CN107769891A - LT code coding/decoding methods based on encoder matrix characteristic - Google Patents
LT code coding/decoding methods based on encoder matrix characteristic Download PDFInfo
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- CN107769891A CN107769891A CN201710995424.XA CN201710995424A CN107769891A CN 107769891 A CN107769891 A CN 107769891A CN 201710995424 A CN201710995424 A CN 201710995424A CN 107769891 A CN107769891 A CN 107769891A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0057—Block codes
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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
- H03M13/37—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35
- H03M13/3761—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35 using code combining, i.e. using combining of codeword portions which may have been transmitted separately, e.g. Digital Fountain codes, Raptor codes or Luby Transform [LT] codes
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0045—Arrangements at the receiver end
- H04L1/0047—Decoding adapted to other signal detection operation
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Abstract
The invention discloses a kind of LT code coding/decoding methods based on encoder matrix characteristic, to realize transmitting of the information in binary erasure channel.Wherein coding method specifically includes：Receive the input bag of initial data；The matrix S for wrapping one k × l of composition will be inputtedk×l, by matrix Sk×lEach row store leu time as encoder matrix Gk×nAdditional column, generate new encoder matrix Gk×(n+l), the line number of newly encoded matrix is still k, and columns adds l row；In encoder matrix Gk×(n+l)Row k after increase mark row, to mark row be labeled and store mark row in；After mark and storage, new encoder matrix G is produced(k+num)×(n+l), wherein num is the line number of mark row；By new encoder matrix G(k+num)×(n+l)Generation coding bag (including common coding bag and " storage bag "), and coding bag is sent.The decoder of receiving terminal is different according to the quantity of " storage is wrapped " that receives, takes different modes to wrap into row decoding input.The present invention can effectively improve the performance of BER of LT codes.
Description
Technical field
The present invention relates to field of channel coding, more particularly to a kind of LT code coding/decoding methods based on encoder matrix characteristic.
Background technology
LT (Luby Transform) code is a kind of sparse linear packet fountain codes.Linear codes fountain codes all have one
The characteristics of obvious is：In an encoding process, an encoder matrix can be generated and come presentation code bag and coupled input bag
Annexation.The method that these link informations pass to decoding end there is many, for example, these information can be put into coding
The head position of bag, or the seed of generation degree and the pseudorandom number generator of " adjoining " is informed in advance into other side, receiving-transmitting sides
Can be by synchronously realizing decoding success.
Traditional LT code coding/decoding algorithms are a kind of second best measures, and complexity is relatively low, but reduces decoding to a certain extent
Success rate.Accordingly, it is considered to a kind of coding and decoding method of the LT codes based on encoder matrix characteristic, it is intended to improve decoding success rate, drop
Low error rate.
The content of the invention
The goal of the invention of the present invention is to provide a kind of coding and decoding method of the LT codes based on encoder matrix characteristic, to realize
Transmitting of the information in binary erasure channel (Binary Erasure Channel, BEC).
The technical solution adopted for the present invention to solve the technical problems is：
A kind of LT code encoding methods based on encoder matrix characteristic are provided, comprised the following steps：
Receive the input bag of initial data；
The matrix S for wrapping one k × l of composition will be inputtedk×l, by matrix Sk×lEach row store leu time as coding
Matrix Gk×nAdditional column, generate new encoder matrix Gk×(n+l), the line number of newly encoded matrix is still k, and columns adds l row；
In encoder matrix Gk×(n+l)Row k after increase mark row, to mark row be labeled and store mark row in；
After mark and storage, new encoder matrix G is produced(k+num)×(n+l), wherein num is the line number of mark row；
By new encoder matrix G(k+num)×(n+l)Generation coding bag, and coding bag is sent.
