CN106656214A - Dynamic distribution sorting algorithm based on successive cancellation list polarization code decoding - Google Patents

Dynamic distribution sorting algorithm based on successive cancellation list polarization code decoding Download PDF

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CN106656214A
CN106656214A CN201611195808.5A CN201611195808A CN106656214A CN 106656214 A CN106656214 A CN 106656214A CN 201611195808 A CN201611195808 A CN 201611195808A CN 106656214 A CN106656214 A CN 106656214A
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node
path
sequence
ncs
fcs
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张川
梁霄
杨俊梅
尤肖虎
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Southeast 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

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  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
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Abstract

The invention discloses a dynamic distribution sorting algorithm based on successive cancellation list polarization code decoding. The algorithm comprises the following steps that two extended child nodes of each father node are set as FC and NC, wherein FC is a better node and NC is a poor node; L FC nodes are taken as L preferred optimal paths, and the final sorting is completed through dynamic replacement of individual FC and NC. The FC node has advantages in SCL decoding, so that the fewer nodes need replacement. The property is utilized, so that the sorting complexity can be reduced to a great extent.

Description

A kind of DYNAMIC DISTRIBUTION sort algorithm that the decoding of list polarization code is offset based on serial
Technical field
The present invention relates to a kind of DYNAMIC DISTRIBUTION sort algorithm that the decoding of list polarization code is offset based on serial.
Background technology
Arlkan proposes that polar code is the first kind of channel coding, is almost capable of achieving the symmetrical discrete nothing of binary system The capacity (B-DMCs) of memory channel.Because its relatively low computation complexity is O (NlogN), wherein N is polarization code length；With And the decoding architecture of fast Fourier transform Fast Fourier Transformation (FFT) forms, serial counteracting decoding Successive cancellation (SC) algorithm has become one of maximally effective polarization decoding algorithm.But compared to most Maximum-likelihood maximum likelihood (ML) decoder, the decoding performance of decoder is offset in serial still larger decline. In order to reduce the performance gap that the suboptimum Path selection for offsetting decoder by traditional serial is brought, decoding is offset in list serial Algorithm (list SC polar decoder) arises at the historic moment.After adding list (L), the chance of more Path selections is brought.
The main thought of SCL decoding algorithms is the L paths that optimum is selected in decoding tree extension, and to optimum L bars Path extends again.Each layer of decoding of level can all be related to one and L optimum node is filtered out from 2L both candidate nodes Sorting operation.The major defect of list decoding device is offset in serial, with the increase of list L sizes, decoder sort sections Complexity nonlinear increase.During Path extension, need to select L with maximum path from 2L extensions path acceptance of the bid The path of metric is used as path candidate.If selecting to be realized similar to bubble sort or selected and sorted method, its computing is answered Miscellaneous degree is O (L2)；If selecting to be realized similar to heapsort method, its computational complexity is O (Llog2L), but while is also increased Required internal storage location.Additionally, the time delay of two kinds of algorithms is larger, the hardware for being unfavorable for high speed is realized.
The content of the invention
Goal of the invention：It is an object of the invention to provide it is a kind of can solve the problem that defect present in prior art based on serial Offset the DYNAMIC DISTRIBUTION sort algorithm of list polarization code decoding.
Technical scheme：To reach this purpose, the present invention is employed the following technical solutions：
The DYNAMIC DISTRIBUTION sort algorithm that the decoding of list polarization code is offset based on serial of the present invention, including following step Suddenly：
S1：It is extended for L paths：Two extension child nodes of each father node are set to FC and NC, wherein FC is that NC is poor path, and the L FC node for obtaining is set to into set FCS, and the L NC node for obtaining is set compared with shortest path For set NCS；
S2：L FC node is set to into L bar optimal paths, is represented with set C；
S3：Initialization i=1, i are sequence wheel number；
S4：The maximum sequence wheel number n of setting, and 1≤n≤L-1 are required according to actual performance；
S5：For the i-th wheel sequence, worst path FC will be selected in L-i+1 FC node remaining in set FCSi, will The path NC of optimum is selected in L-i+1 NC node remaining in set NCSi；
