CN107273088B - Rapid sequencing method and device for polarization codes - Google Patents

Rapid sequencing method and device for polarization codes Download PDF

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CN107273088B
CN107273088B CN201710456345.1A CN201710456345A CN107273088B CN 107273088 B CN107273088 B CN 107273088B CN 201710456345 A CN201710456345 A CN 201710456345A CN 107273088 B CN107273088 B CN 107273088B
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CN107273088A (en
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张小军
隋荣全
崔建明
张德学
曾庆田
董雁飞
高健
张荣才
张作文
陈晨
李俊
烟晓凤
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Shandong University of Science and Technology
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Abstract

The invention discloses a rapid sequencing method and device for a polarization code, and belongs to the technical field of wireless communication. The invention firstly carries out pre-sorting on M paths which are expanded by different types of nodes when the width is L and are searched in a Fast-SSC List decoding algorithm, then carries out simplification on the pre-sorted M paths according to the method provided by the invention, deletes part of redundant candidate paths, then inputs the rest candidate paths into an MSR module for sorting, and finally outputs the minimum L candidate paths. Finally, the invention designs a sequencing architecture compatible with four nodes, and compared with a sequencing method without deletion, the invention greatly saves the resource consumption.

Description

Rapid sequencing method and device for polarization codes
Technical Field
The invention belongs to the technical field of wireless communication.
Background
The polarization code is the only theoretically proven coding scheme that can reach Shannon (Shannon) limit at present and becomes an error correction code for the control channel of 5G communication. Gabi Sarkis, Pascal Giard propose Fast-SSC (Fast simplified serial cancellation) algorithm, which can decode a plurality of code words in one clock cycle, compared with SC (serial cancellation algorithm), improving throughput. To reduce the error rate, they propose a Fast-SSC List (Fast simplified serial cancellation List) algorithm that improves the decoding performance of Fast-SSC, reducing the BLER (ratio of erroneous blocks to the total number of blocks received by the digital circuit). But the number of candidate paths of Fast-SSC List extension is much larger than 2L of SC List (serial cancellation List algorithm), resulting in large resource consumption and path delay of the sorting network.
The Fast-SSC List leaf nodes comprise a plurality of types which are divided into four types, each layer expands a plurality of paths according to the type of the leaf node in the decoding process, each path corresponds to a PM value, the paths are sequenced by utilizing a sequencing network after being expanded each time, L most reliable paths are selected, and L paths with smaller PM absolute values are reserved, namely the searching width is L. It is known that the REP node, the Rate-1 node, and the SPC node extend 2,4, and 8 paths (M is 2,4, and 8), respectively, while the Rate-0 node does not extend the path. Because the upper stage reserves L paths, after expansion, the total number of M X L candidate paths is obtained, corresponding to M X L PM values, and the absolute value of the PM value is used
Figure GDA0002375457240000011
Is shown in which
Figure GDA0002375457240000012
The PM absolute value of the mth path of the l path extension retained by the previous stage is represented.
At present, a Bitonic (Bitonic) network is mainly used as a sorting network for the List algorithm, and L candidate paths with the highest reliability can be selected from 2L candidate paths. A tailored Bitonic network may save 14% of resources when L is 32, relative to a Bitonic network. The simplified Odd-Even (Odd-Even) sorting network divides the sequence to be sorted into two Odd-Even sequences, wherein the Odd sequence is an ordered sequence, the sorted Even sequence is more than or equal to the corresponding Odd sequence unit, the HC (half-cleaner) network in the ordered Even sequence can be deleted, and the number of comparison units (CASU, compare and select unit) is effectively reduced. The sorting networks are designed aiming at the SCL algorithm, the characteristic that the number of candidate paths generated by Fast-SSC List nodes is different is not considered, and the direct application of the sorting networks to the Fast-SSC List causes larger network delay and resource consumption.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a quick sorting method for the polar codes, and partial candidate paths can be deleted through pre-sorting according to the property of Fast-SSC List extended paths, so that the number of the candidate paths participating in subsequent sorting is reduced, the hardware complexity is reduced, the sorting speed and the resource utilization rate are improved, and the quick sorting method has good practical value.
The technical scheme of the invention is as follows:
the sorting method adopted according to different node types in the Fast-SSC List decoding algorithm is as follows:
rate-0 node
Since the path is not expanded by the Rate-0 node, the candidate path does not need to be selected, and the L paths are directly reserved to the next stage.
B.REP node
Each REP node expands two paths, and the expanded paths have 2L paths in total, from which L paths need to be selected. The sorting method uses Odd-even and Bitonic mixed sorting, namely the first half sorting uses two L-input Odd-even sorting networks to sort L candidate paths respectively to obtain two monotonic L sequences, then uses HC network in Bitonic to select L minimum values, and CASU and sorting series (stage) used by the L-input Odd-even sorting network can be expressed by formulas (1) and (2).
Figure GDA0002375457240000021
Figure GDA0002375457240000022
Wherein
Figure GDA0002375457240000023
Representing the number of CASUs used by the parity-ordered network for the L input,
Figure GDA0002375457240000024
representing the sorting progression used by the parity sorting network of the L input;
rate-1 node
For the Rate-1 type nodes, the four paths extended by each node satisfy equation (3),
1) it is first pre-ordered: sorting the mth path expanded by each path in the L paths reserved at the previous stage into four groups by an Odd-even sorting network, respectively sorting the mth path by a comparator I, a comparator II, a comparator III and a comparator IV by using CASU and stage as formulas (1) and (2), respectively outputting L candidate paths meeting the requirement (4),
it is worth noting that when L is<In M, all the candidate paths do not need to be pre-ordered, and only the candidate paths need to be pre-ordered
Figure GDA0002375457240000025
And
Figure GDA0002375457240000026
pre-sorting is performed, and the other four candidate paths do not belong to the minimum 2 candidate paths, so that the two candidate paths need not be considered, and M is equal to L:
Figure GDA0002375457240000027
Figure GDA0002375457240000028
wherein the content of the first and second substances,
Figure GDA0002375457240000029
the mth path representing the expansion of the mth node; formula (3): l is more than or equal to 1 and less than or equal to L, M is more than or equal to 1 and less than or equal to M-1; formula (4): l is more than or equal to 1 and less than or equal to L-1, M is more than or equal to 1 and less than or equal to M, and M is the number of paths expanded by each node.
