CN106209312A - A kind of cyclic code parameter blind recognition algorithm utilizing soft-decision - Google Patents

Abstract

The invention claims to protect a cyclic code parameter blind identification algorithm using soft decision, which belongs to the technical field of signal processing. First find out the parity check matrices corresponding to the factors of all codeword length n and generator polynomial x ⁿ -1, and put them into the parity check matrix library; then use the M ₂ /M ₄ estimator to estimate the signal amplitude and Noise variance; then use the intercepted cyclic code stream to construct the interception matrix, call the check matrix in the check matrix library corresponding to the length of the code word, and obtain the average log likelihood ratio of the posterior probability of the syndrome; finally according to Properties of cyclic codes, identifying codeword lengths, synchronization instants, and generator polynomials. This algorithm can identify the codeword length, synchronization time and generator polynomial at the same time when only the encoding method is known as cyclic code and the signal-to-noise ratio is low, so it is of great significance for the blind identification of cyclic code parameters.

Description

A Blind Identification Algorithm of Cyclic Code Parameters Using Soft Decision

technical field

The invention relates to blind recognition of channel coding parameters, in particular to a problem of blind recognition of cyclic code coding parameters.

Background technique

In recent years, channel coding blind recognition is an important content in the field of non-cooperative signal processing, and plays an important role in the fields of intelligent communication, information countermeasures and information interception. In order to improve the reliability of data transmission, channel coding technology is usually used. Because cyclic codes are very effective in detecting random or burst errors, and the algebraic structure of cyclic codes is based on finite fields, it is easy to find effective encoding and decoding methods. In non-cooperative communication, it is of great practical significance to study how to identify the coding parameters of cyclic codes according to the intercepted code stream.

At present, there are relatively few research documents on the blind recognition of cyclic code parameters. The existing analysis methods usually use the hard decision sequence of the demodulation output for analysis. The document "Jia-feng Wang. A method blind recognition of cyclic generator polynomial, Wireless Communication Networking and MobileComputing , 2010" Assuming that the codeword length is known, or the codeword length is unknown and the frame length is known, the codewords are grouped, and the Euclidean algorithm is used to realize the blind recognition of the binary BCH code. But it must know certain prior knowledge, and in the case of unknown prior knowledge, the amount of calculation is very large. In fact, the soft decision output by demodulation contains not only bit symbol information, but also reliability information of the symbol. Document "Yu Peidong. A new method of channel coding identification using soft decision. Electronic Journal, 2013", this method uses the soft decision information output by demodulation to realize the blind identification of channel coding parameters in the case of low signal-to-noise ratio . However, when this method is applied to linear block codes, there are a large number of candidate checks, a large amount of calculation, and a high requirement for computer memory. Therefore, this patent proposes a blind identification algorithm of cyclic code parameters using soft decision.

Contents of the invention

The technical problem to be solved by the present invention is to solve the problems of the prior art that the cyclic code parameter estimation has a large amount of computation, cannot realize full-blind recognition, and requires high computer memory, and proposes a cyclic code parameter blind recognition algorithm using soft judgment to solve the problem. The problem of blind identification of cyclic code parameters is solved. This method can identify the parameters of cyclic codes, such as codeword length, synchronization time, and generator polynomial, under low SNR. When estimating the parameters of cyclic codes, a check matrix library is established and a check matrix matching method is adopted, which can achieve the purpose of reducing the amount of calculation without reducing the recognition performance.

The technical solution of the present invention to solve the above-mentioned technical problems is: a method for blind identification of cyclic code parameters using soft decision, the steps of which are: firstly find out the correction coefficients corresponding to the factors of all codeword length n and generator polynomial x ⁿ -1 check matrix, put it into the check matrix library; then use the M ₂ /M ₄ estimator (the second-order/fourth-order momentmethod, second-order moment/fourth-order moment method) to estimate the signal amplitude and noise variance in the channel ;Use the intercepted cyclic code stream, construct the interception matrix according to the assumed codeword length and synchronization time, call the parity check matrix in the parity check matrix library corresponding to the codeword length, and obtain the average logarithm of the posterior probability of the syndrome Likelihood ratio; finally, according to the nature of the cyclic code, the length of the code word, the synchronization moment and the generator polynomial are identified.

