CN111884662B - Parameter identification method and system for polarization code under error code condition - Google Patents
Parameter identification method and system for polarization code under error code condition Download PDFInfo
- Publication number
- CN111884662B CN111884662B CN202010896852.9A CN202010896852A CN111884662B CN 111884662 B CN111884662 B CN 111884662B CN 202010896852 A CN202010896852 A CN 202010896852A CN 111884662 B CN111884662 B CN 111884662B
- Authority
- CN
- China
- Prior art keywords
- code
- matrix
- determining
- bit position
- cronecker
- 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
Links
- 230000010287 polarization Effects 0.000 title claims abstract description 107
- 238000000034 method Methods 0.000 title claims abstract description 41
- 239000011159 matrix material Substances 0.000 claims abstract description 191
- 230000009977 dual effect Effects 0.000 claims abstract description 73
- 230000009466 transformation Effects 0.000 claims description 9
- 239000013598 vector Substances 0.000 description 21
- 238000004422 calculation algorithm Methods 0.000 description 11
- 238000010586 diagram Methods 0.000 description 9
- 238000004364 calculation method Methods 0.000 description 7
- 230000000694 effects Effects 0.000 description 6
- 230000008569 process Effects 0.000 description 5
- 238000004088 simulation Methods 0.000 description 5
- 238000013459 approach Methods 0.000 description 4
- 238000004891 communication Methods 0.000 description 4
- 238000010276 construction Methods 0.000 description 4
- 230000000295 complement effect Effects 0.000 description 3
- 238000009928 pasteurization Methods 0.000 description 3
- 238000012360 testing method Methods 0.000 description 3
- 230000007704 transition Effects 0.000 description 3
- 238000012795 verification Methods 0.000 description 3
- 208000011231 Crohn disease Diseases 0.000 description 2
- 230000008030 elimination Effects 0.000 description 2
- 238000003379 elimination reaction Methods 0.000 description 2
- 230000009467 reduction Effects 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 108091026890 Coding region Proteins 0.000 description 1
- 238000000342 Monte Carlo simulation Methods 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000000354 decomposition reaction Methods 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000018109 developmental process Effects 0.000 description 1
- 238000007710 freezing Methods 0.000 description 1
- 230000008014 freezing Effects 0.000 description 1
- 238000007689 inspection Methods 0.000 description 1
- 238000010295 mobile communication Methods 0.000 description 1
- 230000000750 progressive effect Effects 0.000 description 1
- 230000033458 reproduction Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000011218 segmentation Effects 0.000 description 1
- 230000007480 spreading Effects 0.000 description 1
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
Landscapes
- Physics & Mathematics (AREA)
- Probability & Statistics with Applications (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Error Detection And Correction (AREA)
Abstract
The invention relates to a parameter identification method and system for a polarization code under an error code condition. Constructing a polarized code codeword matrix by utilizing the intercepted bit sequence and setting the traversed code length range; determining a Cronecker power matrix according to the polarized code codeword matrix; sequentially removing the row data in the Cronecker power matrix, and determining a corresponding dual matrix by utilizing the Cronecker power matrix after removing the row data each time; judging whether the currently removed data is an information bit position or a frozen bit position according to the dual matrix and the polarized code codeword matrix; counting the code length of the current traversal and determining the code rate corresponding to the code length of the current traversal according to the current information bit positions; performing parameter identification of a polarization code according to the traversed code length corresponding to the minimum code rate and the information bit position corresponding to the minimum code rate; the invention realizes the correct identification of the parameters of the polarization code.
Description
Technical Field
The present invention relates to the field of channel code identification, and in particular, to a method and a system for identifying parameters of a polarization code under an error code condition.
Background
In order to combat the interference of channel noise, channel coding techniques are widely used in modern digital communication systems, and with the rapid development of channel coding theory, a series of coding modes with performances close to shannon limit, such as Turbo codes, LDPC codes, and polarization codes, are found, and these codes have been widely used in 5G mobile communication or satellite communication. For non-cooperative communication parties, channel coding blind identification is always a research hotspot, at present, the literature aiming at coding identification is mainly focused on algebraic structure coding, convolutional codes, turbo codes and LDPC codes, but the literature aiming at polarization code identification alone is not reported, so that the problem of polarization code parameter identification under the condition of high error rate is a problem to be solved urgently for the coding identification field.
Disclosure of Invention
The invention aims to provide a method and a system for identifying parameters of a polarization code under an error code condition, which realize correct identification of the parameters of the polarization code.
In order to achieve the above object, the present invention provides the following solutions:
a parameter identification method of polarization code under error code condition includes:
constructing a polarized code codeword matrix by utilizing the intercepted bit sequence and the set traversed code length range;
determining a Cronecker power matrix according to the polarized code codeword matrix;
sequentially removing the row data in the Cronecker power matrix, and determining a corresponding dual matrix by utilizing the Cronecker power matrix after removing the row data each time;
judging whether the currently removed data is an information bit position or a frozen bit position according to the dual matrix and the polarized code codeword matrix;
counting the current traversed code length and the current determined information bit positions to determine the code rate corresponding to the current traversed code length until the code rates corresponding to all traversed code lengths in the set traversed code length range are determined;
performing parameter identification of a polarization code according to the traversed code length corresponding to the minimum code rate and the information bit position corresponding to the minimum code rate; the parameters of the polarization code include code length, information bit position and freeze bit position.
Optionally, the sequentially removing the row data in the kronecker power matrix, and determining the corresponding dual matrix by using the kronecker power matrix after removing the row data each time specifically includes:
using the formulaDetermining a corresponding dual matrix by determining a Cronecker power matrix after each rejected line data; wherein H is i Determining a corresponding dual matrix for the Cronecker power matrix after the ith rejected line data,is H i Transpose of S i For column transformation matrix, P (n-1) × 1 The conditions are as follows: r is R i ·Q i ·S i ＝[I (n-1)×(n-1) |P (n-1)×1 ]Wherein R is i For a row-transform matrix, Q i To reject the Cronecker power matrix after line I, I (n-1)×(n-1) Is (n-1) x (n-1) identity matrix.
