CN107332571B - A kind of Polar code constructing method and device - Google Patents

A kind of Polar code constructing method and device Download PDF

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Publication number
CN107332571B
CN107332571B CN201710449069.6A CN201710449069A CN107332571B CN 107332571 B CN107332571 B CN 107332571B CN 201710449069 A CN201710449069 A CN 201710449069A CN 107332571 B CN107332571 B CN 107332571B
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row
submatrix
information bit
weight
exchanged
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CN107332571A (en
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肖东亮
储汪兵
刘继文
杨超
孙娜
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China Agricultural University
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China Agricultural University
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    • 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
    • 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

Abstract

The present invention provides a kind of Polar code constructing method and device.The described method includes: Polar code information bit is generated submatrix G in a symmetrical case by S1NIThe smallest row of middle row weight generates submatrix G with position is freezedNFThe maximum row of middle row weight is all exchanged with each other, and by GNIThe corresponding information bit of the smallest row of middle row weight and GNFThe corresponding position of freezing of the maximum row of middle row weight is all exchanged with each other；Polar code information bit is generated submatrix G in asymmetric situation by S2NIThe smallest row of middle row weight generates submatrix G with position is freezedNFThe maximum row part of middle row weight is exchanged with each other, and by GNIThe corresponding information bit of the smallest row of middle row weight and GNFThe corresponding bit position that freezes of the maximum row of middle row weight is exchanged with each other.The present invention is in asymmetric situation, to GNIAnd GNFThe exchange of part row vector is carried out, and then changes the weight Spectral structure of code word, so as to improve the performance of code.It is all suitable for this kind of building method under arbitrary bit rate simultaneously, makes up the deficiency of existing building method.

Description

A kind of Polar code constructing method and device
Technical field
The present invention relates to communication channel coding fields, more particularly, to a kind of Polar code constructing method and device.
Background technique
The good code that can reach shannon limit is illustrated in paper " a mathematical theory of communication " interior symptom-complex delivered from Shannon in 1948 In the presence of since, field of channel coding is always in unremitting effort, to find the building method of such a good code.Arikan is 2007 Year is put forward for the first time-Polar yards of coding method of a kind of channel capacity that can reach binary system discrete memoryless channel(DMC) (B-DMCs), This kind of coding mode possesses lower encoding and decoding complexity, the short code coding mode being confirmed as under 5G communications control channel.
The main indicator for differentiating a kind of performance of coding mode is its error-correcting performance.Arikan is initially proposed with second order nuclear moment Battle array constructs generator matrix, under this building method, as error exponent β < 1/2, code length N → ∞, code rate R < I (W), The mistake frame probabilistic upper bound of Polar code isThen there is scholar to study discovery as code length N → ∞ and uses one Bigger nuclear matrix is come when constructing Polar code, error exponent β is close in 1.There is scholar to go out from the angle of Algorithms of Algebraic Geometric Codes again Hair, constructs nuclear matrix using Hermitte curve, to obtain bigger error exponent and smallest hamming distance.For any Liner code C, its smallest hamming distance are equal to non-zero codeword minimum Hamming weight.Polar code is a kind of linear block codes, therefore its Smallest hamming distance is equal to its minimum Hamming weight.For a code, it is very difficult for seeking its smallest hamming distance.But by There is close connection in Polar code and Reed-Muller code, the smallest hamming distance of Polar code is equal to information submatrix most Small row weight.
Currently, there is scholar to propose a kind of row replacement method based on this to increase the smallest hamming distance of Polar code, improve The performance of Polar code.This method is that Polar code information bit is generated to the smallest row G of row weight in submatrixNISon is generated with position is freezed Matrix GNFThe maximum row of middle row weight is exchanged with each other, and GNIThe corresponding information bit of the smallest row of middle row weight and GNFMiddle row weight is maximum Row corresponding s freeze position also transposition.The applicable precondition of this kind of method is code rate R=1/2.
However, during practical communication, code rate not necessarily 1/2.G at this timeNIThe heavy the smallest number of lines of middle row and GNFIn The maximum number of lines of row weight is unequal, asymmetric situation occurs, therefore cannot increase Polar code with the method replaced completely Hamming distance, thus in asymmetric situation, the error correcting capability of Polar code is lower, needs a kind of asymmetric situation Polar of raising The method of code error correcting capability.
