CN103346858A - System LT code compiling method based on superposition degree - Google Patents

Abstract

The invention provides a system LT code compiling method based on the superposition degree. The method comprises the following compiling steps: conducting initialization, defining input nodes S, middle nodes I and redundancy check nodes R, constructing a BP translatability matrix in advance, and utilizing S=I G<ENC> to generate the I; generating the R by the I in a distribution mode through the superposition degree; using the S and the R as output nodes to be sequentially sent out. SPDD degree distribution is designed and optimized for the middle nodes of system coding, a DD doping level component is arranged in a superposition mode on the basis of WRSD degree distribution, the full coverage probability on information nodes is effectively ensured, and meanwhile the method has the advantages of ensuring linear code compiling complexity and partial recovery of the middle nodes and theoretically proving the asymptotic performance of the SPDD.

Description

System LT sign indicating number Compilation Method based on the stack degree

Technical field

The present invention relates to a kind of system LT sign indicating number Compilation Method, relate in particular to a kind of coding that the LT of limit for length system sign indicating number is arranged, interpretation method based on the stack degree.

Background technology

In recent years, can approach the fountain sign indicating number of erasure channel tolerance limit with lower coding and decoding complexity, receive correlative study person's very big concern.The no code check characteristic of fountain sign indicating number makes transmitting terminal to produce unlimited coding groups to k information block, sprays to receiving terminal; And receiving terminal only need successfully receive and be slightly more than k encoded packets, can (BeliefPropagation, BP) iterative decoding algorithm recovers raw information by a kind of simple message transmission.The fountain sign indicating number has been extended to packet with traditional channel error correction coding, provides a kind of efficient forward direction that need not based on feedback link to entangle and has deleted transmission mechanism.Especially code length 10 ³The long LT sign indicating number of the short code of the order of magnitude, the information block that is applicable to the Delay Tolerant Network scene that the node operational capability is limited is entangled and is deleted (as Internet of Things, survey of deep space etc.).Coding in actual applications often needs to adopt the systematic code structure, namely constitutes transmitted codewords by raw information and redundancy check information.Deletion or probability of erasure do not take place when extremely low at channel, receiving terminal can directly recover raw information to avoid deciphering expense, can reduce processing delay greatly.

But the random coded mode that the LT sign indicating number of Luby design and the Raptor sign indicating number of Shokrollahi adopt makes its original encoding scheme be difficult for obtaining the systematic codeword structure.Therefore, Shokrollahi has designed relevant patented technology, generator matrix by (weak robust solitary wave distributes) LT sign indicating number that the WRSD of cascade is distributed carries out inverse transformation, obtains intermediate node and then tectonic system Raptor sign indicating number, but the inverse transformation action need O (k of generator matrix ²) complexity, information node count k when big encoder complexity exceeded the limited communication node ability of hardware.3GPP utilizes the generator matrix of pseudo random sequence structure input node and intermediate node, the minimum Raptor code system encoding scheme of a kind of redundant decoding expense has been proposed, (decoding this moment end needs O (k for Gaussian Elimination, GE) decoding algorithm but receiving terminal need use gaussian elimination ²) complexity.More than two kinds bigger based on the improved system coding scheme of Raptor sign indicating number complexity, and need the precoding structure.And existing a kind of Barebone doping LT sign indicating number that intermediate node is interweaved (Quasi-Systematic Doped LT Codes, QS-DLT), omitted the precoding structure of Raptor sign indicating number, and obtained asymptotic performance when infinite (be code length level off to) of BP decoding, but its intermediate node interweave need be bigger the buffer memory expense.