Optionally, the determining that the currently rejected data is an information bit position or a frozen bit position according to the dual matrix and the polar code codeword matrix specifically includes:
determining statistics and decision threshold according to the dual matrix and the polarized code codeword matrix;
judging whether the statistic is smaller than the judgment threshold;
if the statistic is smaller than the judgment threshold, determining that the currently removed line data is an information bit position, and judging the next removed line data;
and if the statistic is not smaller than the judgment threshold, determining that the currently removed line data is a frozen bit position, and judging the next removed line data.
Optionally, the counting the code length of the current traversal and determining the code rate corresponding to the code length of the current traversal according to the current determined positions of the information bits until determining the code rate corresponding to the code length of all traversals within the set traversal code length range specifically includes:
and determining the code rate corresponding to the code length of the current traversal according to the ratio of the information bit positions determined currently to the code length of the current traversal.
A system for identifying parameters of a polarization code under error conditions, comprising:
the polarized code codeword matrix constructing module is used for constructing a polarized code codeword matrix by utilizing the intercepted bit sequence and the set traversed code length range;
the Cronecker power matrix determining module is used for determining a Cronecker power matrix according to the polarization code word matrix;
the dual matrix determining module is used for sequentially removing the row data in the Cronecker power matrix and determining a corresponding dual matrix by utilizing the Cronecker power matrix after each row of removed row data;
the bit position determining module is used for judging whether the currently removed data is an information bit position or a frozen bit position according to the dual matrix and the polarized code codeword matrix;
the code rate determining module is used for counting the code length of the current traversal and determining the code rate corresponding to the code length of the current traversal according to the current determined information bit positions until the code rates corresponding to all the traversed code lengths in the set traversal code length range are determined;
the parameter identification module of the polarization code is used for carrying out parameter identification of the polarization code according to the traversed code length corresponding to the minimum code rate and the information bit position corresponding to the minimum code rate; the parameters of the polarization code include code length, information bit position and freeze bit position.
Optionally, the dual matrix determining module specifically includes:
a dual matrix determining unit for using the formulaDetermining a corresponding dual matrix by determining a Cronecker power matrix after each rejected line data; wherein H is i Determining a corresponding dual matrix for the Cronecker power matrix after the ith rejected line data,/for the Cronecker power matrix>Is H i Transpose of S i For column transformation matrix, P (n-1) The x 1 satisfies the condition: r is R i ·Q i ·S i ＝[I (n-1)×(n-1) |P (n-1)×1 ]Wherein R is i For a row-transform matrix, Q i To reject the Cronecker power matrix after line I, I (n-1)×(n-1) Is (n-1) x (n-1) identity matrix.
Optionally, the bit position determining module specifically includes:
the statistic and decision threshold determining unit is used for determining statistic and decision threshold according to the dual matrix and the polarized code codeword matrix;
a first judging unit, configured to judge whether the statistic is smaller than the decision threshold;
the information bit position determining unit is used for determining that the currently removed line data is an information bit position and judging the next removed line data if the statistic is smaller than the judgment threshold;
and the frozen bit position determining unit is used for determining that the currently removed line data is the frozen bit position and judging the next removed line data if the statistic is not smaller than the judgment threshold.
Optionally, the code rate determining module specifically includes:
and the code rate determining unit is used for determining the code rate corresponding to the code length of the current traversal according to the ratio of the information bit positions determined currently to the code length of the current traversal.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the parameter identification method and system for the polarized codes under the error code condition, a codeword matrix and a Crohn's product matrix are constructed by traversing possible code length values, then the suspected information bit positions are traversed, vector rows corresponding to the Crohn's product matrix are removed, and a check vector is solved; secondly, solving a judgment threshold of the information bit position based on a minimum error judgment criterion, so as to estimate the code rate and the information bit position under the traversing code length; the identified code length is the minimum code length corresponding to the minimum code rate, and the position of the information bit under the code length is identified, so that the identification of the parameters is finally completed. Under the condition of error code, the invention can complete the correct identification of the polarization code parameters, has stronger fault tolerance and has the error code rate of 10 -3 Under the condition that the code length is 1024, the parameter identification rate can reach more than 95%, and the calculation complexity of the invention only has a linear relation with the maximum traversing code length and the intercepted data quantity.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for identifying parameters of a polarization code under error conditions according to the present invention;
FIG. 2 is a schematic diagram of a method for identifying parameters of a polarization code under error conditions according to the present invention;
FIG. 3 is a schematic diagram of a system for identifying parameters of a polarization code under error conditions according to the present invention;
FIG. 4 is a diagram illustrating the result of identifying the parameters of the polarization code in a noise-free environment;
FIG. 5 is a diagram showing the result of identifying the parameters of the polarization code in a noisy environment;
FIG. 6 is a diagram illustrating the effect of code length on algorithm performance;
FIG. 7 is a diagram showing the influence of different numbers of intercepted codewords on the algorithm;
fig. 8 is a schematic diagram showing the effect of the code rate of the polar code on the algorithm performance.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a method and a system for identifying parameters of a polarization code under an error code condition, which realize correct identification of the parameters of the polarization code.
The basic principle of the polarization code is as follows:
for any binary symmetrical memory-less channel W, repeatedly using it n times to obtain n mutually independent channels W, then converting these n mutually independent channels into a group of n mutually related channelsDefine the channel therein->X→Y n ×X i-1 Wherein X is channel->Input symbol set of (2), Y n For channel n as the output symbol set, X i-1 Is that i -1-dimensional input symbol set, "×" is a cartesian product. When n is sufficiently large, channel +.>A portion of the capacity of (2) approaches 1 while the remaining portion approaches 0. The information bits are transmitted in a channel with a channel capacity of 1 and the freeze bits are transmitted in a channel with a channel capacity of 0, thereby achieving reliable transmission of information. For polarization codes, the coding process is divided into two parts, namely channel combination and channel splitting, wherein the channel combination is to combine n independent channels W into W n Whereas channel splitting is to divide W n Decomposition into n channels with certain relevance +.>The polarization code principle is briefly described below in terms of two parts, channel combining and channel splitting.
