CN110233628A - The adaptive belief propagation list decoding method of polarization code - Google Patents
The adaptive belief propagation list decoding method of polarization code Download PDFInfo
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- H—ELECTRICITY
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- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/09—Error detection only, e.g. using cyclic redundancy check [CRC] codes or single parity bit
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
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Abstract
The invention discloses a kind of adaptive belief propagation list decoding methods of polarization code, the BP decoder quantity possessed first according to receiving end, determine the maximum list number of this method, calculate by Gaussian approximation method and obtains the BP decoding factor graph that can obtain preferably decoding effect, then different BP decoding factor graphs is selected to the BP decoder recorded in list to decode, cyclic redundancy check is carried out after being ranked up to decoding result, it is then successfully decoded by the result of cyclic redundancy check if it exists and stop decoding, otherwise adjust automatically list size, list number is expanded as into original twice, the BP decoder continued to use in list is decoded.
Description
Technical field
The present invention relates to a kind of adaptive belief propagation list decoding methods of polarization code, belong to the channel in wireless communication
Coding techniques field.
Background technique
Polarization code technology is as a kind of novel channel coding technology, and when code length tends to be infinite, transmission rate can reach
In the channel capacity of the memoryless symmetric channel of binary system.The decoded mode of polarization code more mainstream has two classes at present, a kind of
(Successive Cancellation, SC) interpretation method is offset based on serial, includes the serial counteracting column based on SC decoding
Table (Successive Cancellation List, SCL) interpretation method, the polarization code coding method based on SC belong to sequential translate
Code, the information bit translated have an impact the estimation of follow-up bit, it is therefore necessary to estimate the letter in code word one by one
Bit is ceased, biggish decoding delay is thereby produced.Other a kind of mainstream interpretation method of polarization code is based on belief propagation
(Belief Propagation, BP) interpretation method, including belief propagation list (Belief Propagation List, BPL)
Interpretation method, based on the property that the interpretation method of BP is calculated due to its parallel iteration, decoding delay is substantially less than based on SC's
Interpretation method and insensitive to code word size, therefore BP interpretation method is suitable for the application scenarios more demanding to time delay.But
It is that traditional the BP interpretation method bit error rate and frame error rate performance are poor, BPL interpretation method improves on the basis of BP interpretation method
The bit error rate and frame error rate performance, but bring higher computation complexity and hardware requirement.
Summary of the invention
The present invention provides a kind of adaptive belief propagation list decoding method of polarization code, and the code word used is cyclic redundancy
Verify the concatenated code that (Cyclic Redundancy Check, CRC) code and polarization code are formed.Adaptive belief propagation list is translated
For recording the BP decoder that can be decoded simultaneously, list number is defined as the BP decoder number in list for the list of code method
Mesh, maximum list number are defined as the BP decoder the upper limit of the number that can be decoded simultaneously.
The adaptive belief propagation list decoding method proposed in the present invention, the BP decoder possessed first according to receiving end
Quantity determines the maximum list number of this method, and preferable decoding effect can be obtained by calculate obtaining by Gaussian approximation method
BP decodes factor graph, then selectes different BP decoding factor graphs to the BP decoder recorded in list and decodes, to decoding
As a result cyclic redundancy check is carried out after being ranked up, then successfully decoded by the result of cyclic redundancy check if it exists and stopping is translated
Code, otherwise adjust automatically list size, expands as original twice for list number, and the BP decoder continued to use in list carries out
Decoding.
The existing BP interpretation method bit error rate and frame error rate performance are poor, and BPL interpretation method uses multiple BP decoders
The method decoded simultaneously, improves the bit error rate and frame error rate using higher computation complexity and hardware energy consumption as cost
Energy.The adaptive belief propagation list decoding method of polarization code obtains more for comparing BP interpretation method and BPL interpretation method
The good bit error rate and frame error rate performance, and be the list needed for completing the required list number of decoding under the conditions of middle high s/n ratio
List number of the number significantly less than BPL interpretation method.This illustrates the adaptive belief propagation list decoding method of polarization code in middle height
Need BP decoder number to be started considerably less than the BPL interpretation method using constant list number under the conditions of signal-to-noise ratio, to reach
To computation complexity is significantly reduced, the effect of hardware energy consumption is reduced.
