CN100391141C - Coding parameter blind identification of fault tolerant code communicating channel - Google Patents

Abstract

The present invention belongs to the field of intelligence communication and information safety technology, particularly to a coding parameter blind identification method of a fault-tolerant code communicating channel. In the fields of the future intelligent mobile communication, broadcast multipoint communication and communication acquisition, a channel coding mode needs changing at any time following the change of time and environment in order to obtain the optimal communication efficiency and service quality. In the communication environment, the synchronous communication of persons who need multi-party communication can not be realized by a protocol generally; therefore, multi-part rapid blind identification which can realize channel coding parameters only by signal contents needs receiving so as to achieve the purpose of intelligent communication. Aiming at the requirement of intelligent communication, the present invention provides a coding parameter blind identification model without a protocol of a fault-tolerant code communicating channel; the model is quickly solved by solving a Homogeneous Key Module Equation (HKME); consequently, the quick coding blind identification without the protocol communication of a fault-tolerant channel is realized.

Description

A kind of communication channel blind identification method for coding parameters of error-tolerant code

Technical field

The invention belongs to intelligence communication and field of information security technology, be specifically related to a kind of communication channel blind identification method for coding parameters of error-tolerant code.

Technical background

In intelligent mobile communication, broadcast multipoint communication and the information acquisition field in future, along with the variation of time and environment need change channel coding method at any time, so that obtain optimum communication efficiency and service quality.In this communication environment, generally can't therefore need to receive the quick blind identification that can only realize the chnnel coding parameter in many ways by the agreement person's that realizes the multi-party communication synchronous contact by the content of signal, reach the purpose of intelligence communication.

The blind identification of signal (Blind Identification) technology is the field, forward position of current Communication Studies. and its target is in order to set up normal communication under the prerequisite that does not have training sequence (Training Sequence) equalization channel. and blind recognition technology is in communication, information theory, fields such as cybernetics and systematology have broad application prospects.

If F is a territory, establishing Z is an integer item, and N is a positive integer. the blind identification problem of so-called convolution code specifically describes as follows: establish a part of sequence of known convolution code sign indicating number sequence, with the polynomial repressentation on the integer item Z: C _i(D)=c _I0+ c _I1D+c _I2D ²+ ... + c _IND ^N, i=1,2 ... k.Obtain the generator polynomial g of the encoder for convolution codes that can generate this codeword sequence _i(D)=g _{I, 0}+ g _{I, 1}D+ ... + g _{I, t}D ^t, i=1,2 ... k.For for simplicity, establish k=2.

Can adopt Gaussian elimination method to find the solution g _i(D), but the Gauss elimination is not fault-tolerant, that is, each coefficient in the coefficient matrix in the equation group that find the solution can not be wrong.In the communication of routine, the error rate is 10 ^-2To 10 ^-3Between be recurrent.In order the identification that realize convolution code and other chnnel coding parameters under the situation of error code to be arranged, usually to adopt the lot of data acquisition test to calculate, by hundreds of times even tens thousand of secondary data collections and test calculating, making it possible to take a chance obtains one group of data of not having error code, solves separating of system of linear equations then.And the computation complexity of Gaussian elimination method is O (N ³).For example, the convolution code to 7/8 will be estimated t=60 usually, therefore, needs to gather about N=8 * 9 * 61=4392 the bit of zero defect continuously at least.Like this, be prob (e in the error rate _Ij=1) under the condition=0.005, must carry out 8 * 10 ⁹Repeatedly data are intercepted and captured, and can reach the bit that probability more than 95% is chosen 4392 zero defects.In order to make the Gauss elimination that unique solution be arranged, need 4 * 10 approximately ¹⁰Repeatedly sampling of data and Equation for Calculating.As seen the image data amount is very huge, and computational complexity is 3.2 * 10 ²¹With computing last time.

In order to realize the fast decoding of BCH code, Berlekamp (1968) [Berl] has proposed key equation KE, and to have provided computational complexity be O (N ²) famous KE derivation algorithm .Massey (1969) [Mass] synthtic price index of linear recurring sequence (LRS) summed up in the point that find the solution the KE equation, and provided and iterated algorithm. above-mentioned algorithm now is called Berlekamp-Massey algorithm (abbreviating the BM algorithm as).

