CN108055108A - The encryption algorithm of LT codes - Google Patents
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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
- H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
- H04L1/0009—Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the channel coding
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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
- 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
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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
- 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
- H04L1/0061—Error detection 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
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0061—Error detection codes
- H04L1/0063—Single parity check
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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
- H04L1/0064—Concatenated codes
Abstract
This divisional application is related to a kind of encryption algorithm of LT codes, belongs to satellite channel coding field, and encoding and decoding complexity is higher in solution LT codes, and when incoming symbol number is smaller, decoding performance declines the problems such as apparent, and technical essential is：Initial data is divided into k number according to bag according to isometric l；According to robust solitary wave degree of fixation distribution function Φ (d) is truncated, number of degrees d is randomly selected；In k number according to d data packet of selection of bag equal probability；D data packet of selection is subjected to exclusive or, operation result is denoted as a coding bag；Step is repeated, until receiving terminal receives enough coding bags.
Description
The application is application number 2017105807665, " degree in LT codes is distributed for applying date 2017-07-17, denomination of invention
The divisional application of optimization algorithm and equipment ".
Technical field
The invention belongs to satellite channel coding fields, and emerging digital fountain code is studied, it is proposed that a kind of new
Distribution optimization algorithm is spent, that is, truncates robust solitary wave degree of fixation distribution (Chopped Robust Soliton Stationary
Distribution, C_RSSD).The algorithm is effectively improved the compiling code performance of LT codes in fountain codes.
Background technology
With the fast development of information technology and becoming increasingly abundant for Information application, people are for the quality of satellite communication system
Increasingly higher demands are proposed with capacity, this has pushed directly on the development of satellite communication channel coding.Satellite link have easily by
The features such as space environment is disturbed, time delay is longer, Bandwidth-Constrained affects the overall performance of satellite communication system.Ensure to communicate
Quality, it is necessary to using corresponding channel coding under certain power condition, to achieve the purpose that EDC error detection and correction.Satellite communication
In common channel coding have：Convolutional code, RS codes, serial concatenation of codes, Turbo code, LDPC code, fountain codes etc..Digital fountain code
It is a kind of emerging packet-based forward error correction, has the characteristics that channel adaptability is strong, encoding and decoding complexity is low.In addition,
Its characteristic that need not be fed back avoids network long delay caused by transmitting terminal waits as long for feedback acknowledgment, particularly satellite
In the case that network transfer delay is inherently very big, repeat request mechanism can introduce the time delay of bigger.Fountain codes it is another important
Feature is no rate, can adjust code check at any time with the variation of channel status to adapt to its variation.This feature can make to defend
Star network transmission system makes full use of channel capacity, effectively improve due to satellite channel it is complicated and changeable caused by high bit error etc.
Problem, so having apparent advantage using fountain codes as satellite channel coding, development prospect is boundless.
What is be widely used at present in fountain codes has a LT codes and Raptor codes, wherein Raptor codes be by conventional error correction code with
The cascade generation of LT codes, Raptor codes are used by the MBMS standards of 3GPP at present.It is main to wrap on the research of digital fountain code
Design, the design of coding method and interpretation method design of degree of including distribution etc., the property of moderate distribution function and digital fountain code
Can be directly related, decide decoding success rate, decoding cost, encoding and decoding complexity etc., the key for designing fountain codes is to construct
Suitable degree distribution function.LT codes can be described by source incoming symbol number k and degree distribution Ω (d), be denoted as LT (k, Ω (d)),
Degree distribution is defined in the probability distribution (Ω on set of integers { 1,2 ..., k }1,Ω1,…,Ωk), wherein ΩdRepresent defeated by d
Enter symbol to be encoded and obtain the probability of a coded identification, it is possible to use the form degree of a representation distribution of generator polynomial, i.e.,Luby gives two kinds of common degree distribution forms when proposing the design of LT codes, is preferable respectively
Solitary wave is distributed (Ideal Soliton Distribution, ISD) and on its basis improved robust solitary wave distribution (Robust
Soliton Distribution, RSD).Theoretically ISD distributions make each coded identification in each decoding iteration with identical
Probability discharges, and has and only there are one the coded identification that degree is 1 in iteration every time, in practical work, it is easy to change in decoding
Because of the coded identification that degree of lacking is 1 in generation, so as to cause decoding failure.The distribution of RSD degree is a kind of degree distribution most common at present
Function, it introduces 2 parameters can translate the size of rendezvous value during decoding to change, it causes decoding process more to tend to be steady
It is fixed.But the probability that RSD degree is distributed medium and small angle value is smaller, there may be interruptions for decoding process；And it is compiled when using the distribution of RSD degree
During code, averagely coding degree increases with the increase of code length, so as to which its encoding and decoding complexity also increases therewith；Simultaneously when code length compared with
Hour, decoding failure rate is also higher.