The present invention uses following technical scheme to solve above-mentioned technical problem:
The present invention provides a kind of adaptive belief propagation list decoding method of polarization code, comprising the following steps:
Step 1: the maximum list number L that initialization allowsmax, it is configured to the 2L of BP decodingmax- a kind of factor graph is corresponding
Permutation matrix permutation_matrix, specifically:
(1) the BP decoder quantity possessed according to receiving end, it is autonomous to determine maximum list number Lmax；
(2) search range of Permutation Factor figure needed for reducing: being N=2 for code lengthnPolarization code, coding when need
By n coding stage { l0,...,ln-1, the factor graph and L={ l that when decoding uses0,l1,...,ln-1In element full row
It is classified as mapping relations one by one；Defined parameters k, makes k meet condition: (n-k)！≥Lmax, a subset of note set L is Lh={ lk,
lk+1,...,ln-1, obtain set Lh(n-k) of middle element！Kind fully intermeshing, then plus sequentially constant before every kind of arrangement
Preceding k coding stage { l0,l1,...,lk-1, to obtain (n-k) of all elements in set L！Kind arrangement, by factor graph and L
The mapping relations one by one of middle arrangement of elements obtain corresponding (n-k)！Kind factor graph, thus by the search range of Permutation Factor figure
It is reduced into (n-k)！Kind；
(3) from the factor graph for selecting needs in Permutation Factor graph search range: in set L obtained in step (2)
(n-k) of all elements！Kind arrangement, calculates separately the frame error rate that corresponding factor graph obtains under Gaussian approximation method, selects
The wherein the smallest 2L of frame error ratemax- a kind of factor graph；
(4) 2L is constructedmaxThe corresponding permutation matrix permutation_matrix of-a kind of factor graph: 2L is constructedmax- 1 row n
Every a line in the permutation matrix permutation_matrix, permutation_matrix of column corresponds to be selected in step (3)
2LmaxOne of the fully intermeshing of-a kind of set L；
Second step carries out the adaptive belief propagation list decoding of polarization code, specifically:
(A) initialize: initialization can currently carry out the BP decoder quantity l=that polarization code carries out belief propagation decoding simultaneously
1；
(B) BP decoding is carried out simultaneously using l independent BP decoders, each BP decoder uses permutation_
The corresponding factor graph of not yet used 1 row element separately carries out BP decoding, the output knot of BP decoder in matrix
Fruit isWithCalculate the code word estimation that each decoder obtainsWith reception
SignalBetween Euclidean distance d, whereinIt is to information bit uiEstimation,It is to information bit uiThe code word bits x obtained after concatenated codingiEstimation；
(C) l group information bit obtained in step (B) is estimated according to the ordering rule of corresponding d from small to largeRow
Sequence；
(D) l group information bit collated in step (C) is estimatedCyclic redundancy check is carried out one by one: if current
Decoding result to be verifiedMeet cyclic redundancy check, then adaptive belief propagation list decoding method is successfully decoded, returns
The decoding is as a result, entirely decoding process terminates；Otherwise next group information bit is estimatedCyclic redundancy check is carried out, if l group
Information bit estimationStep (E) is not transferred to then by cyclic redundancy check；
(E) if l >=Lmax, then the first group information bit estimation in step (C) after sequence is exportedIt is tied as decoding
Fruit, the entire process that decodes terminate；Otherwise l=2l is enabled, step (B) is transferred to.
As a further optimization solution of the present invention, in step (1) value of k by receiving end according to itself computing capability and
Delay requirement voluntarily determines.
As a further optimization solution of the present invention, in step (B)
The invention adopts the above technical scheme compared with prior art, has following technical effect that the polarization in the present invention
List number is first set as lesser value by the adaptive belief propagation list decoding method of code, then to the decoding knot in existing list
Fruit carries out cyclic redundancy check, and increases list number after cyclic redundancy check failure and continue to decode.Compared to tradition
BP interpretation method, the adaptive belief propagation list decoding method of polarization code significantly improves the bit error rate and frame error rate performance,
And the average decoding delay in middle high s/n ratio section and computation complexity are only slightly higher than traditional BP interpretation method.Compared to existing
The adaptive belief propagation list decoding method of some BPL interpretation methods, polarization code improves the bit error rate and frame error rate performance, and
And the mode for being stepped up list number avoids a large amount of unnecessary calculating and hardware energy consumption in BPL interpretation method, in middle height
In signal-to-noise ratio section, computation complexity can be reduced an order of magnitude, with approach traditional BP interpretation method computation complexity and
Hardware energy consumption expense obtains the bit error rate performance more than BPL interpretation method.This illustrates that the method in the present invention can be with lesser
Decoding delay is that cost obtains the gain of bit error rate performance and the simplification of computation complexity.
Detailed description of the invention
Fig. 1 is the adaptive belief propagation list decoding method flow diagram of polarization code；
Fig. 2 is that code length is 8, includes 3 coding stage (l0、l1、l2) 3 kinds of different factor graphs schematic diagram, wherein (a)
It is successively by l2、l0、l1Factor graph, be (b) successively by l1、l2、l0Factor graph, be (c) successively by l1、l0、l2's
Factor graph.
