CN106209312B - A kind of cyclic code parameter blind identification using soft-decision - Google Patents

A kind of cyclic code parameter blind identification using soft-decision Download PDF

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CN106209312B
CN106209312B CN201610527274.5A CN201610527274A CN106209312B CN 106209312 B CN106209312 B CN 106209312B CN 201610527274 A CN201610527274 A CN 201610527274A CN 106209312 B CN106209312 B CN 106209312B
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张天骐
王俊霞
宋�莹
宋铁成
江晓磊
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Chongqing University of Post and Telecommunications
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    • H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
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    • 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
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Abstract

A kind of cyclic code parameter blind recognition algorithm using soft-decision is claimed in the present invention, belongs to signal processing technology field.All code word size n are found out first and generator polynomial is xnThe corresponding check matrix of -1 factor, is put into check matrix library；Then M is used2/M4Estimator estimates the signal amplitude and noise variance in channel；The cyclic code code stream intercepted and captured is recycled, construction intercepts and captures matrix, calls the code word size to correspond to the check matrix in check matrix library, obtain the average log-likelihood ratio of the posterior probability of syndrome；Finally according to the property of cyclic code, code word size, synchronization point and generator polynomial are identified.This algorithm can only known coded mode be cyclic code and compared with low signal-to-noise ratio in the case where, while code word size, synchronization point and generator polynomial are identified, to be of great significance to cyclic code parameter blind recognition.

Description

A kind of cyclic code parameter blind identification using soft-decision
Technical field
The present invention relates to Channel coding parameters blind recognition, specially a kind of blind recognition problem of cyclic code coding parameter.
Background technique
In recent years, channel coding blind recognition is the important content of non-co-operation signal process field, in intelligence communication, information pair Anti- and information acquisition field plays an important role.For the reliability of improve data transfer, it will usually use channel coding Technology, since cyclic code detection is random or burst error is highly effective, and the Algebraic Structure of cyclic code is established on finite field basis On, it is easily found effective coding and decoding method.In non-cooperative communication, research how according to intercept and capture code stream identify cyclic code compile Code parameter is of great practical significance.
Fewer for the Research Literature of cyclic code parameter blind recognition at present, existing analysis method is defeated usually using demodulating Hard decision sequence out is analyzed, document " Jia-feng Wang.Amethod blind recognition of cyclic Generator polynomial, Wireless Communication Networking and Mobile Computing, 2010 " assume code word sizes it is known that code word size unknown frame length it is known that being grouped to code word, using Euclid Algorithm realizes the blind recognition of binary BCH codes.But it must be known by certain priori knowledge, in the feelings of unknown priori knowledge Under condition, calculation amount is very big.In fact it demodulates not only containing bit symbol information in the soft-decision of output, but also contains the symbol Reliability information.Document " a kind of channel coding identification new method electronic letters, vol using soft-decision of Yu Peidong, 2013 ", it should Method realizes the blind recognition of Channel coding parameters in low signal-to-noise ratio using the soft decision information of demodulation output.But it should In method application Linear Block Codes, there are many candidate's verification quantity, and calculation amount is very big, require calculator memory very high.Therefore, This patent proposes a kind of cyclic code parameter blind recognition algorithm using soft-decision.
Summary of the invention
The technical problems to be solved by the invention, it is computationally intensive for cyclic code parameter Estimation of the existing technology, no It is able to achieve total blindness's identification, the defects of high is required to calculator memory, proposes a kind of blind knowledge of cyclic code parameter using soft-decision Other algorithm solves the problems, such as cyclic code parameter blind recognition.This method can identify that cyclic code is joined under lower signal-to-noise ratio Number, such as code word size, synchronization point, generator polynomial.When estimating cyclic code parameter, check matrix library is established, uses school Matrix matching technique is tested, can achieve the purpose for reducing operand in the case where not reducing recognition performance.