The content of the invention
It is higher to be distributed in encoding and decoding complexity in LT codes for most practical robust solitary wave, and incoming symbol number compared with
Hour, decoding performance declines the problem of apparent, it is proposed that a kind of new truncation robust solitary wave degree of fixation distribution (C_RSSD).
Its technical solution is as follows：
A kind of degree distribution optimization algorithm in LT codes, step are：By improved truncation robust solitary wave degree distribution with
Degree of fixation distribution after adjustment is combined and is normalized, and is formed and truncates robust solitary wave degree of fixation distribution Φ (d), table
It is up to formula：
Wherein：D is angle value, and α and β are proportionality coefficient, and 0 ＜ α ＜, 1,0 ＜ β ＜ 1；
Degree of fixation distribution expression formula after adjustment：
Z (x)=0.107174x+0.444213x2+0.149598x3+0.065381x4+0.074302x5
+0.050452x8+0.033506x9+0.050031x19+0.022521x65+0.002822x66
The improved expression formula for truncating the distribution of RSD degree：
μ(d)：RSD degree distribution expression formulas；D：The maximum angle value of truncation degree distribution.
Further, it is to the improved method of degree of fixation distribution：The expression formula that degree of fixation is distributed is denoted as S (x) first, it is right
Except the probability value for spending other angle value for 1 all reduces itself 10%, probability value all degree of imparting 1 of reduction, degree of fixation distribution
In all angle value probability and equal to 0.999998, for accuracy distribution expression formula, by remaining 0.000002 also degree of imparting
1。
Further, the distribution of RSD degree is truncated in the method for obtaining truncation degree distribution expression formula is：
1) by k/R compared with maximum angle value d in degree of fixation distribution；
2) if k/R >=d makes D=k/R；If k/R ＜ d, make D=d；
3) angle value of d ＞ D truncates during RSD degree is distributed；
4) distribution of truncation degree is normalized, obtains the degree distribution of truncation robust solitary wave and be denoted as C_RSD.
The invention further relates to the degree distribution optimization equipment in a kind of LT codes, store some instructions, described instruction is by processor
It loads and performs：
It is combined and is normalized by degree of fixation distribution of the improved truncation robust solitary wave degree distribution after adjustment
Reason, forms and truncates robust solitary wave degree of fixation distribution Φ (d), and expression formula is：
Wherein：D is angle value, and α and β are proportionality coefficient, and 0 ＜ α ＜, 1,0 ＜ β ＜ 1；
Degree of fixation distribution expression formula after adjustment：
Z (x)=0.1113591x+0.49357x2+0.16622x3+0.002764x4+0.082558x5
+0.056058x8+0.0037229x9+0.05559x19+0.025023x65+0.003135x66
The improved expression formula for truncating the distribution of RSD degree：
Wherein：μ (d) is distributed for RSD degree；D：The maximum angle value of truncation degree distribution.
Further, it is to the improved method of degree of fixation distribution：The expression formula that degree of fixation is distributed is denoted as S (x) first, it is right
Except the probability value for spending other angle value for 1 all reduces itself 10%, probability value all degree of imparting 1 of reduction, degree of fixation distribution
In all angle value probability and equal to 0.999998, for accuracy distribution expression formula, by remaining 0.000002 also degree of imparting
1。
Further, the distribution of RSD degree is truncated in the method for obtaining truncation degree distribution expression formula is：
1) by k/R compared with maximum angle value d in degree of fixation distribution；
2) if k/R >=d makes D=k/R；If k/R ＜ d, make D=d；
3) angle value of d ＞ D truncates during RSD degree is distributed；
4) RSD distributions will be truncated to be normalized, and will obtain truncation RSD degree distributions and be denoted as C_RSD.
Advantageous effect：The present invention is distributed using the degree of fixation distribution after adjustment and improved truncation RSD degree, and by the two
With reference to normalized is made, the probability of small angle value can be increased, the possibility of generation interruption during decoding is reduced, reduce simultaneously
The average angle value of degree distribution reduces the whole redundant operation of decoding, so as to reduce encoding and decoding complexity, improves its property
Energy.
