CN103944586A - Method for constructing code-rate compatibility QC-LDPC code - Google Patents

Abstract

The invention relates to the technical field of channel coding of a wireless communication system and a satellite communication system, and provides a method for constructing a rate-compatible QC-LDPC code based on matrix row and column deletion. The method comprises: first, constructing a low code rate QC-LDPC code with a large girth length based on the GCDg8 algorithm as the mother code; Short loops appear in high bit rate codewords, because row and column deletion is to delete the corresponding edges in the Tanner graph corresponding to the mother code without short loops, not only will not produce short loops, but also may increase the girth; finally, using concealment The technology processes subcodes separately, which improves the minimum distance and performance of codewords. Compared with the LDPC code constructed by the PEG algorithm, the method adopts a structurally designed rate-compatible QC-LDPC code, which has a simpler structure, less complex hardware implementation, and superior performance.

Description

A Construction Method of Rate Compatible QC-LDPC Codes

technical field

The invention relates to the technical field of channel coding of a wireless communication system and a satellite communication system, in particular to a construction method of a rate-compatible QC-LDPC code.

Background technique

Different from the channel coding technology of traditional wireless and satellite communication systems, low-density parity-check (Low-Density Parity-Check, LDPC) code is a kind of linear block code defined by sparse parity check matrix, using belief propagation (belief propagation, BP) algorithm decoding, not only has good performance close to the Shannon limit, but also has low decoding complexity and flexible structure. It is a research hotspot in the field of channel coding in recent years. Satellite digital video and audio broadcasting and other fields.

In recent years, researchers have found that the introduction of rate-compatible LDPC code coding technology under the time-varying channel conditions of wireless and satellite communication systems can make the error correction capability of channel coding adaptively adjusted according to the channel environment. Using code rate compatible LDPC codes can adjust the error correction capability in real time by adjusting the code rate according to the channel environment under the premise of ensuring the service quality, so as to maximize the channel throughput and improve the data transmission efficiency. From the perspective of implementation complexity, the rate-compatible LDPC code is composed of a nested structure, which can work with a single encoder/decoder within a certain range of bit rate, thus greatly reducing the complexity of the system. In Hybrid Automatic Repeat Request (HARQ), the sender can use rate-compatible LDPC codes to send incremental parity bits to ensure that the decoder at the receiver can decode successfully. In Unequal Error Protection (UEP), it can perform effective error protection according to the importance of information.

At present, the commonly used methods for designing rate-compatible LDPC codes mainly include: (1) Puncture, that is, to punch LDPC codes with low bit rates to obtain subcodes with higher and higher bit rates. In the article "Rate-compatible puncturing of low-density parity-check codes" [Information Theory, IEEE Transactions on, 2004, 50(11): 2824-2836], McLaughlin et al. adopted a Gaussian approximation method for rate-compatible LDPC codes. Research on the optimal porosity distribution of . Although this method is simple to operate, the codewords obtained by puncturing still have the disadvantage that the decoding performance drops very seriously with the increase of the code rate. (2) Based on the method of matrix row and column expansion, that is, the row and column expansion of the high code rate LDPC code is carried out successively to obtain subcodes with smaller and smaller code rates. Aiming at the disadvantage of deteriorating subcode decoding performance in the puncturing process, Jacobsen et al. "Design of rate-compatible irregular LDPCcodes based on edge growth and parity splitting" [Vehicular Technology Conference, 2007.VTC-2007Fall.2007IEEE66th.IEEE, 2007 :1052-1056] In this paper, the degree distribution optimization method using the external information transfer graph (EXIT) is used to study the rate-compatible LDPC codes based on the extension method design. Although this method can avoid the disadvantage of deteriorating subcode decoding performance during the puncturing process, the expansion process is equivalent to adding new check nodes, variable nodes, and edges corresponding to new non-zero elements in the corresponding Tanner graph. , so it is necessary to consider avoiding the newly added non-zero elements to generate new short loops in the corresponding Tanner graph, thus increasing the complexity of degree distribution optimization in the expansion process. Therefore, the construction of rate-compatible LDPC codes with good codeword performance and low complexity has become one of the hot issues in researching the application of rate-compatible LDPC codes in recent years.