The technical solution that the present invention solves above-mentioned technical problem is: a kind of cyclic code parameter blind recognition side using soft-decision Method, step are, find out all code word size n first and generator polynomial is xnThe corresponding check matrix of -1 factor, puts Enter in check matrix library；Then M is used2/M4Estimator (the second-order/fourth-order moment Method, second moment/quadravalence Moment Methods) estimation channel in signal amplitude and noise variance；Recycle the cyclic code intercepted and captured Code stream calls the code word size to correspond in check matrix library according to code word size and synchronization point construction intercepting and capturing matrix is assumed Check matrix obtains the average log-likelihood ratio of the posterior probability of syndrome；Finally according to the property of cyclic code, code word is identified Length, synchronization point and generator polynomial.
The present invention carries out blind estimate to cyclic code parameter using a kind of method of soft-decision, utilizes M2/M4Estimator is effective The amplitude and noise variance for estimating signal, establish check matrix library using the property of cyclic code, so that in check matrix library Quantity greatly reduces, by traversing the check matrix in check matrix, seeking its correspondence in different code word size and synchronization point Syndrome posterior probability average log-likelihood ratio, not only take full advantage of the effective information for receiving symbol, but also candidate Check matrix quantity is small, can be realized under lower state of signal-to-noise, identifies there is certain work to the total blindness of cyclic code parameter Journey application value.
Detailed description of the invention
Below in conjunction with drawings and concrete examples, implementation of the invention is further described.
The flow chart of Fig. 1 code word size of the present invention and synchronization point blind-identification method；
The flow chart of Fig. 2 generator polynomial recognition methods of the present invention；
The former cyclic code of Fig. 3 present invention and new cyclic code inclusion relation；
The basic signal transmission system block diagram of Fig. 4 present invention；
The different cyclic code of Fig. 5 present invention is in different code word sizes, the corresponding average log-likelihood ratio of synchronization point；
Fig. 6 cyclic code of the present invention is in n=30, t0Different irreducible polynomials corresponding average log-likelihood ratio is corresponded to when=5；
The performance map of the different cyclic code identifications of Fig. 7 present invention.
Specific embodiment
Below in conjunction with drawings and concrete examples, implementation of the invention is further described.
Fig. 1 show the flow chart of code word size and synchronization point blind-identification method of the present invention, specific steps:
(1) check matrix library is established, method particularly includes: by xn- 1 is completely decomposed into the product of irreducible polynomial, it is assumed that has w A irreducible polynomial, is denoted as pi(x), 1≤i≤w, thenAssuming that pi(x), there is w in 1≤i≤w1It is a mutually not Identical irreducible polynomial is denoted as g if taking generator polynomial is one of irreducible functioni(x)=pi(x),1≤i≤ w1, then check polynomialBy its corresponding check matrix HiIt is put into check matrix library；
(2) M is used2/M4Estimator estimates parameter signal amplitude avAnd noise variance
(3) assume code word size n, (value is 1 to 2n0- 1), synchronization point d (value is 0 to n-1), construction intercepts and captures square Battle array X, calls the corresponding check matrix H of n in check matrix libraryi1≤i≤w calculates the flat of the posterior probability of its corresponding syndrome Equal log-likelihood ratio Wi,1≤i≤w；
(4) W is takeni, the corresponding average log-likelihood ratio of 1≤i≤w maximum value L conduct (n, d), be put into Q matrix (n, D) corresponding position；
(5) change the value of n, d, Q is the matrix of a 2n × n, asks Q maximum value corresponding n, d, is denoted as n '=n, d '=d；
(6) n=2n ' is enabled, for d value from 0 to n-1, construction intercepts and captures matrix X, calls the corresponding verification square of n in check matrix library Battle array Hi, 1≤i≤w calculates the average log-likelihood ratio of the posterior probability of its corresponding syndrome；
(7) code word size is identifiedSynchronization point
Fig. 2 show the flow chart of generator polynomial recognition methods of the present invention, specific steps:
(1) whenWhen, it calls in check matrix libraryCorresponding check matrix Hi1≤i≤w, calculates it The average log-likelihood ratio W of the posterior probability of corresponding syndromei,1≤i≤w.And take Wi(1≤i≤w) is greater than T pairs of thresholding The generator polynomial g answeredi(x) product of (1≤i≤w), is denoted as g1(x).IfFor odd number, thenIdentification knot Beam.IfIt is even number, then g0(x) it may include repeated root (for the true generator polynomial of cyclic code), turn (3)；
(2) whenWhen, theng0(x) it may include repeated root, turn (3)；
(3) the step of identifying generator polynomial repeated root: (a) willComplete factorization is f, is denoted as pi (x), 1≤i≤f, wherein there is f1A multinomial is contained in g1(x) factor, is denoted as pi(x),1≤i≤f1≤f；If (b) f1= 0, thenEnd of identification.If f1≠ 0, i=1 is initialized, g (x)=g is enabled1(x)pi(x), it finds outCorresponding check matrix Hi, calculate the average log-likelihood ratio W of the posterior probability of its corresponding syndromeiIf Wi > T updates g1(x)=g1(x)pi(x), otherwise, g1(x) it remains unchanged；(c) i=i+1 is enabled, g (x)=g is taken1(x)pi(x), The average log-likelihood ratio W of the posterior probability of corresponding syndromeiIf Wi> T updates g1(x)=g1(x)pi(x), otherwise, g1(x) it remains unchanged；(d) step (c) is repeated, until i > f1, then haveEnd of identification.