On the other hand, existing degree distributes often based on asymptotic optimal design, often is difficult to obtain trading off of desirable complexity and decoding performance for the information block of finite length.Can translate collection by the expectation that introducing is revised in the prior art, divergent density be carried out in the degree distribution of practical code length LT sign indicating number evolve, but the degree of optimizing distribution can only guarantee to recover raw data packets as much as possible rather than recover original document.Also can utilize the derived degree distribution optimal solution of (＜100) LT sign indicating number under the utmost point short code elongate member of multimode Markov Chain in the prior art, but the high complexity of this optimization algorithm can't be found the solution it to the goodness distribution of practical length.Also proposed a kind of degree distribution optimization algorithm in the prior art, the suboptimum LT sign indicating number degree that this algorithm has provided short-and-medium code length distributes.Above-mentioned degree distribution optimization design for the fountain sign indicating number mainly is to be optimized at RSD, can't guarantee the linear complexity of coding and decoding process.Further, adopt the LT sign indicating number of RSD need receive the waterfall district that most code words just can enter BP decoding at the decoding end, namely receiving terminal needs extra wait time delay could begin the code word of recovering deleted in the transmission course.Therefore, utilize the part encoded packets received to recover raw information as early as possible and become in recent years hot research problem.But above-mentioned research all is the LT sign indicating number towards the nonsystematic structure.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the invention provides a kind of system LT sign indicating number Compilation Method based on the stack degree.

Compared to prior art, the present invention is directed to the demand of practical application, designed the long system LT code scheme of a kind of short code.Different with existing scheme, for the precoding computation complexity that reduces coding side or interweave and bring the buffer memory expense, at the design of the intermediate node of system coding and optimized a kind of SPDD degree and distribute, by the basis that distributes at the WRSD degree DD doping level component that superposeed, effectively guarantee the full choosing of information node is covered probability, have simultaneously and guarantee linear coding and decoding complexity and the part recovery characteristics of intermediate node, and theoretical proof the asymptotic performance of SPDD.Then based on the consideration of practicability parameter, under the condition of limited code length according to parameter optimizations such as code length, channel probability of erasure and decoded redundant expenses the stack ratio that distributes of SPDD degree.Simulating, verifying the system LT sign indicating number that proposes of the present invention under limited code length with respect to existing systems fountain code plan, have lower decoding failure probability.The quantitative relationship of following will superpose from theory analysis angle further investigation SPDD ratio p and other parameters with the applicability of extension system LT sign indicating number in the face of the different channels condition, and is further constructed general system LT sign indicating number.

Description of drawings

Fig. 1 is the encoding scheme schematic diagram of the system LT sign indicating number Compilation Method based on the stack degree of the present invention.

Fig. 2 is the best value schematic diagram that the β value is influenced by δ under the short code elongate member among the present invention.

Fig. 3 is the SPDD degree distribution schematic diagram of different stack ratio p among the present invention.

Fig. 4 be among the present invention SPDD and WRSD select the covering performance schematic diagram entirely.

Fig. 5 is the BP decoding failure probability schematic diagram of three kinds of systematic codes among the present invention

Fig. 6 is the decoding performance contrast schematic diagram of the LT of system sign indicating number and other schemes among the present invention.

Embodiment

The present invention is further described below in conjunction with description of drawings and embodiment.

See also Fig. 1 to Fig. 6, the limitation of the design requirement of taking into account system fountain sign indicating number of the present invention and existing degree distribution optimization scheme, for reducing the coding and decoding expense that precoding that existing system structure fountain sign indicating number adopts or intermediate node interweave and bring, at the intermediate node in the LT of the system sign indicating number cataloged procedure, a kind of distribution of new stack degree (Superposing Degree Distribution, SPDD) LT of system code encoding method have been designed.Design has also been optimized a guarantee information node and has been selected the doping level component that covers probability entirely (Doping degree Distribution DD), and has verified that SPDD has BP and deciphers asymptotic performance and linear coding and decoding complexity.Then under the long condition of short code according to parameter optimizations such as code length, channel probability of erasure and decoded redundant expenses the stack ratio of SPDD, the system LT sign indicating number that has obtained to have practical parameter, and carried out emulation relatively with Raptor sign indicating number and QS-DLT sign indicating number.

