CN107947803A - A kind of method for rapidly decoding of polarization code - Google Patents
A kind of method for rapidly decoding of polarization code Download PDFInfo
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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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- H—ELECTRICITY
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- H04L1/00—Arrangements for detecting or preventing errors in the information received
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Abstract
The present invention provides a kind of Fast Decoding Algorithim of polarization code, i.e. EPD (Error Probability Distribution) SSC decoding algorithms.The algorithm is divided into off-line calculation part and online decoding portion：Off-line calculation module estimates the error probability parameter of weak polarization subchannel using the Gaussian approximation under weak polarisation channel, so that generation error probability distribution tree aids in decoding online；Online decoding module calculates the P of current node by error probability distribution treenodeValue, the value represent the characteristic of current Rate R nodes, further filter out Rate R EPD nodes by threshold value.When implementing EPD SSC decoding algorithms, Rate R EPD nodes can carry out fast decoding, so as to reduce decoding delay.
Description
Technical field
The invention belongs to field of communication technology, and in particular to the improvement based on SSC decoding algorithms is calculated in a kind of polarization code
Method --- EPD-SSC (Error-Probability-Distribution-SSC).
Background technology
Polarization code (Polar Codes) is discussed in international information in 2008 by Turkey scientist and proposed first in conference, because
It proves to reach the channel capacity of binary system Discrete Symmetry channel and receive much concern in theory.2015, in 3GPP meetings
Polarization code is set to the encoding scheme of control channel under the 5th third-generation mobile communication eMBB scenes in view.
Polarization code is using different polarisation channel difference transmission information bits and fixed bit, so as to reach with channel capacity
The purpose of reliable transmission information.The it is proposed of polarization code derives from channel-polarization phenomenon, when to N number of channel progress polarization conversion
Afterwards, the channel capacity of part polarization subchannel tends to 1, and the channel capacity of another part polarization subchannel tends to 0.Therefore, may be used
To tend to transmission information bit in 1 subchannel in channel capacity, tend to the fixed ratio of transmission in 0 subchannel in channel capacity
It is special.Further, it is exactly to find sufficiently reliable K sub-channels in N number of polarization subchannel to construct polarization code.
The basic decoding algorithm of polarization code is successive elimination (Successive Cancellation-SC) decoding algorithm, though
The right algorithm complex is low, but can only individual bit serial decoding, therefore larger time delay can be brought.In 5G communication systems
In, the communication of low time delay is particularly significant.Then, simplified successive elimination (Simplified SC-SSC) decoding algorithm is suggested,
A variety of modified versions based on special construction are also suggested.Tree construction of the SSC algorithms based on combinational code, can simplify Rate-1 knots
The decoding of point improves decoding speed, reduces time delay.In order to further reduce decoding delay, patent of the present invention is tied for Rate-R
Point proposes a kind of EPD-SSC algorithms based on probability measure.
The content of the invention
The present invention proposes a kind of EPD-SSC decoding algorithms based on SSC decoding algorithms, can effectively reduce polarization code
Decoding delay, improves decoding speed.
EPD-SSC decoding algorithms are divided into two parts：Offline error probability distribution calculation module and online EPD-SSC are translated
Code module.
Off-line calculation module estimates the error probability ginseng of weak polarization subchannel using the Gaussian approximation under weak polarisation channel
Number.
The definition of weak polarisation channel is：Assuming that there is N=2nA same BDMC channels, are denoted as WN, then aggregate channel set
{WM| M=2m,m<N } it is known as the weak aggregate channel of N number of BDMC channels, WMThe individual channel generated after the separation of channel channel
Referred to as polarisation channelCorresponding weak polarisation channel.
In the tree construction of polarization code SSC decoding algorithms, the node of tree correspond to combinational code.Assuming that Vi,jRepresent i-th layer of jth
A node, the information of storage is respectively α and β, and wherein α represents likelihood value, and β represents hard decision information.Then, { Vi,j| i=t } table
Show all nodes on t layers, its corresponding likelihood value is N is code length.
Consider weak polarisation channelN is code length, and t is the of SSC trees
T layers.As can be seen that weak polarisation channelWith t layers of likelihood value aiOr hard decision information βiIt is one-to-one；Further,
Weak polarisation channel and decoding tree node are closely related it can be seen from polarization code channel-polarization and coding and decoding.Therefore, research is passed through
Weak polarisation channel can analyze the performance of tree node, you can to describe the performance of tree node by probability measure.