Summary of the invention
The present invention provides a kind of Polar code constructing method for overcoming the above problem or at least being partially solved the above problem And device.
According to an aspect of the present invention, a kind of Polar code constructing method is provided, comprising:
Polar code information bit is generated submatrix G in a symmetrical case by S1NIThe smallest row of middle row weight is generated with position is freezed Submatrix GNFThe maximum row of middle row weight is all exchanged with each other, and by GNIThe corresponding information bit of the smallest row of middle row weight and GNF The corresponding position of freezing of the maximum row of middle row weight is all exchanged with each other；
Polar code information bit is generated submatrix G in asymmetric situation by S2NIMiddle row again give birth to position is freezed by the smallest row At submatrix GNFThe maximum row part of middle row weight is exchanged with each other, and by GNIThe corresponding information bit of the smallest row of middle row weight and GNFThe corresponding bit position that freezes of the maximum row of middle row weight is exchanged with each other.
Specifically, the information bit generates submatrix GNISubmatrix G is generated with the position of freezingNFIt is raw by following steps At:
The Polar code for being N for code length, calculates Pasteur's parameter of channel
For any given code rate R, obtains lesser K of Pasteur's parameter and be used as information bit UI, other N-K conducts Freeze a UF, wherein K=N × R；
Index based on the information bit generates the information bit and generates submatrix GNI, raw based on the index for freezing position Submatrix G is generated at the position of freezingNF。
Code rate R ≠ 1/2 specifically, the code rate R=1/2 under the symmetric case, under the asymmetric case.
Further, the S2 further comprises:
Obtain the GNIThe corresponding biggish m row of Pasteur's parameter value and its corresponding m information in the smallest row of middle row weight Position；
Obtain the GNFThe corresponding lesser m row of Pasteur's parameter value and its corresponding m freeze in the maximum row of middle row weight Position；
By the GNIIn the m row and the GNFIn the m row be exchanged with each other, and by the m information bit Freeze position with the m to be exchanged with each other；
Wherein, m is exchange line number, and m is natural number and m≤3.
Specifically, determining the exchange line number m according to the following formula:
If max { a, b }≤3, then m=min { a, b } goes；
If min { a, b }≤3, max { a, b } > 3, then m=min { a, b } row is exchanged；
If min { a, b } >=3, then m=3；
Wherein, a GNIThe smallest row vector number of middle row weight, b GNFThe maximum row vector number of middle row weight.
Specifically, being calculate by the following formula Pasteur's parameter:
Wherein, Z () is Pasteur's parameter, and i=1,2 ... N, N are the code length of Polar code,ε is channel deletion Rate.
Further, the index based on the information bit generates the information bit and generates submatrix GNI, it is based on the jelly The index of knot position freezes position generation submatrix G described in generatingNFThe step of after, before being exchanged with each other further include:
Submatrix G is generated to the information bit respectivelyNISubmatrix G is generated with the position of freezingNFIn row arranged again Sequence, and submatrix G is generated to the information bit respectivelyNISubmatrix G is generated with the position of freezingNFIn the corresponding index of every a line It resequences.
Further, after described the step of being the Polar code of N, calculate Pasteur's parameter of channel for code length further include:
To the information position index of the Polar code and freeze position index based on Pasteur's parameter and be ranked up.
According to another aspect of the present invention, a kind of Polar code constructing apparatus is also provided, including symmetrical Switching Module and non- Symmetrical Switching Module；
The symmetrical Switching Module, in a symmetrical case, Polar code information bit being generated submatrix GNIMiddle row weight is most Small going and freeze position generates submatrix GNFThe maximum row of middle row weight is all exchanged with each other, and by GNIMiddle row weight is the smallest The corresponding information bit of row and GNFThe corresponding position of freezing of the maximum row of middle row weight is all exchanged with each other；
The asymmetric Switching Module, in asymmetric situation, Polar code information bit to be generated submatrix GNIMiddle row The smallest row of weight generates submatrix G with position is freezedNFThe maximum row part of middle row weight is exchanged with each other, and by GNIMiddle row weight is most The corresponding information bit of small row and GNFThe corresponding bit position that freezes of the maximum row of middle row weight is exchanged with each other.