The encryption algorithm flow process of LT sign indicating number of the present invention may further comprise the steps:

Initialization is constructed BP in advance and can be translated matrix

Utilize S=IG ^ENCGenerate I;

Utilize the SPDD degree to distribute and generate R by I;

S and R are sent successively as output node.

The decoding algorithm step of system LT sign indicating number is as follows:

Initialization, structure synchronously

Continue to receive output node, if S does not have deletion, then decoding finishes; If S has deletion, then utilize the S and the R that have received to recover I, by

Construct deleted S;

If all S recovers, decoding finishes;

If there is not new output node, and not full recovery of S, decoding failure announced.

In above step, at first node S is imported in definition, intermediate node I and redundancy check node R, and system LT sign indicating number coding structure is as shown in Figure 1.At first utilize pseudo random sequence to construct a k at specific code length k * k BP decodable code matrix in advance

Notice that receiving terminal and transmitting terminal can obtain by time synchronized or the trigger message of pseudo random sequence generator

To carry out the BP decoding of the LT of system code word.

Intermediate node I is most important factor in the system LT sign indicating number design of the present invention.S (S=IG at first ^ENC) can and reuse previously selected by the BP decoding algorithm with I

Construct; I utilizes SPDD to produce ε k R then, and ε is a nonnegative real number with the successfully decoded probability correlation of expectation of the LT of system sign indicating number.Transmitting terminal sends as output node S and R together to receiving terminal, then need to consider following two problems:

1) guarantees to construct in advance the G of k * k ^ENCBe that BP can translate.In the practical communication process, the G of k * k ^ENCEasily because the deletion of indivedual transmitted codewords causes BP decoding to stop before recovering all I.And be (1+ ε) LT of k system sign indicating number for the decoded redundant expense, can be divided into two situations: 1. when channel probability of erasure δ hour, suppose that δ k input node S is deleted, do not need the I that recovers whole to recover whole S with this then this moment, more wish to recover most of I by the system LT code word that has received the S that the part I structure that probability utilization that namely can be higher recovers is lost; 2. when δ is big, then the shared ratio of R improves (the LT sign indicating number of system LT sign indicating number trend random coded) in (1+ ε) k systematic codeword of receiving of receiving terminal, namely can pass through then by the whole I of BP decoding algorithm recovery

Recover whole S.Therefore, problem turns to and how to recover I reliably by (1+ ε) k output node that receives.

2) as guaranteeing to adopt the decoding success rate of BP decoding.Deciding factor degree of being distribution design, how to design SPDD and can recover I reliably to guarantee (1+ ε) k output node that receives: if adopt RSD need receive the almost encoded packets of k quantity, just can enter BP decoding waterfall district, limit system LT sign indicating number in δ efficient hour; And the characteristics of recovery raw information as much as possible rather than full detail in the linear coding and decoding complexity of WRSD and the BP decode procedure are more suitable for the design object of system LT sign indicating number of the present invention.But the problem that WRSD exists is, and is not high to the full choosing covering probability of information node.The Raptor sign indicating number adopts precoding to address this problem, and the flexibility in order to reduce complexity and to improve the system coding scheme, SPDD solves this problem by design.

(Doping degree Distribution, the key parameter of design and optimization DD): WRSD are parameter preset ε (ε＞0, relevant with reliability of decode and complexity) to the doping level component, its generating function Ω _WRSD(x) be:

${\mathrm{\&Omega;}}_{\mathrm{WRSD}}\left(x\right)=[\mathrm{\&mu;x}+{\mathrm{\&Sigma;}}_{i=2}^S{x}^i/(i\&CenterDot;(i-1))+x^{S+1}/S]/(\mathrm{\&mu;}+1)---\left(1\right)$

Wherein,

μ=ε/2+ (ε/2) ²If δ=ε/4 (1+ ε) then adopts the LT sign indicating number of WRSD to recover (1-δ) n intermediate node with the BP decoded mode by any (1+ ε/2) the n+1 output node that receives, the coding and decoding complexity is O (ln (1/ ε)).

