CN108390677A - A kind of coding and decoding method of polarization code optimization - Google Patents
A kind of coding and decoding method of polarization code optimization Download PDFInfo
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- CN108390677A CN108390677A CN201810228503.2A CN201810228503A CN108390677A CN 108390677 A CN108390677 A CN 108390677A CN 201810228503 A CN201810228503 A CN 201810228503A CN 108390677 A CN108390677 A CN 108390677A
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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
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- 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
- H04L1/0041—Arrangements at the transmitter end
- H04L1/0043—Realisations of complexity reduction techniques, e.g. use of look-up tables
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- 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
- H04L1/0045—Arrangements at the receiver end
- H04L1/0052—Realisations of complexity reduction techniques, e.g. pipelining or use of look-up tables
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- 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
A kind of coding and decoding method of polarization code optimization.Belong to field of communication technology, generator matrix is obtained using the method that circular recursion replicates, the Kronecker product of matrix is avoided in polarization code encoding context and the repetition in space is opened up to save the time, coding information can be treated and carry out Polarization Coding；The decoding information of symbol is calculated using tree construction mode in terms of polarization code decoding, memory space is reduced, in decoding, there are two types of selections for each node messages calculation formula, using tree construction mode can each node layer calculation formula it is identical, a kind of effective easily selection method is proposed, the calculating process of Decoding Message is largely simplified.
Description
Technical field
The present invention relates in the communications field channel coding more particularly to it is a kind of polarization code optimization coding and decoding method.
Background technology
Channel coding is a part important in communication system, and by channel coding, receiving terminal, which can be corrected, to be transmitted across
The information that mistake occurs in journey, so that the communication quality of communicating pair is protected.
People have been devoted to research and find reach the channel coding of shannon limit, and polarization code is currently the only theoretically can
Reach the channel coding method of shannon limit.Under normal conditions, the code length of linear block codes and decoding complexity exponent function relation, when
When code length is very big, it is unable to get actual application, the polarization code with lower encoding and decoding complexity can be to avoid this problem.
The requirement that control channel encodes in the low complex degree of polarization code, high-performance positive adaptation 5G.
The encoding and decoding complexity of exactly polarization code is relatively low, so should be by the way of optimizing as possible during realization.Make
Person Zhang Liang paper " decoding algorithm of polarization code is studied and its application " (《Zhejiang University》Doctoral thesis 2016,15-21) in carry
The generator matrix gone out is all obtained by the Kronecker product by multi-degree matrix, and realization process will repeatedly apply for space, to
More time is spent, and used realization of decoding method is in the selection of node messages calculation formula, each node can only lead to
The odd even of serial number is crossed to judge, and is required for storing the information of each node, so deterministic process is relatively complicated when realizing
And required insufficient memory optimization.
Invention content
In order to overcome defect and deficiency of the existing technology, the present invention to propose a kind of coding and decoding side of polarization code optimization
Method, Kronecker product is avoided during calculating generator matrix, generator matrix is obtained using the method for recursive copying, to keep away
The repetition for exempting from space opens up and saves the time.
Technical scheme is as follows：
A kind of coding and decoding method of polarization code optimization, respectively by the decoder of the encoder of polarization code and polarization code Lai real
It is existing, the party
Method includes polarization code coding and polarization code decoding, is as follows：
Polarization code encodes：
The generator matrix of Polarization Coding is represented byWhereinFor the generation square for completing before bit inverted sequence
Battle array,N is code length, n=log2N,It is the Kronecker product of matrix, BNIt is sequence
Matrix is completing bit inverted sequence reordering operations；In order to avoid n=log2N times Kronecker product and multiple opening space, Shen
Please space size be N × N matrix, recursive copying is carried out to it and obtains generator matrix, process is as follows：
1) the N N matrix upper left corner of application is copied into
2) by N N matrix (2index, o) and coordinate position is copied into(o, 2index) position copies as
(2index, 2index) position is copied intoIt is formed in the N N matrix upper left cornerWherein index is indicated
Counting variable, 1≤index≤log2N operates season index=1 for the first time；
3) index=index+1, withStep 2) is carried out for replicator, is obtained
4) it repeats the above steps 2), 3), until index=log has been calculated2N terminates, and obtains
5) rightIt completes bit inverted sequence reordering operations and obtains generator matrix, information bit is encoded to obtain code word,
Complete polarization code coding work；
Polarization code decodes：
It can be completed by recurrence in the calculating for serially offsetting log-likelihood ratio in decoding algorithm, defined function f and g are such as
Under：
(a, b, u)=(- 1) gua+b (2)
Wherein a, b belong to real number i.e. a, b ∈ R, u ∈ { 0,1 }, a, b, and u is respectively the independent variable of function f and g, log-likelihood
The recursive operation of ratio indicates as follows by function f and g：
U in formula (3), (4) aboveiIndicate the i-th symbol in code word,Indicate the decoding estimated value to the i-th symbol,Table
It is shown asIndicate the message y that decoder receives1..., yN,Indicate 1 to 2i-2 odd numbers index son to
Amount, subscript ο indicate odd number,Indicate also or,Indicate that 1 subvector for arriving 2i-2 even number index, subscript e indicate even
Number,It indicates according to reception signalAnd estimated sequenceCalculate symbol u2i-1Log-likelihood ratio message,It indicates according to reception signalAnd estimated sequenceCalculate symbol u2iLog-likelihood ratio message；
The log-likelihood ratio for being calculated each node using tree structure according to the recursive operation formula of formula (3), (4) is disappeared
Breath, calculating process are as follows：
1) it is log to establish the number of plies2The full binary tree of N, according to the symbol serial number i of decoding, if the number of plies of tree is j, from tree
First layer, that is, j=1 starts to calculate；
2) symbol i%2 indicates i pairs of 2 remainders, judges the value of i%2, and as i%2=1, this node layer message selects formula
(4) it calculates；Formula (3) is then selected to calculate as i%2=0；
3) i=i/2, j=j+1 are enabled, judges the value of j, as j ＞ log2It is transferred to when N in next step, is otherwise transferred to step 2)；
4) j ＞ log2N terminates calculating process.
