CN107273088A - A kind of quicksort network method and device for polarization code - Google Patents
A kind of quicksort network method and device for polarization code Download PDFInfo
- Publication number
- CN107273088A CN107273088A CN201710456345.1A CN201710456345A CN107273088A CN 107273088 A CN107273088 A CN 107273088A CN 201710456345 A CN201710456345 A CN 201710456345A CN 107273088 A CN107273088 A CN 107273088A
- Authority
- CN
- China
- Prior art keywords
- candidate
- path
- path candidate
- row
- odd
- 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.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 33
- 230000010287 polarization Effects 0.000 title claims abstract description 7
- 239000011159 matrix material Substances 0.000 claims description 54
- 238000013138 pruning Methods 0.000 claims description 11
- 230000000717 retained effect Effects 0.000 claims description 9
- 238000012217 deletion Methods 0.000 claims description 5
- 230000037430 deletion Effects 0.000 claims description 5
- FGUUSXIOTUKUDN-IBGZPJMESA-N C1(=CC=CC=C1)N1C2=C(NC([C@H](C1)NC=1OC(=NN=1)C1=CC=CC=C1)=O)C=CC=C2 Chemical compound C1(=CC=CC=C1)N1C2=C(NC([C@H](C1)NC=1OC(=NN=1)C1=CC=CC=C1)=O)C=CC=C2 FGUUSXIOTUKUDN-IBGZPJMESA-N 0.000 claims description 2
- 238000005516 engineering process Methods 0.000 abstract description 3
- 238000004891 communication Methods 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 23
- 241001269238 Data Species 0.000 description 3
- 241000208340 Araliaceae Species 0.000 description 1
- 235000005035 Panax pseudoginseng ssp. pseudoginseng Nutrition 0.000 description 1
- 235000003140 Panax quinquefolius Nutrition 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 235000008434 ginseng Nutrition 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012163 sequencing technique Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/22—Arrangements for sorting or merging computer data on continuous record carriers, e.g. tape, drum, disc
- G06F7/24—Sorting, i.e. extracting data from one or more carriers, rearranging the data in numerical or other ordered sequence, and rerecording the sorted data on the original carrier or on a different carrier or set of carriers sorting methods in general
-
- 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
- H04L1/0054—Maximum-likelihood or sequential decoding, e.g. Viterbi, Fano, ZJ algorithms
Landscapes
- Engineering & Computer Science (AREA)
- General Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Artificial Intelligence (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- Data Exchanges In Wide-Area Networks (AREA)
Abstract
The invention discloses a kind of sort algorithm and its hardware structure for polarization code decoding algorithm, belong to wireless communication technology field.The common M*L bars path candidate of M paths that different type point spread goes out when the present invention is L first to search width in Fast SSC List decoding algorithms is sorted in advance, then the M*L bars path candidate after pre- sequence is subjected to abbreviation according to the proposed method, delete partial redundance path candidate, then remaining path candidate input MSR modules are ranked up, the minimum L bar path candidates of final output.The final present invention devises the sequence framework of compatible four kinds of nodes, and compared to the sort method without deleting, the present invention significantly saves resource consumption.
Description
Technical field
The invention belongs to wireless communication technology field.
Background technology
Polarization code be it is currently the only be proved in theory can reach Shannon (Shannon) limit encoding scheme, and into
For the error correcting code of the 5G control channels communicated.Gabi Sarkis, Pascal Giard propose that Fast-SSC is (quick to simplify serial
Offset) algorithm, it can translate multiple code words in a clock cycle, improve and handle up compared with SC (serial cancellation algorithms)
Rate.In order to reduce the bit error rate, they propose Fast-SSC List (quick to simplify serial counteracting list) algorithm, and the algorithm is improved
Fast-SSC decoding performance, reduces BLER (the ratio between total block data that the block for having mistake is received with digital circuit).But Fast-
The number of the path candidate of SSC List extensions is much larger than SC List (serially offsetting list algorithm) 2L bars, causes sort-net
The larger resource consumption of network and path delay.
Fast-SSC List leaf nodes comprising several and be divided into four types, during decoding every layer all can basis
The Extended-type several ways footpath of leaf node, per paths, one PM value of correspondence, can all be utilized after path has been extended every time
Sorting network is ranked up, the most reliable path of selection L bars, and it is L to retain the less L paths of PM absolute values, i.e. search width.
Known REP nodes, Rate-1 nodes, SPC nodes expand 2,4,8 paths (M=2,4,8) respectively, and Rate-0 nodes are then
Not extensions path.Because upper level remains L paths, expanded rear shared M*L bar path candidates, M*L PM value of correspondence, PM
The absolute value of value is usedRepresent, whereinRepresent the l paths extension that upper level retains
M paths PM absolute values.
Mainly there is Bitonic (double tune) network currently for the sorting network of List algorithms, can be from 2L bar path candidates
Select confidence level highest L bars.The Bitonic networks of cutting, relative to Bitonic networks, 14% can be saved as L=32
Resource.And simplifying Odd-Even (odd even) sorting network will treat that collating sequence is divided into two sequences of odd even, wherein odd-order has been classified as
Sequence sequence, the even sequence after sequence is more than or equal to corresponding odd-order column unit, can delete HC therein (half-cleaner, half
Clear device) network, effectively reduce comparing unit (CASU, compare and select unit) quantity.Above sorting network is all
For the design of SCL algorithms, do not consider the characteristics of path candidate number that Fast-SSC List nodes are produced is different, directly should
For in Fast-SSC List larger network delay and resource consumption will to be caused.
The content of the invention
In order to overcome the shortcomings of that above-mentioned prior art is present, the present invention proposes a kind of quicksort side for polarization code
Method, according to the property of Fast-SSC List extensions paths, can delete part path candidate, so as to reduce ginseng by sorting in advance
Plus the path candidate quantity subsequently sorted, hardware complexity is reduced, sequencing production and resource utilization are improved, with good reality
With value.