So-called key equation KE be to find the solution following element to (f (x), L) ∈ F[x] * Z, satisfy:

f(x)C ₁(x)≡b(x)modx ^N+1，

And make 0≤degb (x)＜L, and f (0) ≠ 0, degf (x)≤L, and L reaches minimum.

Owing to find the solution the importance of KE, the contact of seeking new algorithm and disclosing the various inherences of existing algorithm is a flourishing long time research topic [Chen] in the field such as information theory, [Heyd], [Kail], [Kuij]. the efficiency parameters to the comprehensive relevant algorithm of LRS is one of cryptanalytic important evaluation criterion. and the BM algorithm has also been made special chip as the standard decoding algorithm of RS sign indicating number, be widely used in the storage of various communications and multimedia, improved everyone quality of life.

The present invention is summed up as a homogeneous crucial modular equation HKME with the quick blind identification problem of fault-tolerant chnnel coding of no-protocol contact, and with the polynomial ring F[x of two arguments, y] homogeneous ideal portray homogeneous crucial modular equation.

HKME has promoted KE.But it promotes direction and G.L.Feng[Feng] and S, Sakata[Saka] the popularization direction all different.The new direction of the present invention's research has stem-winding future.In fields such as intelligence communication, information acquisition and cryptanalysises important use is arranged.

List of references

[Adam]W.W.Adams and P.Loustaunau，An Introduction to Gr\″obner Bases，Amer.Math.Society，1994.

[Berl]E.R.Berlekamp，Algebraic Coding Theory，McGrw-Hill，New York，1968.

[Chen]M.H.Cheng，Generalised Berlekamp-Massey Algorithm，IEE Proceedings Communications，Vol.149(4)，207-210，August 2002.

[Feng]G.L.Feng，K.K.Tzeng，A New Procedure for Decoding Cyclic and BCH Codes up to Actual MinimunDistance，IEEE Trans.on Inform.Theory，vol.40，No.5，1994，pp1364-1374.

[Heyd]A.E.Heydtmann and J.M.Jensen，ON the Equivalence of the Berlekamp-Massey and the EuclideanAlgorithms for Decoding，IEEE Trans.Inform.Theory，vol.46(7)，2614-2624，2000.

[Kail]T.Kailath，Encounters with the Berlekamp-Massey Algorithm，in Communication and Cryptography，edited by R.E.Blahut，etl.Kluwer Academic Publisher，pp.209-220，1994.

[Kuij]]M.Kuijper and J.C.Willems，″On constructing a shortest linear recurrence relation，″IEEE Trans.Automat.Contr.vol.42，No.11，p1554-1558，1997.

[Lu05] Lu Peizhong, Shen Li, Zou Yan, Luo Xiangyang, the blind identification of deletion convolution code, Chinese science E collects, and 35 (2), 173-185,2005.

[Mass]Massey，J L，Shift-Register Synthesis and BCH Decoding，IEEE Trans.Info.Theory，15(1)：122-127，1969.

[Saka]S.Sakata，Synthesis of Two-Dimensional Linear Feedback Shift-Registers and Groebner Basis，LectureNotes in Comput.Sci.356，Springer-Verlag，Berlin，1989.

Summary of the invention

The objective of the invention is to propose the error-tolerant code communication channel blind identification method for coding parameters of low, the widely applicable no-protocol contact of a kind of computational complexity.

The communication channel blind identification method for coding parameters of the error-tolerant code that the present invention proposes comprises the structural model of the blind identification of fault-tolerant chnnel coding of a no-protocol contact of design, sets up the homogeneous crucial modular equation HKME of this structural model; And propose to find the solution the pairing algorithm of the SY2SY of this homogeneous crucial modular equation HKME, this model is carried out rapid solving, thereby realize the quick blind identification of fault-tolerant chnnel coding of no-protocol contact.

1, model

Sequence synthtic price index can be described as: known array c=(c ₀, c ₁..., c _N), ask can formation sequence the proper polynomial of number of times minimum of c.Traditional linear recurring sequence collective model such as Fig. 3 represent.

Because the primary signal of being obtained under the information acquisition background must have serious error code.Therefore must seek the problem that new method goes to find the solution the blind identification of signal parameter, determine the signal data form rapidly, entanglement form, error correction coding mode and frame structure form etc.The fault-tolerant analysis-by-synthesis of sequence is the basic problem in the cryptanalysis.