For reducing the expense that adopts precoding or intermediate node to interweave and bring in the existing systems fountain coding scheme, at first need to design a guarantee information node and select the doping level component DD that covers probability entirely, with compensation WRSD for selecting covering problem entirely between output node and the intermediate node.

The asymptotic optimality that obtains after consideration QS-DLT sign indicating number interweaves to intermediate node, adopt heuritic approach design doping level component (Doping degree Distribution, DD) (Jiao J, Zhang Q Y, Guo Q.Packets interleaving CCSDS file delivery protocol in deep space communication[J] .IEEE Aerospace Electronic System Magazine, 2011,26 (2): 5-11.).The degree distribution generating function of definition DD is Ψ (x), and its initial distribution Ψ (x) needs k component, to guarantee that the information node of specific code length is selected covering entirely.Simultaneously, by two harmonic progression components and the degree component β (β=ε k) with maximum weight, the corresponding probability-distribution function of structure DD

For:

Normalization

Obtain the generating function Ψ (x) of DD:

Next discuss under the practical codes elongate member, among the doping level component DD β and Span.Because the value of DD is on the basis of using WRSD, the full choosing that improves information node covers probability to guarantee the success rate of BP decoding, simultaneously for keeping the linear coding and decoding complexity of WRSD, so the parameter value of DD need satisfy β＞S+1 and

Fig. 2 has provided DD parameter value under the short code elongate member to the influence of decoding performance, for selected channel probability of erasure δ=0.5 and decoded redundant ε=0.2, by the performance curve among Fig. 2 as can be seen, the β value of actual optimum is slightly larger than 0.2k, can think that δ is influential for the required ε of reality decoding, cause optimum β value to be offset institute's setting parameter, can further optimize and revise the β value according to δ.

The design and optimization that the stack degree distributes: on the basis of above-mentioned research, at Ω _WRSD(x) Ψ of definition (x) stack ratio p is to obtain SPDD, then the generating function Ω of SPDD _SPDD(x) be:

${\mathrm{\&Omega;}}_{\mathrm{SPDD}}\left(x\right)=\frac{{\mathrm{\&Omega;}}_{\mathrm{WRSD}}\left(x\right)+p\&CenterDot;\mathrm{\&psi;}\left(x\right)}{1+p}---\left(4\right)$

Fig. 3 has provided the SPDD of code length k=500, the SPDD degree distribution probability curve under different p values, and compare with RSD and WRSD.At first, SPDD degree distribution probability value has three peak values, respectively by degree be 2, the maximum weight degree component β of the maximal degree S of WRSD and DD determines; Secondly, after β determined, SPDD stack ratio p only influenced its probable value, to the not influence of each peak value number of degrees; At last, compare with RSD, though the β of DD greater than the second peak value number of degrees of RSD, controls it by p and selects probability, can guarantee that the overall complexity of SPDD is still less than RSD.

Theorem 1: the code parameters that adopts SPDD to generate is (k, Ω _SPDD(x)) LT sign indicating number, definition decoded redundant parameter ε (ε＞0), then there is an arithmetic number c relevant with ε, make the decoding end of this LT sign indicating number can use the BP decoding algorithm, to be not more than exp (probability of failure ck), recover from (1+ ε) k encoded packets of any reception and be no less than (1-p) k information node, the p interval is:

Proof: based on the and/or tree analysis theories, only need prove the bipartite graph of the encoded packets formation that is received by (1+ ε) k success to above-mentioned lemma, the limit distribution generating function λ (x) of its left side information node and the limit distribution generating function ρ (x) of right side check-node, at x ∈ [p, 1) under the condition, satisfies inequality ρ (x)＞1-λ ^-1(1-x), the irreclaimable information node quantity≤pk of decoder then, the probability upper bound be exp (ck).