Description of the drawings
Below in conjunction with attached drawing, the present invention is described in detail；
The flow chart of Fig. 1 optimization degree Distribution Algorithms；
When Fig. 2 k=70, c=0.05, δ=0.05, the probability distribution graphs of three kinds of degree distribution functions；
When being compiled respectively yard using three kinds of degree distributions during Fig. 3 k=500, the relation of decoding success rate and decoding overheads
Figure；
The cataloged procedure of Fig. 4 LT codes；
Fig. 5 is based on LT codes and the cascade satellite network channel coding of LDPC code and transmission plan.
Specific embodiment
A kind of degree distribution optimization algorithm in LT codes, comprises the following steps：
1. a pair degree of fixation distribution is improved
Degree of fixation distribution is that one kind that people sum up in long-term application to engineering practice is very practical
Degree distribution, is mainly suitable for for the longer LT codes of code length, smaller for 1 probability due to spending for the shorter LT codes of code length, causes
It is very little to spend the quantity of the coding bag for 1, so as to easy decoding failure.Stationary distribution is referred to as SD (Stationary
Distribution), S (x) is denoted as, is expressed as with the form of generator polynomial：
In formula (1.1), SdRepresentative degree is the probability value of d.Next degree of fixation distribution is adjusted：Due to degree to be improved
1 probability value, it is necessary to reduce the probability value of other angle value, in order to degree of being kept fixed distribution probability distribution tendency, to except
The probability value for spending other angle value for 1 all reduces itself 10%, probability value all degree of imparting 1 of reduction.An it is understood that degree
The probability of all angle value of distribution function and should be equal to 1, but degree of fixation distribution in all angle value probability and be equal to
0.999998, accurate probability-distribution function in order to obtain, by 0.000002 (remaining probability value) also imparting degree 1.After changing
Degree of fixation distribution (Adjusted_Stationary Distribution, A_SD), Z (x) is denoted as, with the shape of generator polynomial
Formula is expressed as：
The average angle value of degree of fixation distribution is 5.8703, and the average angle value of amended degree of fixation distribution is 5.3833, drop
Low average angle value so as to reduce the computing redundancy and encoding and decoding complexity during coding and decoding, improves the globality of LT codes
Energy.
2. a pair RSD degree distribution truncates
(1) first we provides the expression formula of RSD degree distribution, is denoted as μ (d)：
Wherein,
Wherein, k is incoming symbol number, and d is angle value, and ρ (d) is ISD degree distribution functions, and τ (d) is auxiliary function, and c is normal
Number and 0 ＜ c ＜ 1；When δ receives n coding groups for decoder, whole original data packets can successfully be recovered permitted
The probability of decoding failure, and 0 ＜ δ ＜ 1.
(2) distribution of RSD degree is truncated
It is known that in probability value all very littles of d ＞ k/R angle value, the probability for arriving the angle value more than k/R is chosen in coding
Very little very little, so carrying out appropriate truncation to it.It concretely comprises the following steps：
1) by k/R compared with maximum angle value d in degree of fixation distribution；
2) if k/R >=d makes D=k/R；If k/R ＜ d, make D=d；
3) angle value of d ＞ D truncates during RSD degree is distributed；
4) RSD distributions will be truncated to be normalized.Amended truncation degree is distributed (Chopped_Robust
Soliton Distribution, C_RSD) Ψ (d) is denoted as, expression formula is：
The maximum angle value of amended truncation degree distribution is D, due to eliminating larger angle value, reduces average angle value
Value reduces the whole redundant operation of decoding, so as to reduce encoding and decoding complexity, improves its performance.Improved truncation
The distribution of RSD degree is to truncate the distribution of robust solitary wave degree, is denoted as C_RSD in the present embodiment, using blocking RSD degree point in the present invention
Cloth is expressed.
3. the merging of two kinds of degree distributions
C_RSD degree is distributed is combined and is normalized with the degree of fixation distribution after adjusting, formed it is a kind of newly
Degree distribution, ψ (d) represent the degree distribution after optimization, and expression formula is：
(7) in formula, Φ (d) represents the degree distribution after optimization, when representing to be encoded using this degree distribution, coded data point
Group degree is the probability of d, is denoted as and truncates robust solitary wave degree of fixation distribution (Chopped Robust Soliton Stationary
Distribution, C_RSSD).Wherein α and β is proportionality coefficient, and 0 ＜ α ＜, 1,0 ＜ β ＜ 1 can pass through according to demand
Proportionality coefficient is adjusted to find optimal degree distribution function.Ψ (d) is distributed C_RSD for truncation degree, and Z (d) is the fixation after adjustment
Distribution function is spent, the degree distribution after optimization can combine the advantages of both degree are distributed.As shown in Figure 1, it is distributed and calculates for optimization degree
The flow chart of method, Fig. 2 are the distribution of robust solitary wave degree, degree of fixation distribution and the probability distribution for truncating the distribution of robust solitary wave degree of fixation
Figure.