Technical solution of the present invention is specific as follows：
It is specific as follows according to the sort method that different node types are used in Fast-SSC List decoding algorithms：
A.Rate-0 nodes
Due to Rate-0 nodes not extensions path, therefore path candidate need not be selected, directly retain L paths
To next stage.
B.REP nodes
Each paths of REP point spreads two, have 2L paths, it is necessary to therefrom select L paths after extension.Sequence side
Method is using Odd-even and Bitonic hybrid-sortings, i.e., the Odd-even sorting networks that first half sequence is inputted with two L,
L bar path candidates are ranked up respectively and obtain two dull L sequences, then L are selected using the HC networks in Bitonic
Minimum value, the Odd-even sorting networks of L inputs use CASU and sequence series (stage) to be represented with formula (1), (2).
C.Rate-1 nodes
For Rate-1 type nodes, four paths of each point spread meet formula (3),
1) it is sorted in advance first：The m paths extended in the L paths retained previous stage per paths lead to
Cross Odd-even sorting networks to be ranked up, be divided into four groups, pass through comparator I, comparator II, comparator III and ratio respectively
It is ranked up compared with device IV, it uses CASU and stage such as formulas (1), (2), the path candidate that L bars meet (4) is exported respectively,
It is worth noting that working as L<During M, it is not necessary to which whole path candidates are sorted in advance, a need pairWithSorted in advance, four additional path candidate is necessarily not belonging to 2 path candidates of minimum, therefore be not required to consider, and make M
=L：
Wherein, formula (3)：1≤l≤L,1≤m≤M-1；Formula (4)：1≤l≤L-1,1≤m≤M, M are expanded by each node
The number of paths of exhibition.
And then the obtained path candidate of sorting in advance is deleted 2)：It is made up of path candidate and column and row is met respectively
(3), the matrix of (4) is referred to as ordered candidate path matrix.By the obtained orderly path candidate matrix of path candidate construction that sorts in advance.
The path that need not be sorted is deleted according to the method for deleting, it is specific as follows：The first row isRetain whole path candidates, noteSecond row isThe middle less L/2 path candidate of reservation deletes remaining path candidate, remembersThe third line isRetain less(λ is integer) individual path candidate deletes remaining path candidate, note
(λ is integer)；Fourth line isOnly retain lessIndividual path candidate deletes remaining path candidate, note
It is whole path candidate numbers to remember AL,For the remaining candidate road of ordered candidate path matrix i-th row after deleting
Footpath number,For the remaining path candidate number after Pruning algorithm is deleted, then have
AL=M*L (5)
3) finally to being ranked up through deleting remaining path candidate：The first row is total to the second rowIndividual data are defeated
Enter to Odd-even merger networks are simplified, after being sorted through comparator V, export L minimum value；The third line is remaining with fourth line
Data input after being sorted through comparator VI, exports dullness to another simplification Odd_even merger networkIndividual minmal sequence.
Path candidate after comparator V and comparator VI sequences is inputted after half into Bitonic algorithms clear device, output L is most
Small value.D.SPC nodes
For SPC type nodes, 8 paths that each point spread goes out meet formula (7)：
And
1) sorted in advance firstly the need of to it：It is first rightIt is ranked up.Then the L bars retained respectively previous stage
The m paths extended in path per paths are ranked up by Odd_even sorting networks.So far, all data can be met
Abbreviation condition, you can write as the form of ordered candidate path matrix；
Odd_even sorting networks use CASU and stage to be drawn by formula (1), (2)；
If search width L is less than the number of paths M of point spread, including：As L=4, can directly it deleteAndAs L=1 or 2, a need pairSorted in advance, other data are not necessarily in the row of minimum L, and make
M=L.
And then the obtained path candidate of sorting in advance is deleted 2)：Path candidate is configured to orderly path candidate square
Battle array.The path that need not be sorted is deleted according to the method for deleting, it is specific as follows：The first row isRetain whole path candidates, noteSecond row isThe middle less L/2 path candidate of reservation deletes remaining path candidate, remembersThe third line isRetain less(λ is integer) individual path candidate deletes remaining path candidate, note
(λ is integer)；Fourth line isOnly retain lessIndividual path candidate deletes remaining path candidate, noteFifth line
I.e.Only retain(λ is integer) individual path candidate deletes remaining path candidate, note(λ is integer)；6th row isOnly retain
(λ is integer) individual path candidate deletes remaining path candidate, note(λ is integer)；
7th row isRetain(λ is integer) individual path candidate deletes remaining path candidate, note8th row isRetain lessIndividual path candidate deletes remaining path candidate, note
It is whole path candidate numbers to remember AL,For the remaining candidate road of ordered candidate path matrix i-th row after deleting
Footpath number,For the remaining path candidate number after Pruning algorithm is deleted,
AL=M*L (5)
3) and then to deleting remaining path candidate it is ranked up：Ordered candidate path matrix residual paths are subjected to merger
Sequence, the first row is total to the second rowIndividual data are input to simplified Odd_even merger network, export L minimum value；By
Three rows, to Odd_even merger networks are simplified, are exported in order with the remaining data input of fourth lineIndividual minimum value；Five, the six
Row and the seven, the eight is exercised with Odd_even merger networks merger sequence；It is above-mentioned that the path candidate exported is sorted through merger network still
So formula (3), (4) are met, and can be write as the form of ordered candidate path matrix and it is deleted according to Pruning algorithm, and after input
Continuous simplification Odd_even merger networks are ranked up again, after half clear device of the output result through Bitonic, export L minimum
Value.
In actual applications, it is a greater degree of saving resource, on the basis of the present invention carries Pruning algorithm, design one
Kind of sequence framework, makes its sorting network simultaneously required for compatible different type node, the sequence framework is in M=8, L >=8
Gained under part, including pre-ranking module (presorter) and delete rear order module (MSR).
