A method for open set blind recognition of Gaussian elimination decoding of a multi-element LDPC code

Abstract

The application provides an open set blind identification method suitable for multi-element LDPC code, which recovers the LDPC code check matrix by using soft decision information at the receiving end, and reconstructs the LDPC code channel encoder accordingly. The application firstly evaluates the bit reliability of each code word receiving sequence, sorts the code word receiving signal according to the bit reliability, and obtains hard decision bits, thereby obtaining hard decision symbols, and then applies the Gaussian elimination method to the matrix composed of the hard decision symbols of multiple groups of code words to find the check relationship contained among the code words. After completing one elimination, error code word elimination and replacement of the order of part of the code words are needed, thereby discovering more check relationships. Considering the case that the initial error code rate of the channel input is high, the application adopts the standard soft decision belief propagation QSPA decoding algorithm of the multi-element LDPC code in the identification process, effectively reduces the influence of the input error code rate, makes more check vectors be obtained in the new round of iterative identification, improves the fault tolerance of the algorithm, and thereby optimizes the blind identification performance.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of open set blind identification method of multi-element LDPC code, specifically relates to a kind of open set blind identification method based on iterative Gauss elimination and LDPC decoding suitable for multi-element LDPC code, belong to channel coding blind identification technical field. BACKGROUND

[0002] Low-Density Parity-Check Codes (LDPC) was proposed by Gallager in the early 1960s. Davey and Mackay first studied multi-element LDPC code in 1998. Compared with binary LDPC code, multi-element LDPC code of medium and short code length has better decoding performance, and is better in high-order modulation, burst error correction and other aspects. It is widely used in storage, large-scale mobile communication and other scenarios.

[0003] LDPC code belongs to linear block code, and is named due to the sparsity characteristics of its check matrix H. The blind identification of (n, k) block code aims to reconstruct the parity check matrix H from some received codewords. In most applications, the receiver knows the channel coding used for transmission. However, in non-cooperative scenarios, the channel coding parameters obtained by the receiving end are very limited. Therefore, it is necessary to analyze the intercepted message sequence of the information and monitoring system to blindly identify the coding, and to reconstruct the channel encoder. In addition, the blind identification of LDPC code can also be used in applications such as adaptive modulation and coding (AMC), cognitive radio, etc. In general, the channel coding parameters in the AMC system need to be sent to the receiving end through the control channel. Blind reconstruction of the channel encoder can omit the use of the control channel, saving channel and spectrum resources. The receiver of the cognitive radio needs to adjust according to the change of the channel coding to ensure correct decoding of the received information.

[0004] The research of the previous multi-element LDPC code blind recognition algorithm is mainly for the closed set blind recognition, that is, according to the received code word, the correct check matrix is selected from the given check matrix set. One recognition method is to use the expectation maximization (EM) estimator of unknown parameters (signal amplitude, noise variance and phase offset), the log likelihood ratio (LLR) estimator of the posterior probability and the maximum average LLR detector (see literature: Xia T. Blind LDPC Encoder Identification [J]. 2013.). The method has considerable performance. Another method is also a maximum average LLR based open set blind recognition method of multi-element LDPC code (see literature: Tian X, Wu H C. Blind Identification of Nonbinary LDPC Codes Using Average LLR of Syndrome a Posteriori Probability [J]. IEEE Communications Letters, 2013, 17(7): 1301-1304.). However, the closed set blind recognition needs to obtain the candidate set information in advance, so its use scene is greatly limited. Therefore, in order to solve the recognition problem of the sending end encoder in the non-cooperative scene, it is necessary to study the open set blind recognition algorithm of multi-element LDPC code. SUMMARY