The present invention uses a soft decision method to blindly estimate the parameters of the cyclic code, uses the M ₂ /M ₄ estimator to effectively estimate the signal amplitude and noise variance, and uses the properties of the cyclic code to establish a check matrix library, so that the check The number in the matrix library is greatly reduced. By traversing the parity check matrix in the parity check matrix at different codeword lengths and synchronization moments, the average log-likelihood ratio of the posterior probability of the corresponding syndrome is not only sufficient The effective information of received symbols is utilized, and the number of candidate parity check matrices is small, which can realize the blind identification of cyclic code parameters under the condition of low signal-to-noise ratio, and has certain engineering application value.

Description of drawings

The implementation of the present invention will be further described below in conjunction with the accompanying drawings and specific examples.

Fig. 1 is the flow chart of the code word length and the blind identification method of synchronization moment of the present invention;

Fig. 2 is the flow chart of generating polynomial recognition method of the present invention;

The original cyclic code of the present invention and the new cyclic code contain relationship of Fig. 3;

Fig. 4 basic signal transmission system block diagram of the present invention;

Fig. 5 is the average log likelihood ratio corresponding to different cyclic codes of the present invention at different codeword lengths and synchronization moments;

Fig. 6 is the average log likelihood ratio corresponding to different polynomials corresponding to the cyclic code of the present invention when n=30, t ₀ =5;

Fig. 7 is a performance diagram of different cyclic code recognition in the present invention.

detailed description

The implementation of the present invention will be further described below in conjunction with the accompanying drawings and specific examples.

Fig. 1 shows the flow chart of the present invention's code word length and blind identification method of synchronous moment, concrete steps:

(1) Establish a check matrix library, the specific method is: completely decompose x ⁿ -1 into the product of reduced polynomials, assuming that there are w reduced polynomials, recorded as p _i (x), 1≤i≤w, then Assuming that p _i (x), 1≤i≤w, there are w ₁ different reducing polynomials, if the generator polynomial is taken as one of the irreducible polynomials, write g _i (x)=p _i (x), 1≤i≤w ₁ , then the check polynomial Put its corresponding check matrix H _i into the check matrix library;

(2) Use the M ₂ /M ₄ estimator to estimate the parameter signal amplitude a _v and noise variance

(3) Assuming that the codeword length is n, (the value is 1 to 2n ₀ -1), and the synchronization time d (the value is 0 to n-1), the interception matrix X is constructed, and the calibration corresponding to n in the check matrix library is called For the empirical matrix H _i 1≤i≤w, calculate the average log-likelihood ratio W _i of the posterior probability of the corresponding syndrome, 1≤i≤w;

(4) Take the maximum value L of W _i , 1≤i≤w as the average log likelihood ratio corresponding to (n,d), and put it into the position corresponding to (n,d) in the Q matrix;

(5) change the value of n, d, Q is a matrix of 2n * n, seek n, d corresponding to Q maximum value, denoted as n'=n, d'=d;

(6) Set n=2n′, d ranges from 0 to n-1, construct the intercept matrix X, call the check matrix H _i corresponding to n in the check matrix library, 1≤i≤w, and calculate its corresponding check matrix The average log-likelihood ratio of the posterior probability of the tester;

(7) Identify the codeword length synchronization time

Fig. 2 shows the flowchart of generating polynomial identification method of the present invention, concrete steps:

(1) when When calling the check matrix library For the corresponding check matrix H _i 1≤i≤w, calculate the average log likelihood ratio W _i of the posterior probability of the corresponding syndrome, 1≤i≤w. And take the product of the generator polynomial g _i (x) (1≤i≤w) corresponding to W _i (1≤i≤w) greater than the threshold T, and record it as g ₁ (x). if is an odd number, then Identification is complete. if is an even number, then g ₀ (x) (for the real generator polynomial of the cyclic code) may contain repeated roots, turn to (3);

(2) when when g ₀ (x) may contain repeated roots, go to (3);

(3) Steps to identify multiple roots of generator polynomials: (a) set The complete factorization is decomposed into f items, denoted as p _i (x), 1≤i≤f, among which there are f ₁ polynomials contained in the factor of g ₁ (x), denoted as p _i (x), 1≤i ≤f ₁ ≤f; (b) if f ₁ =0, then Identification is complete. If f ₁ ≠0, initialize i=1, set g(x)=g ₁ (x)p _i (x), find For the corresponding check matrix H _i , calculate the average log-likelihood ratio W _i of the posterior probability of the corresponding syndrome, if W _i >T, update g ₁ (x)=g ₁ (x)p _i ( x), otherwise, g ₁ (x) remains unchanged; (c) Let i=i+1, take g(x)=g ₁ (x)p _i (x), the posterior of its corresponding syndrome The average log-likelihood ratio of probability W _i , if W _i > T, update g ₁ (x) = g ₁ (x) p _i (x), otherwise, g ₁ (x) remains unchanged; (d) repeat Step (c), until i＞f ₁ , then there is Identification is complete.