Contents of the invention

At present, the rate-compatible LDPC codewords designed by punching technology have the disadvantage that the decoding performance decreases seriously with the increase of the code rate, and the rate-compatible LDPC code designed based on the matrix expansion method is proposed to solve this disadvantage. , most of them cannot guarantee low coding complexity due to the need to do a lot of optimization work to avoid new short cycles in the corresponding Tanner graphs caused by newly added non-zero elements and their unstructured design.

For above deficiencies in the prior art, the object of the present invention is to provide a kind of code rate compatible QC-LDPC code that produces multi-code rate, superior performance; The technical scheme of the present invention is as follows: a kind of code rate compatible QC-LDPC code A construction method, which includes the following steps:

101. The initialization sequence S is {0,1}, input the number of rows J and the number of columns L of the exponential matrix E, and obtain the sequence S={a ₀ ,a ₁ ,…,a _J-1 } according to the GCDg8 algorithm, and then calculate according to The formula P≥(a _J-1 -a ₀ )(L-1)+1, the dimension of the cyclic permutation matrix is P×P, and the element a _i j corresponds to each row of the P×P identity matrix to the right cyclically shift a _i j bits, i=0,1,...,J-1; j=0,1,...,L-1, the index matrix E is

$\mathrm{E.}(a_0,a_1,...,a_{J-1})=\left(\begin{array}{cccc}{a}_0\&Center\; Dot;0& a_0\&Center\; Dot;1& ...& a_0\&CenterDot;(L-1)\\ a_1\&Center\; Dot;0& a_1\&Center\; Dot;1& ...& a_1\&Center\; Dot;(L-1)\\ & & & .\\ ...& ...& ...& .\\ & & & .\\ a_{J-1}\&CenterDot;0& a_{J-1}\&Center\; Dot;1& ...& a_{J-1}\&CenterDot;(L-1)\end{array}\right);$ J and L are two integers, J≥3, L≥3, and 0≤a ₀ <a ₁ <…<a _J-1 , a ₀ ,…,a _J-1 are integers;

102. According to the sequence S={a ₀ ,a ₁ ,…,a _J-1 } obtained in step 101 and the dimension P×P of the cyclic permutation matrix, the parity check matrix is obtained according to the construction principle of the exponential matrix in 101, And the girth of the parity check matrix is greater than or equal to 8;

103. Delete the last row and the last column of the index matrix of the quasi-cyclic low density parity check QC-LDPC code mother code LDPC0 obtained in step 102 to obtain the subcode LDPC1, and then delete the last row and the last column of the index matrix of the subcode LDPC1 to obtain the subcode LDPC1. The code LDPC2 is deleted by analogy to obtain multiple high code rate subcodes, and the code rate of the high code rate codeword obtained after the row and column deletion method is

n=1,2,..., represents the number of rows/columns deleted in total for the exponential matrix of the mother code;

104. The index matrix E of the mother code LDPC0 and the subcodes LDPC1 and LDPC2 obtained in step 103 is respectively processed by a concealment matrix M of the same dimension, and the concealment matrix M(J,L,J′)=(m _i,j ) _{0 ≤i<J,0≤j<L} is a J×L binary matrix, hidden operation It is defined as follows: If m _i,j =1, then m _i,j ·E _i,j =E _i,j , otherwise when m _i,j =0, m _i,j ·E _i,j corresponds to a P×P all-zero matrix , use the binary concealment matrix with the same dimension as the exponential matrix to process the exponential matrix of the QC-LDPC code of the corresponding code rate, that is, the position unit corresponding to 0 in the corresponding exponential matrix and the concealment matrix adopts the same dimension The zero matrix is replaced, and the position unit corresponding to 1 in the hidden matrix remains unchanged, and a rate-compatible QC-LDPC code is obtained.