Above-mentioned technical proposal is connect, specifically using ten's digit to matrix Sk×lRow order marked from low to high, so
The decimal system is converted into binary system afterwards；The line number of mark row is determined by the digit of binary flags, by these binary flags point
It is not stored in mark row corresponding to each storage row, and each element of mark row is arranged to 0 corresponding to other row.
Above-mentioned technical proposal is connect, it is all 1 to set and store every bit in coding bag corresponding to row.
Present invention also offers a kind of interpretation method based on above-mentioned coding method, comprise the following steps：
Receiving terminal receives N number of coding bag；
Reconstruct encoder matrix G '(k+2)×N；
The mark row in encoder matrix after detection reconstruct, find the storage row for carrying storage information；
Take out the mark row in each storage row for carrying flag information；
Whether lost according to the storage bag that the mark row of taking-up judges to receive, storage bag is corresponding to each storage row
Coding bag；Such as fruit part storage packet loss, first, remove the storage row in the encoder matrix after reconstruct and mark is gone, composition is new
Encoder matrix G 'k×N, while remove coding bag corresponding to storage row；Then, based on restructuring matrix G 'k×NWith corresponding coding
Bag, enters row decoding using belief propagation BP algorithm；Finally, arranged according to storage and recover some bit not translated in input bag.
Above-mentioned technical proposal is connect, also includes step after taking out mark row：Binary mark row is converted into the decimal system, will
All storage row carry out ascending order arrangement according to corresponding decimal system mark, form matrix S 'k×l′, pass through matrix S 'k×l′Recover defeated
Enter some bit not translated in bag.
Above-mentioned technical proposal is connect, if all storage coating receives, passes through matrix S 'k×l′Directly obtain all original
Data, without entering row decoding process.
Above-mentioned technical proposal is connect, if all storage coating is deleted, row decoding is entered using belief propagation BP algorithm.
Above-mentioned technical proposal is connect, is " 1 " in mark row when detecting the mark row in the encoder matrix after additional row reconstruct
The storage row for carrying storage information are classified as corresponding to element.
Present invention also offers a kind of storage device, the storage device internal memory contain above-mentioned technical proposal based on coding square
The program of the LT code encoding methods of battle array characteristic.
Present invention also offers a kind of storage device, the storage device internal memory contain above-mentioned technical proposal based on coding square
The program of the LT code coding methods of battle array characteristic.
The beneficial effect comprise that：Generating principle of the invention according to LT code encoder matrixs, that is, input the number of bag
Amount is identical with the line number of encoder matrix, according to this characteristic, there is provided a kind of coding and decoding method of the LT codes based on encoder matrix characteristic,
To realize transmitting of the information in binary erasure channel.
Brief description of the drawings
Below in conjunction with drawings and Examples, the invention will be further described, in accompanying drawing：
Fig. 1 is the coding method figure based on encoder matrix characteristic；
Fig. 2 is the interpretation method figure based on encoder matrix characteristic when storage is wrapped and all received；
Fig. 3 is the interpretation method figure based on encoder matrix characteristic when storing packet portion and losing；
Fig. 4 is the LT code encoding methods based on encoder matrix characteristic；
Fig. 5 is the LT code coding methods based on encoder matrix characteristic.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that specific embodiment described herein is only to explain the present invention, not
For limiting the present invention.
The encoder matrix generating principle of the present invention is as follows：
To k input bag S={ Sj| j=1,2 ..., k } encoded, generation coding bag C={ Cn| n=1,2 ...,
Each coding wraps long l bit.Encoder randomly generates k bit coding vector according to degree distributionIn the vector
The value of element is " 0 " or " 1 ", determines whether corresponding input bag is participated in the computing of coding bag generation：
In formula, CnIt is caused n-th of coding bag, is and GI, n=1 corresponding He of input bag step-by-step mould 2.Random generation
Column vectorConstitute a line number and be defined as k, the encoder matrix of columns endlessUnlimited number of coding can be produced by k input packet encoder based on the encoder matrix
Bag.