For the random coded mode of LT sign indicating number, the generating function λ (x) that the information node limit distributes obeys Poisson distribution, for:

λ(x)＝exp(d _l·(x-1)) (5)

D wherein _lThe average degree of expression information node, and the average degree of definition check-node is d _r, d then _r/ d _l=(1+ ε) k/k=1+ ε, and the generating function ρ (x) that the check-node limit distributes be ρ (x)=Ω ' (x)/Ω ' (1), with the generating function Ω of SPDD _SPDD(x) substitution has:

$\mathrm{\&rho;}\left(x\right)={\mathrm{\&Omega;}}^{\&prime;}\left(x\right)/{\mathrm{\&Omega;}}^{\&prime;}\left(1\right)=\frac{{{\mathrm{\&Omega;}}^{\&prime;}}_{\mathrm{WRSD}}\left(x\right)+p\&CenterDot;{\mathrm{\&psi;}}^{\&prime;}\left(x\right)}{d_r\&CenterDot;(1+p)}---\left(6\right)$

Wherein, can get Ω ' by formula (1) _WRSD(x):

${{\mathrm{\&Omega;}}^{\&prime;}}_{\mathrm{WRSD}}\left(x\right)=\frac{1}{\mathrm{\&mu;}+1}(\mathrm{\&mu;}-\ln (1-x))+x^S-\underset{s=S+1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{x^s}{S}---\left(7\right)$ (7)

$>\frac{1}{\mathrm{\&mu;}+1}(\mathrm{\&mu;}-\ln (1-x))$

And for Ψ ' (x),

Deployablely be:

$>\frac{1}{\mathrm{\&beta;}}\underset{i=1}{\overset{\mathrm{\&beta;}}{\mathrm{\&Sigma;}}}{x}^i+\frac{1}{\mathrm{\&beta;}}\underset{i=\mathrm{\&beta;}+1}{\overset{2\&CenterDot;\mathrm{\&beta;}-1}{\mathrm{\&Sigma;}}}{x}^i+\frac{1}{k}\underset{i=2\mathrm{\&beta;}}{\overset{k}{\mathrm{\&Sigma;}}}{x}^i$ (8)

$=\frac{1}{\mathrm{\&beta;}\&CenterDot;(1-x)}-\frac{1}{\mathrm{\&beta;}}\underset{i=2\mathrm{\&beta;}}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{x}^i+\frac{1}{k}\underset{i=2\mathrm{\&beta;}}{\overset{k}{\mathrm{\&Sigma;}}}{x}^i$

$>\frac{1}{2\mathrm{\&beta;}\&CenterDot;(1-x)}$

Then have:

Then the generating function ρ (x) of check-node limit distribution satisfies inequality:

Bring formula (5) and formula (10) into ρ (x)＞1-λ ^-1(1-x), and establish y=1-x, y ∈ (0,1], further obtain following inequality:

Utilize the relational expression d of check-node average degree and information node average degree _r/ d _l=1+ ε, formula (11) can turn to:

Then this SPDD degree asymptotic performance that distributes proves, transfers the establishment of proof inequality (12) to, establishes Q (x) and is:

With WRSD degree distribution Ω _WRSD(x) parameter value μ=ε/2+ (ε/2) ²Bring formula (13) into, verify easily Q (x) for (0,1] in following convex function, and have:

$\underset{x\&RightArrow;0}{\lim }Q\left(x\right)=+\&infin;$

Then to Q (x) differentiate with obtain (0,1] interval minimum value, make it satisfy Q (x)＞0, be equivalent to and find the solution Q ' (x)=0:

When x ∈ (0,1] time, have unique solution to be:

At this moment, if will guarantee inequality Q (x ₀Set up)＞0, works as Ω _SPDD(x) value of the stack ratio p in need satisfy the interval:

Card is finished

The asymptotic performance that theorem 1 has provided SPDD proves.And for limited code length condition, p is relevant simultaneously with δ and ε for the stack ratio, and optimum p value need satisfy p (x)＞1-δ λ ^-1(1-x), can this make up the optimization aim function, utilize the linear programming algorithm to obtain optimum p.When table 1 has provided code length k=500, be target to reach 99.99% decoding success rate, the best p value of different δ and ε correspondence.As can be seen from Table 1:

1) along with the increase of δ, reaching 99.99% the required ε of decoding success rate increases gradually, and when δ surpassed 0.75-0.99, receiving terminal need receive the output node of 1.5k quantity, could recover whole input node S with 99.99% decoding success rate.