Wherein, pre-ranking module (presorter) is used to perform following steps：
For M path according to node type after extension, first the one-level sequence for two 2L inputs, difference
To sequenceWithIt is ranked up, is exported WithThe path candidate of input can be made to meet formula (3) after the sequence.Then exist
It is right on the basis of thisTwo grades of sequences are carried out by Odd_even sorting networks, deleted
Fall part path candidate and export most reliable respectivelyThe orderly path candidate of bar is used as i-th row in ordered candidate path, composition
Ordered candidate path matrix after deleting, specifically deletes method as follows：
1) the first row of path candidate matrix isAll retain, noteSecond row isIt is middle to retain less L/
2 path candidates, delete remaining path candidate, note
2) the third line of path candidate matrix isRetain less(λ is integer) individual path candidate, is deleted
Remaining path candidate is cut, is remembered(λ is integer)；Fourth line isOnly retain lessIndividual candidate road
Footpath, deletes remaining path candidate, note
3) fifth line of path candidate matrix isOnly retain(λ is integer) is individual
Path candidate, deletes remaining path candidate, note(λ is integer)；6th row
I.e.Only retain(λ is integer) individual path candidate, deletes remaining path candidate, note(λ is integer)；7th row isOnly retain(λ is integer) is individual
Path candidate, deletes remaining path candidate,(λ is integer)；8th row isOnly retain less
Individual path candidate, deletes remaining path candidate, note
The Odd_even sorting networks of two grades of sequence L inputs meet (1), (2) using CASU and sequence series (stage),
Deleting rear order module (MSR) is used to perform following steps：
A. by the first row of ordered candidate path matrix and being total to that the second row is exportedIndividual data are input to simplified Odd_
Even merger networks, export L minimum value.
B. merger sequence is carried out with the output of fourth line remainder to the third line of ordered candidate path matrix, output is not
It is more thanIndividual orderly minimum value.
C. the output of fifth line and the 6th row remainder to ordered candidate path matrix carries out merger sequence, outputIndividual orderly minimum value.
D. the output of the 7th row and the 8th row remainder to ordered candidate path matrix carries out merger sequence, outputIndividual orderly minimum value.
E. data input step a and step b exported is individual to Odd_even merger networks merger sequence, output L is simplified
Minimum value.
F. the data input exported step c and step d, which is arrived, simplifies Odd_even merger networks merger sequence, only export compared with
Small
G. data input step e and step f exported carries out Bitonic sequences to HC networks and exports L minimum value.
The beneficial effects of the invention are as follows：Compared with the sort algorithm without deleting, the present invention is effectively reduced comparing unit
Quantity, so as to reduce hardware usable floor area, and then save corresponding hardware resource.Different sort algorithms using CASU and
Stage data are more as shown in table 1, and wherein odd even ordering and Bitonic sequences column are by M*L bars path candidate whole sequence institute
The resource used.Work as M=8, during L=16, carry algorithm and odd even ordering algorithm comparison herein, CASU 57% can be reduced,
Stage reduces 29%, is compared with Bitonic sequences, can reduce CASU 65%, and stage reduces 29%, it is known that the present invention is carried
The more other several sort algorithms of sort method have greater advantage.
Table 1
Brief description of the drawings
Fig. 1 is the sequence block diagram of REP type nodes in the present invention
Fig. 2 is basic CASU functional schematics in the present invention
Fig. 3 is the sorting network of REP type nodes in the present invention
Fig. 4 is L=4 of the present invention, and M=4's deletes schematic diagram
Fig. 5 is the sequence block diagram of Rate-1 node types in the present invention
Fig. 6 is the sequence block diagram of SPC node types in the present invention
Fig. 7 is sorter0 sorting network figures in Fig. 6
Fig. 8 is the Odd_even sorting network figures of 8 inputs
Fig. 9 is the sequence block diagram of compatible four kinds of node types
Figure 10 is the pre- sorting network of sorter01, sorter02
Figure 11 is the Odd_even sorting networks of L=16 inputs
1st, 2 row merger sorting networks after being deleted when Figure 12 is L=16
3rd, 4 row merger sorting networks after being deleted when Figure 13 is L=16
5th, 6 row sorting networks after being deleted when Figure 14 is L=16
7th, 8 row sorting networks after being deleted when Figure 15 is L=16
Figure 16 is Figure 12, the merger sorting network of 13 output datas
Figure 17 is Figure 14, the merger sorting network of 15 output datas
Figure 18 is Figure 16, the sorting network of 17 output datas
Embodiment
The present invention is specific as follows according to different node type sort methods：
A.Rate-0 nodes
Due to Rate-0 nodes not extensions path, therefore path candidate need not be selected, directly retain L paths
To next stage.
B.REP nodes
The paths of REP point spreads two are often run into, 2L paths are had after extension, it is necessary to therefrom select L paths.Sequence
Method is using Odd-even and Bitonic hybrid-sortings, i.e., the Odd-even sort-nets that first half sequence is inputted with two L
Network, is ranked up to L bar path candidates obtains two dull L sequences respectively, the HC networks in then being sorted using Bitonic
Select L minimum value, sequence block diagram such as Fig. 1.By taking L=4 as an example, detailed sorting network is as shown in figure 3, sorting network is by comparator
I (sorter1), comparator II (sorter2) and the half clear part of device (HC) three are constituted, and export 4 minimum values, comparator I
(sorter1) and comparator II (sorter2) is Odd-even sorting networks, the Odd-even sorting networks of L inputs are made
It can be represented with CASU and sequence series (stage) with formula (1), (2).