Fig. 3 shows the original cyclic code and the new cyclic code of the present invention, and their dual code space inclusion relationship. The original cyclic code refers to the (n, k) cyclic code generated by the generator polynomial g(x)=A(x)g′(x), and the new cyclic code refers to the (Mn) generated by the generator polynomial g′(x). , k), M=1, 2, ... cyclic code. The dual code space of the new cyclic code is a subspace of the dual code space of the original cyclic code. This is because cyclic codes have the properties of Proposition 1 and Proposition 2.

Proposition 1 If c _i (x), i=1, 2, ... is the i-th codeword of the (n, k) cyclic code generated by g(x)=A(x)g'(x) as the generator polynomial, Suppose the cyclic code (Mn, k), M=1, 2, ... with g'(x) as the generator polynomial corresponding check polynomial is h'(x), then [c ₁ (x), ..., c _M ( x)]h′(x)mod(x ^Mn -1)=0, M=1, 2,…, where [c ₁ (x),…,c _M (x)] represents the matrix.

Proposition 2 If c(x) is (n,k) generated by g(x) generator polynomial, n=2n ₁ cyclic code word, if That is, the generator polynomial can be decomposed into and Partial factorization of factorization, let c ⁽¹⁾ (x), c ⁽²⁾ (x) respectively denote the code word composed of the first n ₁ code elements and the code word composed of the last n ₁ code elements in c(x), that is but and in,

It can be seen from Proposition 1 that if the cyclic code satisfies the condition of Proposition 2, then for M = 1, 2, ... cyclic codes, assuming that the check polynomial corresponding to g'(x) as the generator polynomial is h'(x), all satisfy

$<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; mod</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, Respectively represent the codeword composed of the first n ₁ symbols and the codeword composed of the last n ₁ symbols of the i-th codeword. For cyclic codes (Mn,k), M=1,2,..., the generator polynomial takes any factor of x ^Mn -1, and the corresponding check polynomial is h″(x), then all satisfy

[c ₁ (x),...,c _M (x)] h″(x) mod (x ^Mn -1) = 0, M = 1, 2, ... (2)

Figure 4 shows the basic transmission model system block diagram. Define the set Z ₂ ={0,1}, Β ₂ ={-1,1}. b _i represents the k information bits of the i-th codeword, denoted as v∈Ζ ⁺ , Ζ ⁺ represents a positive integer. b _i becomes a codeword of length n through the (n,k) cyclic code encoder, denoted as c _i is changed to by BPSK modulator Then after frequency modulation, additive Gaussian white noise channel transmission, and then demodulated to baseband signal, becomes _{Xi = [X i0 ,} X _i1 ,…,X _ij ,…,X _i(n-1) ] ^T , but

X _ij ＝a _v s _ij +w _ij ,j＝0,1,...,n-1 (3)

Among them, a _v is the amplitude gain, w _ij obeys the normal distribution In the case where it is only known that the encoding method of the sending end is a cyclic code, and a string of bit stream L with a length of len is intercepted, the code word length n ₀ , the synchronization time t ₀ and the generator polynomial g ₀ ( x). Assuming that the codeword length is n, the generator polynomial is g(x), and the synchronization time is d, then the first d bits of L are truncated, and the length is n and divided into N codewords, where the i-th codeword is recorded as X _i ＝[X _i1 ,X _i2 ,...,X _ij ,...,X _in ], the corresponding error-free codeword belonging to Ζ ₂ is recorded as C _i =[C _i1 ,C _i2 ,...,C _ij ,... ,C _in ], a matrix in which N codewords of C _i are stacked, denoted as C=[C ₁ ,C ₂ ,...,C _i ,...,C _N ] ^T .