The present invention proposes a kind of Polar code constructing method and device, is changed on the basis of existing Polar code constructing method Into influence of the distribution of weight of the Pasteur's parameter and code word that fully consider information bit to Polar code error-correcting performance, not right It in the case of title, is exchanged by part row vector, changes GNIThe number of lines of middle minimum row weight, so that GNIIn with minimum row weight Row is few as far as possible, and then changes the weight Spectral structure of code word, so as to improve the performance of code.Make this kind of building method in any code simultaneously It is all suitable under rate, makes up the deficiency of existing building method.
Detailed description of the invention
Fig. 1 is a kind of Polar code constructing method flow chart of the embodiment of the present invention；
Front and back Polar code performance contrast schematic diagram is improved when Fig. 2 is R=1/2 of the embodiment of the present invention；
Front and back Polar code performance contrast schematic diagram is improved when Fig. 3 is R=2/3 of the embodiment of the present invention；
Front and back Polar code performance contrast schematic diagram is improved when Fig. 4 is R=3/4 of the embodiment of the present invention.
Specific embodiment
With reference to the accompanying drawings and examples, specific embodiments of the present invention will be described in further detail.Implement below Example is not intended to limit the scope of the invention for illustrating the present invention.
When the code rate of Polar code is 1/2, GNIThe heavy the smallest number of lines of middle row and GNFThe maximum number of lines of middle row weight is not Equal, it is a kind of symmetric case.During practical communication, the code rate of Polar code not necessarily 1/2.When the code of Polar code When rate is not 1/2, GNIThe heavy the smallest number of lines of middle row and GNFThe maximum number of lines of middle row weight is unequal, asymmetric feelings occurs Condition.
When code rate is respectively 1/2 and 2/3, the information bit of the Polar code of part code length generates submatrix GNIIt is raw with position is freezed At submatrix GNFRow weight and the row to reppear existing frequency difference as shown in Table 1 and Table 2.
When 1 R=1/2 of table, generates submatrix and row weight and row reppears existing frequency
When 2 R=2/3 of table, generates submatrix and row weight and row reppears existing frequency
As shown in Table 1, when given code length N, R=1/2, GNIAnd GNFCorresponding row is reppeared existing frequency and is symmetric, however As R ≠ 1/2, GNIAnd GNFCorresponding each row reppears existing frequency in mal-distribution.Such as work as N=512, when R=1/2, GNIRow weight be wt=8,16,32,64, corresponding distribution of weight be D (wt)=2,36,90,82,36,9,1；GNFRow weight is Wt=1,2,4,8,16,32,64, corresponding distribution of weight is D (wt)=1,9,36,82,90,36,2, row weight is minimum and row The maximum number of lines of weight is all 2.For another example N=512, R=2/3, GNIThe row of middle row weight minimum (weight 8) has 13 rows, GNFMiddle row , there is asymmetric situation at this time in 5 row of behavior of weight maximum (weight 32).Therefore cannot be increased with the method replaced completely The Hamming distance of Poalr code.
Therefore the present invention is based on row weight and Pasteur's parameter that Polar code generates submatrix, a kind of improved Polar code is proposed Building method, which is applicable under any code rate, and can significantly improve the error correcting capability of Polar code.
As shown in Figure 1, a kind of Polar code constructing method, comprising:
Polar code information bit is generated submatrix G in a symmetrical case by S1NIThe smallest row of middle row weight is generated with position is freezed Submatrix GNFThe maximum row of middle row weight is all exchanged with each other, and by GNIThe corresponding information bit of the smallest row of middle row weight and GNF The corresponding position of freezing of the maximum row of middle row weight is all exchanged with each other；
Polar code information bit is generated submatrix G in asymmetric situation by S2NIMiddle row again give birth to position is freezed by the smallest row At submatrix GNFThe maximum row part of middle row weight is exchanged with each other, and by GNIThe corresponding information bit of the smallest row of middle row weight and GNFThe corresponding bit position that freezes of the maximum row of middle row weight is exchanged with each other.
Code rate R ≠ 1/2 specifically, the code rate R=1/2 under the symmetric case, under the asymmetric case.
Label S1 and S2 involved in the embodiment of the present invention, only has the function of being identified processing step, not Sequencing relationship between the step of limiting each number.