Understood according to formula (1), encoder matrix Gk×nColumns it is corresponding caused by coding bag quantity n, the member in each row
Plain " 1 " is considered as annexation being present between coding bag and input bag corresponding to the row；The line number of encoder matrix is corresponding to be inputted
The quantity k of bag, it is considered as annexation being present between input bag corresponding to the row and coding wrap per the element " 1 " in a line.
That is, it is each the element G of " 1 " in encoder matrixI, jRepresent that the connection between i-th of input bag and j-th of coding bag is closed
System.As can be seen that the quantity of input bag is identical with encoder matrix line number.Based on this characteristic, the present invention uses following technical side
Case improves encoding and decoding algorithm.
(1) coding method based on encoder matrix characteristic
As shown in figure 4, first, the matrix S for forming a k × l is wrapped by inputtingk×l, using its each leu time as coding square
Battle array Gk×nAdditional column, generate new encoder matrix Gk×(n+l).Now, the line number of newly encoded matrix is still k, and columns adds l
Row.
Then, in order to distinguish additional column and original encoding rectangular array, consider in encoder matrix Gk×(n+l)Row k after increase it is several
Row is as " mark row ".After BEC, order of the coding bag in transmitting procedure is disturbed, in order to input bag
Each original position is correctly returned to per bit information, using ten's digit to matrix Sk×lRow order carry out from low to high
Mark, is then converted to binary system by the decimal system.The line number of " mark row " determined by the digit of binary flags, and these two are entered
Mark processed is stored respectively in each " storage row " corresponding " mark row ", and each element of " mark row " corresponding to other row
It is arranged to " 0 ".
Finally, by above-mentioned memory mechanism, new encoder matrix G is produced(k+num)×(n+l), wherein num is binary flags
Digit." mark row " only serves mark effect, and is not involved in actual coding, that is to say, that originally based on Gk×nCaused coding
Sequence keeps constant.For coding bag corresponding to the increase " storage row " in coded sequence, we directly assume that " storage row " are right
Every bit is " 1 " in the coding bag answered.
The encoder of transmitting terminal can use robust orphan to be distributed (Robust Soliton Distribution, RSD) and produce
Common coding bag, while " the storage bag " for carrying storage information is produced based on encoder matrix characteristic.
(2) interpretation method based on encoder matrix characteristic
Transmitted by BEC, the order for encoding bag is disturbed, and some coding bags may not be received.In Fig. 2 and Fig. 3
Grey parts represent the coding bag deleted and corresponding encoder matrix row." storage bag " inevitably faces deleted possibility
Property, although " storage bag " does not have to participate in decoding, the storage information in " storage bag " can recover some bit in input bag.
As shown in figure 5, receiving terminal receives N number of coding bag, reconstruct encoder matrix G '(k+2)×N, then start to decode.It is first
First, by detecting to be arranged corresponding to the element of " 1 " in additional row, that is, " the storage row " of storage information is carried, find out all " storages
Row ".
Then, " the mark row " in each " storage row " for carrying flag information is taken out, and binary system " mark is gone " is turned
It is changed to the decimal system.All " storage row " are subjected to ascending order arrangement according to corresponding decimal system mark, form matrix S 'k×l′。
Finally, it is different according to the quantity of " storage is wrapped " that receives, take different modes to wrap into row decoding input：(1)
If all " storage bag " is received, pass through matrix S 'k×l′All initial data can be directly obtained, without entering row decoding mistake
Journey；(2) such as fruit part " storage bag " loss, first, remove " storage row " and " mark row " in restructuring matrix, form new volume
Code matrix G 'k×N, while remove coding bag corresponding to " storage row "；Then, based on restructuring matrix G 'k×NWrapped with corresponding coding,
Row decoding is entered using BP algorithm；Finally, matrix S ' is passed throughk×l′Recover some bit not translated in input bag.(3) if all
" storage bag " is deleted, then enters row decoding using belief propagation (Belief Propagation, BP) algorithm.