The channel combination is to combine n independent channels W to generate W n :X n →Y n . Wherein n=2 m (m is a positive integer). G n Generating polynomial matrix for polarization code, u 1 ,u 2 ,…,u n For inputting the sequence of channels, x 1 ,x 2 ,…,x n For input sequence passing G n The latter coding sequence, y 1 ,y 2 ,…,y n A sequence is output for the channel. I.e. Then->And->The method meets the following conditions:
the channel transition probability can be expressed as:
for any code length n (n=2 m M is a positive integer), which generates a polynomial G n Satisfying the relationship of formula (3), namely:
wherein,represents the power of the m-th Cronecker product of the matrix F, let +.>C r×s ＝(b i,j ) Then->And B is connected with r×s The kronecker product of (c) is defined as:
as can be seen from the definition of formula (4),satisfy->And->
In the formula (3), B n Is a bit-reversal permutation matrix for use in a bit-reversal permutation matrixIs a permutation of the row order of (a). When->When the line number of (1, 2, 3) (the actual line number minus 1), the binary number is (00, 01,10, 11), the bit is inverted to obtain (00,10,01,11), and the decimal number is (0,2,1,3), namely +_>Is a permutation order of the rows of (a). Normally +.>Therefore, it isMay be further expressed in recursive form:
combining W for n mutually independent channels n Then split it into n polarized channels with relevanceX→Y n ×X i-1 I is more than or equal to 1 and less than or equal to n, and the transition probability of the ith polarized channel is defined as follows:
in (6)
For the calculation of the channel transition probability in the formula (6), the channel merging structure of the polarization code is generally utilized, and a recursive manner is adopted for calculation, namely:
in the formulas (7) and (8),representation pair sequence (u) 1 ,u 2 ,…,u 2i-2 ) Estimate of odd sequences in ∈ ->Representation pair sequence (u) 1 ,u 2 ,…,u 2i-2 ) An even sequence of the sequence. When n is sufficiently large, channel polarization occurs, i.e., a portion of the polarized channel capacity approaches 1 and the remaining polarized channel capacity approaches 0. For polarization channel reliability, it is mainly measured by the pasteurization parameters, which are defined as:
wherein, W is X-Y, X= {0,1}, Y is the channel output symbol set.
From the definition of the Pasteur parameters, the channel reliability is the worst when Z (W) ≡1; conversely, when Z (W) ≡0, the channel reliability is the best. Binary memoryless channel parameter recurrence calculation expression:
equation (10) equals sign holds if and only if the channel is a binary erasure channel.
The polarization code mainly uses a polarization channel with high reliability to transmit information bits, and transmits frozen bits from the rest polarization channels with poor reliability. The freeze bit position is typically taken to be 0. Combining the above channel combining, channel splitting and pasteurization parameter calculating processes, the polarization code encoding process is as follows:
step 1: constructing a polarization code generation matrix G n ；
Step 2: calculating split polarized channel conversion probability
Step 3: calculating polarized channelsIs a pasteurization parameter of (2);
step 4: sorting the Pasteur parameters from small to large, storing the labels corresponding to the first k parameters in the set, and then for the information sequence u set Freezing sequenceThe code of (2) is:
wherein c is a code word of a polarization code, G n (set) represents G n The median line being a matrix of lines of elements in set c To complement set, symbolRepresenting addition in the binary domain. Typically, the symbol transmitted at the frozen bit position is 0, so equation (12) can be further written as:
c＝u set ·G n (set) (13)
for identifying the polarization code, the parameters to be identified include the code length of the polarization code, the information bit position and the freeze bit position, and the freeze bit position is determined after the information bit position is identified because the information bit position and the freeze bit position are in a complementary relationship. For a communication system, each frame of data is preceded by a synchronization code sequence (typically 1 to 2 bytes in length), and the synchronization of the code words of the polarization code is easily accomplished by using the synchronization code sequence, and the identification of the code length of the polarization code, the information bits and the frozen bit parameters is performed in the presence of errors.
The traversing code length corresponding to the minimum code rate is the code length of the polarization code, and the specific determination process is as follows:
from the coding structure of the polarization code, the code length n of the polarization code satisfies n=2 m (m is a positive integer) and can be used for constructing polarization code words under different m conditions by utilizing intercepted data, and then analyzing the dual space characteristics of the polarization code words and finding rules.
The practical code length is n, the code rate is k/n, the polarized code is divided into code word sequences with the code length of n/2, the divided code words are equivalent to the new polarized code, and the code rate of the new polarized code is greater than k/n.
And (3) proving: let n=2 m Constructing an m-th Cronecker power matrix D n×n The method comprises the following steps:
wherein D is (n/2)×(n/2) Is a Cronecker power matrix of m-1 times, 0 (n/2)×(n/2) An all-zero matrix of (n/2) × (n/2). After bit inversion permutation, extract D n×n The row number of the middle k rows is not limited to: pi (1), pi (2), …, pi (k). Assume that the set { pi (1), pi (2), …, pi (i) } is a subset of the set {1,2, …, n/2}, and the set { pi (i+1), pi (i+2), …, pi (k) } is a subset of the set { n/2+1, n/2+2, …, n }, in which case the polarization code encoding matrix G n (set) can be written as:
wherein element d π(i),j For D (n/2)×(n/2) Medium matrix elements.
After the polarization code is divided into codewords with the code length of n/2, a new codeword coding matrix obtained by dividing becomes:
after the folio in the formula (15) is removed in the formula (16), the row is obviously repeated.
As can be seen from inspection of (16), each row may be at D (n/2)×(n/2) In the middle, so G' n/2 Can be used as a polarization code with a code length of n/2, so that the divided code word is equivalent to a new polarization code. Matrix G 'is discussed further below' n/2 Rank condition.
Case 1: there is no repeat line in formula (16), i.e., G' n/2 Every row is not repeated every other row. Due to G' n/2 Each row in (a) can be at D (n/2)×(n/2) Found in (C) and due to D (n/2)×(n/2) Is a full order matrix, so G' n/2 Must be a full-line matrix, so it is composed of G' n/2 The code rate of the generated polarization code is 2k/n, and the code rate after segmentation is larger than k/n.