In the embodiment of the present invention, on the basis of existing Polar code constructing method, in a symmetrical case, due to GNIMiddle row weight The smallest row generates submatrix G with position is freezedNFThe maximum row number having the same of middle row weight, thus can all be handed over It changes, exchanges one by one.And due to G in asymmetric situationNIThe smallest row of middle row weight generates submatrix G with position is freezedNFMiddle row weight is most The number of big row is not identical, thus can not be exchanged one by one.
The embodiment of the present invention fully considers Pasteur's parameter of information bit and the weight point of code word in asymmetric situation Influence of the cloth to Polar code error-correcting performance, selected section row vector swap, while exchanging corresponding information bit and freezing Position changes GNIThe number of lines of middle minimum row weight, so that GNIIn with minimum row weight row it is few as far as possible, and then change code word weight Spectral structure is measured, so as to improve the performance of code.It is all suitable for this kind of building method under arbitrary bit rate simultaneously, makes up existing construction side The deficiency of method.
In an alternative embodiment, the information bit generates submatrix GNISubmatrix G is generated with the position of freezingNF It is generated by following steps:
The Polar code for being N for code length, calculates Pasteur's parameter of channel
For any given code rate R, obtains lesser K of Pasteur's parameter and be used as information bit UI, other N-K conducts Freeze a UF, wherein K=N × R；
Index based on the information bit generates the information bit and generates submatrix GNI, raw based on the index for freezing position Submatrix G is generated at the position of freezingNF。
It is also wrapped after the step of being the Polar code of N, calculate Pasteur's parameter of channel for code length described in the embodiment of the present invention It includes based on Pasteur's parameter to the information position index of the Polar code and freezes position index and be ranked up.
In an alternative embodiment, it is calculate by the following formula Pasteur's parameter:
Wherein, Z () is Pasteur's parameter, and i=1,2 ... N, N are the code length of Polar code,ε is channel deletion Rate.
Index described in the embodiment of the present invention based on the information bit generates the information bit and generates submatrix GNI, based on institute It states and freezes to freeze described in the index generation of position position generation submatrix GNFA specific example it is as follows:
When Polar code length is N=8, code rate R=1/2, it is computed Pasteur's parameter value
After Pasteur's parameter is sorted from small to large, obtain:
Corresponding index is 8,7,6,4,5,3,2,1 after sequence.
Selecting the small index bit of Pasteur's parameter is information bit, and the big index bit of Pasteur's parameter is to freeze position, then the letter obtained Ceasing position is 4,6,7,8；Freezing position index is 1,2,3,5.
Generator matrix when N=8:
Therefore freeze the corresponding generation submatrix in position are as follows:
The corresponding generation submatrix of information bit are as follows:
In an alternative embodiment, Polar code information bit is generated submatrix in asymmetric situation by the S2 GNIThe smallest row of middle row weight generates submatrix G with position is freezedNFThe maximum row part of middle row weight is exchanged with each other, and by GNIIn The corresponding information bit of the smallest row of row weight and GNFThe corresponding bit position that freezes of the maximum row of middle row weight is exchanged with each other, further Include:
Obtain the GNIThe corresponding biggish m row of Pasteur's parameter value and its corresponding m information in the smallest row of middle row weight Position；
Obtain the GNFThe corresponding lesser m row of Pasteur's parameter value and its corresponding m freeze in the maximum row of middle row weight Position；
By the GNIIn the m row and the GNFIn the m row be exchanged with each other, and by the m information bit Freeze position with the m to be exchanged with each other；
Wherein, m is exchange line number, and m is natural number and m≤3.
Specifically, determining the exchange line number m according to the following formula:
If max { a, b }≤3, then m=min { a, b } goes；
If min { a, b }≤3, max { a, b } > 3, then m=min { a, b } row is exchanged；
If min { a, b } >=3, then m=3；
Wherein, a GNIThe smallest row vector number of middle row weight, b GNFThe maximum row vector number of middle row weight.
In the embodiment of the present invention, in case that asymmetrical, G is rememberedNIThe row vector number and G of middle minimum row weightNFMiddle maximum The row vector number of row weight is denoted as a, b, a≤b respectively.It at this time can be by GNIThe row and G of middle minimum row weightNFThe row of middle maximum row weight Part exchange is carried out, corresponding partial information position and freezes position also transposition.According to channel-polarization theory, information bit is than freezing There is higher channel capacity in knot position, therefore the information bit after exchange is lower than the channel capacity of original information bit, this will lead to friendship Changing rear channel capacity reduces.It needs to consider information bit to be exchanged at this time and freezes Pasteur's parameter value of position, from GNIMinimum row weight Row in choose the biggish m row of corresponding Pasteur's parameter value, from GNFIt is smaller to choose corresponding Pasteur's parameter value in the row of middle maximum row weight M row swap, and make exchange line number m≤3.