[0005] The application aims to: In recent years, some researches are devoted to solving the reconstruction problem of the open set blind encoder of the LDPC code. After the signal passes through the noise channel, some existing methods use Gaussian elimination (GCE) to obtain the parity check relationship, and then delete the code word that does not satisfy the current parity check, so as to obtain the correct code word. In order to improve the fault tolerance of the existing algorithm, the application provides a Gaussian elimination decoding open set blind recognition method suitable for multi-element LDPC code. Firstly, the reliability of the code word is evaluated and the code word is sorted by using the reliability, and then the Gaussian Jordan elimination method is applied to the code word matrix to find the check relationship contained in the code word, and after the elimination operation, the error code word is removed and a part of the code word is replaced. Considering that the error code leads to poor recognition performance in one round of iteration elimination, the application adopts a multi-element LDPC soft decoding algorithm to eliminate the adverse effects caused by the error code to a certain extent. The decoding algorithm of the multi-element LDPC code is similar to that of the binary LDPC code, which is an iterative decoding algorithm based on message passing. The most basic one is the Q-dimensional product-sum algorithm QSPA, and the FFT-QSPA algorithm using fast Fourier transform is derived based on this, and the application adopts this algorithm.

[0006] Technical scheme: In order to achieve the above purpose, the technical scheme adopted by the application is:

[0007] An open set blind identification method suitable for multi-element LDPC codes is defined in q=2 d A multi-element LDPC code with a code length of N in a finite field GF(q) is denoted as m i =[m i,1 ,m i,2 ,…,m i,K ] 1×K ,m i,j ∈GF(q) is an input information symbol sequence of the i-th multi-element code, wherein K is the length of the message symbol sequence. After the symbol sequence is encoded by the multi-element LDPC code, an output symbol sequence c i =[c i,1 ,c i,2 ,…,c i,N ] 1×N ,c i,j ∈GF(q) is obtained. Denote the M×N dimensional parity check matrix of the multi-element LDPC code as H, and h j represents the j-th parity check row vector with a size of 1×N, so c i ·H T =0, The open set blind identification of the multi-element LDPC code is performed according to a plurality of sets of encoded vector received symbols and the parity check relation to obtain the parity check matrix H and all check vectors (the code length N and the synchronization position are known), and the steps 1-3 are specifically executed as follows.

[0008] Step 1: C multi-element symbol code sequences are transmitted in the form of binary mapping bits, and a set of C soft decision output sequences received is denoted as R=[r1,r2,…,r C ], wherein r i =[r i,1 ,r i,2 ,…,r i,dN ]; define a single code word error estimation variable Err esti as the proportion of the received bits of the code word dN whose amplitude is less than a determined threshold Th, wherein card{} represents the number of elements in a set; the C soft decision output sequences received are rearranged in a descending order according to the values of the error estimation variables Err esti (r i ), i=1,…,C, and the rearranged result is denoted as R'; the hard decision bits of the C code words rearranged in R' are converted into a multi-element domain symbol every d bits, and a symbol level matrix V=(v1,v2,…,v C ) T is obtained, wherein v i =(v i,1 ,v i,2 ,…,v i,N )T This is the hard decision symbol column vector of the received signal of the i-th codeword, which corresponds to the i-th column in R′ after rearrangement.

[0009] Step 2:

[0010] Gaussian elimination: Let E = (e1, e2, ..., e N ) represents the N-order identity matrix that records the check vector, where e i It is a column vector of length N; then, the same operation is performed on the columns of V and E using Gaussian elimination in the GF(q) field to obtain new matrices L and E′=(e′1,e′2,…,e′). N Here, Gaussian elimination eliminates V into a column echelon form matrix;

[0011] Analyze the elimination results and determine the verification vector: according to the formula Where L(k,i) is the element in the k-th row and i-th column of matrix L, and by summing each row of matrix L, a new vector set W = (w1, w2, ..., w N );remember The set of verification columns Q can be expressed by the formula Q = {i|Φ} i <β, i = 1, 2, ..., N} are detected, where β is the judgment threshold; assuming there are s elements in Q, let Q = {i1, i2, ..., i...} s}, then the set of verification vectors P can be obtained from the corresponding matrix E′ based on the element symbols.