C.Rate-1 nodes
For Rate-1 type nodes, four paths of each point spread meet formula (3), carry out walkthrough to it first
Sequence：
The m paths extended in the L paths retained previous stage per paths are entered by Odd-even sorting networks
Row sequence, is divided into four groups, respectively sorter1, sorter2, sorter3, sorter4 in corresponding diagram 5, its using CASU and
Stage such as formulas (1), (2), export the path candidate that L bars meet (4) respectively.It is worth noting that working as L<During M, it is not necessary to complete
Portion's path candidate is sorted in advance, only need pairWithSorted in advance, four path candidates are necessarily not belonging in addition
2 minimum path candidates, therefore be not required to consider, and make M=L：
Wherein formula (3)：1≤l≤L,1≤m≤M-1；Formula (4)：1≤l≤L-1,1≤m≤M
Then the obtained path candidate of sorting in advance is deleted：Path candidate is write as to Fig. 4 form, claimed shown in Fig. 4
Be made up of path candidate and column and row meet respectively (3), (4) matrix be ordered candidate path matrix.Deleted according to the method for deleting
The element that need not be sorted is removed, it is specific as follows：The first row of ordered candidate path matrix isRetain whole path candidates, noteSecond row isThe middle less L/2 path candidate of reservation deletes remaining path candidate, remembersThe third line isRetain less(λ is integer) individual path candidate deletes remaining path candidate, note
(λ is integer)；Fourth line isOnly retain lessIndividual path candidate deletes remaining path candidate, note
With M=4, it is necessary to select the minimum value of L minimum value, i.e., 4 exemplified by L=4.Ordered candidate path square shown in Fig. 4
2. the battle array Part I data that 1. middle expression is deleted, frame represents the Part II data deleted, deletes in module Fig. 5
Pruned modules are represented；
It is whole candidate data numbers to remember AL,For the remaining candidate road of ordered candidate path matrix i-th row after deleting
Footpath number,For the remaining path candidate number after Pruning algorithm is deleted,
AL=M*L (5)
Finally to being ranked up through deleting remaining path candidate, the first row is total to the second rowIndividual data are input to
Simplify the sorter5 in Odd-even merger networks, corresponding diagram 5, export L minimum value；The third line is remaining with fourth line
Data input exports dullness to Odd_even merger networks are simplifiedSorter6 in individual minmal sequence, corresponding diagram 5.Will be through
The path candidate of sorter5, sorter6 sequence is inputted to Bitonic after the HC networks in sorting, and exports L minimum value.
D.SPC nodes
For SPC type nodes, 8 paths that each point spread goes out meet formula (7)：
And
To meet abbreviation condition, it is necessary first to which it is sorted in advance：It is first rightIt is ranked up, such as Fig. 7.Whole
Sorter0 is expressed as in sorting network, as shown in Figure 6.Then extended in the L paths retained respectively previous stage per paths
M paths be ranked up by Odd_even sorting networks, be expressed as sorter11~sorter18.So far, all numbers
According to abbreviation condition can be met, you can write as the form in ordered candidate path；Sorter11~sorter18 use CASU and
Stage can be drawn by formula (1), (2)；If L<M, as L=4, can directly be deletedAndWhen L=1,
When 2, a need pairSorted in advance, other data are necessarily not in the row of minimum L, and make M=L.
Path candidate after pre- sequence is write as the form of ordered candidate path matrix, deletes and is not required to according to the method for deleting
The path to be sorted, it is specific as follows：The first row isRetain whole path candidates, noteSecond row isIt is middle retain compared with
L/2 small path candidate deletes remaining path candidate, noteThe third line isRetain less(λ is
Integer) individual path candidate deletes remaining path candidate, remembers(λ is integer)；Fourth line isOnly retain smaller
'sIndividual path candidate deletes remaining path candidate, noteFifth line isOnly retain
(λ is integer) individual path candidate deletes remaining path candidate, note(λ is whole
Number)；6th row isOnly retain(λ is integer) individual path candidate deletes remaining candidate road
Footpath, note(λ is integer)；7th row isRetain(λ is whole
Number) individual path candidate deletes remaining path candidate, remembers8th row isRetain lessIndividual candidate
Remaining path candidate of route deletion, note
Then it is ranked up to deleting remaining path candidate：Ordered candidate path matrix residual paths are subjected to merger row
Sequence, the first row is total to the second rowIndividual data are input to the sorter21 in simplified Odd_even merger network, corresponding diagram 6,
Export L minimum value；By the third line and the remaining data input of fourth line to Odd_even merger networks are simplified, export in orderSorter22 in individual minimum value, corresponding diagram 6；Five, the six rows and the merger network of the seven, the eight enforcements are corresponded to respectively
sorter23、sorter24；The path candidate exported that sorted through sorter2i (1≤i≤4) still meets formula (3), (4), and can
Write as the form of ordered candidate path matrix and it is deleted according to Pruning algorithm, and input follow-up simplification Odd_even merger
Network, respectively sorter31, sorter32, its sort method are identical with sorter21, sorter22 respectively.Then will
Sorter31 and sorter32 output exports L minimum value after the half clear device HC that Bitonic sorts.
Above is the simple declaration for the framework that sorted to different node types, different point spread number of paths such as table 2 is different
Node type needs the number of sequence to be compared as shown in table 3 with the total data number before deleting after deleting network.
Table 2
Table 3
In actual applications, it is a greater degree of saving resource, on the basis of the present invention carries Pruning algorithm, design one
Kind of sequence framework, makes its sorting network simultaneously required for compatible different type node, overall architecture such as Fig. 9, including sort in advance
Module (presorter) and delete rear order module (MSR).Herein compliant architectures are put forward to draw under conditions of L >=8,
Work as L=2, know and whole path candidates need not in advance be sorted according to the sort method of SPC and Rate-1 type nodes when 4,
Therefore accordingly reduced using CASU, the situation is not described in detail, and the framework that hereafter sorted to it carries out labor.