In an alternative embodiment, the index based on the information bit generates the information bit and generates submatrix GNI, submatrix G is generated based on position is freezed described in the index generation for freezing positionNFThe step of after, before being exchanged with each other Further include:
Submatrix G is generated to the information bit respectivelyNISubmatrix G is generated with the position of freezingNFIn row arranged again Sequence, and submatrix G is generated to the information bit respectivelyNISubmatrix G is generated with the position of freezingNFIn the corresponding index of every a line It resequences.
In a specific embodiment of the invention and application, the Polar code constructing method includes the following steps:
(1) Pasteur's parameter of channel is calculatedAnd it is ranked up.Wherein Pasteur's parameter calculates Formula are as follows:
Wherein,ε is channel deletion rate；
(2) for any given code rate R, the number of information bit is K=N × R, and it is K lesser to pick out Pasteur's parameter As information bit UI, remaining N-K as freezing a UF；
(3) information bit generation submatrix G corresponding with position index is freezed is calculatedNIWith generation submatrix GNFIt is each Every trade weight；
(4) to GNIAnd GNFIn row be ranked up respectively again, and GNIAnd GNFIn the corresponding index of every a line also arrange again Sequence；
(5) as code rate R=1/2, GNIAnd GNFRow weight and row reppear existing frequency present it is symmetrical, at this time by GNI The heavy the smallest row of middle row and GNFThe maximum row of middle row weight all exchanges, and corresponding information bit and freezes position also transposition.
(6) as R ≠ 1/2, there is asymmetric situation.The line number for needing to exchange is determined at this time.The line number of note exchange is m.
If max { a, b }≤3, then m=min { a, b } goes；
If min { a, b }≤3, max { a, b } > 3, then m=min { a, b } row is exchanged；
If min { a, b } >=3, then m=3；
(7) from GNIChoose it in the smallest row of row weight and correspond to the maximum m row of Pasteur's parameter, from GNFIn the maximum row of row weight Choose it and correspond to the smallest m row of Pasteur's parameter, then this m row is exchanged with each other.Meanwhile corresponding m information bit and m are freezed position It is exchanged with each other position.
It, can be according to coding formula after constructing Polar code by above stepTo needing to pass Defeated data are encoded.
A kind of Polar code constructing method described in the embodiment of the present invention carry out emulation experiment effect picture such as Fig. 2, Fig. 3 and Shown in Fig. 4.The emulation experiment is that the method is improved to original Polar code and through the embodiment of the present invention under Gaussian channel Polar code performance compare.Polar code code length is respectively 256,512, is decoded using SC decoding algorithm, and work as Accidentally frame number reaches 50 frames and stops emulating.
When code rate R=1/2, it is as shown in Figure 2 that Polar code improves front and back performance comparison.No matter code length is 256 or 512, by When code rate is 1/2, there is symmetrical situation, at this time by GNIThe middle row the smallest row of weight and its corresponding information bit and GNFThe middle row maximum row of weight and its corresponding position of freezing all swap, the smallest hamming distance d of Polar codeminBecome from 8 16, therefore the performance of Polar code is improved.
When code rate R=2/3, Polar code improves front and back performance comparison as shown in figure 3, when code rate R=3/4, and Polar code changes When as shown in Figure 4 into front and back performance comparison.When code rate R=2/3 and 3/4, there is asymmetric situation, with original Polar code phase Than improved Polar code performance is improved.Such as when frame error rate is 10-3, when R=2/3, code length be 256 it is improved Polar code compares the gain for having nearly 0.7dB, the improved Polar code and original Polar that code length is 512 with original Polar code Code is compared to the gain for having nearly 0.2dB.And when Eb/N0 increases, Polar performance improvement is more obvious.In this asymmetric feelings Under condition, although by GNIThe middle row the smallest row of weight and its corresponding information bit and GNFThe maximum row of middle row weight and its corresponding freeze Position has carried out part and has exchanged, but changes the distribution of weight of Polar code code word after exchanging, while considering information to be exchanged Position and freeze the influence of Pasteur's parameter of position to the performance of code, the channel capacity of the information bit after guaranteeing exchange is as big as possible, because The performance of this Polar code is improved.