Specific embodiment
Technical solution of the present invention is described in further detail with reference to the accompanying drawing:
The adaptive belief propagation list decoding method of polarization code in the present invention, with code length N=2048, information bit K
It is illustrated for=1024, cyclic redundancy check code length r=8.The building method of polarization code in this example is Gaussian approximation,
Code construction signal-to-noise ratio is 2.5 decibels, and the generator polynomial of cyclic redundancy check code is g (x)=x8+x6+x3+x2+1。
As shown in Figure 1, including the following steps:
Step 1: the maximum list number L that initialization allowsmax(L in this examplemax=4), it is configured to the 2L of BP decodingmax-1
(2L in this examplemax- 1=7) the corresponding permutation matrix permutation_matrix of kind factor graph.This step includes following process:
(1) the BP decoder quantity possessed according to receiving end, it is autonomous to determine maximum list number Lmax.It is transferred to step (2).
(2) (Permutation Factor figure is existing concept, this step summary construction for the search range of Permutation Factor figure needed for reducing
Method).
It is N=2 for code lengthnPolarization code, coding when need by n coding stage { l0,...,ln-1, note set
L={ l0,l1,...,ln-1}.The fully intermeshing of element is mapping relations one by one in the factor graph and L used when decoding, as Fig. 2 is indicated
Three kinds of different factor graphs when n=3.The fully intermeshing of element shares n in set L！Kind, therefore shared n！Kind different decoding because
Subgraph.Defined parameters k, makes k meet condition: (n-k)！≥Lmax, (value of k is related to the size of factor graph search range, tool
Body value can voluntarily be determined by receiving end according to itself computing capability and delay requirement).The a subset for remembering set L is Lh, Lh=
{lk,lk+1,...,ln-1}.Obtain set Lh(n-k) of middle element！Kind fully intermeshing, then plus sequentially constant before every kind of arrangement
Preceding k coding stage { l0,l1,...,lk-1, to obtain (n-k) of all elements in set L！Kind arrangement, by factor graph
Corresponding (n-k) can be obtained with the mapping relations one by one of arrangement of elements in L！Kind factor graph.This completes Permutation Factor figures
Search range by original n！Kind is reduced into present (n-k)！Kind.It is transferred to step (3).
(3) factor graph of needs is selected from Permutation Factor graph search range.For in set L obtained in step (2)
(n-k) of all elements！Kind arrangement, calculates separately the frame error rate that corresponding factor graph obtains under Gaussian approximation method, selects
The wherein the smallest 2L of frame error ratemaxThe arrangement of all elements in the corresponding set L of-a kind of factor graph.It is transferred to step (4).
(4) the corresponding permutation matrix permutation_matrix of factor graph needed for construction.Constructing size is 2Lmax-
Every a line in the permutation matrix permutation_matrix, permutation_matrix of 1 row n column corresponds in step (3)
The 2L selectedmaxOne of the fully intermeshing of-a kind of set L.This process terminates.Permutation_matrix in this example is such as
A size shown in lower is the matrix of 7 rows 11 column:
Step 2: carrying out the adaptive belief propagation list decoding of polarization code.This step includes following process:
(1) it initializes.Note can currently carry out polarization code and carry out the BP decoder quantity of belief propagation decoding to be l simultaneously.Just
Beginningization parameter l=1, note receive signal and areIt is transferred to step (2).
(2) start l BP decoder simultaneously to be decoded according to different factor graphs.NoteWithFor BP decoder output as a result, whereinRefer to information bit uiEstimation,It is the code word bits x obtained after concatenated coding to information bitiEstimation.It is decoded using l independent BP
Device carries out BP decoding simultaneously, and each BP decoder is corresponding using 1 row element not yet used in permutation_matrix
Factor graph separately carry out BP decoding.Calculate the code word estimation that each decoder obtainsWith reception signalIt
Between Euclidean distance d,It is transferred to step (3).
(3) l group information bit obtained in step (2) is estimatedSequence.According to the sequence of corresponding d from small to large
Rule estimates l group information bit obtained in step (2)It is ranked up.It is transferred to step (4).
(4) l group information bit collated in step (3) is estimatedCyclic redundancy check is carried out one by one.If currently to
The decoding result of verificationMeet cyclic redundancy check, then adaptive belief propagation list decoding method is successfully decoded, and returning should
Decoding is as a result, entirely decoding process terminates.Otherwise next group information bit is estimatedCarry out cyclic redundancy check.If l group is believed
Cease bit estimationStep (5) are not transferred to then by cyclic redundancy check.