S6：Relatively FCiWith NCi：If FCiMore excellent, then sequence terminates, and jumps to step S12；Otherwise, step is proceeded S7；
S7：By the FC in set CiPath replacement is NCiNode；
S8：By the FC in set FCSiElement is deleted, then the element number in set FCS is changed into L-i；
S9：By the NC in set NCSiElement is deleted, then the element number in set NCS is changed into L-i；
S10：Update i values, i=i+1；
S11：If i<N, then jumping to step S5 carries out next round sequence；Otherwise, then step S12 is proceeded；
S12：Sequence is completed, and optimum L paths are the path in set C.
Beneficial effect：Compared with prior art, the present invention has following beneficial effect：
1) it is right the characteristics of choose L bar optimal paths from 2L bar extensions paths present invention utilizes in SCL decoding requirements Order result is required no knowledge about in path selected by L bars, it is to avoid direct sequence；
2) present invention utilizes the very big possibility of L FCs node is final L bar optimal paths in expanding node, with FC Based on node, ranking results are adjusted with the mode for replacing poor FC, greatly reduce sequence complexity；
3) complexity is O (L by the present invention2) bubble sort or complexity be reduced to for the heapsort of O (Llog2L) Complexity is the dynamic distributed sequence of O (L)；
4) present invention is dynamic order, and its sequence time delay is not fixed.Because FC nodes vast scale is better than NC nodes, In every layer of dynamic order for a frame polarization code, great majority sequence only needs to wheel sequence, i.e., without NC nodes and FC nodes Replacement.
Description of the drawings
Fig. 1 is the search code tree of N-bit Polar codes；
Fig. 2 is using specific embodiment of the invention method and the FER performance comparison using general SCL decoding algorithms Figure；
Fig. 3 is the average computation cycle of DS2 algorithms in the specific embodiment of the invention；
Fig. 4 is the average computation cycle of DS3 algorithms in the specific embodiment of the invention.
Specific embodiment
Technical scheme is further introduced with reference to specific embodiment.
1st, code tree is searched for
The SCL decoding algorithms of Polar codes are substantially the tree search algorithms of breadth-first, the search of N-bit Polar codes Code tree is as shown in figure 1, L is surviving path number.The maximum path of path metric value (Path Metric, PM) in n-th layer in Fig. 1 (survivor path) as decodes outputNumber of times represents vector, is numbered 1 to N N number of decoding result.
2nd, SCL algorithms
For parameter isPolar codes, N is code length, and K is information bit quantity.Respective channels WNOutput Vector isRepresent that 1 to N N number of of being numbered for receiving receives data.A is information bit distribution situation set.To freeze The value of knot position, is typically set to 0.The path metric value of decoding is defined as channel transition probabilityFrequently with its logarithm Form.For the complexity for reducing calculating and storing, we are defined as follows using path metric value of equal value：
The recurrence formula of its decoding is as follows：
WhereinI-th decoding PM value of N-bit decoder is represented,Represent corresponding nodePart and.WithRepresent connecting nodeTwo parts of upper strata iteration and.Represent that XOR is calculated, max*Represent Jacobi Logarithm：
Initialization conditionWherein σ2 For noise variance.max(x1,x2) it is to take x1,x2In maximum.
3rd, this specific embodiment
During Path extension, need to select the L road with maximum path metric from 2L extensions path acceptance of the bid Footpath is used as path candidate.If selecting to be realized similar to bubble sort or selected and sorted method, its computational complexity is O (L2)；If selecting to be realized similar to heapsort method, its computational complexity is O (Llog2L), but needed for while also increasing Internal storage location.Additionally, the time delay of two kinds of algorithms is larger, the hardware for being unfavorable for high speed is realized.
This specific embodiment discloses a kind of DYNAMIC DISTRIBUTION sort algorithm that the decoding of list polarization code is offset based on serial Comprise the following steps：
S1：It is extended for L paths：Two extension child nodes of each father node are set to FC and NC, wherein FC is that NC is poor path, and the L FC node for obtaining is set to into set FCS, and the L NC node for obtaining is set compared with shortest path For set NCS；
S2：L FC node is set to into L bar optimal paths, is represented with set C；
S3：Initialization i=1, i are sequence wheel number；
S4：The maximum sequence wheel number n of setting, and 1≤n≤L-1 are required according to actual performance；
S5：For the i-th wheel sequence, worst path FC will be selected in L-i+1 FC node remaining in set FCSi, will The path NC of optimum is selected in L-i+1 NC node remaining in set NCSi；
S6：Relatively FCiWith NCi：If FCiMore excellent, then sequence terminates, and jumps to step S12；Otherwise, step is proceeded S7；
S7：By the FC in set CiPath replacement is NCiNode；