2) And then deleting candidate paths obtained by pre-sorting: the matrix composed of the candidate paths and the columns and rows satisfying (3) and (4) respectively is called an ordered candidate path matrix. And constructing an ordered candidate path matrix by using the candidate paths obtained by pre-ordering. Deleting paths which do not need to be sorted according to a deleting method, which comprises the following specific steps: the first line is
Figure GDA00023754572400000210
All candidate paths are retained and recorded
Figure GDA00023754572400000211
The second line is
Figure GDA00023754572400000212
The L/2 path candidates with smaller number are retained to delete the rest path candidates and record
Figure GDA00023754572400000213
The third line is
Figure GDA00023754572400000214
Reserve less
Figure GDA00023754572400000215
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure GDA00023754572400000216
(λ is an integer); the fourth line is
Figure GDA00023754572400000217
Only remain small
Figure GDA00023754572400000218
Deleting the rest of the candidate paths from the candidate path
Figure GDA00023754572400000219
Note ALThe number of the total candidate paths is,
Figure GDA0002375457240000031
the number of the remaining candidate paths in the ith row after the ordered candidate path matrix is pruned,
Figure GDA0002375457240000032
the number of the remaining candidate paths after being deleted by the deletion algorithm is
AL＝M*L (5)
Figure GDA0002375457240000033
3) And finally, sequencing the deleted residual candidate paths: the first row and the second row are shared
Figure GDA0002375457240000034
Inputting the data into a simplified Odd-even merging network, and outputting L minimum values after the data are sequenced by a comparator V; inputting the rest data of the third row and the fourth row into another simplified Odd _ even merging network, and outputting monotonous data after being sorted by a comparator VI
Figure GDA0002375457240000035
The smallest sequence. And inputting the candidate paths sequenced by the comparator V and the comparator VI into a half-cleaner in the Bitonic algorithm, and outputting L minimum values.
SPC node
For SPC type nodes, the 8 paths each node extends satisfy equation (7):
Figure GDA0002375457240000036
and is
Figure GDA0002375457240000037
1) It first needs to be pre-ordered: first to each other
Figure GDA0002375457240000038
And (6) sorting. Then sorting the mth path expanded by each path in the L paths reserved in the previous stage through an Odd _ even sorting network. All data can meet the simplification conditions, namely the data can be written into the form of an ordered candidate path matrix;
the CASU and the stage used by the Odd _ even sequencing network can be obtained by the formulas (1) and (2);
if the search width L is smaller than the path number M of the node expansion, the method comprises the following steps: when L is 4, it can be deleted directly
Figure GDA0002375457240000039
And
Figure GDA00023754572400000310
when L is 1 or 2, it is only necessary to
Figure GDA00023754572400000311
And performing pre-sorting, wherein other data are not in the minimum L rows, and M is equal to L.
2) And then deleting candidate paths obtained by pre-sorting: the candidate paths are constructed into an ordered candidate path matrix. Deleting paths which do not need to be sorted according to a deleting method, which comprises the following specific steps: the first line is
Figure GDA00023754572400000312
All candidate paths are retained and recorded
Figure GDA00023754572400000313
The second line is
Figure GDA00023754572400000314
The L/2 path candidates with smaller number are retained to delete the rest path candidates and record
Figure GDA00023754572400000315
The third line is
Figure GDA00023754572400000316
Reserve less
Figure GDA00023754572400000317
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure GDA00023754572400000318
(λ is an integer); the fourth line is
Figure GDA00023754572400000319
Only remain small
Figure GDA00023754572400000320
Deleting the rest of the candidate paths from the candidate path
Figure GDA00023754572400000321
The fifth element is
Figure GDA00023754572400000322
Only reserve
Figure GDA00023754572400000323
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure GDA00023754572400000324
(λ is an integer); the sixth line is
Figure GDA00023754572400000325
Only reserve
Figure GDA00023754572400000326
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure GDA0002375457240000041
(λ is an integer); in the seventh row
Figure GDA0002375457240000042
Retention
Figure GDA0002375457240000043
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure GDA0002375457240000044
in the eighth line
Figure GDA0002375457240000045
Reserve less
Figure GDA0002375457240000046
Deleting the rest of the candidate paths from the candidate path
Figure GDA0002375457240000047
Note ALThe number of the total candidate paths is,
Figure GDA0002375457240000048
the number of the remaining candidate paths in the ith row after the ordered candidate path matrix is pruned,
Figure GDA0002375457240000049
for the number of candidate paths remaining after deletion by the pruning algorithm,
AL＝M*L (5)
Figure GDA00023754572400000410
3) and then sorting the deleted residual candidate paths: merging and sorting the rest paths of the ordered candidate path matrix, wherein the first row and the second row are shared
Figure GDA00023754572400000411
Inputting the data into a simplified Odd _ even merging network, and outputting L minimum values; inputting the rest data of the third row and the fourth row into the simplified Odd _ even merging network and outputting the data in order
Figure GDA00023754572400000412
A minimum value; the fifth, sixth and seventh, eighth rows use Odd _ even merge network merge sort; the candidate paths sorted and output by the merging network still satisfy the formulas (3) and (4), can be written into a form of an ordered candidate path matrix, are deleted according to a deletion algorithm, are input into a subsequent simplified Odd _ even merging network for sorting again, and output results are output by a Bitonic half-cleaner and then L minimum values are output.
In practical application, in order to save resources to a greater extent, on the basis of the deletion algorithm provided by the invention, a sorting framework is designed, so that the sorting framework is compatible with sorting networks required by different types of nodes at the same time, and the sorting framework is obtained under the condition that M is 8 and L is more than or equal to 8 and comprises a pre-sorting module (presorter) and a deleted sorting Module (MSR).