[0012] Deleting and replacing codewords: Let L = (l1, l2, ..., l N ), where l j =(l 1,j ,l 2,j ,…,l C,j ) T Let j represent column L; let q represent column L. i =∑ j∈Q l i,j ,i=N+1,…,C to determine if the i-th row of V has an error; if q i If the value is greater than 0, then the i-th row of V contains errors, and these rows need to be deleted; therefore, the set of codewords to be deleted can be represented as D = {i|q}. i >0, i=N+1,N+2,…,C};After deleting these codewords, the codeword order of matrix V needs to be changed, and Change to Where C′=C-card{D} is the number of codewords after deleting erroneous codewords, v i ,i=1,…,C′ are the row vectors of matrix V;

[0013] Inner iteration: after step 1 is executed, step 2 is executed iteratively, and this process is one inner iteration, and the maximum iteration number is n1 times. If the number of identified check vectors is 0 after n1 inner iterations, the algorithm terminates, and the identification fails; if the number of identified check vectors is greater than 0, step 3 is executed;

[0014] Step 3: using part of the check vectors identified in step 2, soft decision decoding is performed on the received signals of the C codewords in R' respectively, such as the belief propagation QSPA decoding of the multi-element LDPC code standard, and the maximum iteration number of each iteration decoding is set to n it , the C' successfully decoded decision output vectors constitute V', which is used as the input matrix V = V' of the next outer iteration Gaussian elimination in step 3.

[0015] Outer iteration: the process of completing one inner iteration and step 3 is one outer iteration, and the maximum iteration number is n2 times. The check vectors obtained in each outer iteration are combined with the check vectors obtained in the previous iteration. After all n2 outer iterations are executed, all identified check vectors are combined as the final identification result, and the identification is completed.

[0016] The open set blind identification method described above can be applied to an adaptive coding modulation system. The adaptive coding modulation system can dynamically select a modulation format and determine a suitable channel coding combination. The blind identification method of the channel code such as the LDPC code is used in the system to detect the change of the channel code, to replace the use of the additional bits in the frame structure, and a part of the spectrum efficiency and channel resources can be saved.

[0017] The open set blind identification method described above can be applied to a cognitive radio receiver. The cognitive radio technology can adapt to the external wireless environment by detecting, analyzing and reasoning the surrounding wireless environment, and adaptively adjusting the transmission parameters (such as power, carrier modulation and coding, etc.), and the like, to find and use the idle spectrum autonomously. Therefore, the blind identification method of the channel code such as the LDPC code can be applied to the cognitive radio receiver to detect and analyze the wireless signal.

[0018] Compared with the prior art, the present application has the following beneficial effects:

[0019] The open set blind identification method provided by the application firstly sorts the code words according to reliability, arranges the more reliable code words in front, and uses them for Gaussian elimination, so as to become the main identification basis of the check vector and increase the identification success rate. Meanwhile, considering the negative influence of the error code word on the Gaussian elimination process, the application deletes the error code word and replaces the order of part of the code word after each iteration, so as to effectively identify more check vectors. In the case of limited iteration times, the application proposes to insert the decoding algorithm in the multiple rounds of Gaussian elimination iteration, and skillfully uses part of the check vectors identified in the previous iteration to decode the received sequence, so as to reduce the input error rate of the next iteration identification, and therefore identify a more complete check matrix in the next iteration, and improve the performance of blind identification.

[0020] The blind identification method provided by the application is based on Gaussian elimination and soft decision decoding, has fast decoding speed, high fault tolerance and good identification performance. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 The flow chart of the blind identification method of the application.

[0022] Figure 2 The simulation verification graph of the application: the average identification accuracy- average input bit error rate relationship curve of the (96, 48)-GF(64) multiple LDPC code.

[0023] Figure 3 The simulation verification graph of the application: the average identification accuracy- average input bit error rate relationship curve of the (16, 8)-GF(256) multiple LDPC code.

[0024] Figure 4 The simulation verification graph of the application: the average identification accuracy- average input bit error rate relationship curve of the (72, 36)-GF(256) multiple LDPC code. DETAILED DESCRIPTION

[0025] In order to make the technical scheme, object and advantages of the application clearer, the application will be further illustrated below in combination with the drawings and specific implementation examples, and it should be understood that these examples are only used to illustrate the application, and are not used to limit the scope of the application.