Further, when J=6 and L=12 are set, the information bit lengths of mother code LDPC0, subcode LDPC1 and subcode LDPC2 in step 103 are all 2514, and the code rates are 1/2 and 6/11 respectively , 3/5, the sequence obtained by GCDg8 algorithm search is (a ₀ ,a ₁ ,…,a ₅ )={0,1,12,13,35,38}, P=419.

Further, the rate-compatible QC-LDPC code is composed of a nested codeword structure, which can work under a single encoder/decoder.

Furthermore, in the wireless communication and satellite communication systems under the time-varying channel environment, after the information to be sent is coded by the source, it adaptively adopts a rate-compatible QC-LDPC coder for channel coding according to the channel environment and transmits it in the channel. That is, when the channel environment is good, a codeword with a high code rate is used for encoding; otherwise, when the channel environment is not ideal, a codeword with a low code rate is used for encoding.

Advantage of the present invention and beneficial effect:

The construction method of the code rate compatible QC-LDPC code based on the index matrix row and column deletion proposed by the present invention considers the time-varying nature of the channel under the wireless and satellite communication environment, and proposes a construction method of the code rate compatible QC-LDPC code, which corrects The error capability can be adaptively adjusted according to the channel environment. Using this code rate compatible QC-LDPC code can adjust its error correction capability in real time by adjusting the code rate according to the channel environment under the premise of ensuring the quality of service, thereby improving the throughput of the channel. This kind of code rate compatible QC-LDPC code based on the idea of exponent matrix row and column deletion can avoid short loops in subcodes, because row and column deletion is to delete the corresponding edges in the Tanner graph corresponding to the mother code without short loops, not only will not Short rings are produced, and the girth is also increased. Therefore, the construction method based on the idea of row and column deletion can well overcome the serious degradation of subcode decoding performance after puncturing and the shortcomings of short loops in the expansion process.

Description of drawings

Fig. 1 is the construction flowchart of code rate compatible QC-LDPC code among the present invention;

Fig. 2 is the exponent matrix structural diagram of code rate compatible QC-LDPC code among the present invention;

Fig. 3 is the exponent matrix structural diagram of the code rate compatible QC-LDPC code based on GCDg8 algorithm among the present invention;

Fig. 4 adopts the wireless, satellite communication system model diagram of code rate compatible QC-LDPC code among the present invention;

Fig. 5 is the BER performance emulation diagram of three kinds of code rates compatible QC-LDPC code among the present invention;

FIG. 6 is a simulation diagram of BER performance comparison between three code rate compatible QC-LDPC codes and PEG algorithm-constructed LDPC codes in the present invention.

Detailed ways

A non-limiting embodiment is given below in conjunction with the accompanying drawings to further illustrate the present invention.

With reference to Fig. 1-shown in Fig. 3, for the structure of the code rate compatible QC-LDPC code, what the present invention selects is based on the QC-LDPC code of GCDg8 algorithm construction as mother code, then its index matrix of J * L successively Rows and columns are deleted to obtain high code rate subcodes with constant information bit length, which are finally processed by concealment matrix.

As shown in FIG. 1, it is a flow chart of the construction of the rate-compatible QC-LDPC code in the present invention. The method comprises the following steps: first constructing a low code rate QC-LDPC code with a large girth length based on the GCDg8 algorithm as a mother code, and then deleting rows and columns of the exponential matrix of the above QC-LDPC mother code to obtain a high code rate code with constant information bit length Finally, the concealment technology is used to process the codewords of each code rate respectively, that is, a rate-compatible LDPC code with good code word performance and low complexity is obtained.

