CN107666325B - Polar code decoding path selection method based on list continuous deletion algorithm - Google Patents

Polar code decoding path selection method based on list continuous deletion algorithm Download PDF

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CN107666325B
CN107666325B CN201710854876.6A CN201710854876A CN107666325B CN 107666325 B CN107666325 B CN 107666325B CN 201710854876 A CN201710854876 A CN 201710854876A CN 107666325 B CN107666325 B CN 107666325B
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陈治宇
林军
王中风
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Nanjing University
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Abstract

The invention provides a polar code decoding path selection method based on a list continuous deletion algorithm, which comprises the following steps: expressing the target polarization code by a binary tree, traversing the binary tree by a decoder until a special node on the binary tree is found, performing decoding judgment on a bit associated under the current special node, and performing decoding path expansion according to a judgment result; the method comprises the steps of carrying out hard judgment on soft information vectors received by any original path in a decoding list of a current special node to obtain a binary reference list, calculating the Hamming distance between a list formed by the jth original path in alternative paths and the reference list, screening the alternative paths of each original decoding path by adopting a Hamming distance filter, and finding out L decoding paths from the remaining alternative paths screened by the Hamming distance filter, so that the sorting space during decoding path selection at the special node can be effectively reduced, the selection efficiency of the decoding paths is improved, the decoding efficiency and the decoding speed of the polarization code are improved, and the decoding accuracy can be effectively guaranteed.

Description

Polar code decoding path selection method based on list continuous deletion algorithm
Technical Field
The invention relates to a method for selecting a polar code decoding path, in particular to a method for selecting a polar code decoding path based on a list continuous deletion algorithm.
Background
The polar code is a linear block code, and is a novel encoding mode, when decoding the polar code, the traditional algorithm generally adopts a continuous deletion algorithm (SC algorithm for short), because of the disadvantages of large time delay and small throughput of the algorithm, a list continuous deletion algorithm (SCL algorithm for short) is also provided, but when decoding the SCL algorithm, two possibilities of the same bit are considered, so that the decoding efficiency is still low, and the speed is slow, therefore, people improve the SCL algorithm to form an improved SCL algorithm, but in the improved SCL algorithm, when selecting the coding and decoding paths of two special nodes, namely rate-1 and rate-R, a very large sequencing space is needed, and the decoding efficiency and the speed of the polar code cannot be improved.
Therefore, a new method for selecting a polarization code path is needed to be provided, which can effectively reduce the sorting space during the selection of the decoding path at a special node, thereby improving the selection efficiency of the decoding path, further improving the decoding efficiency and speed of the polarization code, and effectively ensuring the accuracy of decoding.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a method for selecting a decoding path of a polar code based on a list continuous deletion algorithm, which can effectively reduce a sorting space during selecting the decoding path at a special node, thereby improving the selection efficiency of the decoding path, further improving the decoding efficiency and speed of the polar code, and effectively ensuring the accuracy of decoding.
The invention provides a polar code decoding path selection method based on a list continuous deletion algorithm, which comprises the following steps:
s1, representing a target polarization code by using a binary tree, traversing the binary tree by a decoder until a special node on the binary tree is found, stopping continuously traversing the binary tree downwards on the special node, performing decoding judgment on a bit associated under the current special node, and performing decoding path expansion according to a judgment result;
s2, decoding path expansion: splitting each original path of a decoded list in a list prune algorithm to 2kAlternative paths, whereby the entire coding list has L x 2kA path, wherein k is the number of information bits of the special node, and L is the capacity of the decoding list;
s3, carrying out hard decision on the soft information vector alpha received by any original path in the decoding list of the current special node to obtain a binary reference list, and calculating 2kHamming distance D between list formed by jth strip in strip alternative path and reference listjWherein, in the step (A),
Figure GDA0001524883550000021
m is the length of the special node;
s4, screening the alternative paths of each original decoding path by adopting a Hamming distance filter, and then finding out L decoding paths from the remaining alternative paths screened by the Hamming distance filter.
Further, the special nodes include node rate-0, node rate-1, and node rate-R.
Further, the decoding decision method of the associated bits under the current special node is as follows:
when the special node is a node rate-0, all bits of the node are directly set as 0;
if the special node is not the node rate-0, the process proceeds to the decoding path extension of step S2.