Case 2: there are repeated matrix rows in equation (16). Can not be provided with repeated rowsIs t and the set of repeated row elements is set0. Due to D (n/2)×(n/2) Is a full order matrix, and is composed of G n The (set) structure is known as G' n/2 No repeated lines appear in the 1 st to i st lines, and no repeated lines appear in the (i+1) th to k th lines, so that set0 is equal to G' n/2 Intersection of the first i rows and the last k-i rows, namely:
set 0 ＝{q π(1) ,q π(2) ,…,q π(i) }∩{q π(i+1) ,q π(i+2) ,…,q π(k) } (17)
wherein q π(j) As matrix G' n/2 Is the j-th row of (2).
Since the split channel corresponding to the transmitted information bit is selected according to the reliability of the channel, i is less than or equal to k/2, so long as the code rate of the polarization code is equal to 1, the equal sign is established, at the moment, k=n, and since the code rate of the polarization code actually transmitted is necessarily less than 1, t is less than or equal to i < k/2. After removal of the repeat row at this point, G' n/2 The rank of (2) is k-t, which corresponds to a code rate of 2 (k-t)/n, and since t < k/2, 2 (k-t)/n > k/n, thereby obtaining the evidence.
Theorem 1: the given polarization code property has recursion, namely, when the polarization code with the actual code length of n is divided into n/2, n/4, …,4 and 2, each divided code word is equivalent to a new polarization code, and the code rate of the new polarization code increases gradually along with the reduction of the division length until the code rate increases to 1.
Theorem 2: when the polarized code with the code length of n and the code rate of k/n is expanded into the code word with the code length of 2.n, the polarized code with the code length of 2.n exists, the dual space is the same as the dual space of the expanded code word, and the code rate of the expanded code word is equal to k/n.
And (3) proving: the unexpanded polarization code coding matrix is set as G' n Each row in the matrix has a corresponding row number pi '(1), pi' (2), …, pi '(k) in equation (14), so G' n Can be expressed as:
in the formula, d π′(i),j (1.ltoreq.i.ltoreq.k, 1.ltoreq.j.ltoreq.n) is D n×n Is an element of the group.
When the code length of the polarization code is extended to 2.n, the front n bit sequence and the rear n bit sequence of the newly extended code word are G' n The codeword is generated, so the extended codeword generation matrix can be expressed as:
because of G' n Is a full-order matrix, so G' 2n Also has to be a full-line matrix, so G' 2n The code rate of the corresponding code word is 2 k/(2 n), which is equal to the code rate of the original polarization code.
Since the row transformation does not affect the dual space of the matrix, G 'will be' 2n The first n rows and the last n rows are overlapped to obtain a transformed matrix:
as can be seen from the observation of (20), G 2n Just D (2·n)×(2·n) In part of (A), therefore G', is 2n A polarization code matrix with code length of 2.n can be constructed, and the dual space is exactly matched with G 2 ′ n The corresponding dual spaces are the same, thereby obtaining the evidence.
Theorem 2 is also recursive, i.e.: after spreading the polarization code with code length n to 2.n, 4.n, 8.n and …, the code rate of the spread code word is still equal to k/n.
As can be seen from theorem 1 and theorem 2, when the traversed code length is smaller than the actual polarized code length, the code rate of the constructed code word is larger than the actual polarized code rate; on the contrary, when the traversed code length is larger than the actual code length, the code rate of the constructed code word is equal to the actual polarized code rate, so that the code length of the polarized code is known to be equal to the minimum code length corresponding to the minimum code rate. When the code rate of the constructed code word is obtained, a Gaussian elimination method can be adopted, but the method has poor recognition performance under the condition of error codes, and the calculated amount and the required data amount of the method are also increased sharply along with the increase of the traversing code length. In order to overcome the problem of the elimination method, the method is considered to solve the information bit positions corresponding to the code words from the dual space for constructing the code words, and the ratio of the number of the information bit positions to the traversed code length is exactly equal to the code rate, so that the code rate is solved indirectly, and meanwhile, the information bit positions can be identified.
The information bit position identification specifically includes:
from the construction principle of the polarization code encoding matrix, the code word generating matrix G which actually participates in encoding is known n Each row in (set) corresponds exactly to G n The row in which the information bit position is located, the identification information bit position is equivalent to identifying G n (set) each line at G n Middle position. Due to G n (set) and G n The code word space and the dual space generated by the two are different, and theorem 3 gives the relation between the two coding spaces and the dual space.
Theorem 3: space V of setting 1 Is set by vector set 1 ＝{a 1 ,a 2 ,…,a l Tense and record V 1 ＝L(set 1 ) Set is provided with 1 Some subset of (a) is set 2 ＝{a π(1) ,a π(2) ,…,a π(i) Pi (j) (1.ltoreq.j.ltoreq.i) corresponds to the set 1 Medium reference numerals marked by set 2 The space is V 2 ＝L(set 2 ) ThenAnd the dual space is->
And (3) proving: when (when)Equivalent to the dual space +>Establishment of the actionReason 3 proving->And (3) obtaining the product. Let us say vector V be space V 2 V may be defined by V 2 Medium baseline representation, namely: />Wherein alpha is j (1.ltoreq.j.ltoreq.i). Epsilon.GF (2). Set up set 2 At set 1 The complement of (a) is set 3 ＝{a π(i+1) ,a π(i+2) ,…,a π(l) V can be expressed asSo v can also be set 1 The elements in the Chinese are represented linearly, so V is V 1 Thus there is->Obtaining the evidence.
From theorem 3, the space of the polar code words is equal to G n (set) space formed by row vectors, and the codeword space must be defined by G n The middle row vectors are expanded into subspaces of space. If G is to n When the position of a certain line is not the information bit position, the dual space corresponding to the space formed by the rest lines after being removed is necessarily orthogonal to the codeword space; conversely, when the rejected line is located exactly at the information bit position, this orthogonal relationship will no longer exist. It follows that G can be eliminated by traversing in turn n Then the corresponding dual space is obtained, when the dual matrix and the code word form a check relation, the position can be judged as a frozen bit position; and vice versa, information bit positions. Set G n The row i of the rows which are eliminated, and the matrix formed by the rest row vectors is Q i Due to G n Is a full-order matrix, so Q i For a full rank matrix of dimension (n-1) x n, the row transform and column transform result in:
R i ·Q i ·S i ＝[I (n-1)×(n-1) |P (n-1)×1 ] (21)
wherein R is i For a row transformation matrix, S i For column transformation matrix, I (n-1)×(n-1) Is an identity matrix. Q can be obtained rapidly from the formula (21) i Is a dual matrix H of (2) i The method comprises the following steps:
i.e.Wherein->Represents H i Is a transpose of (a).