The difficult point of problem is fault-tolerance.The progression of different with the problem of finding the solution that contains wrong linear equation on the finite field is linear recurrence without limits.If therefore the progression of linear recurrence is oversize, it is infeasible then studying this problem with DISCRETE W alsh spectral method.

We start with from the desirable global nature of analysis recursion sequence and algebraically, have found many methods of finding the solution this problem.The present invention adopts a new Mathematical Modeling delineation to contain the synthtic price index of incorrect order row.Originally the key equation that was used to describe the BM algorithm is transformed into a homogeneous ideal equation.With a desirable linear recurrence that writes down all local sequences of all different starting points of sequence of reflection of relation.Therefore model of the present invention has been widened the implication of Berlekamp (1968) about the Mathematical Modeling of the comprehensive key equation of sequence widely.Our target is to calculate this homogeneous relation ideal apace, and further analyzes its graded algebra structure.Because the desirable rigid structure of relation has very strong fault-tolerance, therefore, utilize the multiple Syzygy decomposition computation of polynomial algebra mould, with some characteristic parameters of overall importance that utilize graded algebra (for example Hilbert function), can filter out the desirable generator of the most rational linear recurrence, thereby obtain correct answer about the linear recurring sequence synthtic price index that contains error code.Show through a large amount of real analysis of experimental data: the fault-tolerant synthtic price index of linear recurring sequence can change into pure calculating algebraic geometry problem.Can be with calculating algebro geometric Algebraic Structure and algorithm rule, the global nature of delineation linear recurrence.The stochastic variable that so just can overcome on the finite field can't use the method for statistics to disclose the difficulty of global nature.

Fig. 4. the structural model of the blind identification of fault-tolerant chnnel coding that a kind of no-protocol of having illustrated the present invention to propose is got in touch with.Promptly for the burst of receiving, through the syzygies decomposition algorithm, find out the homogeneous ideal structure of the whole recurrence relations all relevant with each part of sequence, graded ideal is cleared up algorithm and is obtained optimal solution then.

2, homogeneous key equation

We adopt the structural model of the blind identification of fault-tolerant chnnel coding of following equation portrayal no-protocol contact:

If F is a territory, F[x, y] be the polynomial ring on the F; If

C _i(x, y)=c _I0y ^N+ c _I1Xy ^N-1+ c _I2x ²y ^N-2+ ... + c _INx ^N, i=1,2 ..., k (1) is F[x, y] in t quantic; If I=＜x ^N+1, y ^N+1Be F[x, y] by x ^N+1, y ^N+1Generated ideal.

Homogeneous crucial modular equation HKME: ask F[x, y]-Mo

Γ ^(k)={ (H ₁..., H _k) ∈ F[x, y] ^k| H ₁C ₁(x, y)+... + H _kC _k(x, y) the minimum standard generator of ≡ 0modI} (2).

In above-mentioned crucial modular equation, work as k=1, problem has become sequence synthtic price index.As shown in Figure 2, the synthtic price index of linear recurring sequence (LRS) is the special case of convolution code identification problem, at this moment, as long as linear recurring sequence is regarded as the code word of a convolution code, wherein LRS is I (D) information output sequence, and the verification road output sequence that complete 0 sequence is a coded sequence, because omit when being the output of identical sequence.This is the code word of a systematic convolutional code.

3, fast algorithm

For understanding the algorithm of this section easily, we introduce GB base theoretical [Adam] briefly.

If F is a territory, F[x ₁..., x _n] be n the indeterminate x that have on the F of territory ₁..., x _nPolynomial ring.At F[x ₁..., x _n] individual event set go up a definition Xiang Xu "＞".Like this, for f ∈ F[x ₁..., x _n], f can be expressed as $f={\mathrm{\α}}_1{X}^{{\mathrm{\α}}_1}+{\mathrm{\α}}_2{X}^{{\mathrm{\α}}_2}+\·\·\·+{\mathrm{\α}}_r{X}^{{\mathrm{\α}}_r},$

0 ≠ α wherein _i∈ F, α _i=(e _I1..., e _In) ∈ Z ₊ ⁿ, $X^{{\mathrm{\α}}_i}={x_1}^{e_{i1}}\·\·\·{x_n}^{e_{\mathrm{in}}}$ , and $X^{{\mathrm{\α}}_1}>X^{{\mathrm{\α}}_2}>\·\·\·>X^{{\mathrm{\α}}_r}$ 。At this moment, claim $\mathrm{lp}\left(f\right)=X^{{\mathrm{\α}}_1}$ The first power that is f is long-pending; Lc (f)=α _iIt is the leading coefficient of f; $\mathrm{lt}\left(f\right)=a_1{X}^{{\mathrm{\α}}_1}$ It is the first term of f.