Wherein the pre-ordering module (presorter) is configured to perform the following steps:
aiming at M paths which are expanded according to node types, firstly, two 2L input first-level sequences are ordered, and sequences are respectively ordered
Figure GDA00023754572400000413
And
Figure GDA00023754572400000414
sorting to obtain output
Figure GDA00023754572400000415
Figure GDA00023754572400000416
And
Figure GDA00023754572400000417
after the sorting, the input candidate path can satisfy the formula (3). Then on the basis of the above-mentioned
Figure GDA00023754572400000418
Performing secondary sorting through the Odd _ even sorting network, deleting part of candidate paths, and respectively outputting the most reliable paths
Figure GDA00023754572400000419
And the ordered candidate paths are used as the ith row of the ordered candidate paths to form a pruned ordered candidate path matrix, and the specific pruning method comprises the following steps:
1) the first row of the candidate path matrix
Figure GDA00023754572400000420
All reserve and remember
Figure GDA00023754572400000421
The second line is
Figure GDA00023754572400000422
The L/2 path candidates with smaller number are reserved, the other path candidates are deleted and recorded
Figure GDA00023754572400000423
2) The third row of the candidate path matrix
Figure GDA00023754572400000424
Reserve less
Figure GDA00023754572400000425
(lambda is an integer) candidate paths, and deleting and recording the rest of the candidate paths
Figure GDA0002375457240000051
(λ is an integer); the fourth line is
Figure GDA0002375457240000052
Only remain small
Figure GDA0002375457240000053
Deleting the other candidate paths and recording
Figure GDA0002375457240000054
3) The fifth row of the candidate path matrix
Figure GDA0002375457240000055
Only reserve
Figure GDA0002375457240000056
(lambda is an integer) candidate paths, and deleting and recording the rest of the candidate paths
Figure GDA0002375457240000057
(λ is an integer); the sixth line is
Figure GDA0002375457240000058
Only reserve
Figure GDA0002375457240000059
(lambda is an integer) candidate paths, and deleting and recording the rest of the candidate paths
Figure GDA00023754572400000510
(λ is an integer); in the seventh row
Figure GDA00023754572400000511
Only reserve
Figure GDA00023754572400000512
(λ is an integer) candidate paths, prune the remaining candidate paths,
Figure GDA00023754572400000513
(λ is an integer); in the eighth line
Figure GDA00023754572400000514
Only remain small
Figure GDA00023754572400000515
Deleting the other candidate paths and recording
Figure GDA00023754572400000516
The Odd _ even sorting network of the secondary sorting L input satisfies (1) and (2) by using CASU and sorting stage number (stage),
a post-pruning ranking Module (MSR) is configured to perform the steps of:
a. outputting a first row and a second row of an ordered candidate path matrix
Figure GDA00023754572400000517
Each data is input to the simplified Odd _ even merging network, and L minimum values are output.
b. Merging and sorting the output of the third row and the rest of the fourth row of the ordered candidate path matrix, wherein the output is not more than
Figure GDA00023754572400000518
A sequential minimum.
c. Merging and sorting the outputs of the rest part of the fifth row and the sixth row of the ordered candidate path matrix, and outputting
Figure GDA00023754572400000519
A sequential minimum.
d. Merging and sorting the outputs of the rest of the seventh row and the eighth row of the ordered candidate path matrix, and outputting
Figure GDA00023754572400000520
A sequential minimum.
e. And (c) inputting the data output by the step (a) and the step (b) into a simplified Odd _ even merging network for merging and sorting, and outputting L minimum values.
f. Inputting the data output by the step c and the step d into a simplified Odd _ even merging network for merging and sorting, and outputting only a smaller data
Figure GDA00023754572400000521
g. And e, inputting the data output in the step e and the step f into the HC network for Bitonic sorting and outputting L minimum values.
The invention has the beneficial effects that: compared with the non-deleted sorting algorithm, the method can effectively reduce the number of comparison units, thereby reducing the hardware use area and further saving corresponding hardware resources. The different ranking algorithms use CASU and stage data comparisons as shown in table 1, where the parity and Bitonic ranking columns are the resources used to rank all M x L candidate paths. When M is 8 and L is 16, the algorithm provided herein can reduce CASU by 57% and stage by 29% compared with the parity sorting algorithm, and can reduce CASU by 65% and stage by 29% compared with the Bitonic sorting algorithm.
TABLE 1
Figure GDA0002375457240000061
Drawings
FIG. 1 is a block diagram of the sequencing of REP type nodes in the present invention
FIG. 2 is a schematic diagram of the basic CASU function of the present invention
FIG. 3 is a sequencing network of REP type nodes in the present invention
Fig. 4 is a schematic diagram of the present invention with L-4 and M-4 being omitted
FIG. 5 is a block diagram of the ordering of the type of Rate-1 node in the present invention
FIG. 6 is a block diagram of the ordering of SPC node types in the present invention
FIG. 7 is a diagram of the sorter0 sorting network of FIG. 6
FIG. 8 is a diagram of an 8-input Odd _ even ranking network
FIG. 9 is a block diagram of an ordering scheme compatible with four node types
FIG. 10 is a sorter01, sorter02 pre-ordered network
Fig. 11 is an Odd _ even ranking network with L ═ 16 inputs
Fig. 12 shows the merging and sorting network of the 1 st and 2 nd rows after the deletion when L is 16
Fig. 13 shows the merging and sorting network of the 3 rd and 4 th rows after the deletion when L is 16
Fig. 14 shows the sorted network of the 5 th and 6 th rows after the deletion when L is 16
Fig. 15 shows the 7 th and 8 th row sorting networks after the deletion when L is 16
FIG. 16 is a merging and sorting network of the output data of FIGS. 12 and 13
FIG. 17 is a merging and sorting network of the output data of FIGS. 14 and 15
FIG. 18 is a sequencing network of the output data of FIGS. 16 and 17
Detailed Description
The sorting method according to different node types is concretely as follows:
rate-0 node
Since the path is not expanded by the Rate-0 node, the candidate path does not need to be selected, and the L paths are directly reserved to the next stage.
B.REP node
When two paths are expanded when a REP node is encountered, the expanded paths have 2L paths in total, and L paths need to be selected from the expanded paths. The sorting method uses Odd-even and Bitonic mixed sorting, namely the first half sorting uses two L-input Odd-even sorting networks to sort L candidate paths respectively to obtain two monotonous L sequences, then uses HC networks in the Bitonic sorting to select L minimum values, and the sorting block diagram is shown in FIG. 1. Taking L ═ 4 as an example, the detailed sorting network is shown in fig. 3, the sorting network is composed of three parts, namely, a comparator I (sorter1), a comparator II (sorter2) and a half-cleaner (HC), 4 minimum values are output, the comparator I (sorter1) and the comparator II (sorter2) are Odd-even sorting networks, and CASU and sorting stages (stage) used by the L-input Odd-even sorting network can be represented by expressions (1) and (2).