When the dual vector is solved, whether the dual vector and the code word space form an orthogonal relation or not is needed to be judged, and under the condition of error codes, the judgment is mainly based on the condition that the dual vector and the non-dual vector enable the code word verification relation to be established as a basis. First two types of hypothesis testing are given:
H i the dual vector of the codeword, namely the row position of the rejection is the frozen bit position;
H i the positions of the rows that are not dual vectors of the codeword, i.e., the culled rows are information bit positions.
Conditions under assumptionWhen error code exists, the check relation is still established, and the position of error code in the code word corresponds to H i The number of the error codes is required to be even when the element in the data is 1, and the check relation is still established through the modulo 2 operation. Setting channel error rateIs p e ，H i The code weight of (2) is w i The probability of establishment of the check relation is:
in the method, in the process of the invention,the value is downward, and C is the operation of taking the combination number.
Assuming that the number of codewords constructed is N by taking the average T of the differences between the number of established codeword check relations and the number of non-established codeword check relations as statistics, under the assumption conditionThe mean value of the statistic T is: 2P-1, variance 4P (1-P)/N, when N is sufficiently large, T approximately follows a Gaussian distribution:
conditions under assumptionUnder the condition of H i Instead of the dual vector, the check relation is random at this time, the probability of establishment is 0.5, so the mean value of the statistic T is 0, the variance is 1/N, and when the number N of codewords is sufficiently large, the check relation is at +.>Under the condition, obeys Gaussian distribution:
for convenience of explanation, mu is recorded 1 ＝2P-1，μ 0 ＝0，/>Let the decision threshold under two assumption conditions be Λ, then the false alarm probability is:
the false alarm probability is:
under the condition of no priori knowledge, the probability of occurrence of the two kinds of assumption conditions is the same, so the average error judgment probability P t The method comprises the following steps:
will P t Taking the derivative of Λ and letting it equal to 0 yields:
taking logarithms from two sides, converting the logarithms into a unitary quadratic equation, and solving a minimum error judgment threshold as follows:
in order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Fig. 1 is a flow chart of a method for identifying parameters of a polarization code under an error condition, which is provided by the invention, as shown in fig. 1, and the method for identifying parameters of a polarization code under an error condition, which is provided by the invention, comprises the following steps:
s101, constructing a polarized code codeword matrix by using the intercepted bit sequence and the set traversed code length range.
S102, determining a Cronecker product power matrix according to the polarized code word matrix.
And S103, sequentially removing the row data in the Cronecker power matrix, and determining a corresponding dual matrix by using the Cronecker power matrix after removing the row data each time.
Using the formulaDetermining a corresponding dual matrix by determining a Cronecker power matrix after each rejected line data; wherein H is i Determining a corresponding dual matrix for the Cronecker power matrix after the ith rejected line data,is H i Transpose of S i For column transformation matrix, P (n-1) The x 1 satisfies the condition: r is R i ·Q i ·S i ＝[I (n-1)×(n-1) |P (n-1)×1 ]Wherein R is i For a row-transform matrix, Q i To reject the Cronecker power matrix after line I, I (n-1)×(n-1) Is (n-1) x (n-1) identity matrix.
S104, judging whether the currently removed data is an information bit position or a frozen bit position according to the dual matrix and the polarization code word matrix.
S104 specifically comprises:
and determining statistics and decision thresholds according to the dual matrix and the polarized code word matrix.
And judging whether the statistic is smaller than the judgment threshold.
And if the statistic is smaller than the judgment threshold, determining that the currently removed line data is an information bit position, and judging the next removed line data.
And if the statistic is not smaller than the judgment threshold, determining that the currently removed line data is a frozen bit position, and judging the next removed line data.
S105, counting the code length of the current traversal and the positions of all the information bits determined currently to determine the code rate corresponding to the code length of the current traversal until the code rates corresponding to all the traversed code lengths in the set traversal code length range are determined.
And determining the code rate corresponding to the code length of the current traversal according to the ratio of the information bit positions determined currently to the code length of the current traversal.
S106, carrying out parameter identification of the polarization code according to the traversed code length corresponding to the minimum code rate and the information bit position corresponding to the minimum code rate; the parameters of the polarization code include code length, information bit position and freeze bit position.
Fig. 2 is a schematic diagram of a parameter identification method of a polarization code under an error condition, as shown in fig. 2, in which a true polarization code length is distinguished, and information bit positions under the code length are obtained, and specific algorithm steps are as follows:
step 1: setting the traversing code length range n as n min To n max Wherein n=2 m (m is a positive integer);
step 2: constructing a data matrix with a codeword length of n by using intercepted data, and then constructing an m-order Cronecker power matrix D by using a polarization code generation matrix construction method n×n ；
Step 3: i takes values from 1 to n in turn, and D is removed each time n×n Then, the dual vector is obtained by using the formula (21) and the formula (22);
step 4: calculating statistics T by utilizing a data matrix and a dual vector, and simultaneously calculating a decision threshold lambda opt If T < lambda opt Judging the position i as an information bit position, and returning to the step 3 until i=n, wherein i=i+1;
step 5: counting the number of information bit positions under the condition that the traversing code length is n, calculating the corresponding code rate, traversing the next code length, and returning to the step 2 until n=n max ；
Step 6: and outputting the minimum code length and the information bit position corresponding to the minimum code rate to finish the identification of the polarization code parameters.
Because the structure of the polarization code is relatively fixed, the dual vector under each traversing code length and information bit position can be solved and stored before identification, and the dual vector can be directly loaded when statistic is calculated, so that the calculation of a large number of reproductions can be reduced.