Specifically include the following steps:

1. Based on the GCDg8 algorithm to construct a low code rate QC-LDPC mother code with a large girth length: In this step, the QC-LDPC code constructed based on the GCDg8 algorithm is selected as the mother code, and other methods can also be selected to construct an LDPC that meets the above requirements mother code. The construction of the QC-LDPC code based on the GCDg8 algorithm is as follows:

Each element in the index matrix E can be expressed as: P _r,c =f(r,c). According to the GCDg8 algorithm given by Wang X et al. in "Construction of youth-eight QC-LDPC codes from greatest commondivisor" [Communications Letters, IEEE, 2013, 17(2): 369-372], P _r,c =g( r)h(c), where g(r _i )=a _i (i=0,1,…,J-1),h(c _j )=j(j=0,1,…,L-1) . Then, a J×L exponential matrix corresponds to a block cyclic check matrix without zero elements:

$\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</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">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left(\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; L</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><span\; class="notranslate">\; .</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>& <span\; class="notranslate">\; .</span>\\ & & & <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>& {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\end{array}\right)<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>$

Where J and L (J≥3, L≥3) are two integers, and 0≤a ₀ <a ₁ <…<a _J-1 (a ₀ ,…,a _J-1 are integers). When the index matrix is converted into a check matrix, the element a _i j (i=0,1,…,J-1;j=0,1,…,L-1) corresponds to each row of the P×P identity matrix Circularly shift a _i · j (mod P) bits to the right.

In the above exponential matrix, we need to search for the sequence a _i and determine the dimensionality of the cyclic permutation matrix. To construct a QC-LDPC code with a girth of at least 8, first, we search the sequence a _i according to the GCDg8 algorithm. The steps of the GCDg8 algorithm are as follows:

Input: column weight J and row weight L.

Output: sequence S={a ₀ ,a ₁ ,...,a _J-1 }.

Initialization: The set S is initialized to {0,1}. Initializej=0.

Step 1: If j<(J-2), go to step 2. Otherwise end and the search is complete.

Step 2: Initialization: Y = value of the last element of S + 1.

Step 3: Traverse and select two numbers S(i) and S(j) in the current S set, and S(j)>S(i), if for any two S(i) and S(j) , if both satisfy:

(Y-S(i))/gcd(Y-S(i),S(j)-S(i))≥L (gcd(a,b) represents the greatest common factor of a,b) (2) Then set check=1 ; Otherwise, set check=0.

Step 4: If check=0, Y=Y+1, and return to step 3; if check=1, S=S∪Y, j=j+1, and return to step 1.

Then we determine the dimension of the cyclic permutation matrix as P×P according to P≥(a _J-1 -a ₀ )(L-1)+1(3).

Finally, the parity check matrix H of the QC-LDPC code based on the GCDg8 algorithm can be uniquely determined by formulas (1), (2), and (3) according to the construction principle of the exponential matrix.

2. The index matrix based on the QC-LDPC mother code is deleted row-by-row and column-by-row: starting from the last row and column of the J×L index matrix constructed by the GCDg8 algorithm or other algorithms, the high-code-rate subcode is obtained by row-column deletion. This method of successive deletion is to delete one row and one column of the exponential matrix at a time, which ensures that the length of the information remains unchanged, and its code rate is compatible with the exponential matrix structure of the QC-LDPC code as shown in Figure 2. Since the row and column deletion is performed successively on the basis of the large girth length LDPC code, that is, the variable nodes and check nodes and the corresponding edges are deleted in the Tanner graph, which will not only avoid short loops in the expansion process, but also reduce The sides of will help to increase the girth, thereby ensuring the performance of the codeword.

3. Using concealment technology to process the codewords of each code rate respectively: the index matrix of each code rate subcode is respectively processed by the concealment matrix of the same dimension. Concealment techniques are usually used simply to replace the cyclic permutation matrices at the corresponding positions with some all-zero matrices. We set M(J,L,J′)=(m _i,j ) _{0≤i<J,0≤j<L} as a J×L binary matrix, and we define the operation of concealment technology on the exponential matrix E as follows:

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; E.</span>}\stackrel{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}{<span\; class="notranslate">\; =</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

If m _i,j =1, then m _i,j ·E _i,j =E _i,j , otherwise when m _i,j =0, m _i,j ·E _i,j corresponds to a P×P all-zero matrix .