Figure GDA0002375457240000071
Figure GDA0002375457240000072
Rate-1 node
For the Rate-1 type node, the four paths extended by each node satisfy equation (3), which is first pre-ordered:
the mth path expanded by each path in the L paths reserved at the previous stage is sorted by an Odd-even sorting network, and is divided into four groups, which respectively correspond to the sorter1, the sorter2, the sorter3 and the sorter4 in fig. 5, and the mth path is divided into four groups, and uses CASU and stage such as CASU and stageAnd (3) respectively outputting L candidate paths meeting the requirement (4) by the formulas (1) and (2). It is worth noting that when L is<In M, all the candidate paths do not need to be pre-ordered, and only the candidate paths need to be pre-ordered
Figure GDA0002375457240000073
And
Figure GDA0002375457240000074
pre-sorting is performed, and the other four candidate paths do not belong to the minimum 2 candidate paths, so that the four candidate paths need not be considered, and M is equal to L:
Figure GDA0002375457240000075
Figure GDA0002375457240000076
wherein formula (3): l is more than or equal to 1 and less than or equal to L, M is more than or equal to 1 and less than or equal to M-1; formula (4): l is more than or equal to 1 and less than or equal to l-1, M is more than or equal to 1 and less than or equal to M
And then deleting candidate paths obtained by pre-sorting: writing the candidate paths into the form shown in fig. 4 refers to the matrix shown in fig. 4, which is composed of the candidate paths and has columns and rows satisfying (3) and (4), respectively, as an ordered candidate path matrix. Deleting the elements which do not need to be sorted according to a deleting method, which comprises the following specific steps: the first row of the ordered candidate path matrix
Figure GDA0002375457240000077
All candidate paths are retained and recorded
Figure GDA0002375457240000078
The second line is
Figure GDA0002375457240000079
The L/2 path candidates with smaller number are retained to delete the rest path candidates and record
Figure GDA00023754572400000710
The third line is
Figure GDA00023754572400000711
Reserve less
Figure GDA00023754572400000712
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure GDA00023754572400000713
(λ is an integer); the fourth line is
Figure GDA00023754572400000714
Only remain small
Figure GDA00023754572400000715
Deleting the rest of the candidate paths from the candidate path
Figure GDA00023754572400000716
In the ordered candidate path matrix ① shown in fig. 4, the deleted first part data is represented, the deleted second part data is represented by a block ②, and the deletion module is represented by a Pruned module in fig. 5;
the AL is expressed as the number of all candidate data,
Figure GDA0002375457240000081
the number of the remaining candidate paths in the ith row after the ordered candidate path matrix is pruned,
Figure GDA0002375457240000082
for the number of candidate paths remaining after deletion by the pruning algorithm,
AL＝M*L (5)
Figure GDA0002375457240000083
finally, the deleted residual candidate paths are sorted, and the first row and the second row are shared
Figure GDA0002375457240000084
Inputting the data into a simplified Odd-even merging network, corresponding to a sorter5 in FIG. 5, and outputting L minimum values; inputting the data of the third row and the fourth row into the simplified Odd _ even merging network and outputting the data which is monotonous
Figure GDA0002375457240000085
The smallest sequence, corresponding to sorter6 in fig. 5. And inputting the candidate paths sorted by the sorter5 and the sorter6 into an HC network in the Bitonic sorting, and outputting L minimum values.
SPC node
For SPC type nodes, the 8 paths each node extends satisfy equation (7):
Figure GDA0002375457240000086
and is
Figure GDA0002375457240000087
To satisfy the simplification conditions, it is first pre-ordered: first to each other
Figure GDA0002375457240000088
Sorting is performed as in fig. 7. Denoted sorter0 throughout the ranking network, as shown in fig. 6. Then, the mth path expanded by each path in the L paths reserved at the previous stage is sorted through the Odd _ even sorting network, which is represented as sorter 11-sorter 18. All data can meet the simplification conditions, namely the data can be written into the form of ordered candidate paths; the CASU and the stage used by the sorters 11-18 can be obtained from the formulas (1) and (2); if L is<M, when L is 4, can be deleted directly
Figure GDA0002375457240000089
And
Figure GDA00023754572400000810
when L is 1, 2, only need to be paired
Figure GDA00023754572400000811
And performing pre-sorting, wherein other data are not in the minimum L rows, and M is equal to L.
Writing the pre-ordered candidate paths into an ordered candidate path matrix form, and deleting paths which do not need to be ordered according to a deletion method, wherein the method specifically comprises the following steps: the first line is
Figure GDA00023754572400000812
All candidate paths are retained and recorded
Figure GDA00023754572400000813
The second line is
Figure GDA00023754572400000814
The L/2 path candidates with smaller number are retained to delete the rest path candidates and record
Figure GDA00023754572400000815
The third line is
Figure GDA00023754572400000816
Reserve less
Figure GDA00023754572400000817
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure GDA00023754572400000818
(λ is an integer); the fourth line is
Figure GDA00023754572400000819
Only remain small
Figure GDA00023754572400000820
Deleting the rest of the candidate paths from the candidate path
Figure GDA00023754572400000821
The fifth element is
Figure GDA00023754572400000822
Only reserve
Figure GDA00023754572400000823
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure GDA00023754572400000824
(λ is an integer); the sixth line is
Figure GDA0002375457240000091
Only reserve
Figure GDA0002375457240000092
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure GDA0002375457240000093
(λ is an integer); in the seventh row
Figure GDA0002375457240000094
Retention
Figure GDA0002375457240000095
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure GDA0002375457240000096
in the eighth line
Figure GDA0002375457240000097
Reserve less
Figure GDA0002375457240000098
Deleting the rest of the candidate paths from the candidate path
Figure GDA0002375457240000099
And then sorting the deleted residual candidate paths: merging and sorting the rest paths of the ordered candidate path matrix, wherein the first row and the second row are shared
Figure GDA00023754572400000910
Inputting the data into a simplified Odd _ even merging network, corresponding to a sorter21 in FIG. 6, and outputting L minimum values; inputting the rest data of the third row and the fourth row into the simplified Odd _ even merging network and outputting the data in order
Figure GDA00023754572400000911
A minimum value, corresponding to sorter22 in fig. 6; the merging networks used in the fifth line, the sixth line, the seventh line and the eight line respectively correspond to the sorter23 and the sorter 24; the candidate paths sorted and output by the sorter2i (i is more than or equal to 1 and less than or equal to 4) still satisfy the formulas (3) and (4), can be written into the form of an ordered candidate path matrix, are deleted according to a deletion algorithm, and are input into a subsequent simplified Odd _ even merging network, namely the sorter31 and the sorter32 respectively, and the sorting methods of the sorter21 and the sorter22 are completely the same. The outputs of sorters 31 and 32 are then passed through a Bitonic sorted half cleaner HC to output L minimum values.