Under MATLAB emulation tools, simulating, verifying, as a comparison, incoming symbol 0 are carried out to new degree distribution function
Or 1 binary sequence, the parameter of C_RSSD and RSD degree distribution is all for c=0.05, δ=0.05.Proportionality coefficient be set to α=
0.5, β=0.5, Ψ (d) is identical with Z (d) weights.Table 1 is the average angle value of RSD, SD and C_RSSD degree distribution, and attached drawing 3 is to work as
When being compiled respectively yard using these three degree distributions during incoming symbol number k=500, the pass of decoding success rate and decoding overheads
It is analogous diagram.
1 three kinds of degree of table are distributed in the average angle value under different code length k
| Incoming symbol k | The average angle value of RSD | The average angle value of SD | The average angle value of C_RSSD |
| 200 | 9.3339 | 5.8703 | 6.9511 |
| 500 | 10.9507 | 5.8703 | 7.3728 |
| 1000 | 12.2258 | 5.8703 | 7.6948 |
The present invention is the optimization carried out to the degree distribution in LT codes, it is proposed that a kind of new degree Distribution Algorithm is next right
The application being distributed in LT codes is spent to be introduced.
(1) effect of the coding principle of LT codes and degree distribution
Assuming that input raw data packets are X=(x1,x2…xk), LT coding bags are Y=(y1,y2…yk), LT cataloged procedures
As shown in Figure 4, algorithm flow is as follows：
1) initial data is divided into k number according to bag (insufficient to mend 0 completion) according to isometric l；
2) according to robust solitary wave degree of fixation distribution function Φ (d) is truncated, number of degrees d is randomly selected, wherein C_RSSD degree is distributed
Probability distribution graph as shown in Figure 2；
3) in k number according to d data packet of selection of bag equal probability；
4) d data packet of selection is subjected to exclusive or, operation result is denoted as a coding bag；
5) repeat 2), 3), 4) step, until receiving terminal receives enough coding bags.
(2) decoding algorithm of LT codes
Decoding algorithm of the generally use belief propagation compiler algorithm (abbreviation BP decoding algorithms) as fountain codes, algorithm flow
It is as follows：
1) the direct restoring degree of decoder is 1 coded identification, if not spending the coded identification for 1, decoding failure；
2) neighbours that the coded identification after recovery is connected with it carry out exclusive or respectively, update the coded identification of its neighbour,
Remove their adjacent sides simultaneously；
3) repeat above step 2), 3) until recovering all original input symbols, then it is successfully decoded.
If the average angle value that can be seen that degree distribution function by LT coding and decoding processes is higher, during coding and decoding into
Capable XOR operation is just more with iterations, so as to considerably increase the time of coding and decoding and complexity.But if average degree
It is worth relatively low, raw data packets are not it is possible that be all covered, so as to cause decoding failure or need more decoding overheads.
So degree distribution function is directly related with the performance of digital fountain code, decide that decoding success rate, decoding cost, coding and decoding are complicated
Degree etc. constructs the key point that suitable degree distribution function is fountain codes.
LT codes and LDPC code are cascaded the channel coding as satellite network by we, and the degree distribution wherein in LT codes, which uses, to cut
Short robust solitary wave degree of fixation is distributed C_RSSD.Application scheme in satellite network channel coding is as shown in Figure 5.
The above is only the preferable specific embodiment of the invention, but the protection domain of the invention is not
This is confined to, in the technical scope that any one skilled in the art discloses in the invention, according to the present invention
The technical solution of creation and its inventive concept are subject to equivalent substitution or change, should all cover the invention protection domain it
It is interior.
Claims (1)
1. a kind of encryption algorithm of LT codes, it is characterised in that：
1) initial data is divided into k number according to bag according to isometric l；
2) according to robust solitary wave degree of fixation distribution function Φ (d) is truncated, number of degrees d is randomly selected；
3) in k number according to d data packet of selection of bag equal probability；
4) d data packet of selection is subjected to exclusive or, operation result is denoted as a coding bag；
5) repeat 2), 3), 4) step, until receiving terminal receives enough coding bags.
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| CN108055108B (en) | 2020-06-16 |
| CN107994974B (en) | 2020-09-22 |
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