As shown in figure 1, exemplified by inputting packet length l=3 bit, the encryption algorithm based on encoder matrix characteristic is as follows：
Step1：The degree d of a coding bag is randomly choosed in being distributed from degree.Random and equably d input bag conduct of selection
" adjoining " of the coding bag.This d " adjoining " is subjected to XOR and generates a coding bag.Meanwhile this coding bag wraps to input
Annexation be expressed as the respective column of encoder matrix.
Step2：Repeat Step1 and produce the individual coding bags of n (n=1,2 ...) and encoder matrix Gk×n。
Step3：By the former matrix for inputting one k × 3 of bag compositionBy its each row
Encoder matrix G is used as successivelyk×nAdditional column, generate new encoder matrix：
Wherein,Referred to as " storage row ".
Step4：" 1 ", " 2 ", " 3 " are ranked up as mark to storage row, other row are masked as " 0 ".First, by ten
System " 0 ", " 1 ", " 2 ", " 3 " are converted to binary system " 00 ", " 01 ", " 10 ", " 11 ".Then, these binary flags are stored
In the additional row of encoder matrix, new encoder matrix is generated：
In formula, the row of kth+1 and the behavior of kth+2 " mark row ".[G(k+1), m, G(k+2), m]=[0,1], [G(k+1), (m+1),
G(k+2), (m+1)]=[1,0], [G(k+1), (m+2), G(k+2), (m+2)]=[1,1], and the other elements of " mark row " are arranged to " 0 ".
Step5：" 1 " is both configured to corresponding to the 3bit in each coding bag of " storage row ", is referred to as " storage bag ".
As shown in Figures 2 and 3, the decoding algorithm based on encoder matrix characteristic is as follows：
Step1：Detect G '(k+2)×NAdditional row in the presence or absence of mark.
Step2：All it is detected if all of mark " 01 ", " 10 ", " 11 ", then it represents that " storage bag " is all received, and is owned
What input bag can be transferred through " storage row " 1 directly obtains to k rows.First, binary system " 01 ", " 10 ", " 11 " be converted to the decimal system " 1 ", " 2 ",
“3”.Then, own " storage row " to be arranged according to the ascending order of decimal system mark, and delete additional row, form Finally, S 'k×3S is returned to successivelyk×3, i.e.,
Step3：If only some marks are detected, then it represents that some " storage bags " are lost, by combining " storage
Bag " and BP decoding algorithms are wrapped into row decoding to input.For example, only mark " 01 " and " 11 " is detected.First, pass through
Step2 method obtainsWithFinally, based on the restructuring matrix G ' for resetting " storage row " and " mark row "k×N, adopt
Enter row decoding with BP algorithm to obtain
Step4：If all marks are not detected, then it represents that all " storage bags " are lost, and are translated using BP algorithm
Code.
The coding and decoding method of the LT codes based on encoding characteristics of above-described embodiment, can be realized by multiple programs language,
And stored by storage device.
It should be appreciated that for those of ordinary skills, can according to the above description be improved or converted,
And all these modifications and variations should all belong to the protection domain of appended claims of the present invention.
Claims (10)
1. a kind of LT code encoding methods based on encoder matrix characteristic, it is characterised in that comprise the following steps：
Receive the input bag of initial data；
The matrix S for wrapping one k × l of composition will be inputtedk×l, by matrix Sk×lEach row store leu and time be used as encoder matrix
Gk×nAdditional column, generate new encoder matrix Gk×(n+l), the line number of newly encoded matrix is still k, and columns adds l row；
In encoder matrix Gk×(n+l)Row k after increase mark row, to mark row be labeled and store mark row in；
After mark and storage, new encoder matrix G is produced(k+num)×(n+l), wherein num is the line number of mark row；
By new encoder matrix G(k+num)×(n+l)Generation coding bag, and coding bag is sent.