The present invention also provides a kind of Polar code constructing apparatus, including symmetrical Switching Module and asymmetric Switching Module；
The symmetrical Switching Module, in a symmetrical case, Polar code information bit being generated submatrix GNIMiddle row weight is most Small going and freeze position generates submatrix GNFThe maximum row of middle row weight is all exchanged with each other, and by GNIMiddle row weight is the smallest The corresponding information bit of row and GNFThe corresponding position of freezing of the maximum row of middle row weight is all exchanged with each other；
The asymmetric Switching Module, in asymmetric situation, Polar code information bit to be generated submatrix GNIMiddle row The smallest row of weight generates submatrix G with position is freezedNFThe maximum row part of middle row weight is exchanged with each other, and by GNIMiddle row weight is most The corresponding information bit of small row and GNFThe corresponding bit position that freezes of the maximum row of middle row weight is exchanged with each other.
Code rate R ≠ 1/2 specifically, the code rate R=1/2 under the symmetric case, under the asymmetric case.
Polar code constructing apparatus described in the embodiment of the present invention is for realizing Polar code construction side described in the embodiment of the present invention Method, the two beneficial effect having the same and specific embodiment, then this repeats no more.
The information bit generates submatrix GNISubmatrix G is generated with the position of freezingNFIt specifically includes:
The Polar code for being N for code length, calculates Pasteur's parameter of channel
For any given code rate R, obtains lesser K of Pasteur's parameter and be used as information bit UI, other N-K conducts Freeze a UF, wherein K=N × R；
Index based on the information bit generates the information bit and generates submatrix GNI, raw based on the index for freezing position Submatrix G is generated at the position of freezingNF。
Further, submatrix G is generated to the information bit respectivelyNISubmatrix G is generated with the position of freezingNFIn row weight It is ranked up, and submatrix G is generated to the information bit respectivelyNISubmatrix G is generated with the position of freezingNFIn every a line it is corresponding Index resequence.
After described the step of being the Polar code of N, calculate Pasteur's parameter of channel for code length further include: based on described Pasteur's parameter is ranked up the Polar code.
The embodiment of the present invention is calculate by the following formula Pasteur's parameter:
Wherein, Z () is Pasteur's parameter, and i=1,2 ... N, N are the code length of Polar code,ε is channel deletion Rate.
The asymmetric Switching Module further comprises:
Obtain the GNIThe corresponding biggish m row of Pasteur's parameter value and its corresponding m information in the smallest row of middle row weight Position；
Obtain the GNFThe corresponding lesser m row of Pasteur's parameter value and its corresponding m freeze in the maximum row of middle row weight Position；
By the GNIIn the m row and the GNFIn the m row be exchanged with each other, and by the m information bit Freeze position with the m to be exchanged with each other；
Wherein, m is exchange line number, and m is natural number and m≤3.
Wherein, the exchange line number m is determined according to the following formula:
If max { a, b }≤3, then m=min { a, b } goes；
If min { a, b }≤3, max { a, b } > 3, then m=min { a, b } row is exchanged；
If min { a, b } >=3, then m=3；
Wherein, a GNIThe smallest row vector number of middle row weight, b GNFThe maximum row vector number of middle row weight.
In conclusion the embodiment of the present invention in Polar asymmetry situation, passes through selection GNIAnd GNFPart row vector into Row exchange, while exchanging corresponding information bit and freezing position, change GNIThe number of lines of middle minimum row weight, so that GNIIn have most The row of small row weight is few as far as possible, and then changes the weight Spectral structure of code word, so as to improve the performance of code.Described in the embodiment of the present invention Polar code constructing method can be applicable under arbitrary bit rate, and Polar code performance significantly improves, and be had good beneficial to effect Fruit.
Finally, the present processes are only preferable embodiment, it is not intended to limit the scope of the present invention.It is all Within the spirit and principles in the present invention, any modification, equivalent replacement, improvement and so on should be included in protection of the invention Within the scope of.