The above is a simple description of the sorting architecture of different node types, the number of the extension paths of different nodes is shown in table 2, and the comparison between the number of different node types needing sorting after being deleted from the network and the total number of data before deletion is shown in table 3.
TABLE 2
Figure GDA00023754572400000912
TABLE 3
Figure GDA00023754572400000913
In practical applications, in order to save resources to a greater extent, on the basis of the deletion algorithm provided by the present invention, a sorting architecture is designed to be compatible with the sorting networks required by different types of nodes, and the overall architecture is as shown in fig. 9, and includes a pre-sorting module (presorter) and a deleted sorting Module (MSR). The compatible structure provided by the present invention is obtained under the condition that L is greater than or equal to 8, and when L is 2,4, it is known that all candidate paths do not need to be pre-sorted according to the sorting method of SPC and Rate-1 type nodes, so that the number of CASU used is correspondingly reduced, which is not described in detail, and the sorting structure thereof is analyzed in detail below.
The pre-ordering module (presorter) is used for executing the following steps:
firstly, for M paths which are expanded according to node types, two 2L input first-level sequences are respectively expanded for each node corresponding to sorters 01 and 02 in FIG. 9
Figure GDA0002375457240000101
To correspond to
Figure GDA0002375457240000102
And
Figure GDA0002375457240000103
to correspond to
Figure GDA0002375457240000104
And (4) sorting, wherein after primary sorting, the input candidate path can satisfy the formula (3). Then, on the basis, the M-th (M is more than or equal to 1 and less than or equal to M) path expanded by each path in the L paths reserved at the previous stage is subjected to secondary sorting through an Odd _ even sorting network, and corresponding to sorter1i in FIG. 9, the most reliable candidate paths are respectively output by deleting part of candidate paths
Figure GDA0002375457240000105
And (3) forming a pruned ordered candidate path matrix by taking the ordered candidate paths as the ith row of the ordered candidate paths, wherein i is more than or equal to 1 and less than or equal to 8, the sorter1i satisfies (1) and (2) by using resources, and when L is 8, the sorter1i sorts the network as shown in fig. 8. The method for pruning the ordered candidate path matrix specifically comprises the following steps:
1) the first row of the candidate path matrix
Figure GDA0002375457240000106
All reserve and remember
Figure GDA0002375457240000107
The second line is
Figure GDA0002375457240000108
The L/2 path candidates with smaller number are reserved, the other path candidates are deleted and recorded
Figure GDA0002375457240000109
2) The third row of the candidate path matrix
Figure GDA00023754572400001010
Reserve less
Figure GDA00023754572400001011
(lambda is an integer) candidate paths, and deleting and recording the rest of the candidate paths
Figure GDA00023754572400001012
(λ is an integer); the fourth line is
Figure GDA00023754572400001013
Only remain small
Figure GDA00023754572400001014
Deleting the other candidate paths and recording
Figure GDA00023754572400001015
3) The fifth row of the candidate path matrix
Figure GDA00023754572400001016
Only reserve
Figure GDA00023754572400001017
(lambda is an integer) candidate paths, and deleting and recording the rest of the candidate paths
Figure GDA00023754572400001018
(λ is an integer); the sixth line is
Figure GDA00023754572400001019
Only reserve
Figure GDA00023754572400001020
(lambda is an integer) candidate paths, and deleting and recording the rest of the candidate paths
Figure GDA00023754572400001021
(λ is an integer); in the seventh row
Figure GDA00023754572400001022
Only reserve
Figure GDA00023754572400001023
(λ is an integer) candidate paths, prune the remaining candidate paths,
Figure GDA00023754572400001024
(λ is an integer); in the eighth line
Figure GDA00023754572400001025
Only remain small
Figure GDA00023754572400001026
Deleting the other candidate paths and recording
Figure GDA00023754572400001027
A post-pruning ranking Module (MSR) is configured to perform the steps of:
the ordered candidate path matrix after the deletion can be obtained through the steps, the candidate path after the deletion is input into the MSR module, and L minimum values are finally output, wherein the MSR module comprises the following steps:
a. the first row and the second row of the ordered candidate path matrix, namely the sorters 11 and 12 are output together
Figure GDA00023754572400001028
Each data is input to a simplified Odd _ even merging network, corresponding to the sorter21 network in fig. 9, and L minimum values are output.
b. Sorting the outputs of sorters 13, 14 for the remaining third and fourth rows of the ordered candidate path matrixAnd sorting, outputting no more than
Figure GDA00023754572400001029
The ordered minimum, corresponding to the sorter22 network in fig. 9.
c. Merging and sorting the outputs of the remaining parts of the fifth row and the sixth row of the ordered candidate path matrix, namely sorter15 and sorter16, and outputting
Figure GDA00023754572400001030
The ordered minimum, corresponding to the sorter23 network in fig. 9.
d. Merging and sorting the outputs of the seventh row and the residual parts of the eighth row of the ordered candidate path matrix, namely sorter17 and sorter18, and outputting
Figure GDA0002375457240000111
The ordered minimum, corresponding to the sorter24 network in fig. 9.