Fig. 3 show former cyclic code and new cyclic code and their antithesis code space inclusion relation of the invention.Former cyclic code Refer to that by generator polynomial be g (x)=A (x) g ' (x) generation (n, k) cyclic code, new cyclic code refers to that generator polynomial is g ' (x) (Mn, the k) generated, M=1,2 ... cyclic codes.New cyclic code antithesis code space is that the son of former cyclic code antithesis code space is empty Between.This is because cyclic code has the property of proposition 1 and proposition 2.
If 1 c of propositioni(x), i=1,2 ... it is to be followed with g (x)=A (x) g ' (x) to generate Polynomial generation (n, k) I-th of code word of ring code, it is assumed that cyclic code (Mn, k), M=1,2 ... with g ' (x) be that the corresponding check polynomial of generator polynomial is H ' (x), then [c1(x),…,cM(x)]h′(x)mod(xMn- 1)=0, M=1,2 ..., wherein [c1(x),…,cM(x)] it indicates The matrix being made of M code word.
If 2 c (x) of proposition is generated (n, k) with g (x) generator polynomial, n=2n1Cyclic code code word, ifI.e. generator polynomial can be decomposed intoWithThe part factor of factorization, ifc(1)(x)、c(2)(x) before respectively indicating in c (x) n1The code word and rear n that symbol is constituted1The code word that symbol is constituted, i.e.,
Then have
WithWherein,
By proposition 1 it is found that if cyclic code meets 2 condition of proposition, forCyclic code, Assuming that it is h ' (x) that it, which is the corresponding check polynomial of generator polynomial with g ' (x), it is all satisfied
In formula,Respectively indicate the preceding n of i-th of code word1The code word and rear n that symbol is constituted1Symbol is constituted Code word.For cyclic code (Mn, k), M=1,2 ..., generator polynomial takes xMn- 1 any one factor,
If its corresponding check polynomial is that h " (x) is then all satisfied
[c1(x),…,cM(x)]h″(x)mod(xMn=0, M=1,2, -1) ... (2)
Fig. 4 show basic mode system block diagram.Definition set Z2={ 0,1 }, B2={ -1,1 }.biIndicate i-th K information bit of a code word, is denoted asv∈Z+, Z+Indicate positive integer.biBecome long by (n, k) encoder for cyclic codes Degree is the code word of n, is denoted asciBecome through BPSK modulatorThen pass through frequency modulation, and additive Gaussian white noise Acoustic channel transmission, is demodulated into baseband signal again later, becomes Xi=[Xi0,Xi1,…,Xij,…,Xi(n-1)]T, then
Xij=avsij+wij, j=0,1 ..., n-1 (3)
Wherein, avIt is amplitude gain, wijNormal DistributionIn the coding mode of only known transmitting terminal For cyclic code, and in the case where intercepting and capturing the bit stream L that a string length is len, the code word according to algorithm estimation cyclic code in text is long Spend n0, synchronization point t0With generator polynomial g0(x).Assuming that code word size be n, generator polynomial be g (x), synchronization point d, The bit of front d then is truncated in L, is that n is divided into N number of code word with length, wherein i-th of code word is denoted as Xi=[Xi1,Xi2,…, Xij,…,Xin], corresponding thereto belong to Z2Without error code code word, be denoted as Ci=[Ci1,Ci2,…,Cij,…,Cin], by N number of Ci The matrix that code word stacks, is denoted as C=[C1,C2,…,Ci,…,CN]T。
And if only if H ∈ C⊥When, then C, H meet parity check equations are as follows:
CHT=0 (4)
In formula, C is the matrix of N × n, and H is the matrix of m × n, and 0 is the full null matrix of N × m.Define Ci, 1≤i≤N expression The i-th row vector of C, is denoted as Ci=[Ci1,Ci2,…,Cij,…,Cin], 1≤j≤n, Ha, 1≤a≤m expression H a row vector, It is denoted as Ha=[Ha1,Ha2,…,Haj,…,Han], 1≤j≤n.Then haveI.e.