In offline error probability distribution calculation module, following steps are applicable in：
Step 1, error probability distribution tree P={ node | node ∈ P }, wherein node={ p are initializedi|0<pi<1, i=
2n-t, 0=<T≤n }, n represents the depth of tree, and t represents the number of plies of tree.Assuming that sending code word is all zero, Initial Channel Assignment exports seemingly
So ratio is
Step 2, error probability distribution tree P is traveled through, and updates the estimating bit error rate p in nodei：
According to Gaussian approximation iterative formulaCalculate with it is weak
The corresponding channel likelihood ratio average of polarisation channel
According to formulaCalculate estimating bit error rate pi, and update nodal value；
If P does not update all, step 2 is continued to execute, otherwise off-line calculation terminates；
In the case where obtaining channel condition information, can obtain error probability distribution tree P, P according to above step can make
To inquire about storehouse additional interpretations；
The online decoding stage makes decisions Rate-R nodes according to the node bit error probability characteristic of off-line calculation, finds foot
Enough reliable nodes, so as to carry out rapidly Hard decision decoding；
In decoding tree, a certain node n ode={ p are consideredi|0<I≤k }, inquiry probability distribution tree P is known that pi's
Value, and piCorresponding hard decision result βi；
If βiBetween be independent, then have So as to obtain at least one βiThe probability of error is denoted as pnode；
Similar, multiple β can be obtainediThe probability of error, but we only consider a wrong situation herein；
Further, by setting appropriate threshold value Δ p come screening to Rate-R nodes, special Rate- is drawn
R-EPD nodes；
Threshold value Δ p is the desired bit error rate, can be set according to communicating requirement；
In online decoding module, following steps are applicable in：
Step 1, initialization decoding tree T=node | and node ∈ T }, node={ αi, βi|αi∈ R, βi∈ { 0,1 } }, just
Beginningization root node likelihood value
Step 2, traversal decoding tree decoding：
Rate-0 nodes：Directly return to βi；
Rate-1 nodes：βi=h (αi), μ=β G, h are hard decision function, and G is corresponding generator matrix；
Rate-R nodes:The p of current node is calculated according to probability distribution tree P firstnode：
If pnode<Δ p, then be marked as Rate-R-EPD nodes, and βi=h (αi), μ=β G, h are hard decision letter
Number, G is corresponding generator matrix；
If pnode>Δ p, then update the α of current node, and jumps to next pending node；
Step 3, if node whole processing terminates, terminates decoding, and draw final decoding as a result, otherwise continuing
Perform step 2.
Beneficial effect
Present invention contrast prior art has following innovative point：
The Rate-R nodes in decoding tree are analyzed from the angle in bit error probability space first herein, it is proposed that
Rate-R-EPD nodes.By exploring more Rate-R-EPD nodes, this decoding algorithm can effectively improve decoding speed, drop
Low decoding delay.
In the case of known channel state information (CSI), this method can calculate weak polarization letter off-line manner
The error ratio characteristic in road, generation error probability distribution tree, foundation is provided for online fast decoding.In mobile edge calculations, this
Algorithm has more advantage.
Brief description of the drawings
Fig. 1 calculates schematic diagram for the distribution of offline error probability.
Fig. 2 is online decoding schematic diagram.
EPD-SSC decoding trees when Fig. 3 is N=8.
Embodiment
Below in conjunction with attached drawing 3 and embodiment, the present invention will be further described.
Code length N=8, spatial distribution of nodes are as shown in Figure 3.First, the structure of off-line calculation error probability distribution tree P, P can use figure
3 tree graphs represent.Calculating process is：Assuming that channel output likelihood value isAs m=1,
Calculate accordinglyThat is the root node information of P；As m=2, the second layer first of P
The input likelihood value of a node isIt can obtainAnd pi, i=1, the input of 2,3,4, second node is seemingly
So value isIt can obtainAnd pi=i=5,6,7,8；And so on, it can draw error probability distribution tree P.
Online decoding：Initialize root node informationLeft sibling is Rate-0 nodes, then directly returns to βi=0；Meter
Calculate the right node α of the second layeri, by formula αvr[i]=αv[2i](1-2βvl[i])+αv[2i+1] can be calculated；The right node of the second layer
It is Rate-R nodes, if its corresponding bit error probability is pi, i=5,6,7,8, thenAssuming that pnode<Δ p,
Hard decision then can be directly carried out, i.e.,
The above description is merely a specific embodiment, but protection scope of the present invention is not limited to this, any ripe
Those skilled in the art are known in technical scope proposed by the present invention, the change or replacement that can be readily occurred in, all should
This is included within the scope of the present invention.
Claims (5)
1. the EPD-SSC Fast Decoding Algorithims of a kind of polarization code, it is characterised in that offline error probability distribution calculates and online
EPD-SSC decoding, special Rate-R-EPD nodes can be found out according to off-line data and carry out fast decoding.The decoding side
Method comprises the following steps：
Step 1, decoding tree T={ node | node ∈ T }, node={ α are initializedi, βi|αi∈ R, βi∈ { 0,1 } }, initialize root
Node likelihood value
Step 2, decoding tree decoding is traveled through：If current node is Rate-0 nodes, β is directly returnedi=0；If current node
Rate-1 nodes, then βi=h (αi), μ=β G, h are hard decision function, and G is corresponding generator matrix；If current node is
Rate-R nodes, then calculate current node according to probability distribution tree P
Step 3, if pnode＜ Δ p, then be marked as Rate-R-EPD nodes, and βi=h (αi), μ=β G, h are hard decision
Function, G are corresponding generator matrix；If pnode＞ Δ p, then update the α of current node, and jumps to next pending node；
Step 4, if node whole processing terminates, decoding is terminated, and draw final decoding as a result, otherwise continuing to execute step
Rapid 2.
