045A (en) Improved polarization code SCF decoder based on genetic algorithm
CN103731157B (en) The combined structure method of Quasi-cyclic Low-density Parity-check Codes
CN103944585B (en) Cycle-entropy-based nonbinary quasi-cyclic low density parity check code construction method
CN101465655B (en) Method for encoding ultra short code length density parity check code
CN108206722B (en) High-bit-rate data sending method and device

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