If and only if H∈C ^⊥ , then C and H satisfy the parity check equation:

CH ^T =0 (4)

In the formula, C is an N×n matrix, H is an m×n matrix, and 0 is an N×m all-zero matrix. Define C _i , 1≤i≤N to represent the i-th row vector of C, denoted as C _i =[C _i1 ,C _i2 ,…,C _ij ,…,C _in ], 1≤j≤n, H _a ,1 ≤a≤m represents the a-th row vector of H, denoted as H _a =[H _a1 , H _a2 ,...,H _aj ,...,H _an ], 1≤j≤n. then there is which is

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CirclePlus;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CirclePlus;</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; \&CirclePlus;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

If H _a contains N _a non-zero elements, the subscript vector of non-zero elements is

${\mathrm{<span\; class="notranslate">\; l</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; <</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; l</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Then formula (5) can be transformed into

${\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; il</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}}<span\; class="notranslate">\; \&CirclePlus;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; il</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; \&CirclePlus;</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; \&CirclePlus;</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; il</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Since the probability of sending a 0 at the sender is equal to the probability of sending a 1, then

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

And according to the document "Tian xia.novel blind identification of LDPC codes using average LLR of syndrome a posteriori probability.IEEE Transactions on Signal Processing, 2014":

$\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CirclePlus;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CirclePlus;</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; \&CirclePlus;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; tanh</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Pi;</span>}}\mathrm{<span\; class="notranslate">\; tanh</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Then the log-likelihood ratio of the posterior probability of the a-th parity bit of the i-th codeword is:

Because y=tanh ^-1 (x), it is a monotonically increasing function at -1<x<1, and Therefore, the formula (10) is simplified as

According to the definition of likelihood ratio and formula (11), when H∈C ^⊥ , the log-likelihood ratio of the posterior probability of verification is a positive number. If H∈C ^⊥ , the average log-likelihood ratio of the posterior probability of the corresponding syndrome is a positive number, and the higher the signal-to-noise ratio is, the closer it is to 1. when When , the log-likelihood ratio of the posterior probability of the syndrome Some are positive and some are negative. The average log-likelihood ratio of all syndromes is

Then when H∈C ^⊥ , W is greater than 0 and less than or equal to 1; when When , W is approximately equal to 0.

According to the system model obtained by formula (3), it can be known that:

$\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{{\mathrm{<span\; class="notranslate">\; il</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; il</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; ln</span>}\frac{\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; il</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&rsqb;</span>}{\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; il</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{{\mathrm{<span\; class="notranslate">\; il</span>}}_{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

In the formula, y=L(x) means that y is the log likelihood ratio of x. From (11), (12) and (13), the log likelihood ratio of the posterior probability of the syndrome can be obtained, but a _v and unknown, need to use M ₂ /M ₄ estimator to estimate a _v and value.

_{Estimate a v and} because

X _ij ＝a _v s _ij +w _ij , j＝0,1,...,n-1 (14)

Then the second moment of the received signal X _ij :

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\stackrel{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}}{<span\; class="notranslate">\; =</span>}\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \{</span>{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

The fourth moment of the received signal X _ij :

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\stackrel{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}}{<span\; class="notranslate">\; =</span>}\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \{</span>{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

Combining formula (15) and formula (16), we can get:

${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; =</span>\frac{\sqrt[\mathrm{<span\; class="notranslate">\; 4</span>}]{\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}}{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; v</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\sqrt{\mathrm{<span\; class="notranslate">\; 6</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

Actually, _M2 and _M4 can be estimated by the ith codeword of the received signal, namely:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

Estimated a _v and When , it can be estimated based on all received signal samples to increase the accuracy of estimation and eliminate randomness.

Fig. 5 shows that different cyclic codes of the present invention correspond to logarithmic likelihood ratios at different codeword lengths and synchronization moments; wherein, (a) represents the generator polynomial g ₀ (x)=(x ² +x+1)( (15,9) cyclic code of x ⁴ +x+1); (b) represents generator polynomial g ₀ (x)=(x ¹⁵ +1)(x ² +x+1)(x ⁴ +x+1) (30,9) of the cyclic code; (c) represents the (30,24) cyclic code of the generator polynomial g ₀ (x)=(x ² +x+1)(x ⁴ +x+1); Transmitting in a channel with a noise ratio of SNR=10db, the synchronization time t ₀ at the time of interception is 5. The x-axis represents the synchronization time, the y-axis represents the length of the code word, and the z-axis represents the result of obtaining the syndrome when constructing an interception matrix with different code word lengths and synchronization time. The maximum value of the average log-likelihood ratio of the test probability is denoted as L.