2. the EPD-SSC Fast Decoding Algorithims of a kind of polarization code according to claim 1, it is characterised in that general in step 2
The off-line calculation step of rate distribution tree P is as follows：
Step 1, error probability distribution tree P={ node | node ∈ P }, wherein node={ p are initializedi| 0 ＜ pi＜ 1, i=2n-t,
0=＜ t≤n }, n represents the depth of tree, and t represents the number of plies of tree；Assuming that sending code word is all zero, Initial Channel Assignment output likelihood
Than for
Step 2, error probability distribution tree P is traveled through, and updates the estimating bit error rate p in nodei：According to Gaussian approximation iterative formulaCalculate equal with the corresponding channel likelihood ratio of weak polarisation channel
ValueAccording to formulaCalculate estimating bit error rate pi, and update nodal value；
Step 3, if P does not update all, step 2 is continued to execute, otherwise off-line calculation terminates.
3. the EPD-SSC Fast Decoding Algorithims of a kind of polarization code according to claim 1, it is characterised in that in step 2Represent at least one wrong probability of the β value of current node.
A kind of 4. EPD-SSC Fast Decoding Algorithims of polarization code according to claim 1, it is characterised in that threshold in step 3
Value Δ p is the desired bit error rate, can be set according to communicating requirement.
5. the EPD-SSC Fast Decoding Algorithims of a kind of polarization code according to claim 1, it is characterised in that in step 3
Rate-R-EPD nodes are drawn by bit error probability space P, therefore correspond to a variety of Rate-R node structures in decoding tree.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108777584A (en) * | 2018-07-06 | 2018-11-09 | 中国石油大学(华东) | A kind of fast Optimization of polarization code decoding parameter |
| CN108900198A (en) * | 2018-06-29 | 2018-11-27 | 中国石油大学(华东) | A kind of serial fast determination method for offsetting list decoding parameter |
| CN110336639A (en) * | 2019-06-23 | 2019-10-15 | 西安电子科技大学 | A kind of polarization code multi-layer coding modulator approach and application based on capacity distribution |
| WO2020052537A1 (en) * | 2018-09-14 | 2020-03-19 | 华为技术有限公司 | Decoding method and device for polar codes |
| CN112953555A (en) * | 2021-01-29 | 2021-06-11 | 北京航空航天大学 | Error probability assistance-based method for constructing polarization code under deleted channel |
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| US20160241355A1 (en) * | 2015-02-13 | 2016-08-18 | Samsung Electronics Co., Ltd. | Apparatus and method of constructing polar code |
| CN106788453A (en) * | 2016-11-11 | 2017-05-31 | 山东科技大学 | A kind of parallel polarization code coding method and device |
| CN106803759A (en) * | 2016-12-27 | 2017-06-06 | 南京邮电大学 | Polar yards of effective adaptive decoding method based on Gauss construction |
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| US20160241355A1 (en) * | 2015-02-13 | 2016-08-18 | Samsung Electronics Co., Ltd. | Apparatus and method of constructing polar code |
| CN106788453A (en) * | 2016-11-11 | 2017-05-31 | 山东科技大学 | A kind of parallel polarization code coding method and device |
| CN106803759A (en) * | 2016-12-27 | 2017-06-06 | 南京邮电大学 | Polar yards of effective adaptive decoding method based on Gauss construction |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108900198A (en) * | 2018-06-29 | 2018-11-27 | 中国石油大学(华东) | A kind of serial fast determination method for offsetting list decoding parameter |
| CN108777584A (en) * | 2018-07-06 | 2018-11-09 | 中国石油大学(华东) | A kind of fast Optimization of polarization code decoding parameter |
| WO2020052537A1 (en) * | 2018-09-14 | 2020-03-19 | 华为技术有限公司 | Decoding method and device for polar codes |
| CN110912567A (en) * | 2018-09-14 | 2020-03-24 | 华为技术有限公司 | Decoding method and device of polarization code |
| CN110336639A (en) * | 2019-06-23 | 2019-10-15 | 西安电子科技大学 | A kind of polarization code multi-layer coding modulator approach and application based on capacity distribution |
| CN110336639B (en) * | 2019-06-23 | 2021-08-17 | 西安电子科技大学 | Polar code multilayer coding modulation method based on capacity distribution and application |
| CN112953555A (en) * | 2021-01-29 | 2021-06-11 | 北京航空航天大学 | Error probability assistance-based method for constructing polarization code under deleted channel |
| CN112953555B (en) * | 2021-01-29 | 2022-06-10 | 北京航空航天大学 | Error probability assistance-based method for constructing polarization code under deleted channel |
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