If 0 ≠ f, g ∈ F[x ₁..., x _n], L=lcm (lp (f), lp (g)), promptly L is lp (f), the least common multiple of lp (g) then claims $S(f,g)=\frac{L}{\mathrm{lt}\left(f\right)}f-\frac{L}{\mathrm{lt}\left(g\right)}g$ It is the S multinomial of f and g.

Given F[x ₁..., x _n] in two polynomial f, h and a subclass G={f ₁..., f _t, if h=f-is (c ₁X ₁f ₁+ ... + c _tX _tf _t), c wherein _i∈ F, X _iBe the power product term, satisfy lp (f)=X _iLp (f _i), lp (h)＜lp (f) then is designated as $f\stackrel{G}{\→}h.;$ If there is h _i∈ F[x ₁..., x _n], make $f\stackrel{G}{\→}{h}_1\stackrel{G}{\→}\·\·\·\stackrel{G}{\→}{h}_s\stackrel{G}{\→}h,$ Then be designated as $f{\stackrel{G}{\→}}_{+}h.$

To K={f ₁, f ₂..., f _k∈ F[x ₁..., x _n], the syzygies of K is following F[x ₁..., x _n] on finitely generated module:

Syzygy(K)＝{(h ₁，...，h _k)∈F[x ₁，…，x _n] ^k|h ₁f ₁+…+h _kf _k＝0}

Below fast algorithm, ask homogeneous ideal＜K〉GB base and corresponding syzygies Syzygy (K).

Sy2Sy pairing algorithm concrete steps:

Input: the homogeneous set K={f of strict ordering ₀, f ₁..., f _l}

Output: GB base G makes＜G 〉=＜K〉and the generators set of syzygies Syzygy (K).

(1) initial:

If (f _0,0, f _1,0..., f _{L, 0})=(f ₀, f ₁..., f _l).And establish:

(deg _yLp (f ₀), deg _xLp (f ₀))=min _{I=0,1 ..., l}(deg _yLp (f _i), deg _xLp (f _i)), here, integer vectors (n ₁, m ₁)≤(n ₂, m ₂), and if only if n ₁＜n ₂, perhaps n ₁=n ₂And m ₁≤ m ₂If g ₀=f ₀, A ⁽⁰⁾=I is a unit matrix, G={g ₀, K ₀={ f ₁..., f _l.

(2) suppose that k step finished following algorithm:

Selected go out to gather G and by G reduction residual polynomial set K _k, satisfy following relation:

<G∪K _k>＝<K>，

K=0 wherein, 1 ..., l.G={g ₀, g ₁..., g _k, K _k={ f _{1, k}, f _{2, k}..., f _{L, k},

And calculated coefficient matrices A ^(k)Satisfy

$\left(\begin{array}{c}{f}_{0,k}\\ f_{1,k}\\ .\\ .\\ .\\ f_{l.k}\end{array}\right)=A^{\left(k\right)}\left(\begin{array}{c}{f}_{\mathrm{0,0}}\\ f_{\mathrm{1,0}}\\ .\\ .\\ .\\ f_{l.0}\end{array}\right),$

And note A _i ^(k)It is matrix A ^(k)I capable, i=0,1 ..., l.

(3) the k+1 step will be carried out following calculating:

1) selects f _{0, k+1}, f _{0, k+1}Be K _kIn a special polynomial f _{S, k}, satisfy

$({\mathrm{deg}}_y\mathrm{lp}\left(f_{s,k}\right),{\mathrm{deg}}_x\mathrm{lp}\left(f_{s,k}\right))={\min }_{f\&Element;K_k}({\mathrm{deg}}_y\mathrm{lp}\left(f_{i,k}\right),{\mathrm{deg}}_y\mathrm{lp}\left(f_{i,k}\right)),$