S8：By the FC in set FCSiElement is deleted, then the element number in set FCS is changed into L-i；
S9：By the NC in set NCSiElement is deleted, then the element number in set NCS is changed into L-i；
S10：Update i values, i=i+1；
S11：If i<N, then jumping to step S5 carries out next round sequence；Otherwise, then step S12 is proceeded；
S12：Sequence is completed, and optimum L paths are the path in set C.
Distributed sorting algorithm disclosed in this specific embodiment (DS) is similar to general sort algorithm, but its storage and More complicated degree is below general sort algorithm.When above, when being relatively unsatisfactory for condition, algorithm is exited, and is no longer subsequently compared Compared with greatly reducing average more complicated degree.From analysis and related emulation, the corresponding path degree of i values larger in PMs Value is less, it is more likely that is to need to abandon, accounts for leading to the influence factor of algorithm.Only take i=L-1～L-n and complete path Extension and metric sequence, referred to as DSn, setup parameter n relatively takes turns number for high specific.Now, it is right in algorithm 1Row Sequence operation is unwanted, it is only necessary to if searching the dry values such as its maximum, minimum, secondary big and sub-minimum.During hardware is realized, I Can further be changed, searchMinimum, sub-minimum come replace searchMinimum, sub-minimum, In the case of complexity identical, decoding performance is improved.By emulation, based on DS2 (L=4) or the SCL of DS3 (L=8) After decoding algorithm is in combination with CRC check, the misdiagnosis rate performance loss of decoding almost can be ignored.When L is larger, such as L=16, 32, the performance loss that simple DS2 or DS3 algorithms bring is larger, to front N/2 bits using completely DS algorithms, rear N/2 bits Realized using DS3 algorithms.
By taking L=4 as an example, the Path extension process based on DS2 algorithms is as follows：1, four paths are distinguished into respectively four FC Node and four NC nodes；2, worst node FC is found out in four FC nodes1, the section of optimum is found out in four NC nodes Point NC1；3, compare FC1With NC1If, FC1Larger, then sequence terminates, and four of selection is the corresponding road of four FC compared with shortest path Footpath, it is not necessary to carry out following operation, otherwise carry out following operation；4, use NC1Corresponding path replacement FC1, and the two values are not Enter back into and compare operation；5, select worst node FC in remaining three FC2, find out most in remaining three NC nodes Excellent node NC2；6, compare FC2With NC2If, FC2Larger, then sequence terminates, four of selection compared with shortest path be three FC with NC1Corresponding path, conversely, four paths chosen are remaining two FC and NC1And NC2Corresponding path, sequence terminates.DS2 Algorithm is by the more complicated degree of metric by O (L2) it is reduced to O (L).DS2 algorithms are easy to the parallel of hardware and realize with regard to streamline, Complexity can be reduced, PDR is improved.
For different L values, improved SCL decodes the FER performance comparison decoded with general SCL as shown in Fig. 2 Fig. 2 In for the effective information position 512 of code length 1024 polarization code.During L=4, the SCL based on DS2 algorithms is decoded and decoded with general SCL With almost consistent FER performance, can be used as the hard-wired preferably selection of low complex degree；During L=8, based on DS3 The SCL of algorithm is decoded has almost consistent FER performance with general SCL decodings, can be hard-wired as low complex degree One preferably choosing.
This specific embodiment another advantage is that this sequence is a dynamic sequencer procedure, and sequence to be entered Capable wheel number is uncertain.Because SCL decodes the property that process has in itself, each FC nodes under the extension in L paths Very big possibility is exactly the final L bar optimal paths for being filtered out.Therefore during decoding most of distributed sequencer procedures Only need to carry out a wheel sequence.May certify that sequence length is extremely low by emulation.
From Fig. 3 emulation it can be seen that during as L=4 using this specific embodiment in DS2 sort algorithms averagely only need 1.075 wheel sequences (8 cycles) are carried out, also than strict order has very big lifting (if using traditional bubbling in sequential The sequence clock that sequence needs is L2The cycle of the order of magnitude, i.e., 16).Using this tool when can be seen that as L=8 from Fig. 4 emulation DS3 sort algorithms in body embodiment averagely only need to carry out 1.074 wheel sequences (16 cycles), also than strict in sequential Sequence has very big lifting (if the sequence clock needed using traditional bubble sort is L2The cycle of the order of magnitude, i.e., 64).This Distributed sorting algorithm in specific embodiment averagely sorts consumption in a wheel left and right, greatly reduces what sequence was wasted Time delay.