If HaInclude NaThe subscript vector of a nonzero element, nonzero element is
Then formula (5) can turn to
Because the probability that transmitting terminal sends 0 is equal with the probability for sending 1, then have
And according to document " Tian xia.novel blind identification of LDPC codes using average LLR of syndrome a posteriori probability.IEEE Transactions on Signal Processing, known to 2014 ":
The then posterior probability log-likelihood ratio of a-th of parity check bit of i-th of code word are as follows:
Because of y=tanh-1It (x), is monotonic increasing function in -1 < x < 1, and
Therefore formula (10) is reduced in text
According to the definition of likelihood ratio and formula (11), as H ∈ C⊥When, the log-likelihood ratio Υ of the posterior probability of verificationi′a It is positive number.If H ∈ C⊥, the average log-likelihood ratio Υ of the posterior probability of corresponding syndromeiaIt is positive number, and signal-to-noise ratio is higher Closer to 1.WhenWhen, the log-likelihood ratio Υ of the posterior probability of syndromeiaHave plenty of positive number, has plenty of negative.Institute The average log-likelihood ratio of syndrome is
Then as H ∈ C⊥When, W is greater than 0 and is less than or equal to 1；WhenWhen, W is approximately equal to 0.
The system model obtained according to formula (3), it is known that:
In formula, y=L (x) indicates that y is the log-likelihood ratio of x.Combined after syndrome can be obtained by (11), (12), (13) Test the log-likelihood ratio of probability, but avWithIt is unknown, it needs using M2/M4Estimator estimates avWithValue.
According to M2/M4Estimator estimates avWithDue to
Xij=avsij+wij, j=0,1 ..., n-1 (14)
Then receive signal XijSecond moment:
Receive signal XijFourth-order moment:
It can be obtained by formula (15) and formula (16) joint:
In fact, M2And M4It can be estimated by i-th of code word of reception signal, it may be assumed that
A is estimated in textvWithWhen, it can increase the accuracy of estimation according to sample of signal estimation is all received, eliminate random Property.
Fig. 5 show the different cyclic code of the present invention in different code word sizes, the corresponding log-likelihood ratio of synchronization point；Its In, (a) indicates generator polynomial g0(x)=(x2+x+1)(x4+ x+1) (15,9) cyclic code；(b) generator polynomial g is indicated0 (x)=(x15+1)(x2+x+1)(x4+ x+1) cyclic code (30,9)；(c) generator polynomial g is indicated0(x)=(x2+x+1)(x4+ X+1 (30,24) cyclic code)；It is transmitted in Signal to Noise Ratio (SNR)=10db channel, synchronization point t when intercepting and capturing0=5.x Axis indicates synchronization point, and y-axis indicates code word size, and z-axis is when different code word sizes, synchronization point construction being taken to intercept and capture matrix, to adjust The check matrix in check matrix library is corresponded to code word size, obtains the average log-likelihood ratio of the posterior probability of syndrome most Big value, is denoted as L.