Pre-ranking module (presorter) is used to perform following steps：
It is the one-level sequence of two 2L inputs first against M path according to node type after extension, it is right
Sorter01 and sorter02 in Fig. 9 is answered, respectively to each point spreadWith it is correspondingAndWith it is correspondingCarry out
Sequence, can make the path candidate of input meet formula (3) after being sorted through one-level.Then the L bars retained on this basis upper level
M (1≤m≤M) paths extended in path per paths carry out two grades of sequences, corresponding diagram by Odd_even sorting networks
Sorter1i in 9, deletes part path candidate and exports most reliable respectivelyThe orderly path candidate of bar is simultaneously used as time in order
I-th row in routing footpath, you can constitute the ordered candidate path matrix after deleting, 1≤i≤8, sorter1i is met using resource
(1), (2), as L=8, sorter1i sorting networks such as Fig. 8.Ordered candidate path matrix to delete method specific as follows：
1) the first row of path candidate matrix isAll retain, noteSecond row isIt is middle to retain less L/2
Individual path candidate, deletes remaining path candidate, note
2) the third line of path candidate matrix isRetain less(λ is integer) individual path candidate, is deleted
Remaining path candidate is cut, is remembered(λ is integer)；Fourth line isOnly retain lessIndividual candidate road
Footpath, deletes remaining path candidate, note
3) fifth line of path candidate matrix isOnly retain(λ is integer) individual time
Routing footpath, deletes remaining path candidate, note(λ is integer)；6th row isOnly retain(λ is integer) individual path candidate, deletes remaining path candidate, note(λ is integer)；7th row isOnly retain(λ is integer) is individual
Path candidate, deletes remaining path candidate,(λ is integer)；8th row isOnly retain less
Individual path candidate, deletes remaining path candidate, note
Deleting rear order module (MSR) is used to perform following steps：
It is the ordered candidate path matrix after being deleted through above-mentioned steps, the path candidate input MSR after deleting
Module, L minimum value of final output, MSR modules are comprised the steps of：
A. it is being total to for sorter11, sorter12 output by the first row of ordered candidate path matrix and the second row
Individual data are input to sorter21 networks in simplified Odd_even merger network, corresponding diagram 9, export L minimum value.
B. it is sorter13, sorter14 output to the third line of ordered candidate path matrix and fourth line remainder
Merger sequence is carried out, output is not more thanSorter22 networks in individual orderly minimum value, corresponding diagram 9.
C. fifth line and the 6th row remainder to ordered candidate path matrix is sorter15, sorter16 output
Carry out merger sequence, outputSorter23 networks in individual orderly minimum value, corresponding diagram 9.
D. it is sorter17, sorter18 output to the 7th row of ordered candidate path matrix and the 8th row remainder
Carry out merger sequence, outputSorter24 networks in individual orderly minimum value, corresponding diagram 9.
Note：A, b, c, d sorting data have no dependence, can perform parallel, can have been write as sorter2i output
The form of sequence path candidate matrix continues to delete method deletion redundancy path candidate according to of the invention carry, or sorter2i direct
OutputIndividual orderly minimum value.
E. by being total to that sorter21, sorter22 are exportedIndividual data are input to simplified Odd_even merger network, right
Sorter31 networks in Fig. 9 are answered, L minimum value is exported.
F. sorter23, sorter24 output are input to simplified Odd_even merger network, only need to export lessSorter32 networks in corresponding diagram 9.
Note：E, f sorting data have no dependence, can perform parallel.
G. sorter31, sorter32 output are input to HC networks bitonic sorting and export L minimum value.
It is worth noting that, sorter1i-sorter3i is all on the basis of Odd_even sort algorithms in sorting network
Upper to develop, the HC networks that only afterbody is used are to come from Bitonic sort algorithms.The compatibility sorts framework for M
When=8, M*L bar path candidates can be fully entered, work as M<When 8,Max is mended in (8-M) * L inputs to input port altogether
Value, max is the maximum that can be inputted.The present invention is carried sorting network and sorted using stage after sorting and deleting in advance two parts
Composition, is usedWithThe used stage that sorted after sorting and delete in advance is represented respectively, can be calculated with formula (8), (9).
Operation principle：All sorting networks of the present invention are all made up of one or more CASU, and CASU such as Fig. 2 is inputted as a left side
In1, in2 of side, right side is output, big descending of data, small up of data.In sequence framework under the output conduct of previous stage
The input of one-level, between connected with wire.
To make the object, technical solutions and advantages of the present invention clearer, below with reference to accompanying drawing and specific by taking L=16 as an example
Example, sort method proposed by the present invention is described in detail：
The first step, pre- sequence：
Input sorter01, sorter01 in the one-level sorting network for two 2L inputs, corresponding diagram 9, sorting network point
Not such as Figure 10 (a), (b), output element meets W01_2i-1≤W01_2i, W02_2i-1≤W02_2i respectively.And each network
Need 16 CASU, stage=1；
The m paths extended in the L paths retained upper level per paths are entered by Odd_even sorting networks
Sorter1i, sorting network such as Figure 11 in row sequence, corresponding diagram 9,63 CASU, stage=10, calculating side are needed per paths
Method meets formula (1), (2).Sorter11 input is the W01_2i-1 that sorter01 is exported, and Sorter12 input is
The W01_2i of sorter01 outputs；Sorter13 input isSorter14 input is that sorter02 is defeated
The W01_2i that the W02_2i-1 gone out, Sorter15 input export for sorter02, Sorter16~Sorter18 input point
It is not All 16 paths of each network inputs, according to Pruning algorithm, sorter1i pairs
The network answered deletes part path candidate and exports most reliable respectivelyThe orderly path candidate of bar, constitutes having after deleting
Sequence path candidate matrix, output is designated as W1i_j, wherein 1≤i≤8,
Second step：Sorted after deleting：
A1. sorter21 networks in sorting network corresponding diagram shown in Figure 12 9, left side input for sorter11 with
Sorter12 output, sort method used is actual use to simplify filled circles in Odd_even merger sorting networks, Figure 12
CASU, open circles represent deletable CASU；
B1. sorter22 networks in sorting network corresponding diagram shown in Figure 13 9, left side input for sorter13 with
Sorter14 output, sort method used is to simplify Odd_even merger sorting networks, and totally 8 CASU, stage=3, hollow
Circle represents deletable CASU；
C1. sorter23 networks in sorting network corresponding diagram shown in Figure 14 9, left side input for sorter15 with
Sorter16 output, sort method used is to simplify Odd_even merger sorting networks, and totally 3 CASU, stage=2, hollow
Circle represents deletable CASU；
D1. sorter24 networks in sorting network corresponding diagram shown in Figure 15 9, left side input for sorter17 with
Sorter18 output, sort method used is to simplify Odd_even merger sorting networks, and totally 1 CASU, stage=1, hollow
Circle represents deletable CASU, meets formula (15), (16)；
Because A1, B1, C1, D1 sorting data are without dependence, so parallel perform, stage is using most one
I.e.
Stage used in A1 is 4, totally 44 CASU.