If the check matrix of the QC-LDPC code is a J×L matrix composed of a cyclic permutation matrix and a zero matrix, then such codewords with the same column weight have a larger minimum distance. Combining the masking matrix (Masking Matrix) and the exponential matrix to design a large girth QC-LDPC, that is, by multiplying the "0" and "1" elements in different positions in the masking matrix with the elements in the corresponding positions in the exponential matrix to obtain New exponent matrix for better performing codes.

Below through embodiment, further illustrate the present invention in conjunction with accompanying drawing, but do not limit the scope of the present invention in any way.

The following describes in detail the use of the construction method stated in the present invention to construct three kinds of QC-LDPC codes with code rate compatibility, the information bit length of which is k=2514, and the code rates are 1/2, 6/11, and 3/5 respectively.

1) First, search through the GCDg8 algorithm to obtain (a ₀ ,a ₁ ,…,a ₅ )={0,1,12,13,35,38}, and determine P=419 according to (3), and according to (1) Construct an exponential matrix of J=6, L=12, R=1/2 as mother code. Thus, a (5028, 2514) QC-LDPC mother code with a column weight of 3 is obtained.

2) Then, after deleting the last row and column for the first time, the first (4609, 2514) QC-LDPC subcode with code rate R=6/11 can be obtained, and then delete the last row and column for the second time to obtain the code rate The second (4190, 2514) QC-LDPC subcode of R=3/5. The row-column deletion process is shown in Figure 3.

3) Finally, the exponential matrix of each code rate is processed by the concealment matrix of the corresponding dimension. That is, M(6,12,3), M(5,11,3), and M(4,10,3) given in the previous part are used to process code rates of 1/2, 6/11, and 3/5, respectively. . For a J×L exponential matrix, set the corresponding hidden matrix M(J,L,J′) as a J×L binary matrix with column weight equal to (approximately) J′. The concealment matrix of the QC-LDPC code with code fetch rate R=1/2 is as follows:

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6,12,3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left(\begin{array}{cccccccccccc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right)<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>$

The concealment matrix of the QC-LDPC code with code fetch rate R=6/11 is as follows:

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 11</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left(\begin{array}{ccccccccccc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right)<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>$

The concealment matrix of the QC-LDPC code with code fetch rate R=3/5 is as follows:

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left(\begin{array}{cccccccccc}\mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right)<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>$

The matrices processed by the above series of hidden matrices are a series of check matrixes H of rate-compatible QC-LDPC codes with large girth length and large minimum distance proposed in this part.

For the encoding of the above code rate compatible QC-LDPC code, the parity check matrix H constructed above is used to generate a lower triangular matrix by using the Gaussian elimination method, and then further elementary transformation is performed to obtain the form of the right unit matrix: H=[P|I ] (I is the unit matrix of (NK)×(NK), P is the matrix of (NK)×K), the generator matrix G is obtained by G=[I|P ^T ], and the encoding is directly performed by C=M·G The encoded codeword is obtained (M is an information vector with a length of K, and N is an encoded code length).

In systems with time-varying channels such as wireless communication and satellite communication, after the information to be sent is coded by the source, it adaptively adopts a single rate-compatible QC-LDPC coder to perform channel coding and transmits in the channel according to the channel environment, so that The throughput rate of the channel is greatly improved, and a single code rate compatible QC-LDPC decoder is also used at the receiving end, and a set of encoder/decoder is used for encoding and decoding at the same time, which greatly reduces the complexity of the system. The wireless and satellite communication system model using this code rate compatible QC-LDPC code is shown in Figure 4.