It can be seen from (a) that for the cyclic code (15,9), when n=15α, α=1,2,3, d=5, the value of L is the largest; when n=15α, α=1,2,3 , when d≠5, L is greater than ( Indicates a number approximately equal to 0) is less than the maximum value; when n≠15α, α=1,2,3, L is equal to It can be seen from (c) that for the cyclic code (30,24), when n=30, d=5, the value of L is the largest; when n=30, d≠5, L is greater than is less than the maximum value; when n≠30, L is equal to It can be seen from (b) that for the cyclic code (30,9), when n=15α, α=1, 2, 3, d=5 or d=20, the value of L is the largest; when n=15α, α=1 ,2,3, when d≠5 or d≠20, L is greater than less than the maximum value. The experimental phenomenon is completely consistent with the theoretical analysis.

According to Proposition 1, when the cyclic code does not satisfy the condition of Proposition 2, that is, n ₀ =2n ₁ , , when n=αn ₀ ,α=1,2,..., g(x) traverses the factors of x ⁿ -1, (n,g(x)) corresponds to the parity check matrix H, and there exists H that satisfies C( n,d)H ^T =0; when n≠αn ₀ , α=1,2,..., g(x) traverses the factors of x ⁿ -1, and the check matrix corresponding to (n,g(x)) is H, the absence of H satisfies C(n,d)H ^T =0. When the cyclic code satisfies the condition of Proposition 2, that is, n ₀ =2n ₁ , when When α=1,2,..., if g(x) is a factor of g′(x), set the parity check matrix corresponding to (n,g(x)) as H, satisfying C(n,d)H ^T =0. When n=αn ₀ , α=1,2,..., g(x) takes any factor of x ⁿ -1, let the parity check matrix corresponding to (n,g(x)) be H, there exists H satisfying C (n,d) ^HT =0. Therefore, if H satisfies C(n,d)H ^T =0, the L obtained at this time is closer to 1; if there is no H and satisfies C(n,d)H ^T =0, the L obtained at this time equal

However, according to Figure 5, the codeword length and synchronization time cannot be correctly identified, and further experimental judgment is required.

Fig. 6 shows the average log-likelihood ratios corresponding to different reducing polynomials of the cyclic code of the present invention when n=30, t ₀ =5. (a) is the (15,9) cyclic code of the generator polynomial g ₀ (x)=(x ² +x+1)(x ⁴ +x+1); (b) represents the generator polynomial g ₀ (x)=( The cyclic code (30,9) of x ¹⁵ +1)(x ² +x+1)(x ⁴ +x+1); the x-axis represents the approximate polynomial numbers 1 to 5 respectively p ₁ (x)=x+ 1, p ₂ (x)=x ² +x+1, p ₃ (x)=x ⁴ +x+1, p ₄ (x)=x ⁴ +x ³ +1, p ₅ (x)=x ⁴ +x ³ +x ² +x+1; the y-axis represents the synchronization time, and the value ranges from 0 to 29; the z-axis is the value of L, assuming d=0, g(x)=p ₁ (x), representing n =30, d=0 constructs the interception matrix X, calls the check matrix corresponding to p ₁ (x) in the check matrix library, and obtains the average log likelihood ratio of the posterior probability of the syndrome.

It can be seen from (a) that when g(x)=p ₂ (x), or g(x)=p ₃ (x), and d=5, or d=20, L is the largest; when g(x )=p ₂ (x), or g(x)=p ₃ (x), but when d≠5, or d≠20, L is greater than or equal to is less than the maximum value; when g(x)≠p ₂ (x), or g(x)≠p ₃ (x), therefore, It can be seen from (b) that when d=5, g(x) takes any factor of x ³⁰ -1, L is the largest; when d=20, g(x)=p ₂ (x), or g When (x)=p ₃ (x), L is the largest. therefore, The identification is correct, and it is consistent with the theoretical analysis of Proposition 1 and Proposition 2.

Fig. 7 shows the performance diagram of different cyclic code recognition using the algorithm in the text in the present invention. (a) is the (15,9) cyclic code whose generator polynomial is g ₀ (x)=(x ² +x+1)(x ⁴ +x+1); (b) is the generator polynomial is g ₀ (x) =(x ² +x+ ¹ )(x ⁴ +x+ ¹ ) (30,24) cyclic code; use the algorithm in the text to identify the code word length, synchronization time and generator polynomial, according to the signal-to-noise ratio from -5db to 10db, The step size is 1, the Monte Carlo simulation results of 200 times, where the parameters are selected as N=200, T=0.25.