[0026] Reference Figure 1 , the application provides an open set blind identification method of a multiple LDPC code, comprising:

[0027] Suppose a multiple LDPC code defined in q=2 d finite field GF(q), denoted as m i =[m i,1 ,m i,2 ,…,m i,K ]1×K ,m i,j ∈GF(q) is the input information sequence of the i-th multi-symbol code. The output symbol sequence of the LDPC coded sequence is c i = [c i,1 ,c i,2 ,…,c i,N ] 1×N ,c i,j ∈GF(q). Denote the check matrix of the multi-symbol LDPC code M x N as H, h j represents the j-th parity check vector of size 1 x N.

[0028] In this embodiment, the check bit length M = 48, the code length N = 96, the multi-symbol LDPC code C1 defined in the finite field GF(64); the check bit length M = 8, the code length N = 16, the multi-symbol LDPC code C2 defined in the finite field GF(256); and the check bit length M = 36, the code length N = 72, the multi-symbol LDPC code C3 defined in the finite field GF(256) are selected to test the decoding performance of the algorithm, the code word number C = 10 4 , the code word reliability threshold Th = 0.5, the check column determination threshold β = 0.5, the number of iterations of Gaussian elimination n1 = 50, the total number of iterations of iterative Gaussian elimination n2 = 2, and the maximum decoding iteration number n it = 30. Taking the code C1 as an example, the entire decoding process of the algorithm is described in detail.

[0029] Step S1:

[0030] 10 4 multi-symbol symbol coded sequences are transmitted in the form of binary mapping bits, and the received 10 4 soft decision output sequence set is denoted as wherein r i = [r i,1 ,r i,2 ,…,r i,576 ], and the single code word error estimation variable Err esti is defined as the proportion of the symbols with an amplitude less than the determined threshold Th = 0.5 in the 576 received symbols of the code word, The received 10 4 soft decision output sequences are rearranged from small to large according to the values of the error estimation variable Err esti (r i ), i = 1, …, 10 4 , and the rearranged result is denoted as R'; the hard decision of the 10 4 rearranged received signals in R' is performed, and the hard decision bit result is converted into a multi-symbol domain symbol every 6 bits to obtain the symbol level matrix wherein vi =(v i,1 ,v i,2 ,…,v i,96 ) T This is the hard decision symbol column vector of the received signal of the i-th codeword, which corresponds to the i-th column in R′ after rearrangement.

[0031] Step S2:

[0032] Gaussian elimination: Let E = (e1, e2, ..., e 96 ) represents the 96th-order identity matrix that records the check vector, where e i It is a column vector of length 96; then, the same operation is performed on the columns of V and E by Gaussian elimination in the GF(64) field to obtain new matrices L and E′=(e′1,e′2,…,e′). 96 );

[0033] Analyze the elimination results and determine the verification vector: according to the formula Summing each row of matrix L yields a new vector set W = (w1, w2, ..., w 96 );remember The set of verification columns Q can be expressed by the formula Q = {i|Φ} i <β, i = 1, 2, ..., 96} are detected, where β = 0.5 is the judgment threshold; assuming there are s elements in Q, let Q = {i1, i2, ..., i...} s}, then the set of verification vectors P can be obtained from the corresponding matrix E′ based on the symbols of the elements.