Next, performance simulation results of constructing three rate-compatible QC-LDPC codes based on the matrix row and column deletion method in the embodiment of the present invention are provided. The simulation is carried out under the AWGN channel, modulated by BPSK, decoded by BP algorithm, and the maximum number of iterations is set equal to 100.

Figure 5 shows the simulation results of the BER performance curves of the three code rates compatible codewords under the additive Gaussian white noise channel. It can be seen from the figure that in the embodiment of the present invention, the performance curves of the three code rate compatible QC-LDPC codes are from right to left, and as the code rate decreases, the codeword performance becomes better and better.

In order to illustrate the advantages of the rate-compatible QC-LDPC code construction method based on matrix row and column deletion of the present invention under wireless and satellite communication channels, the present invention has selected the LDPC code based on the PEG algorithm construction and the GCDg8 algorithm construction based on the present invention. Code rate compatible codewords for comparison.

Figure 6 shows the BER of 3 code rate compatible QC-LDPC codes in the embodiment of the present invention and LDPC codes of equal code length, equal code rate, equal code weight, and equal girth length constructed by the PEG algorithm under the additive Gaussian white noise channel Performance comparison simulation results. The performance of the three code rate compatible QC-LDPC codes in the embodiment of the present invention is slightly improved with the performance of the LDPC constructed by the PEG algorithm corresponding to equal code length, code rate, code weight, and girth, which illustrates the proposed method of the present invention. Based on large-gauge LDPC codes, the rate-compatible QC-LDPC codes constructed by successive row-column deletion method can effectively guarantee the performance of each code rate. The construction method based on exponent matrix row and column deletion can construct the code rate compatible LDPC code with the same performance as the random code constructed by PEG algorithm with low implementation complexity.

The row-column deletion of the exponential matrix refers to the deletion of the last row and column of the exponential matrix of the mother code (deleting one row and one column or the same number of rows and columns each time) to obtain high-bit-rate codes. Assuming that the dimension of the mother code index matrix constructed by the large girth construction algorithm is J×L, the code rate of the high code rate code word obtained after the row and column deletion method is:

(n=1,2,..., indicates the total number of deleted rows/columns of the exponential matrix of the mother code) (8)

This method of constructing code-rate compatible QC-LDPC codes avoids short loops in high-rate codewords, because the deletion of rows and columns of the matrix is to delete the corresponding Edges, not only will not produce short loops, but may also increase the girth. Therefore, the construction method based on the idea of row and column deletion can well overcome the serious degradation of subcode decoding performance after puncturing and the shortcomings of short loops in the expansion process.

The method for constructing a rate-compatible QC-LDPC code based on matrix row and column deletion stated in the present invention has been introduced and illustrated in detail above. The above specific implementation description can be used to help understand the core idea of the present invention. The present invention is closely related to the time-varying characteristics of wireless and satellite communication system channels, considering that the decoding performance of high codewords generated by the puncturing technology of constructing code rate compatible LDPC codes is easy to deteriorate, and due to the need for a large number of optimizations based on matrix row and column expansion Work and unstructured design can't guarantee its low coding complexity, these shortcoming, drawbacks, the present invention proposes a kind of code rate compatible QC-LDPC code construction method based on matrix row and column deletion, and punching, expanding these traditional Compared with the code rate compatible implementation scheme, this method can effectively overcome the serious degradation of high code rate codeword decoding performance after puncturing and the disadvantages of short loops that are prone to appear in the expansion process. Compared with the code words with the same code rate and code length constructed by the PEG algorithm, this method uses a structured construction method to adjust the block matrix of the parity check matrix of the code rate compatible QC-LDPC code, thus ensuring a relatively smooth construction process. low complexity.

The above embodiments should be understood as only for illustrating the present invention but not for limiting the protection scope of the present invention. After reading the content of the present invention, the skilled person can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the method claims of the present invention.