Note that: a. b, c and d sequencing data have no dependency relationship and can be executed in parallel, the output of the sorter2i can be written into the form of an ordered candidate path matrix, redundant candidate paths are deleted continuously according to the deletion method provided by the invention, or the sorter2i directly outputs
Figure GDA0002375457240000112
A sequential minimum.
e. The sorters 21 and 22 output together
Figure GDA0002375457240000113
Each data is input to a simplified Odd _ even merging network, corresponding to the sorter31 network in fig. 9, and L minimum values are output.
f. The outputs of the sorters 23 and 24 are input into the simplified Odd _ even merging network, and only a small output is needed
Figure GDA0002375457240000114
Corresponding to the sorter32 network in fig. 9.
Note that: e. the f sorting data has no dependency relationship and can be executed in parallel.
g. And the outputs of the sorters 31 and 32 are input into the HC network bitonic ordering and output L minimum values.
It is noted that sorters 1i-sorter3i in the sorting network all evolve on the basis of the Odd _ even sorting algorithm, and only the HC network used by the last stage is from the Bitonic sorting algorithm. The compatible sorting architecture may input all M × L candidate paths when M is 8, and when M is 8<When the pressure is higher than 8 times, the pressure is lower than the reference pressure,
Figure GDA0002375457240000115
the input ports have (8-M) × L input supplementary max values, and max is the maximum value which can be input. The sequencing network using stage provided by the invention consists of two parts of pre-sequencing and deletion-and-post-sequencing
Figure GDA0002375457240000116
And
Figure GDA0002375457240000117
the stages used for pre-sorting and post-deletion sorting are represented by equations (8) and (9), respectively.
Figure GDA0002375457240000118
Figure GDA0002375457240000119
The working principle is as follows: all sequencing networks of the invention are composed of one or more CASUs (coherent access units), as shown in FIG. 2, the inputs of the CASUs are in1 and in2 on the left side, the right side is output, and the data is large downlink and small uplink. The output of the previous stage in the sequencing framework is used as the input of the next stage and is connected with the input of the next stage by a wire.
In order to make the objects, technical solutions and advantages of the present invention more clear, the following takes L ═ 16 as an example to describe in detail the sequencing method proposed by the present invention with reference to the accompanying drawings and specific examples:
step one, pre-sequencing:
the input is two 2L input first-level sorting networks, corresponding to sorter01 and sorter01 in FIG. 9, the sorting networks are respectively shown in FIGS. 10(a) and (b), the output elements respectively satisfy W01_2i-1 ≤ W01_2i, and W02_2i-1 ≤ W02_2 i. Each network needs 16 CASUs, and stage is 1;
sequencing the mth path expanded by each path in the L paths reserved at the previous stage through an Odd _ even sequencing network, corresponding to sorter1i in fig. 9, where the sequencing network is as shown in fig. 11, each path needs 63 CASUs, and stage is 10, and the calculation method satisfies equations (1) and (2). The input of the Sorter11 is W01_2i-1 output by the Sorter01, and the input of the Sorter12 is W01_2i output by the Sorter 01; the input to Sorter13 is
Figure GDA0002375457240000121
The input of the Sorter14 is W02_2i-1 output by the Sorter02, the input of the Sorter15 is W01_2i output by the Sorter02, and the inputs of the Sorter16 to the Sorter18 are respectively
Figure GDA0002375457240000122
Figure GDA0002375457240000123
Each network input is all 16 paths, and according to the deletion algorithm, the network corresponding to the sorter1i deletes part of candidate paths and respectively outputs the most reliable paths
Figure GDA0002375457240000124
Forming a pruned ordered candidate path matrix by ordered candidate paths, and recording the output as W1i _ j, wherein i is more than or equal to 1 and less than or equal to 8,
Figure GDA0002375457240000125
the second step is that: sorting after deletion:
A1. the sorting network shown in fig. 12 corresponds to the sorter21 network in fig. 9, the left inputs are the outputs of sorter11 and sorter12, the sorting method is to simplify Odd _ even merging sorting network, the solid circles in fig. 12 are CASUs actually used, and the open circles represent deletable CASUs;
B1. the sorting network shown in fig. 13 corresponds to the sorter22 network in fig. 9, the left inputs are the outputs of the sorter13 and the sorter14, the sorting method is to simplify the Odd _ even merging sorting network, total 8 CASUs, stage is 3, and the open circles indicate deletable CASUs;
C1. the sorting network shown in fig. 14 corresponds to the sorter23 network in fig. 9, the left inputs are the outputs of the sorter15 and the sorter16, the sorting method is to simplify the Odd _ even merging sorting network, 3 CASUs are used, the stage is 2, and the open circles indicate deletable CASUs;
D1. the sorting network shown in fig. 15 corresponds to the sorter24 network in fig. 9, the left inputs are the outputs of the sorter17 and the sorter18, the sorting method is to simplify the Odd _ even merging sorting network, 1 CASU is provided, stage is 1, and the open circles indicate deletable CASUs, which satisfy the equations (15) and (16);
since A1, B1, C1 and D1 have no dependency relationship in the ordering data, the data are executed in parallel, and the stage is the most used item, namely the stage
Stage used in A1 was 4, for a total of 44 CASUs.
E1. Fig. 16 shows that the sorting network is the sorter31 network in fig. 9, and the left inputs are the outputs of sorter21 and sorter22 in fig. 9, that is, the outputs of the merging networks in fig. 12 and 13, which are sorted and output smaller 16 ordered values, which totally require 32 CASUs, and have 4 stages;
F1. fig. 17 shows that the sorting network is the sorter32 network in fig. 9, the left inputs are the outputs of sorter23 and sorter24 in fig. 9, that is, the outputs of the merging networks in fig. 14 and 15, sorting the outputs and outputting 8 ordered values, which require 8 CASUs in total, and stage is 3;
the data in E1 and F1 have no dependency relationship, and can be executed in parallel, and the maximum stage is used, namely stage is 4, and CASU is the sum of the two, and the total number of the two is 40 CASUs.
G1. The sorting network shown in fig. 18 is the HC network in fig. 9, and the left inputs are the outputs of sorter31 and sorter32 in fig. 9, that is, the outputs of the merging networks in fig. 16 and 17, which are sorted and output smaller L-16 sorted values. A total of 8 CASUs, 1 stage are required.