To further determine the usability of the present invention, an analysis of computational complexity was further performed, the analysis procedure was as follows:
the intercepted data quantity is L, and the traversed code length range isTo->When the traversing code length is 2 m (m min ≤m≤m max ) When it is needed to be 2 m Traversing each information bit position, and traversing each information bit position, the method needs to be carried out +.>Sub-vector multiplication>And performing addition operation and threshold solution 1 time. For convenience of description, the threshold 1 calculation is approximately equivalent to the vector multiplication operation of 5 times, so that the code length is 2 m Traversing requires 5.2 m +L vector multiplications and L addition operations. Summing the calculated amounts under different traversing code lengths to obtain the total multiplication calculation complexity of +.>The addition complexity is (m max -m min +1) L. It can be seen that the computation of the method herein increases approximately linearly with the length of the intercepted data and the maximum code length traversed.
Fig. 3 is a schematic structural diagram of a parameter identification system for a polarization code under an error condition provided by the present invention, as shown in fig. 3, and the parameter identification system for a polarization code under an error condition provided by the present invention is characterized in that the system includes: a polarization code codeword matrix construction module 301, a kronecker power matrix determination module 302, a dual matrix determination module 303, a bit position determination module 304, a code rate determination module 305 and a parameter identification module 306 of the polarization code.
The polarization code codeword matrix construction module 301 is configured to construct a polarization code codeword matrix by using the intercepted bit sequence and the set traversed code length range. .
The kronecker power matrix determination module 302 is configured to determine a kronecker power matrix from the polarization code codeword matrix.
The dual matrix determining module 303 is configured to sequentially reject the row data in the kronecker power matrix, and determine a corresponding dual matrix by using the kronecker power matrix after each reject of the row data.
The bit position determining module 304 is configured to determine that the currently removed data is an information bit position or a freeze bit position according to the dual matrix and the polar code codeword matrix.
The code rate determining module 305 is configured to count a currently traversed code length and all currently determined information bit positions to determine a code rate corresponding to the currently traversed code length, until determining code rates corresponding to all traversed code lengths within the set traversed code length range.
The parameter identification module 306 of the polarization code is configured to identify the parameter of the polarization code according to the traversed code length corresponding to the minimum code rate and the information bit position corresponding to the minimum code rate; the parameters of the polarization code include code length, information bit position and freeze bit position.
The dual matrix determining module 303 specifically includes: and a dual matrix determining unit.
The dual matrix determining unit is used for utilizing the formulaDetermination ofDetermining a corresponding dual matrix by using the Cronecker power matrix after each row of data is removed; wherein H is i Determining a corresponding dual matrix for the Cronecker power matrix after the ith rejected line data,/for the Cronecker power matrix>Is H i Transpose of S i For column transformation matrix, P ( n-1). Times.1 satisfies the condition: r is R i ·Q i ·S i ＝[I (n-1)×(n-1) |P (n-1)×1 ]Wherein R is i For a row-transform matrix, Q i To reject the Cronecker power matrix after line I, I (n-1)×(n-1) Is (n-1) x (n-1) identity matrix.
The bit position determining module 304 specifically includes: the device comprises a statistic and decision threshold determining unit, a first judging unit, an information bit position determining unit and a frozen bit position determining unit.
And the statistic and decision threshold determining unit is used for determining statistic and decision threshold according to the dual matrix and the polarized code codeword matrix.
The first judging unit is used for judging whether the statistic is smaller than the judging threshold.
And the information bit position determining unit is used for determining that the currently removed line data is the information bit position and judging the next removed line data if the statistic is smaller than the judgment threshold.
And the frozen bit position determining unit is used for determining that the currently removed line data is the frozen bit position and judging the next removed line data if the statistic is not smaller than the judgment threshold.
The code rate determining module 304 specifically includes:
and the code rate determining unit is used for determining the code rate corresponding to the code length of the current traversal according to the ratio of the information bit positions determined currently to the code length of the current traversal.
In order to further explain the validity of the parameter identification method and system of the polarization code under the error code condition provided by the invention, the following provides relevant verification:
the code length of the simulation selected polarization code is 256, the code rate is 1/2, the Babbitt parameters are calculated according to the formula (10) and the formula (11), the calculated Babbitt parameters are ordered from small to large, the first 1/2 position is selected to transmit information bits, and the later 1/2 position is selected to transmit frozen bits. The algorithm verifies the correctness of the algorithm under the two environments of no error code and error code. Under the condition of error code, the channel error rate is set to be 0.01, the number of intercepted code words is 10000, and the traversed code length is 2 m (2.ltoreq.m.ltoreq.10), i.e. code lengths ranging from 4 to 1024. According to the algorithm steps, firstly, the code rate value under the traversing code length is obtained, then the information bit position corresponding to the identified code length is output, and the identification result under two noise environments is shown in fig. 4 and 5.
Firstly, as seen from the result of fig. 4 (a), under the condition of no error, when the estimated code length is smaller than 256, the solved code rate is obviously larger than 0.5, and when the code length is larger than 256, the code rate is exactly equal to 0.5, which is consistent with the conclusion of theorem 1 and theorem 2, and the code length of the polarization code is recognized to be 256; under the condition that the code length is 256, traversing the information bit position, and because the error code is 0, the solved threshold is equal to 1, and when the traversed position is a frozen bit position, the statistic T is equal to 1 because the verification relation is established; conversely, the check is not true, and the statistic T can only wander around 0, which is consistent with the derived statistical properties, which indicates that the conclusion of theorem 3 is correct.
And then under the condition that the error rate is 0.01, traversing the code length of the polarization code, when m=8, the code rate has the minimum value of 0.5, identifying that the code length of the polarization code is 256 at the moment, and traversing the information bit position under the error rate condition, when the traversed position is just the information bit position, the statistic is smaller than the threshold value, and the analyzed statistic characteristics and the solved minimum error judgment threshold are reasonable. In a comprehensive view, the method provided by the invention can finish correct identification of the polarization code parameters under the condition of error codes.
The simulation sets 5 types of polarization codes, the code length n of the polarization codes is 64, 128, 256, 512 and 1024 respectively, the number of intercepted code words is 5000 corresponding to the code rate R=1/2, the range of the channel error rate is 0 to 0.15, the interval is 0.005, 1000 Monte Carlo tests are carried out under each error rate, and the identification rate of the parameters of the polarization codes and the information bits is counted respectively, so that the result is shown in fig. 6.