It can be seen from (a) that when the signal-to-noise ratio of the cyclic code (15,9) is 3db, the correct recognition rate of codeword length and synchronization time can reach 80%; when the signal-to-noise ratio is 5db, the correct recognition rate of the generating polynomial The rate can reach more than 90%. When the SNR of cyclic code (30,24) is 5db, the correct recognition rate of code word length and synchronization time can reach more than 75%, and when the SNR is 7db, the correct recognition rate of generator polynomial can reach 100%. The longer the codeword length, the worse the anti-noise performance, and the algorithm in this paper has good anti-noise performance.

Claims (5)

1. A blind identification algorithm for cyclic code parameters by soft decision includes such steps as finding out the length n of all code words and generating polynomial as xⁿA check matrix corresponding to the factor of-1 is put into a check matrix library; then use M₂/M₄The estimator estimates the signal amplitude and the noise variance in the channel; then, constructing an interception matrix according to the assumed code word length and the synchronous moment by using the intercepted cyclic code stream, calling a check matrix in a check matrix library corresponding to the code word length, and obtaining the average log-likelihood ratio of the posterior probability of the syndrome; finally according to the cycleThe nature of the ring code, the codeword length, the synchronization instant and the generator polynomial are identified.

2. Identification method according to claim 1, characterized in that a check matrix library is established, the generator polynomial mainly according to the cyclic code (n, k) must be xⁿ-1 factor, thus xⁿ-1, completely factorizing into a plurality of known polynomials, and if the generator polynomial is a known polynomial, finding the corresponding check matrix and putting the check matrix into a check matrix library.

3. Identification method according to claim 1, characterized in that with samples of the received signal, M is used₂/M₄The estimator estimates the signal amplitude and noise variance in the channel. Since the cyclic code is subjected to BPSK modulation and is affected by white Gaussian noise in the channel, the received signal is X_ij＝a_vs_ij+w_ijJ is 0,1, …, n-1, wherein X_ijJ-th signal, a, representing i-th code word_vIs the amplitude gain, s_ijBPSK-modulated signal of the jth symbol of the ith code word of a cyclic code, w_ijObeying that the mean is 0 and the variance isThe normal distribution of (a), wherein,is the variance of the noise. Receiving signal X_ijSecond order moment of (c):X_ijfourth order moment of (d):thus, it is possible to providePractice ofUpper, M₂And M₄Can be estimated from the ith codeword of the received signal.

4. The recognition method according to claim 1, wherein the average log-likelihood ratio of the posterior probabilities of the syndromes is determinedWherein Nm is the number of syndromes,representing a posterior probability log-likelihood ratio of the a-th parity bit of the i-th codeword. According to the document "Tianxia. novel labeling of LDPC codes using average LLR of syndrome probability. IEEE Transactions on Signal Processing, 2014", the log-likelihood ratio of the posterior probability of the syndrome is:because y is tan h^-1(x) In-1<x<1 is a monotonically increasing function, andthe log-likelihood ratio of the posterior probability of the syndrome is therefore reduced to:

because of the fact thatAnd according to the identification method of claim 3, the average log-likelihood ratio of the posterior probabilities of the syndromes is estimated.

5. Root of herbaceous plantThe estimation method according to claims 1-4, combined with the properties of cyclic codes, can implement blind identification of cyclic code parameters, including codeword length, synchronization time and check matrix. According to proposition 1, if c_i(x) The code word of (n, k) cyclic code generated by generating polynomial in g (x), a (x), g '(x) is used as i ═ 1,2, …, and if the check matrix corresponding to polynomial in g' (x) is h '(x) cyclic code (Mn, k), M ═ 1,2, … is used as g' (x), then [ c ═ 1,2, …₁(x)，…，c_M(x)]h′(x)mod(x^Mn-1) ═ 0, M ═ 1,2, …. Constructing an interception matrix by assuming the length of a code word and the synchronization time, calling a check matrix of the length of the code word in a check matrix library, and calculating the mean log-likelihood ratio LLR of the posterior probability of a syndrome, wherein the LLR is the largest and is close to 1 when the length of the code word and the synchronization time are correct; when the code word length is incorrect, the LLR is equal to 0; the code word length is correct, and the LLR is more than or equal to a number which is approximately equal to 0 when the synchronization time is incorrect and is less than the maximum value, so that the identification of the code word length, the synchronization time and the check matrix is realized.