(5) if l >=Lmax, then export it is collated in step (3) after the first group information bit estimationIt is tied as decoding
Fruit, the entire process that decodes terminate.Otherwise l → 2l is updated, that is, is adaptively adjusted list size, list size is adjusted to former column
Twice of table size.It is transferred to step (2).
Specific embodiment described herein is only an example for the spirit of the invention.The neck of technology belonging to the present invention
The technical staff in domain can make various modifications or additions to the described embodiments or replace by a similar method
In generation, however, it does not deviate from the spirit of the invention or beyond the scope of the appended claims.
Claims (3)
1. the adaptive belief propagation list decoding method of polarization code, which comprises the following steps:
Step 1: the maximum list number L that initialization allowsmax, it is configured to the 2L of BP decodingmaxThe corresponding displacement of-a kind of factor graph
Matrix permutation_matrix, specifically:
(1) the BP decoder quantity possessed according to receiving end, it is autonomous to determine maximum list number Lmax；
(2) search range of Permutation Factor figure needed for reducing: being N=2 for code lengthnPolarization code, coding when need by n
A coding stage { l0,...,ln-1, the factor graph and L={ l that when decoding uses0,l1,...,ln-1In the fully intermeshing of element be
Mapping relations one by one；Defined parameters k, makes k meet condition: (n-k)！≥Lmax, a subset of note set L is Lh={ lk,
lk+1,...,ln-1, obtain set Lh(n-k) of middle element！Kind fully intermeshing, then plus sequentially constant before every kind of arrangement
Preceding k coding stage { l0,l1,...,lk-1, to obtain (n-k) of all elements in set L！Kind arrangement, by factor graph and L
The mapping relations one by one of middle arrangement of elements obtain corresponding (n-k)！Kind factor graph, thus by the search range of Permutation Factor figure
It is reduced into (n-k)！Kind；
(3) from the factor graph for selecting needs in Permutation Factor graph search range: for owning in set L obtained in step (2)
(n-k) of element！Kind arrangement, calculates separately the frame error rate that corresponding factor graph obtains under Gaussian approximation method, selects wherein
The smallest 2L of frame error ratemax- a kind of factor graph；
(4) 2L is constructedmaxThe corresponding permutation matrix permutation_matrix of-a kind of factor graph: 2L is constructedmax- 1 row n column
Every a line in permutation matrix permutation_matrix, permutation_matrix, which corresponds to, to be selected in step (3)
2LmaxOne of the fully intermeshing of-a kind of set L；
Second step carries out the adaptive belief propagation list decoding of polarization code, specifically:
(A) initialize: initialization can currently carry out the BP decoder quantity l=1 that polarization code carries out belief propagation decoding simultaneously；
(B) BP decoding is carried out simultaneously using l independent BP decoders, each BP decoder uses permutation_matrix
In the corresponding factor graph of not yet used 1 row element separately carry out BP decoding, the output result of BP decoder isWithCalculate the code word estimation that each decoder obtainsWith reception signalBetween Euclidean distance d, whereinIt is to information bit uiEstimation,
It is to information bit uiThe code word bits x obtained after concatenated codingiEstimation；
(C) l group information bit obtained in step (B) is estimated according to the ordering rule of corresponding d from small to largeSequence；
(D) l group information bit collated in step (C) is estimatedCyclic redundancy check is carried out one by one: if currently to school
The decoding result testedMeet cyclic redundancy check, then adaptive belief propagation list decoding method is successfully decoded, returns to this and translates
Code is as a result, entirely decoding process terminates；Otherwise next group information bit is estimatedCyclic redundancy check is carried out, if l group information
Bit estimationStep (E) is not transferred to then by cyclic redundancy check；
(E) if l >=Lmax, then the first group information bit estimation in step (C) after sequence is exportedAs decoding as a result, whole
A decoding process terminates；Otherwise l=2l is enabled, step (B) is transferred to.
2. the adaptive belief propagation list decoding method of polarization code according to claim 1, which is characterized in that step
(1) value of k is voluntarily determined by receiving end according to itself computing capability and delay requirement in.
3. the adaptive belief propagation list decoding method of polarization code according to claim 1, which is characterized in that step
(B) in
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| CN114448575A (en) * | 2022-03-17 | 2022-05-06 | 东南大学 | Polar code retransmission decoding method based on dynamic copy mapping |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110798284A (en) * | 2019-11-25 | 2020-02-14 | 安徽大学 | Polarization code transmission method based on double BP decoding graph parallel decoding technology |
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| WO2021208244A1 (en) * | 2020-04-17 | 2021-10-21 | 北京交通大学 | List polar code propagation decoding method |
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