Claims (1)

  1. It is 1. a kind of that the DYNAMIC DISTRIBUTION sort algorithm that list polarization code is decoded is offset based on serial, it is characterised in that：Including following step Suddenly：
    S1：It is extended for L paths：Two extension child nodes of each father node are set to FC and NC, and wherein FC is Compared with shortest path, NC is poor path, and the L FC node for obtaining is set to into set FCS, and the L NC node for obtaining is set to into collection Close NCS；
    S2：L FC node is set to into L bar optimal paths, is represented with set C；
    S3：Initialization i=1, i are sequence wheel number；
    S4：The maximum sequence wheel number n of setting, and 1≤n≤L-1 are required according to actual performance；
    S5：For the i-th wheel sequence, worst path FC will be selected in L-i+1 FC node remaining in set FCSi, will gather The path NC of optimum is selected in L-i+1 NC node remaining in NCSi；
    S6：Relatively FCiWith NCi：If FCiMore excellent, then sequence terminates, and jumps to step S12；Otherwise, step S7 is proceeded；
    S7：By the FC in set CiPath replacement is NCiNode；
    S8：By the FC in set FCSiElement is deleted, then the element number in set FCS is changed into L-i；
    S9：By the NC in set NCSiElement is deleted, then the element number in set NCS is changed into L-i；
    S10：Update i values, i=i+1；
    S11：If i<N, then jumping to step S5 carries out next round sequence；Otherwise, then step S12 is proceeded；
    S12：Sequence is completed, and optimum L paths are the path in set C.
CN201611195808.5A 2016-12-22 2016-12-22 Dynamic distribution sorting algorithm based on successive cancellation list polarization code decoding Pending CN106656214A (en)

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Cited By (6)

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Publication number Priority date Publication date Assignee Title
CN107248866A (en) * 2017-05-31 2017-10-13 东南大学 A kind of method for reducing polarization code decoding delay
CN107273088A (en) * 2017-06-16 2017-10-20 山东科技大学 A kind of quicksort network method and device for polarization code
CN108462558A (en) * 2018-03-01 2018-08-28 西安电子科技大学 A kind of polarization code SCL interpretation methods, device and electronic equipment
CN110138497A (en) * 2018-02-02 2019-08-16 中兴通讯股份有限公司 Enhance method, apparatus, equipment and the computer readable storage medium of FAR performance
CN110601700A (en) * 2019-08-09 2019-12-20 中国地质大学（武汉） Hardware sequencer suitable for polar code serial offset list decoding algorithm
CN115987302A (en) * 2023-02-03 2023-04-18 中国传媒大学 Parity check supported dynamic serial offset list flip decoding method and system

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CN105720992A (en) * 2016-01-22 2016-06-29 哈尔滨工业大学深圳研究生院 Polarized code simplifying and decoding method
CN105933010A (en) * 2016-04-15 2016-09-07 华南理工大学 Low-complexity polarization code decryption SCL algorithm based on segmented verification assistance
CN106209113A (en) * 2016-07-29 2016-12-07 中国石油大学(华东) A kind of decoding method of polarization code

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KR101496182B1 (en) * 2013-12-16 2015-03-09 성균관대학교산학협력단 Methods and apparatuses of generating polar encode with extended minimum distance
CN105720992A (en) * 2016-01-22 2016-06-29 哈尔滨工业大学深圳研究生院 Polarized code simplifying and decoding method
CN105933010A (en) * 2016-04-15 2016-09-07 华南理工大学 Low-complexity polarization code decryption SCL algorithm based on segmented verification assistance
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Cited By (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107248866A (en) * 2017-05-31 2017-10-13 东南大学 A kind of method for reducing polarization code decoding delay
CN107273088A (en) * 2017-06-16 2017-10-20 山东科技大学 A kind of quicksort network method and device for polarization code
CN107273088B (en) * 2017-06-16 2020-04-24 山东科技大学 Rapid sequencing method and device for polarization codes
CN110138497A (en) * 2018-02-02 2019-08-16 中兴通讯股份有限公司 Enhance method, apparatus, equipment and the computer readable storage medium of FAR performance
CN110138497B (en) * 2018-02-02 2021-08-17 中兴通讯股份有限公司 Method, device, equipment and computer readable storage medium for enhancing FAR performance
CN108462558A (en) * 2018-03-01 2018-08-28 西安电子科技大学 A kind of polarization code SCL interpretation methods, device and electronic equipment
CN108462558B (en) * 2018-03-01 2020-12-18 西安电子科技大学 Method and device for decoding polarization code SCL and electronic equipment
CN110601700A (en) * 2019-08-09 2019-12-20 中国地质大学（武汉） Hardware sequencer suitable for polar code serial offset list decoding algorithm
CN110601700B (en) * 2019-08-09 2021-05-04 中国地质大学（武汉） Hardware sequencer suitable for polar code serial offset list decoding algorithm
CN115987302A (en) * 2023-02-03 2023-04-18 中国传媒大学 Parity check supported dynamic serial offset list flip decoding method and system
CN115987302B (en) * 2023-02-03 2023-11-21 中国传媒大学 Parity-check-supported dynamic serial cancellation list overturning decoding method and system

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