Outputting 16 minimum values through the sequencing of A1-G1, using 92 CASU, taking the maximum value in each step by stage, and 9 stages in total; while the undeleted Odd even ranking network uses 207 CASUs. The sequencing network uses 628 CASUs in total and has 20 sequencing stages, while the Odd _ even sequencing network without deletion uses 727 CASUs in total and has 23 sequencing stages; compared with the undeleted sequencing network, the deleted sequencing network not only reduces the CASU, but also reduces the CASU stage.

Claims (2)

1. A rapid ordering method for a polar code is disclosed, which specifically comprises the following steps according to the ordering method adopted by different node types in a rapid simplified serial offset list algorithm:
rate-0 node
Directly reserving the L paths to the next stage;
B.REP node
Each REP node expands two paths, 2L paths are shared after expansion, and L paths need to be selected from the extended paths; the ordering method uses odd-even ordering and double-tone mixed ordering, namely the first half ordering uses two L-input odd-even ordering networks to respectively order L candidate paths to obtain two monotonous L sequences, then L minimum values are selected by using a half cleaner network in the double-tone ordering, and the CASU and the ordering series used by the L-input odd-even ordering network can be represented by formulas (1) and (2);
Figure FDA0002408263190000011
Figure FDA0002408263190000012
wherein
Figure FDA0002408263190000013
Representing the number of CASUs used by the parity-ordered network for the L input,
Figure FDA0002408263190000014
representing the sorting progression used by the parity sorting network of the L input;
rate-1 node
For the Rate-1 type nodes, the four paths extended by each node satisfy equation (3),
1) it is first pre-ordered: the mth path expanded by each path in the L paths reserved at the previous stage is sorted into four groups by an odd-even sorting network, the mth path is sorted by a comparator I, a comparator II, a comparator III and a comparator IV respectively, the mth path is sorted by using CASU and sorting progression formula (1) and (2), L candidate paths meeting the requirement (4) are output respectively,
it is worth noting that when L is<In M, all the candidate paths do not need to be pre-ordered, and only the candidate paths need to be pre-ordered
Figure FDA0002408263190000015
And
Figure FDA0002408263190000016
pre-sorting is performed, and the other four candidate paths do not belong to the two smallest candidate paths, so that the two smallest candidate paths do not need to be considered, and M is equal to L:
Figure FDA0002408263190000017
Figure FDA0002408263190000018
wherein the content of the first and second substances,
Figure FDA0002408263190000019
the mth path representing the expansion of the mth node; formula (3): l is more than or equal to 1 and less than or equal to L, M is more than or equal to 1 and less than or equal to M-1; formula (4): l is more than or equal to 1 and less than or equal to L-1, M is more than or equal to 1 and less than or equal to M, and M is the number of paths expanded by each node;
2) and then deleting candidate paths obtained by pre-sorting: writing the candidate path into an ordered candidate path matrix of a matrix which consists of the candidate paths and satisfies (3) and (4) in columns and rows respectively; deleting paths which do not need to be sorted according to a deleting method, which comprises the following specific steps: the first line is
Figure FDA00024082631900000110
Reserve allPartial candidate route, memory
Figure FDA00024082631900000111
The second line is
Figure FDA00024082631900000112
The L/2 path candidates with smaller number are retained to delete the rest path candidates and record
Figure FDA00024082631900000113
The third line is
Figure FDA00024082631900000114
Reserve less
Figure FDA00024082631900000115
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure FDA00024082631900000116
(λ is an integer); the fourth line is
Figure FDA00024082631900000117
Only remain small
Figure FDA00024082631900000118
Deleting the rest of the candidate paths from the candidate path
Figure FDA00024082631900000119
Note ALThe number of the total candidate paths is,
Figure FDA0002408263190000021
the number of the remaining candidate paths in the ith row after the ordered candidate path matrix is pruned,
Figure FDA0002408263190000022
after being deleted by a deletion algorithmThe number of remaining candidate paths is
AL＝M*L (5)
Figure FDA0002408263190000023
3) And finally, sequencing the deleted residual candidate paths: the first row and the second row are shared
Figure FDA0002408263190000024
Inputting the data into a simplified Odd-even merging network, and outputting L minimum values after the data are sequenced by a comparator V; inputting the rest data of the third row and the fourth row into another simplified Odd _ even merging network, and outputting monotonous data after being sorted by a comparator VI
Figure FDA0002408263190000025
A minimum sequence; inputting the candidate paths sequenced by the comparator V and the comparator VI into a semi-cleaner network, and outputting L minimum values;
SPC node
For SPC type nodes, the 8 paths each node extends satisfy equation (7):
Figure FDA0002408263190000026
and is
Figure FDA0002408263190000027
1) It first needs to be pre-ordered: first to each other
Figure FDA0002408263190000028
Sorting is carried out; then, sequencing the mth path expanded by each path in the L paths reserved at the previous stage through an odd-even sequencing network; all data can meet the simplification conditions, namely the data can be written into the form of an ordered candidate path matrix; CASU and sorting used by parity sorting networks can be of the following formulas(1) And (2) obtaining;
if the search width L is smaller than the path number M of the node expansion; the method comprises the following steps: when L is 4, it can be deleted directly
Figure FDA0002408263190000029
And
Figure FDA00024082631900000210
when L is 1 or 2, it is only necessary to
Figure FDA00024082631900000211
Pre-sorting, wherein other data are not in the minimum L rows, and M is equal to L;
2) and then deleting candidate paths obtained by pre-sorting: writing the candidate path into an ordered candidate path matrix of a matrix which consists of the candidate paths and satisfies (3) and (4) in columns and rows respectively; deleting paths which do not need to be sorted according to a deleting method, which comprises the following specific steps: the first row of the ordered candidate path matrix
Figure FDA00024082631900000212
All candidate paths are retained and recorded
Figure FDA00024082631900000213
The second line is
Figure FDA00024082631900000214
The L/2 path candidates with smaller number are retained to delete the rest path candidates and record
Figure FDA00024082631900000215
The third line is
Figure FDA00024082631900000216
Reserve less
Figure FDA00024082631900000217
(lambda is an integer) candidate paths delete remaining candidate pathsRadial and radical memory