2) for specific δ, p increases along with the increase of ε because when ε hour, can't satisfy 99.99% decoding success rate, can only recover more I by BP decoding as far as possible, thereby improve the decoding success rate of S by increasing the ratio of WRSD in SPDD; Increase gradually and work as ε, DD doping level component can better guarantee the full choosing of information node is covered, to guarantee the decoding success rate of S.

3) and for specific ε, p reduces along with the increase of δ, when δ hour, receiving terminal has only a spot of S deleted, mainly select covering power to recover a small amount of deleted S entirely can to finish decoding by the information node of DD this moment; And increase gradually as δ, receiving terminal receive a large amount of R, needing to increase the ratio of WRSD in SPDD could recover more I, and then the decoding success rate of raising S.

The best value that table 1. stack ratio p changes along with channel probability of erasure δ and decoded redundant ε

Simulation result is discussed: the ratio that among the present invention the decoding failure number of times is accounted for total simulation times, be that decoding failure probability (Decoding Failure Rate) is as the important indicator of weighing the LT of system code performance, the system LT sign indicating number that the SPDD degree that proposes by the emulation comparative analysis distributes and the Raptor of system sign indicating number, QS-DLT sign indicating number are in time-limited performance, and table 2 provides the simulation parameter configuration.

Table 2. Monte Carlo simulation parameter configuration

Parameter	Value
		Input number of nodes amount k	500，800，1000
Decoded redundant ε	0.1～0.5
		Channel probability of erasure δ	0.01，0.1，0.25，0.5，0.75，0.99
Encryption algorithm	System LT sign indicating number, system Raptor sign indicating number, QC-DLT sign indicating number
		Decoding algorithm	BP (iteration 20 times)
The simulation times of different decoded redundant	Success			10 4Inferior or fail 10 3Inferior

The SPDD degree distributes for the improvement of selecting covering performance entirely of information node: according to matrix theory as can be known, the capable full rank of decoding matrix G of and if only if receiving terminal just might be successfully decoded, and importing namely that node selects entirely is its necessary condition.The Raptor sign indicating number has the precoding structure simultaneously, can recover the small number of nodes that the WRSD degree distribution LT sign indicating number of cascade can not be deciphered, therefore in simulation process, system Raptor sign indicating number covers for the full choosing of information node and reaches 95% and think that namely the full choosing of having finished information node covers.Fig. 4 has provided the system LT sign indicating number that adopts SPDD and the system Raptor sign indicating number that adopts WRSD, at code length k=500, and 800,1000, channel probability of erasure δ=0.5 o'clock, the corresponding covering performance curve that selects entirely of different decoded redundant.The result shows that SPDD obviously is better than WRSD, has proved than the WRSD of the Raptor of system sign indicating number, and the system LT sign indicating number of use SPDD can effectively promote and select covering performance entirely.

Decoding performance emulation and the contrast of the LT of SPDD system sign indicating number: δ and ε changed p the best value down when the LT of SPDD system code parameters was taken from the k=500 that table 1 lists.Because the QS-DLT sign indicating number is that the node ratio that interweaves of its design is fixed value 0.015 (k=65536) or 0.01 (k=∞) at the progressive best performance of long code design, performance is not good under short code is long.For justice carry out performance relatively, in emulation, optimized the node ratio that interweaves of QS-DLT sign indicating number again.Simultaneously, for the Raptor of system sign indicating number, its BP decoding has recovered 95% information node and has namely thought successfully decoded.The BP decoding performance of system LT sign indicating number, QS-DLT sign indicating number and the Raptor of system sign indicating number under Fig. 5 difference emulation relevant parameter.