Further, in step S3, a hard decision is made according to:
Figure GDA0001524883550000022
wherein the content of the first and second substances,
Figure GDA0001524883550000023
for reference list, i ═ 0,1, …, m-1.
Further, in step S4, L decoding paths are screened out from the candidate paths by the following method:
calculating the number of alternative paths left by each original path after being screened by a Hamming distance filter, and recording the number as cnt [ l ];
if the cnt [ L ] is less than or equal to the capacity L of the decoding list, taking the remaining alternative paths under the current original path after being screened by the Hamming distance filter as the decoding paths to be used;
if cnt [ l]Greater than the capacity L of the decoding list, the path metric p of the remaining alternative paths after filtering through the Hamming distance filterjSorting the sizes and selecting L path metrics pjThe minimum alternative path is used as a standby decoding path;
path metric p of all to-be-decoded pathsjAnd sorting the L paths according to the size, and selecting the standby decoding path with the minimum path metric value as a final decoding path.
Further, the Hamming distance D of the alternative pathjThe set threshold value T is in the range of
Figure GDA0001524883550000031
The invention has the beneficial effects that: the invention can effectively reduce the sequencing space during the selection of the decoding path at the special node, thereby improving the selection efficiency of the decoding path, further improving the decoding efficiency and speed of the polarization code, and effectively ensuring the accuracy of decoding.
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The invention is further described below with reference to the following figures and examples:
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a diagram illustrating simulation results of the polarization code (1024,512) of the present invention using the conventional method and the present method.
Fig. 3 is a diagram illustrating simulation results of the polarization code (8192,4096) of the present invention using the conventional method and the present method.
Fig. 4 is a diagram illustrating simulation results of the polarization code (32768,29504) of the present invention using the conventional method and the present method.
Detailed Description
The invention is described in further detail below with reference to the drawings, in which:
the invention provides a polar code decoding path selection method based on a list continuous deletion algorithm, which comprises the following steps:
s1, representing a target polarization code by using a binary tree, traversing the binary tree by a decoder until a special node on the binary tree is found, stopping continuously traversing the binary tree downwards on the special node, performing decoding judgment on a bit associated under the current special node, and performing decoding path expansion according to a judgment result; the polarization code of the binary tree is represented as follows: p (N, K), wherein N represents the length of the polarization code, and K represents the information bit of the polarization code; such as (1024,512), (8192,4096), (32768,29504), etc. in the present embodiment; the special nodes comprise a node rate-0, a node rate-1 and a node rate-R, and specifically: node rate-0 means that all leaf nodes under that node are frozen bits; node rate-1 means that all leaf nodes under this node are information bits; the node rate-R means that the leaf node under the node has both frozen bits and information bits.
The decoding decision method of the associated bit under the current special node is as follows:
when the special node is a node rate-0, all bits of the node are directly translated into 0;
if the special node is not the node rate-0, the process proceeds to the decoding path extension of step S2.
S2, decoding path expansion: splitting each original path of a decoded list in a list prune algorithm to 2kAlternative paths, whereby the entire coding list has L x 2kA path, wherein k is the number of information bits of the special node, and L is the capacity of a decoding list in an SCL algorithm;
s3, carrying out hard decision on the soft information vector alpha received by any original path in the decoding list of the current special node to obtain a binary reference list, and calculating 2kHamming distance D between list formed by jth strip in strip alternative path and reference listjWherein, in the step (A),
Figure GDA0001524883550000041
m is the length of the special node; wherein the hard decision is made according to:
Figure GDA0001524883550000042
wherein the content of the first and second substances,
Figure GDA0001524883550000051
for reference list, i ═ 0,1, …, m-1.