$g_{k+1}\stackrel{\mathrm{\&Delta;}}{=}{f}_{0,k+1}\stackrel{\mathrm{\&Delta;}}{=}{f}_{s,k},G=G\&cup;\left\{g_{k+1}\right\}$

2) calculate $S(g_k,g_{k+1}){\stackrel{G}{\&RightArrow;}}_{+}{f}_{s,k+1}=y^{l_{k+1}}{f}_{0,k}-q_{s,k}{f}_{0,k+1}$

3) calculate $f_{i,k}{\stackrel{G}{\&RightArrow;}}_{+}{f}_{i,k+1}=f_{i,k}-q_{i,k}{f}_{0,k+1},$ I ≠ 0 wherein, i ≠ s.

Above-mentioned each step has been finished following calculating

$\left(\begin{array}{c}{f}_{0,k+1}\\ .\\ .\\ .\\ f_{i,k+1}\\ .\\ .\\ .\\ f_{s,k+1}\\ .\\ .\\ .\\ f_{j,k+1}\\ .\\ .\\ .\end{array}\right)=\left(\begin{array}{c}{f}_{s.k}\\ .\\ .\\ .\\ f_{i,k}-q_{i,k}{f}_{s,k}\\ .\\ .\\ .\\ y^{l_{k+1}}{f}_{0,k}-q_{s,k}{f}_{s,k}\\ .\\ .\\ .\\ f_{i,k}-q_{j,k}{f}_{s,k}\\ .\\ .\\ .\end{array}\right),$

K _k+1＝{f _1，k+1，…，f _l，k+1}

4) corresponding above-mentioned each step, the design factor matrix:

$A^{(k+1)}=\left[\begin{array}{c}{A_0}^{(k+1)}\\ .\\ .\\ .\\ {A_i}^{(k+1)}\\ .\\ .\\ .\\ {A_s}^{(k+1)}\\ .\\ .\\ .\\ {A_j}^{(k+1)}\\ .\\ .\\ .\end{array}\right]=\left[\begin{array}{c}{A_s}^{\left(k\right)}\\ .\\ .\\ .\\ {A_i}^{\left(k\right)}-q_{i,k}{A_s}^{\left(k\right)}\\ .\\ .\\ .\\ y^{l_{k+1}}{A_0}^{\left(k\right)}-q_{s,k}{A_s}^{\left(k\right)}\\ .\\ .\\ .\\ {A_j}^{\left(k\right)}-q_{i,k}{A_s}^{\left(k\right)}\\ .\\ .\\ .\end{array}\right]$

(4) stop condition:, make f up to l step _{1, l}=f _{2, l}=...=f _{L, l}=0.

(5) output: G and coefficient matrices A ^(l)

Sy2Sy realizes following the generator A that calculates syzygies Syzygy (K) by the GB base G of calculating K ₁ ^(l)..., A _l ^(l), at the vectorial A of each row _i ^(l)In choose the row of degree of polynomial minimum, comprehensive exactly needed the separating of (Synthesis) construction problem.

So the blind identification problem of convolution code is changed into the computational problem of Syzygy, and the computation complexity of Sy2Sy algorithm is O (N ²).

If sequence is comprehensive, ask sequence C ₁(x, feature ideal y) are then asked following desirable GB base and corresponding Syzygy:

K＝{f ₀＝x ^N+1，f ₁＝C ₁(x，y)，f ₂＝y ^N+1}

If require the blind identification of convolution code, then ask following desirable GB base and corresponding Syzygy:

K＝{x ^N+1，C ₁(x，y)，...，C _k(x，y)，y ^N+1}

As long as calculate the GB base, then corresponding Syzygy also just follows simultaneously and obtains, and the major event of computational complexity is exactly to calculate the computational complexity of GB base.

We prove theoretically that the computation complexity of SY2SY algorithm is O (N ²), wherein N is the sampling input data volume that observes.Therefore the SY2SY algorithm has reached almost ideal degree at aspects such as computational complexity and space complexities.

To sum up, the present invention proposes a kind of structural model of the blind identification of fault-tolerant chnnel coding of no-protocol contact, set up the homogeneous key equation (HKME) of describing this structural model, provided the quick SY2SY algorithm of finding the solution this HKME.This algorithm has utilized the Algebraic Structure of HKME, by finding the solution the computational process of the desirable GB base of binary polynomial, determines this desirable syzygies of following out to reach synthesis structure by syzygies in computational process.