As seen from Figure 5, the BP decoding performance of three kinds of systematic codes is subjected to the influence of channel probability of erasure δ bigger, along with the increase of δ, for reaching 10 ^-4The needed decoded redundant of decoding failure probability just more big.This architectural characteristic with systematic code is relevant:

1) obvious, systematic code is suitable for the lower communication scenes of channel probability of erasure, and for the code length of k=500, system Raptor sign indicating number and the LT of system sign indicating number all o'clock reach design object in δ=0.01, and QS-DLT is slightly poor, o'clock has also reached 10 in ε=0.25 ^-4The decoding failure probability.This is that (SPDD WRSD) constructs G because the LT of system sign indicating number and the Raptor of system sign indicating number have all adopted the degree with fast quick-recovery information node to distribute at coding side ^ENC, the input node that the I structure that can utilize part to recover when the S of minute quantity is deleted is lost.And the precoding of the Raptor of system sign indicating number can return at S and can recover full detail at 95% o'clock.

2) still, when δ is 0.1 and when above, the performance of system Raptor sign indicating number descends rapidly, and this is because systematic codeword structure when occurring damaging, the redundancy check node R that WRSD generates can't guarantee the recovery fully to intermediate node I, and then has influenced the whole successfully decoded of S.And this moment, system LT sign indicating number of the present invention obviously is better than the Raptor of system sign indicating number, this is because the robust property of the doping level component DD that the SPDD degree distributes, make that more S is deleted after, still can utilize R stable recover I, finish decoding.And the intermediate node interleaving technology that the QS-DLT sign indicating number adopts, in δ=0.1 o'clock similar to the decoding performance of system LT sign indicating number of the present invention (after optimizing the ratio of node in output node that interweave of QS-DLT sign indicating number), when δ further increases, also be much better than the Raptor of system sign indicating number, proved the QS-DLT sign indicating number to the interleaving technology of intermediate node effectively.But because the QS-DLT sign indicating number at the long code design, is not optimized the long parameter of short code, compared to system LT sign indicating number of the present invention, decoding performance is relatively poor.Fig. 6 has provided the BP decoding performance advantage of system LT sign indicating number compared to other two kinds of system's fountain code plans intuitively.

As can be seen from Figure 6, near design object ε=0.2, the decoding performance of system LT sign indicating number is with the obvious advantage.And δ is more big, and system LT sign indicating number is more big with respect to the decoding performance lifting of other two kinds of system's fountain sign indicating numbers, has verified that the simulation performance that the SPDD degree distributes conforms to the target of theoretical optimization design.

The present invention is directed to the demand of practical application, designed the long system LT code scheme of a kind of short code.Different with existing scheme, for the precoding computation complexity that reduces coding side or interweave and bring the buffer memory expense, at the design of the intermediate node of system coding and optimized a kind of SPDD degree and distribute, by the basis that distributes at the WRSD degree DD doping level component that superposeed, effectively guarantee the full choosing of information node is covered probability, have simultaneously and guarantee linear coding and decoding complexity and the part recovery characteristics of intermediate node, and theoretical proof the asymptotic performance of SPDD.Then based on the consideration of practicability parameter, under the condition of limited code length according to parameter optimizations such as code length, channel probability of erasure and decoded redundant expenses the stack ratio that distributes of SPDD degree.Simulating, verifying the system LT sign indicating number that proposes of the present invention under limited code length with respect to existing systems fountain code plan, have lower decoding failure probability.The quantitative relationship of following will superpose from theory analysis angle further investigation SPDD ratio p and other parameters with the applicability of extension system LT sign indicating number in the face of the different channels condition, and is further constructed general system LT sign indicating number.