E1. sorting network shown in Figure 16 be Fig. 9 in sorter31 networks, left side input be Fig. 9 in sorter21 and
Sorter22 output, i.e. Figure 12, the output of 13 merger networks, are ranked up to it and export less 16 ordinal values, altogether
32 CASU are needed, totally 4 grades；
F1. sorting network shown in Figure 17 be Fig. 9 in sorter32 networks, left side input be Fig. 9 in sorter23 and
Sorter24 output, i.e. Figure 14, the output of 15 merger networks, 8 ordinal values of output are ranked up to it, 8 are needed altogether
CASU, stage are 3；
Data can be performed parallel without dependence in E1, F1, the use of stage be that the maximum, i.e. stage are that 4, CASU is
Both sums, totally 40 CASU.
G1. sorting network shown in Figure 18 be Fig. 9 in HC networks, left side input be Fig. 9 in sorter31 and
Sorter32 output, i.e. Figure 16, the output of 17 merger networks, are ranked up to it and export less L=16 ordinal value.
8 CASU, 1 stage are needed altogether.
By A1-G1 sequence, 16 minimum values are exported, using CASU totally 92, stage takes the maximum in each step
Value, totally 9 grades；And use CASU 207 without the Odd_even sorting networks of deletion.The sorting network uses CASU altogether
628, sequence series is 20, and uses CASU 727 altogether without the Odd_even sorting networks of deletion, and sequence series is
23 grades；It can be seen that putting forward the method for deleting through the present invention, compared with the sorting network do not deleted, the sorting network after deleting not only is reduced
CASU, also reduces CASU stage.
Claims (2)
1. a kind of quicksort network method for polarization code, different nodes in serial counteracting list algorithm are simplified according to quick
The sort method that type is used is specific as follows：
A.Rate-0 nodes
L paths are directly remained into next stage；
B.REP nodes
Each paths of REP point spreads two, have 2L paths, it is necessary to therefrom select L paths after extension；Sort method makes
Hybrid-sorting, i.e. the first half sequence odd-even sorting network of two L inputs are adjusted with double with odd even ordering, L bars are waited respectively
Routing footpath, which is ranked up, obtains two dull L sequences, then selects L minimum using half clear device network in bitonic sorting
Value, the odd-even sorting network of L inputs uses CASU and sequence series to be represented with formula (1), (2)；
C.Rate-1 nodes
For Rate-1 type nodes, four paths of each point spread meet formula (3),
1) it is sorted in advance first：The m paths extended in the L paths retained previous stage per paths pass through strange
Even sorting network is ranked up, and is divided into four groups, is entered respectively by comparator I, comparator II, comparator III and comparator IV
Row sequence, it exports the path candidate that L bars meet (4) respectively using CASU and sequence series such as formula (1), (2),
It is worth noting that working as L<During M, it is not necessary to which whole path candidates are sorted in advance, a need pairWithEnter
The pre- sequence of row, four additional path candidate is necessarily not belonging to two path candidates of minimum, therefore is not required to consider, and makes M=L：
Wherein, formula (3)：1≤l≤L,1≤m≤M-1；Formula (4)：1≤l≤L-1,1≤m≤M, M are expanded by each node
Number of paths；
And then the obtained path candidate of sorting in advance is deleted 2)：Path candidate is write as and is made up of path candidate and column and row
(3), the ordered candidate path matrix of the matrix of (4) are met respectively；The path that need not be sorted is deleted according to the method for deleting, is had
Body is as follows：The first row isRetain whole path candidates, noteSecond row isIt is middle to retain less L/2 candidate road
Remaining path candidate is deleted in footpath, noteThe third line isRetain less(λ is integer) individual path candidate
Remaining path candidate is deleted, is remembered(λ is integer)；Fourth line isOnly retain lessIndividual path candidate
Remaining path candidate is deleted, is remembered
It is whole path candidate numbers to remember AL,For the remaining path candidate of ordered candidate path matrix i-th row after deleting
Number,For the remaining path candidate number after Pruning algorithm is deleted, then have
AL=M*L (5)
3) finally to being ranked up through deleting remaining path candidate：The first row is total to the second rowIndividual data are input to letter
Change Odd-even merger networks, after being sorted through comparator V, export L minimum value；The remaining data of the third line and fourth line are defeated
Enter to another simplification Odd_even merger network, after being sorted through comparator VI, output dullnessIndividual minmal sequence；Will through than
Inputted compared with the path candidate after device V and comparator VI sequences to half clear device network, export L minimum value；
D.SPC nodes
For SPC type nodes, 8 paths that each point spread goes out meet formula (7)：
And
1) sorted in advance firstly the need of to it：It is first rightIt is ranked up；Then in the L paths retained respectively previous stage
The m paths extended per paths are ranked up by odd-even sorting network；So far, all data can meet abbreviation condition,
It can be write as the form of ordered candidate path matrix；Odd-even sorting network uses CASU and sorted and can be obtained by formula (1), (2)
Go out；
If search width L is less than the number of paths M of point spread；Including：As L=4, can directly it deleteAndAs L=1 or 2, a need pairSorted in advance, other data are not necessarily in the row of minimum L, and make
M=L；
And then the obtained path candidate of sorting in advance is deleted 2)：Path candidate is write as and is made up of path candidate and column and row
(3), the ordered candidate path matrix of the matrix of (4) are met respectively；The path that need not be sorted is deleted according to the method for deleting, is had
Body is as follows：The first row of ordered candidate path matrix isRetain whole path candidates, noteSecond row isIt is middle to retain
Less L/2 path candidate deletes remaining path candidate, noteThe third line isRetain less(λ
For integer) individual path candidate deletes remaining path candidate, remembers(λ is integer)；Fourth line isOnly retain
It is lessIndividual path candidate deletes remaining path candidate, noteFifth line isOnly retain (λ is integer) individual path candidate deletes remaining path candidate, note(λ
For integer)；6th row isOnly retain(λ is integer) individual path candidate deletes remaining time
Routing footpath, note(λ is integer)；7th row isRetain(λ is
Integer) individual path candidate deletes remaining path candidate, remembers8th row isRetain lessIndividual candidate
Remaining path candidate of route deletion, note
It is whole path candidate numbers to remember AL,For the remaining path candidate of ordered candidate path matrix i-th row after deleting
Number,For the remaining path candidate number after Pruning algorithm is deleted,
AL=M*L (5)
3) and then to deleting remaining path candidate it is ranked up：Ordered candidate path matrix residual paths are subjected to merger row
Sequence, the first row is total to the second rowIndividual data are input to simplified odd-even merging network, export L minimum value；By the third line with
The remaining data input of fourth line is exported in order to odd-even merging network is simplifiedIndividual minimum value；Five, the six rows and the seven, the eight
Exercise and sorted with the merger of merger network；The above-mentioned path candidate exported that sorted through merger network still meets formula (3), (4), and can
Write as the form of ordered candidate path matrix and it is deleted according to Pruning algorithm, and input follow-up simplification odd-even merging network
It is ranked up again, after output result sorts through half clear device, exports L minimum value.