Claims (9)

1. a kind of Polar code constructing method characterized by comprising
Polar code information bit is generated submatrix G in a symmetrical case by S1NIThe smallest row of middle row weight generates sub- square with position is freezed Battle array GNFThe maximum row of middle row weight is all exchanged with each other, and by GNIThe corresponding information bit of the smallest row of middle row weight and GNFMiddle row The corresponding position of freezing of the maximum row of weight is all exchanged with each other；
Polar code information bit is generated submatrix G in asymmetric situation by S2NIThe smallest row of middle row weight generates son with position is freezed Matrix GNFThe maximum row part of middle row weight is exchanged with each other, and by GNIThe corresponding information bit of the smallest row of middle row weight and GNFIn The corresponding bit position that freezes of the maximum row of row weight is exchanged with each other.
2. the method as described in claim 1, which is characterized in that the information bit generates submatrix GNIIt is generated with the position of freezing Submatrix GNFIt is generated by following steps:
The Polar code for being N for code length, calculates Pasteur's parameter of channel
For any given code rate R, obtains lesser K of Pasteur's parameter and be used as information bit UI, other N-K as freezing Position UF, wherein K=N × R；
Index based on the information bit generates the information bit and generates submatrix GNI, institute is generated based on the index for freezing position It states and freezes position generation submatrix GNF。
3. the method as described in claim 1, which is characterized in that the code rate R=1/2 under the symmetric case, it is described asymmetric In the case of code rate R ≠ 1/2.
4. method as claimed in claim 3, which is characterized in that the S2 further comprises:
Obtain the GNIThe corresponding larger m row of Pasteur's parameter value and its corresponding m information bit in the smallest row of middle row weight；
Obtain the GNFThe corresponding lesser m row of Pasteur's parameter value and its corresponding m freeze position in the maximum row of middle row weight；
By the GNIIn the m row and the GNFIn the m row be exchanged with each other, and by the m information bit and institute It states m and freezes position and be exchanged with each other；
Wherein, m is exchange line number, and m is natural number and m≤3.
5. method as claimed in claim 4, which is characterized in that determine the exchange line number m according to the following formula:
If max { a, b }≤3, then m=min { a, b } goes；
If min { a, b }≤3, max { a, b } > 3, then m=min { a, b } row is exchanged；
If min { a, b } >=3, then m=3；
Wherein, a GNIThe smallest row vector number of middle row weight, b GNFThe maximum row vector number of middle row weight.
6. method according to claim 2, which is characterized in that be calculate by the following formula Pasteur's parameter:
Wherein, Z () is Pasteur's parameter, and i=1,2 ... N, N are the code length of Polar code, Z (W1 1)=ε, ε are channel deletion rate.
7. method according to claim 2, which is characterized in that the index based on the information bit generates the information bit Generate submatrix GNI, submatrix G is generated based on position is freezed described in the index generation for freezing positionNFThe step of after, carry out phase Before interchangeable further include:
Submatrix G is generated to the information bit respectivelyNISubmatrix G is generated with the position of freezingNFIn row be ranked up again, and point It is other that submatrix G is generated to the information bitNISubmatrix G is generated with the position of freezingNFIn the corresponding index of every a line carry out again Sequence.
8. method according to claim 2, which is characterized in that the Polar code for being N for code length calculates bar of channel After the step of family name's parameter further include:
To the information position index of the Polar code and freeze position index based on Pasteur's parameter and be ranked up.
9. a kind of Polar code constructing apparatus, which is characterized in that including symmetrical Switching Module and asymmetric Switching Module；
The symmetrical Switching Module, in a symmetrical case, Polar code information bit being generated submatrix GNIMiddle row weight is the smallest It goes and freezes position and generate submatrix GNFThe maximum row of middle row weight is all exchanged with each other, and by GNIThe smallest row pair of middle row weight The information bit and G answeredNFThe corresponding position of freezing of the maximum row of middle row weight is all exchanged with each other；
The asymmetric Switching Module, in asymmetric situation, Polar code information bit to be generated submatrix GNIMiddle row weight is most Small going and freeze position generates submatrix GNFThe maximum row part of middle row weight is exchanged with each other, and by GNIMiddle row weight is the smallest The corresponding information bit of row and GNFThe corresponding bit position that freezes of the maximum row of middle row weight is exchanged with each other.
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