S4, screening alternative paths of each original decoding path by adopting a Hamming distance filter, and then finding out L decoding paths from the remaining alternative paths screened by the Hamming distance filter; specifically, the method comprises the following steps:
hamming distance filter screening is realized by the following method:
computing alternative path metrics pjAnd the Hamming distance D of the alternative path to the reference listj：
Wherein p isjThe initial value of the path metric of the jth alternative path in the alternative paths is the path metric PM of the original path; djThe initial value is 0, and j represents the jth alternative path;
when in use
Figure GDA0001524883550000052
When the temperature of the water is higher than the set temperature,
Figure GDA0001524883550000053
and is
Figure GDA0001524883550000054
When in use
Figure GDA0001524883550000055
When the temperature of the water is higher than the set temperature,
Figure GDA0001524883550000056
and is
Figure GDA0001524883550000057
In this formula, pjP only if the alternative path is different from a bit of the reference codingjIs increased by an amount of
Figure GDA0001524883550000058
Thus, a Hamming distance D resultsjThen 1 will be added; when the Hamming distance D of the alternative pathjWhen the value is 0, the alternative path can be directly marked as a reliable path;
in the alternative paths, if any path has a Hamming distance DjIf the value is larger than the set threshold value T, directly abandoning the current alternative path;
wherein the content of the first and second substances,
Figure GDA0001524883550000059
the influence of Hamming distance is fully considered in the screening for the binary value of the ith bit of the jth alternative path, so that the accuracy of the final path selection can be effectively ensured, and the accuracy of decoding is ensured;
wherein, screening out L decoding paths from the alternative paths by the following method:
calculating the number of alternative paths left by each original path after being screened by a Hamming distance filter, and recording the number as cnt [ l ];
if the cnt [ L ] is less than or equal to the capacity L of the decoding list, taking the remaining alternative paths under the current original path after being screened by the Hamming distance filter as the decoding paths to be used;
if cnt [ l]Greater than the capacity L of the decoding list, the path metric p of the remaining alternative paths after filtering through the Hamming distance filterjSorting the sizes and selecting L path metrics pjThe minimum alternative path is used as a standby decoding path; after the above-mentioned processing, the total number of the decoding paths to be used is Σ cnt [ l [ ]]Then, in the next ordering, it is the sum of ∑ cnt [ l ] that will be sorted]Sorting the path metric values of the decoding paths to be used;
path metric p of all to-be-decoded pathsjSorting according to size, and selecting L standby decoding paths with the minimum path metric value as final decoding paths; by the method, the sequencing space during the selection of the decoding path at the special node can be effectively reduced, so that the selection efficiency of the decoding path is improved, the decoding efficiency and speed of the polar code are improved, and the decoding accuracy can be effectively ensured.
In this embodiment, the hamming distance D of the alternative pathjThe set threshold value T is in the range of
Figure GDA0001524883550000061
Preferably: hamming distance D of alternative pathjSet threshold value T of
Figure GDA0001524883550000062
If D of an alternative pathjGreater than a predetermined threshold T, which means p for this pathjThe probability of a large value is higher, and pjThe larger the value the more unreliable the path; by comparing the Hamming distance of the alternative path with a set threshold T, a part of unreliable decoding paths are directly rejected, so that guarantee is further provided for reducing the sequencing space, the efficiency is improved for selecting the decoding paths, and the decoding efficiency is further improved;
and T is selected. If Tselect is too small, then too many alternative paths are dropped, which may increase the bit error rate. If Tselect is too large, then the alternate paths are hardly filtered and the decoder efficiency improvement is insignificant, therefore, when the value of T is chosen to be too large
Figure GDA0001524883550000063
And meanwhile, the error rate can be ensured, and the accuracy of alternative path extraction can be ensured.
In a specific experiment, in the decoding using (8192,4096) polar code, the relationship between the block error rate (FER) and the signal-to-noise ratio (SNR) of the decoding result is shown in fig. 2-4, in which HDF-L4-T4 represents that the hamming distance filter is used, the capacity of the decoding list is 4, and the hamming distance D of the set alternative path is 4jThe set threshold value of (4) is a decoding result simulation diagram; SCL-L4 represents a decoding result simulation diagram with the capacity of 4 in the decoding list under the traditional way selection method, and as can be seen from the diagram, under the condition that the node length is 8, the threshold T is reasonably selected and set, under the condition that the path selection efficiency can be effectively improved, in a relation curve of block error rate (FER) and signal-to-noise ratio (SNR), HDF-L4-T4 and SCL-L4 are basically overlapped, and the decoding accuracy is ensured.
