CN101567697A - Coder and method for coding rate-compatible low-density parity-check codes - Google Patents

Abstract

The invention discloses a method for obtaining parity check matrix of rate-compatible low-density parity-check codes, comprising the following steps of: selecting a mother code matrix and determining the size of a basic extension matrix; dividing the basic extension matrix into six sub-matrixes (see the formula at right side); according to a minimum ring maximum principle, respectively determining the value of each sub-matrix; subsequently combining each sub-matrix to form the basic extension matrix; finally correcting the obtained basic extension matrix by using a current extension factor z and extending the corrected basic extension matrix by using a matrix P with the size of z*z, thus obtaining a parity check matrix; and using the parity check matrix to carry out the LDPC coding to the data to be coded. When the method and the coder are applied,on one hand, the rate compatibility can be realized; on the other hand, as the minimum and maximum principle is adopted to determine the value of each sub-matrix in each basic extension matrix, the decoding performance can be improved compared to the LDPC codes realizing rate-compatibility by a punching way.

Description

A kind of low density parity check code encoding method of rate-compatible and encoder

Technical field

The present invention relates to the coding techniques of low density parity check code (LDPC), particularly a kind of LDPC coding method and encoder of rate-compatible.

Background technology

Low density parity check code (Low-Density Parity-Check Codes, LDPC) be a class linear block codes, its check matrix can be represented with binary matrix, as shown in Figure 1, each shows j 1 (being that the column weight amount is j), and each row has k 1 (weight be k at once), and other elements all are zero, j 〉=3 wherein, k＞j, j, k are less integer.The check matrix of LDPC can also be represented with a kind of two-dimensional plot, is commonly referred to as Tanner figure now.Tanner figure is directly corresponding with the binary system check matrix.As shown in Figure 2, below among the Tanner figure is variable node (s ₀, s ₁..., s ₉), can think bit in the code word or the row in the check matrix; Be check-node (c above ₀, c ₁..., c ₄), each node is represented the delegation in a check equations or the check matrix.When a certain bit in the code word is included in a certain check equations, there is line among Fig. 2 between the respective nodes.For each node, the number on the limit that is attached thereto is called the degree of this node (degree).The structure of low-density check matrix has conclusive effect for the performance of sign indicating number.Different building methods all is in order to realize following purpose: optimize the non-regular code node number of degrees and distribute; Increase the cycle among the figure, reduce encoder complexity.If the node among the Tanner figure is built into form as shown in Figure 3, then the becate cycle among the figure is 4.

At present, quasi-cyclic LDPC sign indicating number is applied in the practical communication field more and more.The check matrix of this yard is that a size is (m _b* z) * (n _b* z) matrix represents that with H wherein, z represents spreading factor.This check matrix H is cycle specificity matrix and the complete zero battle array formation of z * z by many sizes.The generation type of concrete this check matrix is: definition P is a shift matrix that size is the unit matrix of z * z, and its form is as follows:

$P=\left[\begin{array}{ccccc}0& 1& 0& ...& 0\\ 0& 0& 1& ...& 0\\ ...& ...& ...& ...& ...\\ 0& 0& 0& ...& 1\\ 1& 0& 0& ...& 1\end{array}\right]$

The cyclic shift that above-mentioned P matrix carries out different side-play amounts obtains the cycle specificity matrix that a plurality of sizes are z * z, and check matrix H just is made of these cycle specificity matrixes and complete zero battle array.The form of concrete check matrix is shown below:

$H_b=\left[\begin{array}{ccccc}{P}^{h_{00}^b}& P^{h_{01}^b}& P^{h_{02}^b}& ...& P^{h_{{0n}_b}^b}\\ P^{h_{10}^b}& P^{h_{11}^b}& P^{h_{12}^b}& ...& P^{h_{{1n}_b}^b}\\ ...& ...& ...& ...& ...\\ P^{h_{m_{b}0}^b}& P^{h_{m_{b}1}^b}& P^{h_{m_{b}2}^b}& ...& P^{h_{m_b{n}_b}^b}\end{array}\right]$

Wherein, Expression is carried out h to matrix P _Ij ^bThe matrix that obtains after the inferior cyclic shift, if $h_{\mathrm{ij}}^b=-1,$ Then $P^{h_{\mathrm{ij}}^b}=0.$ Definition

$H_b=\left[\begin{array}{ccccc}{h}_{00}^b& h_{01}^b& h_{02}^b& ...& h_{{0n}_b}^b\\ h_{10}^b& h_{11}^b& h_{12}^b& ...& h_{{1n}_b}^b\\ ...& ...& ...& ...& ...\\ h_{m_{b}0}^b& h_{m_{b}1}^b& h_{m_{b}2}^b& ...& h_{m_b{n}_b}^b\end{array}\right]$

Then check matrix can be expressed as $H=P^{H_b},$ Wherein, the size of check matrix H is M * N, and N=n _b* z, M=m _b* z.With H _bThe basis matrix that is called check matrix just can obtain check matrix according to this basis matrix and replacement matrix P.