The significant key equation KE that is proposed by Berlekamp is the special case of HKME of the present invention when k=1.

The BM algorithm that is proposed by Berlekamp and Massey is the special case of SY2SY algorithm of the present invention at k=1 the time.

The present invention has utilized HKME and has become application software and chip with the SY2SY algorithm development.And, be made into the various products in communication and the information security field, comprise: utilize the limited data from the sample survey of observing, realize that the synthesis structure device of minimal linear recurrence generating apparatus, the key of stream cipher generate the application software of integration unit, the blind identification of algebraic coding parameter, the decoder of cyclic code, the big number of rapid solving involved extensive sparse linear equation group in decomposing.

Description of drawings

The coding of Fig. 1 convolution code.g ₁(D), g ₂(D) be the multinomial that unknown needs are found the solution, I (D) is unknown information sequence multinomial, and C ₁(D), C ₂(D) be the codeword sequence multinomial of known finite length.How only from the sequence C of finite length ₁(D), C ₂(D) the anti-generator polynomial g that releases convolution code ₁(D), g ₂(D) be the problem that homogeneous crucial modular equation that the present invention proposes will be described.

Fig. 2 shows that LRS synthtic price index is the special case of the blind identification problem of convolution code.

Fig. 3. conventional not fault-tolerant synthesis structure model.

Fig. 4. illustrated the model of the blind identification of fault-tolerant chnnel coding of a kind of no-protocol contact.

Embodiment

Below by a Practical Calculation example, computational process of the present invention is described.

Example calculation

We have obtained the two-way sequence: 111110111000001101

001011110010000111

Ask the generator polynomial of the convolution code of 1/2 code check that can generate this two-way sequence.Establish for this reason

f ₀＝x ¹⁷+x ¹⁶y+x ¹⁵y ²+x ¹⁴y ³+x ¹³y ⁴+x ¹¹y ⁶+x ¹⁰y ⁷

+x ⁹y ⁸+x ³y ¹⁴+x ²y ¹⁵+y ¹⁷

f ₁＝x ¹⁸

f ₂＝x ¹⁵y ²+x ¹³y ⁴+x ¹²y ⁵+x ¹¹y ⁶+x ¹⁰y ⁷

+x ⁷y ¹⁰+x ²y ¹⁵+xy ¹⁶+y ¹⁷

f ₃＝y ¹⁸

Step 0

f _0,0=f ₀, this goes on foot corresponding pairing algorithm steps (1)

(1，0)	f 0，0＝f 0	＝x 17+x 16y+x 15y 2+x 14y 3+x 13y 4+x 11y 6 +x 10y 7+x 9y 8+x 3y 14+x 2y 15+y 17
			(0，0)-(x+y)(1，0)	f 1，0＝f 1，-1-(x+y)f 0	＝x 13y 5+x 12y 6+x 9y 9+x 4y 4+x 2y 16+xy 17
(0，1)	f 2，0＝f 2	＝x 15y 2+x 13y 4+x 12y 5+x 11y 6+x 10y 7 +x 7y 10+x 2y 15+xy 16+y 17
			(0，0)	f 3，0＝f 3	＝y 18

Wherein matrix A is shown in first tabulation of the form of k in the step ^(k+1)The 1st row and the 3rd be listed as.

Step 1

f _0,1=f _2,0=f ₂, this step is a corresponding SY2SY algorithm steps (3), 1) and the step

(0，1)	f 0，1＝f 2，0	＝x 15y 2+x 13y 4+x 12y 5+x 11y 6 +x 10y 7+x 7y 10+x 2y 15+xy 16+y 17
			(0，0)-(x+y，0)	f 1，1＝f 1，0	＝x 13y 5+x 12y 6+x 9y 9+x 4y 4+x 2y 16+xy 17
y 2(1，0) +(x 2+xy)(0，1)	f 2，1＝y 2f 0，0 +(x 2+xy)f 2，0	＝x 14y 5+x 13y 6+x 10y 9+x 8y 11 +x 4y 15+x 3y 16+x 2y 17
			(0，0)	f 3，1＝f 3，0	＝y 18

Step 2

f _0,2=f _1,1, this step is a corresponding SY2SY algorithm steps (3), 1) and the step