By (a) it is found that for cyclic code (15,9), as n=15 α, α=1,2,3, d=5, the value of L is maximum；Work as n=15 α, α=1, when 2,3, d ≠ 5, L is greater than(Expression one is approximately equal to 0 number) it is less than maximum value；When the α of n ≠ 15, α=1,2,3 When, L is equal toBy (c) it is found that for cyclic code (30,24), work as n=30, when d=5, the value of L is maximum；Work as n=30, d ≠ 5 When, L is greater thanLess than maximum value；As n ≠ 30, L is equal toBy (b) it is found that for cyclic code (30,9), as n=15 α, α= When 1,2,3, d=5 or d=20, the value of L is maximum；As n=15 α, α=1,2,3, d ≠ 5 or d ≠ 20, L is greater thanLess than maximum Value.Experimental phenomena is completely the same with theory analysis.
According to proposition 1 it is found that when cyclic code is unsatisfactory for 2 condition of proposition, i.e. n0=2n1,When, As n=α n0, α=1,2 ..., g (x) traverse xn- 1 factor, (n, g (x)) corresponding check matrix be H, there are H meet C (n, d)HT=0；As n ≠ α n0, α=1,2 ..., g (x) traverse xn- 1 factor, (n, g (x)) corresponding check matrix are H, are not present H meets C (n, d) HT=0.When cyclic code meets 2 condition of proposition, i.e. n0=2n1,When, whenWhen, if g (x) is the factor of g ' (x), if (n, g (x)) corresponding check matrix is H, meet C (n,d)HT=0.As n=α n0, α=1,2 ..., g (x) take xn- 1 any one factor, if (n, g (x)) corresponding verification square Battle array is H, and there are H to meet C (n, d) HT=0.Therefore, meet C (n, d) H if there is HTWhen=0, the L that obtains at this time closer to 1；Meet C (n, d) H if there is no HTWhen=0, the L obtained at this time is equal to
But code word size and synchronization point can not correctly be identified according to Fig. 5 (a), (b), it is also necessary to make further real Test judgement.
Fig. 6 show cyclic code of the present invention in n=30, t0Different irreducible polynomials corresponding average log is corresponded to when=5 Likelihood ratio.It (a) is generator polynomial g0(x)=(x2+x+1)(x4+ x+1) (15,9) cyclic code；(b) generator polynomial is indicated g0(x)=(x15+1)(x2+x+1)(x4+ x+1) cyclic code (30,9)；It is respectively p that x-axis, which represents irreducible polynomial serial number 1~5,1 (x)=x+1, p2(x)=x2+ x+1, p3(x)=x4+ x+1, p4(x)=x4+x3+ 1, p5(x)=x4+x3+x2+x+1；Y-axis represents same The moment is walked, value is from 0 to 29；Z-axis is the value of L, it is assumed that d=0, g (x)=p1(x), it represents with n=30, the intercepting and capturing of d=0 construction Matrix X calls p in check matrix library1(x) corresponding check matrix, the average log of the posterior probability of obtained syndrome is seemingly So ratio.
Work as g (x)=p it can be seen from (a)2(x) or g (x)=p3(x), and when d=5 or d=20, L is maximum；Work as g (x)=p2(x) or g (x)=p3(x), but when d ≠ 5 or d ≠ 20, L is more than or equal toLess than maximum value；As g (x) ≠ p2 (x) or g (x) ≠ p3(x) when,Therefore,Work as d=5 it can be seen from (b), G (x) takes x30When -1 any factor, L is maximum；As d=20, g (x)=p2(x) or g (x)=p3(x) when, L is maximum.Cause This,Identification is correct, and consistent with proposition 1,2 theory analysis of proposition.
Fig. 7 show the performance map that the present invention identifies different cyclic codes using algorithm in text.It (a) is that generator polynomial is g0(x)=(x2+x+1)(x4+ x+1) (15,9) cyclic code；(b) be generator polynomial be g0(x)=(x2+x+1)(x4+x+1) (30,24) cyclic code；The identification that code word size, synchronization point and generator polynomial are carried out using algorithm in text, according to noise Than from -5db to 10db, the simulation result of 1,200 Monte Carlos of step-length, wherein parameter is chosen for N=200, T=0.25.