Basis matrix H _bConstitute by two parts, $H_b=\left[{\left(H_{b1}\right)}_{m_b\×k_b}\right|{\left(H_{b2}\right)}_{m_b\×m_b}],$ H wherein _B1Corresponding to system bits bit, H _B2Corresponding to the check digit bit.

(Rate-Compatible, LDPC sign indicating number RC) has important role to rate-compatible in the block data communication of reality.A major advantage of rate-compatible code is exactly only to need a pair of volume, decoder can finish coding, the work decoding of each speed.Except advantage with low complex degree, rate-compatible code also be automatic re-send request may (Automatic Repeat Request, ARQ)/(ForwardError Correction, FEC) agreement provides an effective framework in forward error correction.

Present rate-compatible code all is that this mode can not guarantee the performance of the LDPC sign indicating number in a very big range of code rates by the coding and decoding operation of the different rates of hole knockout realization.This is because under the situation of high code check, has destroyed the soft information that most of decoder needs, thereby has caused decoding failure.

Summary of the invention

In view of this, the invention provides a kind of LDPC coding method and encoder of rate-compatible, utilize the LDPC coding that carries out rate-compatible by this method and encoder, the coding efficiency that can greatly improve.

For achieving the above object, the present invention adopts following technical scheme:

A kind of check matrix acquisition methods of low density parity check code of rate-compatible comprises:

Select female sign indicating number matrix, and the size (m of definite basic extension matrix _b+ Δ m) * (n _b+ Δ m), wherein, Δ m=Δ xm _b,

Expression rounds up, R ₀Be female sign indicating number matrix corresponding code rate, m _bAnd n _bBe respectively the line number and the columns of female sign indicating number matrix, R is a target bit rate;

With basic extension matrix H ^ExtensionBe divided into six submatrixs, $H^{\mathrm{extension}}=\left[\begin{array}{ccc}{H}_b^{\mathrm{system}}& H_b^{\mathrm{parity}}& H^{\mathrm{upper}\_\mathrm{right}}\\ H^{\mathrm{lower}\_\mathrm{left}}& H^{\mathrm{lower}\_\mathrm{mid}}& H^{\mathrm{lower}\_\mathrm{right}}\end{array}\right],$ Wherein, H _b ^SystemBe the information submatrix of described female sign indicating number matrix, H _b ^ParityBe the syndrome matrix of described female sign indicating number matrix, H ^Upper_right, H ^Lower_left, H ^Lower_mid, H ^Lower_rightSize is respectively m _b* Δ m, Δ m * (n _b-m _b), Δ m * m _b, Δ m * Δ m;

With submatrix H ^Upper_rightAll elements be set to-1;

For submatrix H ^Lower_mid, all elements on the default diagonal is set to 0, and all the other elements are set to-1, and described default diagonal is for connecting the

Row the 0th column element and nm _b-1 row The diagonal of column element, and connect (n-1) m _bRow

Element and

Row m _bThe diagonal of-1 column element, wherein, n=1 ..., Δ x, and n is a positive integer;

The constructor matrix H ^Lower_rightMask code matrix H _MASK ^Lower_rightFor possessing many cornerwise lower triangular matrixs, comprise mask code matrix H in described many diagonal _MASK ^Lower_rightLeading diagonal and Δ x bar counter-diagonal, wherein, described Δ x bar counter-diagonal is described matrix H ^Lower_midDescribed in default cornerwise extended line, all elements on described many diagonal is set to 1, all the other elements are set to 0;

According to submatrix H _b ^System, H _b ^Parity, H ^Upper_right, H ^Lower_midWith submatrix H ^Lower_rightMask code matrix determine submatrix H ^Lower_leftMask code matrix H _MASK ^Lower_leftDegree distribute structure mask code matrix H _MASK ^Lower_left

With mask code matrix H _MASK ^Lower_rightIn all values be that 0 element is at submatrix H ^Lower_rightMiddle corresponding element is set to " 1 ", with matrix H _MASK ^Lower_rightElement on the middle leading diagonal is at submatrix H ^Lower_rightMiddle corresponding element is set to " 0 ", with mask code matrix H _MASK ^Lower_leftIn all values be that 0 element is at submatrix H ^Lower_leftMiddle corresponding element is set to " 1 "; According to the long maximization of minimum ring criterion, be matrix H _MASK ^Lower_rightElement on the middle counter-diagonal is in matrix H ^Lower_rightMiddle corresponding element and matrix H _MASK ^Lower_leftThe element that middle value is " 1 " is at submatrix H ^Lower_leftMiddle corresponding element is provided with corresponding side-play amount;

Six submatrixs determining are merged obtain described basic extension matrix;

Utilize current spreading factor z that described basic extension matrix is carried out correcting process, and utilize big or small replacement matrix P that revised basic extension matrix is expanded, obtain check matrix for z * z, wherein,

Expression rounds up, and K is the information bit length of present encoding, k _b=n _b-m _b

The check matrix that utilization obtains carries out the LDPC coding to data to be encoded.