(x+y，0)	f 0，2＝f 1，1	＝x 13y 5+x 12y 6+x 9y 9+x 4y 4+x 2y 16+xy 17
			y 3(0，1) +(x 2+xy)(x+y，0)	f 1，2＝y 3f 0，1 +(x 2+xy)f 1，1In the corresponding algorithm (3), 2) step	＝x 12y 8+x 7y 13+x 6y 14+x 5y 15+x 4y 16
(y 2，x 2+xy) +x(x+y，0)	f 2，2＝f 2，1+xf 1，1In the corresponding algorithm (3), 3) step	＝x 8y 11+x 4y 15+x 5y 14
			(0，0)	f 3，1＝f 3，0	＝y 18

Step 3

f _0，3＝f _1，2

(x 3+xy 2，y 3)	f 0，3＝f 1，2	＝x 12y 8+x 7y 13+x 6y 14+x 5y 15+x 4y 16
			y 3(x+y，0) +(x+y)(x 3+xy 2，y 3)	f 1，3＝y 3f 0，2 +(x+y)f 1，2	＝x 9y 11+x 8y 13
(y 2+x 2+x 2，x 2+xy)	f 2，3＝f 2，2	＝x 8y 11+x 4y 15+x 5y 14
			(0，0)	f 3，3＝f 3，2	＝y 18

Step 4

f _0，4＝f _2，3

(y 2+x 2+xy，x 2+xy)	f 0，4＝f 2，3	＝x 8y 11+x 4y 15+x 5y 14
			(x 4+x 2y 2+x 3y+y 4，xy 3+y 4) +(xy+y 2)(y 2+x 2+xy，x 2+xy)	f 1，4＝f 1，3 +(xy+y 2)f 2，3	＝x 6y 15+x 4y 17
y 3(x 3+xy 2，y 3) +(x 4+xy 3+y 4)(y 2+x 2+xy，x 2+xy)	f 2，4＝y 3f 0，3 +(x 4+xy 3+y 4)f 2，3	＝x 7y 16
			(0，0)	f 3，4＝f 3，3	＝y 18

Step 5

f _0，5＝f _1，4

(x 4+x 2y 2，y 4+x 3y)	f 0，5＝f 1，4	＝x 6y 15+x 4y 17
			y 4(y 2+x 2+xy，x 2+xy) +(x 2+y 2)(x 4+x 2y 2，y 4+x 3y)	f 1，5＝y 4f 0，4+(x 2+y 2)f 1，4	＝0
(xy 5+x 4y 2+x 6+x 5y+y 6，y 6+x 6+x 5y+x 3y 3+xy 5) +xy(x 4+x 2y 2，y 4+x 3y)	f 2，5＝f 2，4+xyf 1，4	＝0
			(0，0)	f 3，4＝f 3，3	＝y 18

Step 6

f _0，6＝f _3，5

(0，0)	f 0，6＝f 3，5	＝y 18
			(x 6+xy 5+y 6，x 5y+x 3y 3+xy 5+y 6)	f 1，6＝f 1，5	＝0
(x 6+x 4y 2+x 3y 3+xy 5+y 6，x 6+x 5y +x 4y 2+x 3y 3+y 6)	f 2，6＝f 2，5	＝0
			y 3(x 4+x 2y 2，y 4+yx 3)	f 3，6＝y 3f 0，5+(x 6+x 2y 4)f 3，5	＝0

Obtain GB base G={f _0,0, f _0,1, f _0,2, f _0,3, f _0,4, f _0,5, f _0,6, in the above-mentioned frame, first row have constituted matrix A ^(l)At A ^(l)In select the row (promptly the 2nd row) of number of times minimum, be exactly separating of SY2SY algorithm,, also just obtain the generator polynomial of convolution code here:

H ₁＝x ⁶+x ⁴y ²+x ³y ³+xy ⁵+y ⁶，H ₂＝x ⁶+x ⁵y+x ⁴y ²+x ³y ³+y ⁶.