From (a) as can be seen that cyclic code (15,9) are when signal-to-noise ratio is 3db, the correct identification of code word size, synchronization point Rate can reach 80%；When signal-to-noise ratio is 5db, the correct recognition rata of generator polynomial can reach 90% or more.Cyclic code (30,24) When signal-to-noise ratio is 5db, code word size, synchronization point correct recognition rata can reach 75% or more, it is raw when signal-to-noise ratio is 7db 100% can be reached at polynomial correct recognition rata.Code word size is longer, and noise robustness is poorer, and in text algorithm have it is good Good noise robustness.

Claims (5)

1. a kind of cyclic code parameter blind identification using soft-decision, step are, find out first all code word size n and Generator polynomial is xnThe corresponding check matrix of -1 factor, is put into check matrix library；Then M is used2/M4Estimator estimation Signal amplitude and noise variance in channel；The cyclic code code stream intercepted and captured is recycled, according to hypothesis code word size and synchronization point Construction intercepts and captures matrix, calls the code word size to correspond to the check matrix in check matrix library, obtains the posterior probability of syndrome Average log-likelihood ratio；Finally according to the property of cyclic code, code word size, synchronization point and generator polynomial are identified.
2. blind-identification method according to claim 1, which is characterized in that check matrix library is established, according to cyclic code (n, k) Generator polynomial must be xn- 1 factor, therefore by xn- 1 complete factorization is several irreducible polynomials, it is assumed that is generated Multinomial is irreducible polynomial, finds out its corresponding check matrix and is put into check matrix library.
3. blind-identification method according to claim 1, which is characterized in that using the sample for receiving signal, use M2/M4Estimator estimates signal amplitude and noise variance in channel；Since cyclic code will be modulated by BPSK, and believing It is influenced in road by white Gaussian noise, reception signal is Xij=avsij+wij, j=0,1 ..., n-1, wherein XijIndicate i-th J-th of signal of a code word, avIt is signal amplitude, sijJ-th of symbol for i-th of code word of cyclic code is modulated by BPSK Signal, wijBe obey mean value be that 0 variance isNormal distribution noise, whereinFor the variance of noise；Receive signal XijSecond moment:XijFourth-order moment:ThereforeIn fact, M2And M4Estimated by i-th of code word of reception signal Meter；
4. blind-identification method according to claim 1, which is characterized in that find out the average log of the posterior probability of syndrome seemingly So ratioWherein, Nm is the quantity of syndrome,Indicate the The posterior probability log-likelihood ratio of a-th of parity check bit of i code word, wherein NaIndicate a-th of candidate check matrix H The number for the nonzero element that row vector includes,It indicates in no error code, the of i-th code wordA signal, whereinIndicate the subscript of j-th of nonzero element in a-th of row vector of candidate check matrix H；Indicate the of i-th of code wordA signal；The log-likelihood ratio of the posterior probability of syndrome are as follows: Because of y=tanh-1It (x), is monotonic increasing function in -1 < x < 1, andTherefore The log-likelihood ratio of the posterior probability of syndrome is simplified are as follows:BecauseWherein, avIndicate letter Number amplitude,Indicate noise variance, so, estimate the average log-likelihood ratio of the posterior probability of syndrome.
5. blind-identification method according to claim 1 realizes cyclic code parameter, including code word in conjunction with the property of cyclic code The blind recognition of length, synchronization point and check matrix；According to proposition 1, if ci(x), i=1,2 ... it is with g (x)=A (x) g ' (x) (n, k) cyclic code code word to generate Polynomial generation, it is assumed that cyclic code (Mn, k), M=1,2 ...；It is to generate with g ' (x) The corresponding check matrix of multinomial is h ' (x), then [c1(x),…,cM(x)]h′(x)mod(xMn=0, M=1,2, -1) ...； By assuming that code word size, synchronization point, construction intercepts and captures matrix, calls verification square of the code word size in check matrix library Battle array, calculates the average log-likelihood ratio LLR of the posterior probability of syndrome, when according to code word size and correct synchronization point, LLR Maximum, close to 1；When code word size is incorrect, LLR is approximately equal to 0；Code word size is correct, and when synchronization point is incorrect, LLR is big In being equal to the number for being approximately equal to 0, it is less than maximum value, thus realizes the identification of code word size, synchronization point and check matrix.
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