[0034] Deleting and replacing codewords: Let L = (l1, l2, ..., l 96 ),in Let j represent column L; let q represent column L. i =∑ j∈Q l i,j i = 97, ..., 10 4 To determine if there is an error in the i-th row of V; if q i If the value is greater than 0, then the i-th row of V contains errors, and these rows need to be deleted; therefore, the set of codewords to be deleted can be represented as D = {i|q}. i >0, i = 97, 98, ..., 10 4 After deleting these codewords, the codeword order of matrix V needs to be changed. Change to Where C′=C-card{D} is the number of codewords after deleting erroneous codewords;

[0035] Inner iteration: after step S1 is executed, step S2 is iteratively executed, and this process is one inner iteration, and the maximum iteration number is n1=50 times. If the number of the check vectors identified after 50 inner iterations is 0, the algorithm is terminated, and the identification fails; if the number of the check vectors identified is greater than 0, step S3 is executed;

[0036] Step S3: using part of the check vectors identified in step S2, soft decision decoding is performed on the received signals of the C codewords in R', such as the belief propagation QSPA decoding of the multi-element LDPC code standard, and the maximum iteration number of each iteration decoding is set as n it =30, and the C' successfully decoded decision output vectors constitute V'.

[0037] Outer iteration: the process of completing one inner iteration and step S3 is one outer iteration, and the maximum iteration number is n2=2 times. After all 2 outer iterations are executed, all the identified check vectors are combined as the final identification result, and the identification is completed.

[0038] The blind identification method proposed in the application divides the whole blind identification process into two stages by using decoding, and the second stage is the optimization and supplement of the first stage. The first stage is to identify the received sequence itself after Gaussian elimination, and a certain number of check vectors are obtained, as described in S2. This part of the check vectors is used for soft decision decoding before the second stage, and the constraint relationship of the check vectors is used to reduce the error rate of the received sequence, so that the second round and even the next several rounds of iteration can identify the check vectors as comprehensively as possible, as described in S3. The whole blind identification process fully considers the order of the code elements and their error conditions, so that the application can have higher fault tolerance and better identification performance.

[0039] Figure 2 、 Figure 3 and Figure 4 respectively represent the average identification correct rate-average input error bit rate relationship curve diagram obtained after 30 times of simulation of codes C1, C2 and C3 under the algorithm proposed in the application under the same E b / N0. From Figure 2 , it can be seen that when the average input error bit rate is 4.25x10 -3 , two rounds of iteration can identify the complete check matrix of code C1, and the average identification correct rate of the second round has a relatively large improvement compared with the first round, and the maximum improvement ratio can reach 0.5. From Figure 3 , it can be seen that when the average input error bit rate is 1.95x10 -2 , two rounds of iteration can identify the complete check matrix of code C2, and the identification performance has an order of magnitude improvement compared with code C1, because the code length of code C2 is shorter. From Figure 4 , it can be seen that when the average input error bit rate is 4.4x10-3 When the two iterations can identify the complete check matrix of the code C3, the identification performance is similar to that of the code C1, because the equivalent binary check matrix of the code C1 and the code C3 has the same size, i.e., (576, 288).

[0040] In summary, the open set blind identification method for the multi-element LDPC code proposed in the application evaluates the reliability of the code word, iteratively uses the Gaussian elimination method, eliminates the error code word after elimination, and replaces part of the code word. Considering the optimization of the error code, the application adds the belief propagation QSPA decoding algorithm to eliminate part of the adverse effects caused by the error code, thereby improving the overall check vector identification rate and having a higher fault tolerance. The open set blind identification method for the multi-element LDPC code proposed in the application not only expands the binary open set blind identification of the LDPC code to the multi-element, but also expands the closed set blind identification of the multi-element LDPC code to the open set blind identification, so that the application scene of the algorithm is more flexible and flexible.

[0041] The above is the preferred embodiment of the application, it should be pointed out that for those skilled in the art, without departing from the principles of the application, a number of improvements and refinements can be made, these improvements and refinements should also be considered as the protection scope of the application.