2. coding method according to claim 1, it is characterised in that specifically using ten's digit to matrix Sk×lRow
Order is marked from low to high, and the decimal system then is converted into binary system；Indicate the line number of row by the digit of binary flags
It is determined that these binary flags are stored respectively in mark row corresponding to each storage row, and mark row corresponding to other row
Each element be arranged to 0.
3. coding method according to claim 1, it is characterised in that set storage row corresponding to coding bag in per bit all
For 1.
4. a kind of interpretation method based on claim 1, it is characterised in that comprise the following steps：
Receiving terminal receives N number of coding bag；
Reconstruct encoder matrix G '(k+2)×N；
The mark row in encoder matrix after detection reconstruct, find the storage row for carrying storage information；
Take out the mark row in each storage row for carrying flag information；
Whether lost according to the storage bag that the mark row of taking-up judges to receive, storage bag is the coding corresponding to each storage row
Bag；Such as fruit part storage packet loss, first, remove storage row and mark row in the encoder matrix after reconstruct, form new volume
Code matrix G 'k×N, while remove coding bag corresponding to storage row；Then, based on restructuring matrix G 'k×NWith corresponding coding bag, adopt
Enter row decoding with belief propagation BP algorithm；Finally, arranged according to storage and recover some bit not translated in input bag.
5. interpretation method according to claim 4, it is characterised in that also include step after taking out mark row：By binary system
Mark row be converted to the decimal system, by it is all storage row according to corresponding decimal system mark carry out ascending order arrangement, form matrix
S′k×l′, pass through matrix S 'k×l′Recover some bit not translated in input bag.
6. interpretation method according to claim 5, it is characterised in that if all storage coating receives, pass through square
Battle array S 'k×l′All initial data are directly obtained, without entering row decoding process.
7. interpretation method according to claim 4, it is characterised in that if all storage coating is deleted, using confidence
Propagate BP algorithm and enter row decoding.
8. interpretation method according to claim 4, it is characterised in that the mark in encoder matrix after detection additional row reconstruct
During aspirations and conduct, arranged in mark row to be classified as the storage of carrying storage information corresponding to the element of " 1 ".
9. a kind of storage device, it is characterised in that the storage device internal memory, which contains, realizes the special based on encoder matrix of claim 1
The program of the LT code encoding methods of property.
A kind of 10. storage device, it is characterised in that the storage device internal memory contain realize claim 4 based on encoder matrix
The program of the LT code coding methods of characteristic.
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Cited By (3)
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| CN111064544A (en) * | 2019-10-16 | 2020-04-24 | 中国船舶重工集团公司第七一五研究所 | Cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding |
| CN116366074A (en) * | 2023-03-17 | 2023-06-30 | 武汉大学 | LT code mixed coding and decoding method and system based on binary spread domain and improving fullness ratio |
| CN117118462A (en) * | 2023-09-07 | 2023-11-24 | 重庆大学 | Neural network BP decoding method based on coding distributed computation |
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| CN103888225A (en) * | 2014-04-17 | 2014-06-25 | 李婧婧 | Method for fountain codes under binary erasure channel |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111064544A (en) * | 2019-10-16 | 2020-04-24 | 中国船舶重工集团公司第七一五研究所 | Cross-subcarrier underwater acoustic communication filtering multi-tone modulation method based on digital fountain coding |
| CN116366074A (en) * | 2023-03-17 | 2023-06-30 | 武汉大学 | LT code mixed coding and decoding method and system based on binary spread domain and improving fullness ratio |
| CN116366074B (en) * | 2023-03-17 | 2024-02-09 | 武汉大学 | LT code mixed coding and decoding method and system based on binary spread domain and improving fullness ratio |
| CN117118462A (en) * | 2023-09-07 | 2023-11-24 | 重庆大学 | Neural network BP decoding method based on coding distributed computation |
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