From the results of fig. 6, the code length has a larger effect on the algorithm, and the recognition performance of the algorithm gradually decreases as the code length increases. The main reason is that when the code length is increased, the positions of the information bits to be identified are necessarily increased under the same code rate condition, and the misjudgment probability of the positions of the information bits is increased, which leads to the reduction of the algorithm performance; meanwhile, as can be seen from comparing the results of fig. 6 (a) and fig. 6 (b), the code length recognition performance is significantly better than that of the recognition of the information bit positions, and the main reason is that the recognition of the information bit positions is not only required to recognize the number of the information bits but also specific positions, but only required to recognize the code rate at the actual code length to be minimum, so that the recognition of the information bit positions has more severe requirements on the algorithm.
The simulation sets the code length of the polarized code to 128, the code rate R=1/2, and the number of intercepted code blocks is 1000, 5000, 10000, 15000 and 20000,5. The error rate of the channel ranges from 0 to 0.14, the interval is 0.005, the accuracy of parameter identification under different numbers of intercepted code words and error rates of the channel is counted, the number of Monte Carlo tests in simulation is 1000, and the obtained result is shown in figure 7.
From the result of fig. 7, the code rate has a larger influence on code length identification, and the code length identification performance tends to be reduced with the increase of the code rate; for information bit identification, the code rate has little effect on the code length after the correct identification is completed. The main reason is that the larger the actual code rate is, the estimated code rate between the traversed adjacent code lengths is very close, and once the error code is increased, the code length identification has larger error identification probability; for information bit positions, after the code length is correctly identified, the parameter identification depends on whether the judgment of each information bit position is accurately completed, and the number of the information bit positions is not greatly different under the actual code length and code rate, so that the code rate has less influence on the identification of the information bit positions.
In the simulation, the code length of the polarization code is set to 128, the number of the codes R of 4 coding rates is set to 1/3,1/2,2/3 and 3/4, the number of intercepted codes is set to 5000, the range of the error rate of a channel is set to 0 to 0.15, the interval is 0.005, the number of Monte Carlo simulation times is 1000, the accuracy of parameter identification under different code rates and error rates is counted, and the result is shown in figure 8.
From the result of fig. 8, the code rate has a larger influence on code length identification, and the code length identification performance tends to be reduced with the increase of the code rate; for information bit identification, the code rate has little effect on the code length after the correct identification is completed. The main reason is that the larger the actual code rate is, the estimated code rate between the traversed adjacent code lengths is very close, and once the error code is increased, the code length identification has larger error identification probability; for information bit positions, after the code length is correctly identified, the parameter identification depends on whether the judgment of each information bit position is accurately completed, and the number of the information bit positions is not greatly different under the actual code length and code rate, so that the code rate has less influence on the identification of the information bit positions.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (6)
1. A parameter identification method of polarization code under error code condition is characterized by comprising the following steps:
constructing a polarized code codeword matrix by utilizing the intercepted bit sequence and the set traversed code length range;
determining a Cronecker power matrix according to the polarized code codeword matrix;
sequentially removing the row data in the Cronecker power matrix, and determining a corresponding dual matrix by utilizing the Cronecker power matrix after removing the row data each time;
judging whether the currently removed data is an information bit position or a frozen bit position according to the dual matrix and the polarized code codeword matrix;
counting the current traversed code length and the current determined information bit positions to determine the code rate corresponding to the current traversed code length until the code rates corresponding to all traversed code lengths in the set traversed code length range are determined;
performing parameter identification of a polarization code according to the traversed code length corresponding to the minimum code rate and the information bit position corresponding to the minimum code rate; the parameters of the polarization code comprise code length, information bit positions and frozen bit positions;
the method sequentially eliminates the row data in the Cronecker power matrix, and determines a corresponding dual matrix by utilizing the Cronecker power matrix after each eliminated row data, and specifically comprises the following steps:
using the formulaDetermining a corresponding dual matrix by determining a Cronecker power matrix after each rejected line data; wherein H is i Determining a corresponding dual matrix for the Cronecker power matrix after the ith rejected line data,/for the Cronecker power matrix>Is H i Transpose of S i For column transformation matrix, P (n-1) The x 1 satisfies the condition: r is R i ·Q i ·S i ＝[I (n-1)×(n-1) |P (n-1)×1 ]Wherein R is i For a row-transform matrix, Q i To reject the Cronecker power matrix after line I, I (n-1)×(n-1) Is (n-1) x (n-1) identity matrix.
2. The method for identifying parameters of a polarization code under an error condition according to claim 1, wherein said determining that the currently rejected data is an information bit position or a freeze bit position according to the dual matrix and the polarization code word matrix specifically comprises:
determining statistics and decision threshold according to the dual matrix and the polarized code codeword matrix;
judging whether the statistic is smaller than the judgment threshold;
if the statistic is smaller than the judgment threshold, determining that the currently removed line data is an information bit position, and judging the next removed line data;
and if the statistic is not smaller than the judgment threshold, determining that the currently removed line data is a frozen bit position, and judging the next removed line data.
3. The method for identifying parameters of polarization codes under error conditions according to claim 1, wherein said counting the currently traversed code length and determining all the currently determined information bit positions determines the code rate corresponding to the currently traversed code length until determining the code rate corresponding to all traversed code lengths within the set traversed code length range, specifically comprising:
and determining the code rate corresponding to the code length of the current traversal according to the ratio of the information bit positions determined currently to the code length of the current traversal.