Beneficial effects of the present invention are：
1, realize generator matrix when avoid multiple Kronecker product and do not need multiple opening space, memory space by
2(N2- 1) it is reduced to N2；
2, the generation method of generator matrix need to only be recycled to N rank matrix assignment, be reduced largely with the increase of code length
The computation complexity and time that Kronecker product is brought；
3, the log-likelihood ratio message that tree construction mode calculate node is used in terms of polarization code realization of decoding, to next code
The information of tree node need to be only recalculated when member decoding, memory space is by Nlog2N is reduced to N-1；
4, the formula selection method proposed on the basis of using tree construction mode, keeps each node layer calculation formula identical,
The calculating process of Decoding Message is largely simplified, the decoding algorithm of other improvements is built upon on gradually elimination algorithm,
So simplicity realization method proposed by the present invention also tries out other decoding algorithms；
5, with the increase of code length N, the above advantageous effect is more notable.
Description of the drawings
Fig. 1 is that the present invention asks in generator matrixSchematic diagram.
Wherein：Be calculate for the first time obtain obtained as a result, then carrying out circulate operation again as unit of it
Fig. 2 is the schematic diagram for realizing decoding in the present invention with tree construction.
Wherein：For selecting code length N=8, the i-th symbol is decoded, tree contains log28=3 layers, y1..., y8For decoder
The information received.
Fig. 3 is the schematic process flow diagram of the calculating tree node message in the present invention.
Wherein：J is the number of plies of tree, calculates arrive last one layer of log always2N end loops.
Specific implementation mode
The invention will be further described with reference to the accompanying drawings and examples, but not limited to this.
Embodiment：
The embodiment of the present invention is as follows：A kind of coding and decoding method of polarization code optimization, respectively by the encoder of polarization code and pole
Change code
Decoder realizes that this method includes polarization code coding and polarization code decoding, is as follows：
Polarization code encodes：
The generator matrix of Polarization Coding is represented byWhereinFor the generation square for completing before bit inverted sequence
Battle array,N is code length, n=log2N,It is the Kronecker product of matrix, BNIt is sequence
Matrix is completing bit inverted sequence reordering operations；In order to avoid n=log2N times Kronecker product and multiple opening space, Shen
Please space size be N × N matrix, recursive copying is carried out to it and obtains generator matrix, process is as follows：
1) the N N matrix upper left corner of application is copied into
2) by N N matrix (2index, o) and coordinate position is copied into(o, 2index) position copies as(2index, 2index) position is copied intoIt is formed in the N N matrix upper left cornerAs shown in Figure 1, its
Middle index indicates counting variable, 1≤index≤log2N operates season index=1 for the first time；
3) index=index+1, withStep 2) is carried out for replicator, is obtained
4) it repeats the above steps 2), 3), until index=log has been calculated2N terminates, and obtains
5) rightIt completes bit inverted sequence reordering operations and obtains generator matrix, information bit is encoded to obtain code word, it is complete
Polarization code coding work；
Polarization code decodes：
It can be completed by recurrence in the calculating for serially offsetting log-likelihood ratio in decoding algorithm, defined function f and g are such as
Under：
(a, b, u)=(- 1) gua+b (2)
Wherein a, b belong to real number i.e. a, b ∈ R, u ∈ { 0,1 }, a, b, and u is respectively the independent variable of function f and g, log-likelihood
The recursive operation of ratio indicates as follows by function f and g：
U in formula (3), (4) aboveiIndicate the i-th symbol in code word,Indicate the decoding estimated value to the i-th symbol,Table
It is shown asIndicate the message that decoder receivesIndicate 1 to 2i-2 odd numbers index son to
Amount, subscript o indicate odd number,Indicate also or,Indicate that 1 subvector for arriving 2i-2 even number index, subscript e indicate even
Number,It indicates according to reception signalAnd estimated sequenceCalculate symbol u2i-1Log-likelihood ratio message,It indicates according to reception signalAnd estimated sequenceCalculate symbol u2iLog-likelihood ratio message；
The log-likelihood ratio for being calculated each node using tree structure according to the recursive operation formula of formula (3), (4) is disappeared
Breath, as shown in figure 3, its calculating process is as follows：
1) it is log to establish the number of plies2The full binary tree of N, according to the symbol serial number i of decoding, if the number of plies of tree is j, from tree
First layer, that is, j=1 starts to calculate；
2) symbol i%2 indicates i pairs of 2 remainders, judges the value of i%2, and as i%2=1, this node layer message selects formula
(4) it calculates；Formula (3) is then selected to calculate as i%2=0；
3) i=i/2, j=j+1 are enabled, judges the value of j, as j ＞ log2It is transferred to when N in next step, is otherwise transferred to step 2)；
4) j ＞ log2N terminates calculating process.