Claims (2)

1. the communication channel blind identification method for coding parameters of an error-tolerant code, it is characterized in that designing the structural model of the blind identification of fault-tolerant chnnel coding of a no-protocol contact, set up the homogeneous crucial modular equation HKME of this structural model, the SY2SY pairing algorithm of this homogeneous crucial modular equation HKME is found the solution in proposition, this model is carried out rapid solving, thereby realize the quick blind identification of the fault-tolerant chnnel coding of no-protocol contact; Wherein homogeneous crucial modular equation HKME is:

Ask F[x, y]-Mo

Γ ^(k)＝{(H ₁，...，H _k)∈F[x，y] ^k|H ₁C ₁(x，y)+…+H _kC _k(x，y)≡0mod I} (2)

Minimum standard generator:

Wherein, F is a territory, F[x, y] be the polynomial ring on the F;

C _i(x，y)＝c _i0y ^N+c _i1xy ^N-1+c _i2x ²y ^N-2+…+c _iNx ^N，i＝1，2，…，k (1)

Be F[x, y] in t quantic; I=＜x ^N+1, y ^N+1Be F[x, y] by x ^N+1, y ^N+1Generated ideal;

The concrete steps of said SY2SY pairing algorithm are as follows:

Input: the homogeneous set K={f of strict ordering ₀, f ₁..., f _l}

Output: GB base G makes＜G 〉=＜K〉and the generators set of syzygies Syzygy (K);

(1) initial:

If (f _0,0, f _1,0..., f _{L, 0})=(f ₀, f ₁..., f _l), and establish:

(deg _ylp(f ₀)，deg _xlp(f ₀))＝min _{i＝0，1，...，l}(deg _ylp(f _i)，deg _xlp(f _i))，

If g ₀=f ₀, A ⁽⁰⁾=I is a unit matrix, G={g ₀, K ₀={ f ₁..., f _l;

(2) suppose that k step finished following algorithm:

Selected go out to gather G and by G reduction residual polynomial set K _k, satisfy following relation:

<G∪K _k>＝<K>，

K=0 wherein, 1 ..., l. G={g ₀, g ₁..., g _k, K _k={ f _{1, k}, f _{2, k}..., f _{L, k},

And calculated coefficient matrices A ^(k)Satisfy

$\left(\begin{array}{c}{f}_{0,k}\\ f_{1,k}\\ .\\ .\\ .\\ f_{l,k}\end{array}\right)=A^{\left(k\right)}\left(\begin{array}{c}{f}_{\mathrm{0,0}}\\ f_{1,0}\\ .\\ .\\ .\\ f_{l,0}\end{array}\right),$

And note A _i ^(k)It is matrix A ^(k)I capable, i=0,1 ..., l,

(3) the k+1 step will be carried out following calculating:

1. select f _{0, k+1}, f _{0, k+1}, be K _kIn a special polynomial f _{S, k}, satisfy

$({\mathrm{deg}}_y\mathrm{lp}\left(f_{s,k}\right),{\mathrm{deg}}_x\mathrm{lp}\left(f_{s,k}\right))={\min }_{f\&Element;K_k}({\mathrm{deg}}_y\mathrm{lp}\left(f_{i,k}\right),{\mathrm{deg}}_y\mathrm{lp}\left(f_{i,k}\right)),$

$g_{k+1}\stackrel{\mathrm{\&Delta;}}{=}{f}_{0,k+1}\stackrel{\mathrm{\&Delta;}}{=}{f}_{s,k},G=G\&cup;\left\{g_{k+1}\right\}$

2. calculate $S(g_k,g_{k+1}){\stackrel{G}{\&RightArrow;}}_{+}{f}_{s,k+1}=y^{l_{k+1}}{f}_{0,k}-q_{s,k}{f}_{0,k+1}$

3. calculate $f_{i,k}{\stackrel{G}{\&RightArrow;}}_{+}{f}_{i,k+1}=f_{i,k}-q_{i,k}{f}_{0,k+1},$ I ≠ 0 wherein, i ≠ s;

1., 2., 3. above-mentioned steps has finished following calculating

K _k+1＝{f _1，k+1，…，f _l，k+1)

4) corresponding above-mentioned steps 1., 2., 3., the design factor matrix:

(4) stop condition:, make f up to l step _{1, l}=f _{2, l}=...=f _{L, l}=0;

(5) output: GB base G and coefficient matrices A ^(l), be separating of homogeneous key equation HKME, wherein, coefficient matrices A ^(l)Generators set for syzygies Syzygy (K).

2. method according to claim 1 is characterized in that at the vectorial A of each row _i ^(l)In pick out the row of degree of polynomial minimum, promptly get separating of synthesis structure problem.

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