And then carrying out quantitative analysis: in the experiment, when the node length of a special node is 8 and the threshold T is set to be 4, the proportion of the filtered paths before the sorting is as follows:
Figure GDA0001524883550000071
where 8 is the node length, and the numbers 5, 6, 7, and 8 represent hamming distances; wherein the content of the first and second substances,
Figure GDA0001524883550000072
representing a combination
Figure GDA0001524883550000073
Similarly, when T is 3, the proportion of the filtered alternative paths is about 64%. As can be seen from FIGS. 2-4, the experimental results show that L is obtained by applying the method of the present inventionThe filtering ratio is about 57% when L is 2, and about 70% when L is 4, so the ordering space is greatly reduced, the decoding rate is significantly increased, but the error rate is still very low, and substantially coincides with the decoding result of the conventional path.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (3)

1. A polar code decoding path selection method based on a list continuous deletion algorithm is characterized in that: the method comprises the following steps:
s1, representing a target polarization code by using a binary tree, traversing the binary tree by a decoder until a special node on the binary tree is found, stopping continuously traversing the binary tree downwards on the special node, performing decoding judgment on a bit associated under the current special node, and performing decoding path expansion according to a judgment result;
s2, decoding path expansion: splitting each original path of a decoded list in a list prune algorithm to 2kAlternative paths, whereby the entire coding list has L x 2kA path, wherein k is the number of information bits of the special node, and L is the capacity of the decoding list;
s3, carrying out hard decision on the soft information vector alpha received by any original path in the decoding list of the current special node to obtain a binary reference list, and calculating 2kHamming distance D between list formed by jth strip in strip alternative path and reference listjWherein, in the step (A),
Figure FDA0002980836930000011
m is the length of the special node;
s4, screening alternative paths of each original decoding path by adopting a Hamming distance filter, and then finding out L decoding paths from the remaining alternative paths screened by the Hamming distance filter;
the special nodes comprise a node rate-0, a node rate-1 and a node rate-R;
the decoding decision method of the associated bit under the current special node is as follows:
when the special node is a node rate-0, all bits of the node are directly translated into 0;
when the special node is not the node rate-0, the process proceeds to the decoding path expansion of step S2;
in step S3, a hard decision is made as follows:
Figure FDA0002980836930000012
wherein the content of the first and second substances,
Figure FDA0002980836930000013
for reference list, i ═ 0,1, …, m-1;
in step S4, hamming distance filter screening is implemented by the following method:
computing alternative path metrics pjAnd the Hamming distance D of the alternative path to the reference listj：
Wherein p isjThe initial value of the path metric of the jth alternative path in the alternative paths is the path metric PM of the original path; djThe initial value is 0, and j represents the jth alternative path;
when in use
Figure FDA0002980836930000021
When the temperature of the water is higher than the set temperature,
Figure FDA0002980836930000022
and is
Figure FDA0002980836930000023
When in use
Figure FDA0002980836930000024
When the temperature of the water is higher than the set temperature,
Figure FDA0002980836930000025
and is
Figure FDA0002980836930000026
In the alternative paths, if any path has a Hamming distance DjIf the value is larger than the set threshold value T, directly abandoning the current alternative path;
wherein the content of the first and second substances,
Figure FDA0002980836930000027
is the binary value of the ith bit of the jth alternative path.
2. The method for selecting a decoding path of a polar code based on a list sequential elimination algorithm according to claim 1, wherein: in step S4, L decoding paths are screened out from the candidate paths by the following method:
calculating the number of the remaining alternative paths after the path is screened by the Hamming distance filter, and recording the number as cnt [ l ];
if the cnt [ L ] is less than or equal to the capacity L of the decoding list, directly taking the remaining alternative paths after being filtered by the Hamming distance filter as decoding paths;
if cnt [ l]Greater than the capacity L of the decoding list, the path metric p of the remaining alternative paths after filtering through the Hamming distance filterjSorting the sizes and selecting L path metrics pjThe smallest alternative path serves as the decoding path.
3. The method for selecting a decoding path of a polar code based on a list sequential elimination algorithm according to claim 2, wherein: hamming distance D of alternative pathjThe set threshold value T is in the range of
Figure FDA0002980836930000028
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CN109194338A (en) * 2018-11-07 2019-01-11 桂林电子科技大学 A kind of polarization code coding method of the more bit process of mixed node
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CN111654291B (en) * 2020-07-02 2023-08-01 重庆邮电大学 Polarization code rapid serial offset list decoding algorithm based on bit flipping
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