Claims (4)

1. a building method for code-rate-compatible QC-LDPC code, is characterized in that comprising the following steps:

101, initialization sequence S is that { columns L, obtains sequence S={a according to GCDg8 algorithm for 0,1}, the line number J of input exponential matrix E ₀, a ₁..., a _j-1, then according to calculating formula P>=(a _j-1-a ₀) (L-1)+1, the dimension that draws cyclic permutation matrices is P * P, element a _ij circulates to the right and moves a corresponding to every row of P * P unit matrix _ij position,, i=0,1 ..., J-1; J=0,1 ..., L-1, described exponential matrix E is

$E(a_0,a_1,...,a_{J-1})=\left(\begin{array}{cccc}{a}_0\&CenterDot;0& a_0\&CenterDot;1& ...& a_0\&CenterDot;(L-1)\\ a_1\&CenterDot;0& a_1\&CenterDot;1& ...& a_1\&CenterDot;(L-1)\\ & & & .\\ ...& ...& ...& .\\ & & & .\\ a_{J-1}\&CenterDot;0& a_{J-1}\&CenterDot;1& ...& a_{J-1}\&CenterDot;(L-1)\end{array}\right);$ J and L are two integers, J>=3, L>=3, and 0≤a ₀<a ₁< ... <a _j-1, a ₀..., a _j-1for integer;

102, according to the sequence S={a obtaining in step 101 ₀, a ₁..., a _j-1and the dimension P * P of cyclic permutation matrices, according to the structure principle of 101 Exponential matrixes, obtain its check matrix, and enclosing of this check matrix is longly more than or equal to 8;

103, exponential matrix last column and last row of the female code of the quasi-circulating low-density parity check QC-LDPC code of delete step 102 gained LDPC0 obtain subcode LDPC1, last column and last row of deleting the exponential matrix of subcode LDPC1 obtain subcode LDPC2 again, delete by that analogy the high code check subcode that obtains a plurality of code checks, through the code check of the high rate codewords that obtains after ranks delet method successively, be

n=1,2 ..., represent the row/column number that the exponential matrix of female code is deleted altogether;

104, to the exponential matrix E of female code LDPC0 of gained in step 103 and subcode LDPC1, LDPC2, adopt the hidden matrix M of same dimension to process respectively, hidden matrix M (J, L, J ')=(m _i,j) _{0≤i<J, 0≤j<L}be the binary matrix of a J * L, hidden operation be defined as follows: if m _i,j=1, m _i,je _i,j=E _i,j, otherwise m _i,j=0 o'clock, m _i,je _i,jthe full null matrix of corresponding P * P, the hidden matrix of binary of employing and exponential matrix same dimension is processed the exponential matrix of the QC-LDPC code of phase code rate, be in corresponding exponential matrix, to adopt the null matrix of equal dimension to replace with 0 corresponding position units in hidden matrix, remain unchanged with 1 corresponding position units in hidden matrix, obtain the QC-LDPC code of code-rate-compatible.

2. the building method of code-rate-compatible QC-LDPC code according to claim 1, it is characterized in that: when setting J=6, during L=12, female code LDPC0, the subcode LDPC1 in step 103, the information bit length of subcode LDPC2 are 2514, code check is respectively 1/2,6/11,3/5, and the sequence obtaining by GCDg8 algorithm search is (a ₀, a ₁..., a ₅)={ 0,1,12,13,35,38}, P=419.

3. the building method of code-rate-compatible QC-LDPC code according to claim 1, is characterized in that: described code-rate-compatible QC-LDPC code is comprised of a nested codeword structure, and it can work under single encoder/decoder.

4. according to building method and the coding and decoding mode of the code-rate-compatible QC-LDPC code one of claim 1～3 Suo Shu, it is characterized in that: in radio communication and satellite communication system under time varying channel environment, information to be sent is after information source coding, adaptively according to channel circumstance, adopt code-rate-compatible QC-LDPC encoder to carry out chnnel coding to transmit in channel, when channel circumstance is good, adopt high rate codewords to encode, otherwise when channel circumstance is undesirable, adopt low rate codewords to encode.