Claims

1. A method for open-set blind identification of multivariate LDPC codes, characterized in that, Defined at q=2 d For a multi-element LDPC code with a finite field GF(q) and a coding length of N, the parity check matrix H and all check vectors are obtained based on multiple sets of coded vectors, received signals, and check relational formulas. The specific steps include the following: Step S1: Evaluate the bit reliability of each codeword received sequence, and sort the codeword received signals accordingly to obtain hard decision bits, thereby obtaining hard decision symbols; Step S2: Apply Gaussian elimination to the matrix formed by the hard decision symbols of multiple sets of codewords to find the check relationships contained between codewords, and remove erroneous codewords and replace some codewords after the elimination operation; the process of completing steps S1 and S2 is called one inner iteration. If the number of check vectors identified after the maximum number of inner iterations is 0, the algorithm terminates and the identification fails; if the number of check vectors identified is greater than 0, then proceed to step S3. Step S3: Using the partial check vectors identified in Step S2, perform soft-decision decoding on the received signals of the codewords in the sorting results of the codeword received signals in Step S1; denote the completion of one inner iteration and the process of Step S3 as one outer iteration, and merge the check vectors obtained in each outer iteration with the check vectors obtained in the previous iteration; after all outer iterations are completed, merge all the identified check vectors as the final identification result, and the identification is completed.

2. The method for open-set blind identification of multivariate LDPC codes according to claim 1, characterized in that, Step S1 specifically includes: transmitting C multi-element symbol encoding sequences in binary mapped bit form, and denoting the set of the received C soft-decision output sequences as R = [r1, r2, ..., r...]. C ], where r i =[r i,1 ,r i,2 ,…,r i,dN Define a single codeword error estimation variable Err. esti This refers to the proportion of the received bits of the codeword dN whose amplitude is less than a predetermined threshold Th. Where card{} represents the number of elements in a set; the received C soft-decision output sequences are then processed according to the error estimation variable Err. esti (r i The values ​​of i = 1, ..., C are rearranged in ascending order, and the result is denoted as R. ′ ; For R ′ The received signal after rearranging the C codewords undergoes hard decision processing, and the hard decision bit result is converted into a multi-domain symbol for every d bits, resulting in a symbol-level matrix V = (v1, v2, ..., v C ) T , where v i =(v i,1 ,v i,2 ,…,v i,N ) T For rearrangement and R ′ The i-th column corresponds to the hard decision symbol column vector of the i-th codeword received signal.

3. The method for open-set blind identification of multivariate LDPC codes according to claim 2, characterized in that, Step S2 specifically includes: Gaussian elimination: Let E = (e1, e2, ..., e N ) represents the N-order identity matrix that records the check vector, where e i It is a column vector of length N; then, the same operation is performed on the columns of V and E using Gaussian elimination in the GF(q) field to obtain new matrices L and E′=(e′1,e′2,…,e′). N Here, Gaussian elimination eliminates V into a column echelon form matrix; Analyze the elimination results and determine the verification vector: according to the formula Where L(k,i) is the element in the k-th row and i-th column of matrix L, and summing each row of matrix L yields a new vector set W = (w1, w2, ..., w...). N );remember The set of verification columns Q is expressed by the formula Q = {i|Φ} i <β, i = 1, 2, ..., N} are detected, where β is the judgment threshold; assuming there are s elements in Q, let Q = {i1, i2, ..., i...} s }, then based on the element signs, from the corresponding matrix E ′ The set of verification vectors P is obtained from this. Deleting and replacing codewords: Let L = (l1, l2, ..., l N ), where l j =(l 1,j ,l 2,h ,…,l C,j ) T Let j represent column L; let q represent column L. i =∑ j∈Q l i,j ,i=N+1,…,C to determine if the i-th row of V has an error; if q i If the value is greater than 0, then the i-th row of V contains errors, and the set of codewords to be deleted is represented as D = {i|q}. i >0, i=N+1,N+2,…,C};After deleting these codewords, change the codeword order of matrix V, and Change to Where C′=C-card{D} is the number of codewords after deleting erroneous codewords, v i ,i=1,…,C′ are the row vectors of matrix V.

4. The method for open-set blind identification of multivariate LDPC codes according to claim 3, characterized in that, The soft-decision decoding in step S3 is the FFT-QSPA algorithm using Fast Fourier Transform.

5. An adaptive coding and modulation system based on the open set blind identification method according to any one of claims 1-4.

6. A cognitive radio receiver based on the open-set blind identification method of any one of claims 1-4.

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