Above content be in conjunction with concrete preferred implementation to further describing that the present invention does, can not assert that concrete enforcement of the present invention is confined to these explanations.For the general technical staff of the technical field of the invention, without departing from the inventive concept of the premise, can also make some simple deduction or replace, all should be considered as belonging to protection scope of the present invention.

Claims (10)

1. system LT sign indicating number Compilation Method based on the stack degree is characterized in that: comprise following coding step:

Initialization, definition input node S, intermediate node I and redundancy check node R are constructed BP in advance and can be translated matrix

Utilize S=IG ^ENCGenerate I;

Described I distributes by the stack degree and generates R;

S and R are sent successively as output node.

2. according to the described system LT sign indicating number Compilation Method based on the stack degree of claim 1, it is characterized in that: described system LT sign indicating number Compilation Method based on the stack degree also comprises following decoding step:

Initialization, structure synchronously

Continue to receive output node, if S does not have deletion, then decoding finishes; If S has deletion, then utilize the S and the R that have received to recover I, by

Construct deleted S;

If all S recovers, decoding finishes;

If there is not new output node, and not full recovery of S, decoding failure announced.

3. according to the described system LT sign indicating number Compilation Method based on the stack degree of claim 2, it is characterized in that: in the initialization step in the described cataloged procedure, utilize the pseudo random sequence of obeying the distribution of stack degree to construct a k at specific code length k * kBP decodable code matrix in advance

By time synchronized or the trigger message of pseudo random sequence generator, obtain

To carry out BP decoding.

4. according to the described system LT sign indicating number Compilation Method based on the stack degree of claim 3, it is characterized in that: in the described coding step, S and I are previously selected by BP decoding algorithm and recycling

Construct; Described I utilizes the stack degree to distribute and produces ε k R, and ε is nonnegative real number.

5. according to the described system LT sign indicating number Compilation Method based on the stack degree of claim 4, it is characterized in that: described based on adopting the stack degree to distribute in the system LT sign indicating number Compilation Method cataloged procedure of stack degree, it satisfies following formula:

${\mathrm{\&Omega;}}_{\mathrm{SPDD}}\left(x\right)=\frac{{\mathrm{\&Omega;}}_{\mathrm{WRSD}}\left(x\right)+p\&CenterDot;\mathrm{\&psi;}\left(x\right)}{1+p}$

Wherein,

μ=ε/2+ (ε/2) ²

6. according to the described system LT sign indicating number Compilation Method based on the stack degree of claim 5, it is characterized in that: utilize the stack degree to distribute in the described coding step and generate in the process of R by I, set the doping level component and distribute with weak robust solitary wave and superpose, be used for the compensate for channel probability of erasure for selecting covering problem entirely between output node and the intermediate node.

7. according to the described system LT sign indicating number Compilation Method based on the stack degree of claim 6, it is characterized in that: the corresponding probability-distribution function of described doping level component

For:

Normalization

Obtain the generating function Ψ (x) of doping level component:

β is the degree component with maximum weight, β=ε k, and described β＞S+1, described

8. according to the described system LT sign indicating number Compilation Method based on the stack degree of claim 7, it is characterized in that: the generating function Ω that described stack degree distributes _SPDD(x) for satisfying:

${\mathrm{\&Omega;}}_{\mathrm{SPDD}}\left(x\right)=\frac{{\mathrm{\&Omega;}}_{\mathrm{WRSD}}\left(x\right)+p\&CenterDot;\mathrm{\&psi;}\left(x\right)}{1+p}---\left(4\right)$

P is Ψ (x) stack ratio.

9. described system LT sign indicating number Compilation Method based on the stack degree according to Claim 8, it is characterized in that: the interval of described p is:

10. according to the described system LT sign indicating number Compilation Method based on the stack degree of claim 9, it is characterized in that:

Described for limited code length condition, the p value satisfies ρ (x)＞1-δ λ ^-1(1-x).

Images