2. a kind of device for being used to realize the quicksort network method described in claim 1 for polarization code, it is characterised in that
The sorting network of compatible difference node type, including pre-ranking module and delete rear order module；
Wherein, pre-ranking module is used to perform following steps：
It is right respectively for M path according to node type after extension, first the one-level sequence for two 2L inputs
Each point spreadWith it is correspondingAndWith it is correspondingIt is ranked up, the candidate road of input can be made after being sorted through one-level
Footpath meets formula (3)；Then the m (1≤m≤M) article extended in the L paths retained on this basis upper level per paths
Path carries out two grades of sequences by odd-even sorting network, while delete part path candidate exports most reliable respectivelyBar has
The path candidate of sequence and as the i-th row of ordered candidate path matrix, composition delete after ordered candidate path matrix；Wherein delete
The specific method for subtracting path candidate is as follows：
1) the first row of path candidate matrix isAll retain, noteSecond row isIt is middle to retain less L/2 time
Routing footpath, deletes remaining path candidate, note
2) the third line of path candidate matrix isRetain less(λ is integer) individual path candidate, is deleted
Remaining path candidate, note(λ is integer)；Fourth line isOnly retain lessIndividual path candidate, is deleted
Remaining path candidate is cut, is remembered
3) fifth line of path candidate matrix isOnly retain(λ is integer) individual candidate road
Footpath, deletes remaining path candidate, note(λ is integer)；6th row isOnly protect
Stay(λ is integer) individual path candidate, deletes remaining path candidate, note(λ is integer)；7th row isOnly retain(λ is integer) is individual
Path candidate, deletes remaining path candidate,(λ is integer)；8th row isOnly retain less
Individual path candidate, deletes remaining path candidate, note
The odd-even sorting network of L inputs meets (1), (2) using CASU and sequence series,
Deleting rear order module is used to perform following steps：
A. by the first row of ordered candidate path matrix and being total to that the second row is exportedIndividual data are input to simplified odd-even merging
Network carries out and returns sequence, exports L minimum value；
B. simplified odd-even merging network is input to the third line of ordered candidate path matrix and the output of fourth line remainder
Carry out and return sequence, output is not more thanIndividual orderly minimum value；
C. the output of fifth line and the 6th row remainder to ordered candidate path matrix is input to simplified odd-even merging network
Carry out and return sequence, exportIndividual orderly minimum value；
D. the output to the 7th row and the 8th row remainder of ordered candidate path matrix is input to simplified odd-even merging network
Carry out and return sequence, exportIndividual orderly minimum value；
E. data input step a and step b exported exports L minimum value to odd-even merging network merger sequence is simplified；
F. data input step c and step d exported is only exported less to odd-even merging network merger sequence is simplified
G. data input step e and step f exported is to half clear device network and exports L minimum value, completes sequence.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710456345.1A CN107273088B (en) | 2017-06-16 | 2017-06-16 | Rapid sequencing method and device for polarization codes |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710456345.1A CN107273088B (en) | 2017-06-16 | 2017-06-16 | Rapid sequencing method and device for polarization codes |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107273088A true CN107273088A (en) | 2017-10-20 |
| CN107273088B CN107273088B (en) | 2020-04-24 |
Family
ID=60066570
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710456345.1A Expired - Fee Related CN107273088B (en) | 2017-06-16 | 2017-06-16 | Rapid sequencing method and device for polarization codes |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107273088B (en) |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109995382A (en) * | 2017-12-29 | 2019-07-09 | 华为技术有限公司 | A kind of polarization code decoder |
| CN110620587A (en) * | 2019-09-20 | 2019-12-27 | 上海大学 | Polarization code BP decoding unit based on different data type transmission |
| CN110635808A (en) * | 2018-06-22 | 2019-12-31 | 华为技术有限公司 | Polar code decoding method and decoding device |
| CN111076736A (en) * | 2020-01-02 | 2020-04-28 | 清华大学 | Vehicle-mounted system based on FPGA design and A star path searching method |
| CN112104412A (en) * | 2020-11-17 | 2020-12-18 | 四川九洲电器集团有限责任公司 | Accelerator suitable for low-orbit satellite broadband communication |
| CN113630126A (en) * | 2020-05-07 | 2021-11-09 | 大唐移动通信设备有限公司 | Polar code decoding processing method, device and equipment |
| TWI785122B (en) * | 2018-01-11 | 2022-12-01 | 南韓商三星電子股份有限公司 | Apparatus for constituent code processing in polar successive cancellation list decoding and a method |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20020169835A1 (en) * | 2000-12-30 | 2002-11-14 | Imarcsgroup.Com,Llc | E-mail communications system, method and program |
| CN102122966A (en) * | 2011-04-15 | 2011-07-13 | 北京邮电大学 | Channel-polarization-based encoder for staggered structure duplication code, and encoding and decoding methods thereof |
| CN102318288B (en) * | 2011-07-29 | 2014-11-05 | 华为技术有限公司 | Method, equipment and system of node sorting and selection |
| CN105281785A (en) * | 2015-10-22 | 2016-01-27 | 东南大学 | List successive cancellation decoding method and apparatus for polar codes |