Claims (1)
1. a kind of coding and decoding method of polarization code optimization, is realized by the decoder of the encoder of polarization code and polarization code respectively,
This method includes polarization code coding and polarization code decoding, is as follows：
Polarization code encodes：
The generator matrix of Polarization Coding is represented byWhereinFor complete bit inverted sequence before generator matrix,N is code length, n=log2N,It is the Kronecker product of matrix, BNIt is sequence square
Battle array is completing bit inverted sequence reordering operations；In order to avoid n=log2N times Kronecker product and multiple opening space, application
Space size is the matrix of N × N, carries out recursive copying to it and obtains generator matrix, process is as follows：
1) the N N matrix upper left corner of application is copied into
2) by N N matrix (2index, 0) and coordinate position is copied into(0,2index) position copies as
(2index, 2index) position is copied intoIt is formed in the N N matrix upper left cornerWherein index, which indicates to count, to be become
Amount, 1≤index≤log2N operates season index=1 for the first time；
3) index=index+1, withStep 2) is carried out for replicator, is obtained
4) it repeats the above steps 2), 3), until index=log has been calculated2N terminates, and obtains
5) rightIt completes bit inverted sequence reordering operations and obtains generator matrix, information bit is encoded to obtain code word, completes pole
Change code coding work；
Polarization code decodes：
It can be completed by recurrence in the calculating for serially offsetting log-likelihood ratio in decoding algorithm, defined function f and g is as follows：
(a, b, u)=(- 1) gua+b (2)
Wherein a, b belong to real number i.e. a, b ∈ R, u ∈ { 0,1 }, a, b, and u is respectively the independent variable of function f and g, log-likelihood ratio
Recursive operation indicates as follows by function f and g：
U in formula (3), (4) aboveiIndicate the i-th symbol in code word,Indicate the decoding estimated value to the i-th symbol,It is expressed as Indicate the message y that decoder receives1..., yN,Indicate 1 subvector indexed to 2i-2 odd numbers,
Subscript o indicates odd number,Indicate also or,Indicate that 1 subvector for arriving 2i-2 even number index, subscript e indicate even number,It indicates according to reception signalAnd estimated sequenceCalculate symbol u2i-1Log-likelihood ratio message,It indicates according to reception signalAnd estimated sequenceCalculate symbol u2iLog-likelihood ratio message；
The log-likelihood ratio message of each node is calculated using tree structure according to the recursive operation formula of formula (3), (4),
Calculating process is as follows：
1) it is log to establish the number of plies2The full binary tree of N, according to the symbol serial number i of decoding, if the number of plies of tree is j, from the first layer of tree
That is j=1 starts to calculate；
2) symbol i%2 indicates i pairs of 2 remainders, judges the value of i%2, and as i%2=1, this node layer message selection formula (4) is counted
It calculates；Formula (3) is then selected to calculate as i%2=0；
3) i=i/2, j=j+1 are enabled, judges the value of j, as j ＞ log2It is transferred to when N in next step, is otherwise transferred to step 2)；
4) j ＞ log2N terminates calculating process.
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| CN111698060A (en) * | 2020-06-24 | 2020-09-22 | 京信通信系统（中国）有限公司 | Encoding method, apparatus, device and storage medium |
| CN112534724A (en) * | 2018-09-13 | 2021-03-19 | 华为技术有限公司 | Decoder and method for decoding polarization code and product code |
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