4. A system for identifying parameters of a polarization code under error conditions, comprising:
the polarized code codeword matrix constructing module is used for constructing a polarized code codeword matrix by utilizing the intercepted bit sequence and the set traversed code length range;
the Cronecker power matrix determining module is used for determining a Cronecker power matrix according to the polarization code word matrix;
the dual matrix determining module is used for sequentially removing the row data in the Cronecker power matrix and determining a corresponding dual matrix by utilizing the Cronecker power matrix after each row of removed row data;
the bit position determining module is used for judging whether the currently removed data is an information bit position or a frozen bit position according to the dual matrix and the polarized code codeword matrix;
the code rate determining module is used for counting the code length of the current traversal and determining the code rate corresponding to the code length of the current traversal according to the current determined information bit positions until the code rates corresponding to all the traversed code lengths in the set traversal code length range are determined;
the parameter identification module of the polarized code is used for carrying out parameter identification of the polarized code according to the traversed code length corresponding to the minimum code rate and the information bit position corresponding to the minimum code rate; the parameters of the polarization code comprise code length, information bit positions and frozen bit positions;
the dual matrix determining module specifically comprises:
a dual matrix determining unit for using the formulaDetermining a corresponding dual matrix by determining a Cronecker power matrix after each rejected line data; wherein H is i Determining a corresponding dual matrix for the Cronecker power matrix after the ith rejected line data, H i T Is H i Transpose of S i For column transformation matrix, P (n-1) The x 1 satisfies the condition: r is R i ·Q i ·S i ＝[I (n-1)×(n-1) |P (n-1)×1 ]Wherein R is i For a row-transform matrix, Q i To reject the Cronecker power matrix after line I, I (n-1)×(n-1) Is (n-1) x (n-1) identity matrix.
5. The system for identifying parameters of a polarization code under error conditions of claim 4, wherein said bit position determining module comprises:
the statistic and decision threshold determining unit is used for determining statistic and decision threshold according to the dual matrix and the polarized code codeword matrix;
a first judging unit, configured to judge whether the statistic is smaller than the decision threshold;
the information bit position determining unit is used for determining that the currently removed line data is an information bit position and judging the next removed line data if the statistic is smaller than the judgment threshold;
and the frozen bit position determining unit is used for determining that the currently removed line data is the frozen bit position and judging the next removed line data if the statistic is not smaller than the judgment threshold.
6. The system for identifying parameters of a polarization code under error conditions according to claim 4, wherein said code rate determining module specifically comprises:
and the code rate determining unit is used for determining the code rate corresponding to the code length of the current traversal according to the ratio of the information bit positions determined currently to the code length of the current traversal.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010896852.9A CN111884662B (en) | 2020-08-31 | 2020-08-31 | Parameter identification method and system for polarization code under error code condition |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010896852.9A CN111884662B (en) | 2020-08-31 | 2020-08-31 | Parameter identification method and system for polarization code under error code condition |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111884662A CN111884662A (en) | 2020-11-03 |
| CN111884662B true CN111884662B (en) | 2024-01-19 |
Family
ID=73199868
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010896852.9A Active CN111884662B (en) | 2020-08-31 | 2020-08-31 | Parameter identification method and system for polarization code under error code condition |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111884662B (en) |
Families Citing this family (1)
| 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 (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107147400A (en) * | 2017-04-08 | 2017-09-08 | 西安电子科技大学 | A kind of IRA codes opener blind-identification method |
| CN110708079A (en) * | 2019-10-25 | 2020-01-17 | 北京邮电大学 | Polarization code construction method and device |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US10651973B2 (en) * | 2017-03-22 | 2020-05-12 | Huawei Technologies Co., Ltd. | Method and apparatus for error-correction encoding using a polar code |
-
2020
- 2020-08-31 CN CN202010896852.9A patent/CN111884662B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107147400A (en) * | 2017-04-08 | 2017-09-08 | 西安电子科技大学 | A kind of IRA codes opener blind-identification method |
| CN110708079A (en) * | 2019-10-25 | 2020-01-17 | 北京邮电大学 | Polarization code construction method and device |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111884662A (en) | 2020-11-03 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Condo et al. | Improved successive cancellation flip decoding of polar codes based on error distribution | |
| Jafarpour et al. | Efficient and robust compressed sensing using optimized expander graphs | |
| CN107147400B (en) | IRA code open set blind identification method | |
| WO2018133215A1 (en) | Lsc-crc decoding-based segmented polar code encoding and decoding method and system | |
| US8677222B2 (en) | Method and device for decoding Reed-Solomon (RS) code | |
| CN106712898B (en) | Channel coding blind identification method based on Gaussian iteration column elimination element | |
| JP2002353946A (en) | Method for evaluating error-correcting code for data block of finite size | |
| CN111884662B (en) | Parameter identification method and system for polarization code under error code condition | |
| WO2022039818A2 (en) | Quantum repeaters for concatenated quantum error correction, and associated methods | |
| Ding et al. | An improved blind recognition method for synchronization position and coding parameters of k/n rate convolutional codes in a noisy environment | |
| CN113037299A (en) | LDPC code sparse check matrix reconstruction method and device based on iterative decoding | |
| US8069015B2 (en) | Pseudo noise sequence acquisition in spread spectrum systems | |
| Murata et al. | Performance analysis of CRC codes for systematic and nonsystematic polar codes with list decoding | |
| Li et al. | On the error performance of systematic polar codes | |
| Condo et al. | Sparse superposition codes: A practical approach | |
| Kim et al. | Novel algorithm for blind estimation of scramblers in DSSS systems | |
| CN113965292B (en) | Low-complexity polarization code SC decoding method based on aggregation structure | |
| US20220337269A1 (en) | Block code encoding and decoding methods, and apparatus therefor | |
| ZHANG | Reconstruction of feedback polynomial of synchronous scrambler based on triple correlation characteristics of M-sequences | |
| CN113078914A (en) | Blind identification method for parameters of single incomplete Turbo code component encoder | |
| Wang et al. | A new joint source-channel coding for short-packet communications | |
| Anisimov et al. | Robust prefix encoding using lower (2, 3) number representation | |
| Jamshidi et al. | Estimation of convolutional interleaver parameters in the burst and BSC channels | |
| CN113114273B (en) | Check matrix extraction method, system and equipment of LDPC code | |
| RU2616180C1 (en) | Method for diagnosing convolutional codes |
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 | ||
| CB03 | Change of inventor or designer information | ||
| CB03 | Change of inventor or designer information |
Inventor after: Zhong Zhaogen Inventor after: Wu Zhaojun Inventor after: Zhang Limin Inventor after: Dan Bo Inventor after: Jin Kun Inventor before: Wu Zhaojun Inventor before: Zhang Limin Inventor before: Zhong Zhaogen Inventor before: Dan Bo Inventor before: Jin Kun |
|
| GR01 | Patent grant | ||
| GR01 | Patent grant |