Figure FDA00024082631900000218
(λ is an integer); the fourth line is
Figure FDA00024082631900000219
Only remain small
Figure FDA00024082631900000220
Deleting the rest of the candidate paths from the candidate path
Figure FDA00024082631900000221
The fifth element is
Figure FDA00024082631900000222
Only reserve
Figure FDA00024082631900000223
Figure FDA00024082631900000224
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure FDA00024082631900000225
(λ is an integer); the sixth line is
Figure FDA00024082631900000226
Only reserve
Figure FDA00024082631900000227
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure FDA0002408263190000031
(λ is an integer); in the seventh row
Figure FDA0002408263190000032
Retention
Figure FDA0002408263190000033
(lambda is an integer) candidate paths delete the remaining candidate paths, and
Figure FDA0002408263190000034
in the eighth line
Figure FDA0002408263190000035
Reserve less
Figure FDA0002408263190000036
Deleting the rest of the candidate paths from the candidate path
Figure FDA0002408263190000037
Note ALThe number of the total candidate paths is,
Figure FDA0002408263190000038
the number of the remaining candidate paths in the ith row after the ordered candidate path matrix is pruned,
Figure FDA0002408263190000039
for the number of candidate paths remaining after deletion by the pruning algorithm,
AL＝M*L (5)
Figure FDA00024082631900000310
3) and then sorting the deleted residual candidate paths: merging and sorting the rest paths of the ordered candidate path matrix, wherein the first row and the second row are shared
Figure FDA00024082631900000311
Inputting the data into a simplified odd-even merging network, and outputting L minimum values; inputting the remaining data of the third and fourth rows to the reduced parityParallel network, output ordered
Figure FDA00024082631900000312
A minimum value; the fifth line, the sixth line and the seventh line and the eight lines are merged and sorted by using a merging network; the candidate paths sorted and output by the merging network still satisfy the formulas (3) and (4), can be written into a form of an ordered candidate path matrix, are deleted according to a deletion algorithm, are input into a subsequent simplified odd-even merging network for sorting again, and output results are sorted by a half-cleaner and then output L minimum values.
2. An apparatus for implementing the method for fast sequencing for polar codes according to claim 1, wherein the sequencing network compatible with different node types comprises a pre-sequencing module and a post-puncturing sequencing module;
wherein, the pre-ordering module is used for executing the following steps:
for M paths which are expanded according to node types, firstly, two 2L input first-level sequences are arranged, and each node is expanded
Figure FDA00024082631900000313
To correspond to
Figure FDA00024082631900000314
And
Figure FDA00024082631900000315
to correspond to
Figure FDA00024082631900000316
Sorting is carried out, and after primary sorting, the input candidate path can satisfy the formula (3); then, on the basis, the M (M is more than or equal to 1 and less than or equal to M) th path expanded by each path in the L paths reserved at the previous stage is subjected to secondary sorting through a parity sorting network, and meanwhile, the most reliable paths are respectively output by deleting part of candidate paths
Figure FDA00024082631900000317
Forming a pruned ordered candidate path matrix by taking the ordered candidate paths as the ith row of the ordered candidate path matrix; the specific method for deleting the candidate paths is as follows:
1) the first row of the candidate path matrix
Figure FDA00024082631900000318
All reserve and remember
Figure FDA00024082631900000319
The second line is
Figure FDA00024082631900000320
The L/2 path candidates with smaller number are reserved, the other path candidates are deleted and recorded
Figure FDA00024082631900000321
2) The third row of the candidate path matrix
Figure FDA00024082631900000322
Reserve less
Figure FDA00024082631900000323
(lambda is an integer) candidate paths, and deleting and recording the rest of the candidate paths
Figure FDA00024082631900000324
(λ is an integer); the fourth line is
Figure FDA00024082631900000325
Only remain small
Figure FDA00024082631900000326
Deleting the other candidate paths and recording
Figure FDA0002408263190000041
3) The fifth row of the candidate path matrix
Figure FDA0002408263190000042
Only reserve
Figure FDA0002408263190000043
(lambda is an integer) candidate paths, and deleting and recording the rest of the candidate paths
Figure FDA0002408263190000044
(λ is an integer); the sixth line is
Figure FDA0002408263190000045
Only reserve
Figure FDA0002408263190000046
(lambda is an integer) candidate paths, and deleting and recording the rest of the candidate paths
Figure FDA0002408263190000047
(λ is an integer); in the seventh row
Figure FDA0002408263190000048
Only reserve
Figure FDA0002408263190000049
(λ is an integer) candidate paths, prune the remaining candidate paths,
Figure FDA00024082631900000410
(λ is an integer); in the eighth line
Figure FDA00024082631900000411
Only remain small
Figure FDA00024082631900000412
Deleting the other candidate paths and recording
Figure FDA00024082631900000413
The parity sorting network of the L input uses CASU and the sorting order number satisfies (1) and (2),
the post-pruning sorting module is used for executing the following steps:
a. outputting a first row and a second row of an ordered candidate path matrix
Figure FDA00024082631900000414
Inputting the data into a simplified odd-even merging network for merging and sorting, and outputting L minimum values;
b. inputting the output of the third row and the rest of the fourth row of the ordered candidate path matrix into the simplified odd-even merging network for merging and sorting, and outputting the output not more than
Figure FDA00024082631900000415
A number of ordered minima;
c. the outputs of the rest parts of the fifth row and the sixth row of the ordered candidate path matrix are input into the simplified odd-even merging network for merging and sorting, and the output
Figure FDA00024082631900000416
A number of ordered minima;
d. the outputs of the rest parts of the seventh row and the eighth row of the ordered candidate path matrix are input into the simplified odd-even merging network for merging and sorting, and the output
Figure FDA00024082631900000417
A number of ordered minima;
e. inputting the data output in the step a and the step b into a simplified odd-even merging network for merging and sequencing, and outputting L minimum values;
f. inputting the data output in the step c and the step d into a simplified odd-even merging network for merging and sorting, and outputting only a small quantity
Figure FDA00024082631900000418
g. And e, inputting the data output in the step e and the step f into the half-cleaner network and outputting L minimum values to finish the sequencing.
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