| CN105281814A (en) * | 2014-07-23 | 2016-01-27 | 重庆重邮信科通信技术有限公司 | Basic odd-even merge grid unit and survivor path selection and construction method and device |
| CN106656214A (en) * | 2016-12-22 | 2017-05-10 | 东南大学 | Dynamic distribution sorting algorithm based on successive cancellation list polarization code decoding |
-
2017
- 2017-06-16 CN CN201710456345.1A patent/CN107273088B/en not_active Expired - Fee Related
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20020169835A1 (en) * | 2000-12-30 | 2002-11-14 | Imarcsgroup.Com,Llc | E-mail communications system, method and program |
| CN102122966A (en) * | 2011-04-15 | 2011-07-13 | 北京邮电大学 | Channel-polarization-based encoder for staggered structure duplication code, and encoding and decoding methods thereof |
| CN102318288B (en) * | 2011-07-29 | 2014-11-05 | 华为技术有限公司 | Method, equipment and system of node sorting and selection |
| CN105281814A (en) * | 2014-07-23 | 2016-01-27 | 重庆重邮信科通信技术有限公司 | Basic odd-even merge grid unit and survivor path selection and construction method and device |
| CN105281785A (en) * | 2015-10-22 | 2016-01-27 | 东南大学 | List successive cancellation decoding method and apparatus for polar codes |
| CN106656214A (en) * | 2016-12-22 | 2017-05-10 | 东南大学 | Dynamic distribution sorting algorithm based on successive cancellation list polarization code decoding |
Non-Patent Citations (1)
| Title |
|---|
| 张亮: "极化码的译码算法研究及其应用", 《中国博士学位论文全文数据库信息科技辑》 * |
Cited By (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109995382B (en) * | 2017-12-29 | 2021-01-05 | 华为技术有限公司 | Polar code decoder |
| CN109995382A (en) * | 2017-12-29 | 2019-07-09 | 华为技术有限公司 | A kind of polarization code decoder |
| TWI785122B (en) * | 2018-01-11 | 2022-12-01 | 南韓商三星電子股份有限公司 | Apparatus for constituent code processing in polar successive cancellation list decoding and a method |
| CN110635808B (en) * | 2018-06-22 | 2021-11-30 | 华为技术有限公司 | Polar code decoding method and decoding device |
| CN110635808A (en) * | 2018-06-22 | 2019-12-31 | 华为技术有限公司 | Polar code decoding method and decoding device |
| CN110620587A (en) * | 2019-09-20 | 2019-12-27 | 上海大学 | Polarization code BP decoding unit based on different data type transmission |
| CN110620587B (en) * | 2019-09-20 | 2023-02-17 | 上海大学 | Polarization code BP decoding unit based on different data type transmission |
| CN111076736B (en) * | 2020-01-02 | 2020-10-27 | 清华大学 | Vehicle-mounted system based on FPGA design and A star path searching method |
| CN111076736A (en) * | 2020-01-02 | 2020-04-28 | 清华大学 | Vehicle-mounted system based on FPGA design and A star path searching method |
| CN113630126A (en) * | 2020-05-07 | 2021-11-09 | 大唐移动通信设备有限公司 | Polar code decoding processing method, device and equipment |
| CN113630126B (en) * | 2020-05-07 | 2023-11-14 | 大唐移动通信设备有限公司 | Polar code decoding processing method, device and equipment |
| CN112104412A (en) * | 2020-11-17 | 2020-12-18 | 四川九洲电器集团有限责任公司 | Accelerator suitable for low-orbit satellite broadband communication |
| CN112104412B (en) * | 2020-11-17 | 2021-02-02 | 四川九洲电器集团有限责任公司 | Accelerator suitable for low-orbit satellite broadband communication |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107273088B (en) | 2020-04-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107273088A (en) | A kind of quicksort network method and device for polarization code | |
| Tarjan | Finding optimum branchings | |
| Hubert | Monotone invariant clustering procedures | |
| CN105119834B (en) | A kind of source address destination address joint lookup method based on compound trie tree constructions | |
| CN104036324B (en) | Optimal design method of communication network capacity based on genetic algorithm | |
| CN106253913B (en) | The block encoder of polarization code and its coding method | |
| Wright | Graphs on unlabelled nodes with a given number of edges | |
| CN106301387A (en) | A kind of distributed sort method and the method using the method composition CRC auxiliary polarization code successive elimination list decoding device | |
| CN106656214A (en) | Dynamic distribution sorting algorithm based on successive cancellation list polarization code decoding | |
| CN110138390A (en) | A kind of polarization code SSCL algorithm decoder based on deep learning | |
| CN105515997A (en) | BF_TCAM (Bloom Filter-Ternary Content Addressable Memory)-based high-efficiency range matching method for realizing zero range expansion | |
| CN107896137A (en) | A kind of sort method suitable for the division of polarization code decoding path | |
| CN105959224A (en) | Bit vector-based high-speed routing lookup apparatus and method | |
| CN108833052A (en) | Channel-polarization decoding path metric sort method | |
| Jasmon et al. | A method for evaluating all the minimal cuts of a graph | |
| CN103701590B (en) | Dictionary-based complex password traversing method and device | |
| CN106708532B (en) | Multilevel regular expression matching method based on TCAM | |
| Han et al. | Parallel integer sorting is more efficient than parallel comparison sorting on exclusive write PRAMs | |
| CN102333116B (en) | P2P (peer-to-peer) network building method and data positioning method | |
| CN110765730A (en) | Method for simplifying combined logic circuit | |
| CN102456073A (en) | Partial extremum inquiry method | |
| CN104866678A (en) | FPGA timing constraint layout method | |
| CN104683806B (en) | MQ arithmetic encoder high speed FPGA implementation methods based on depth flowing water | |
| WO2021255171A1 (en) | Architecture for classification of a decision tree ensemble and method | |
| CN107679010B (en) | Operator mapping system and method for reconfigurable computing array |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20200424 |