Preferably, minimize criterion, structure mask code matrix H according to long maximization of minimum ring and becate number _MASK ^Lower_left, satisfy minimum ring and grow up in equaling 6.

Preferably, according to $h_{\mathrm{ij}}^{\mathrm{lower}\_\mathrm{left}}=\begin{array}{c}({\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="A20091008551600261.png"\; state="\{\{state\}\}">C</figure-callout>}}_1\&times;i^2\&times;{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\&times;i^2\&times;j+{\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">C</figure-callout>}}_3\&times;i\&times;{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+{\mathrm{<figure-callout\; id="4"\; label="C"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">C</figure-callout>}}_4\&times;{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">i</figure-callout>}}^2+{\mathrm{<figure-callout\; id="5"\; label="C"\; filenames="A20091008551600262.png,A20091008551600291.png"\; state="\{\{state\}\}">C</figure-callout>}}_5\&times;{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">j</figure-callout>}}^2\\ +{\mathrm{<figure-callout\; id="6"\; label="C"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">C</figure-callout>}}_6\&times;i\&times;j+{\mathrm{<figure-callout\; id="7"\; label="C"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">C</figure-callout>}}_7\&times;i+C_8\&times;j+C_9)\mathrm{mod}\left(z_{\max }\right)\end{array}$

With

$h_{i^{\&prime;}{j}^{\&prime;}}^{\mathrm{lower}\_\mathrm{right}}=\begin{array}{c}({\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="A20091008551600261.png"\; state="\{\{state\}\}">D</figure-callout>}}_1\&times;i^{\&prime;2}\&times;j^{\&prime;2}+{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">D</figure-callout>}}_2\&times;i^{\&prime;2}\&times;j^{\&prime;}+{\mathrm{<figure-callout\; id="3"\; label="D"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">D</figure-callout>}}_3\&times;i^{\&prime;}\&times;j^{\&prime;2}+{\mathrm{<figure-callout\; id="4"\; label="D"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">D</figure-callout>}}_4\&times;i^{\&prime;2}+{\mathrm{<figure-callout\; id="5"\; label="D"\; filenames="A20091008551600262.png,A20091008551600291.png"\; state="\{\{state\}\}">D</figure-callout>}}_5\&times;j^{\&prime;2}\\ +{\mathrm{<figure-callout\; id="6"\; label="D"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">D</figure-callout>}}_6\&times;i^{\&prime;}\&times;j^{\&prime;}+{\mathrm{<figure-callout\; id="7"\; label="D"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">D</figure-callout>}}_7\&times;i^{\&prime;}+D_8\&times;j^{\&prime;}+D_9)\mathrm{mod}\left(z_{\max }\right)\end{array}$ Configuration integer quotient C ₁..., C ₉, D ₁..., D ₉, the minimum ring of described basic extension matrix is grown up in equaling 6, wherein, C ₁..., C ₉Be nonnegative integer, z _MaxBe the maximum of spreading factor, h _{I ' j '} ^Lower_rightBe submatrix H ^Lower_rightIn the element value of the i ' row j ' row, and i ' and j ' be the index of element on the described counter-diagonal, h _Ij ^Lower_leftBe submatrix H ^Lower_leftIn the element value of the capable j of i row, and i and j are submatrix H ^Lower_leftIn with mask code matrix H _MASK ^Lower_leftMiddle value is the element index of the element correspondence of " 1 ".

Preferably, described correcting process is:

Wherein, h _Ij ^bBe basic extension matrix H ^ExtensionIn the element value of the capable j of i row, (h _Ij ^b) _ModifiedBe h _Ij ^bRevised element value.

Preferably, in advance according to the basic extension matrix under a plurality of optional target bit rate select target matrixes and definite each target bit rate;

When carrying out the LDPC coding, according to the corresponding basic extension matrix of current target code rate selection, and carry out described correcting process and extended operation, obtain check matrix.

A kind of encoder of low density parity check code of rate-compatible comprises:

The basic extension matrix determining unit is used to select female sign indicating number matrix, and the size (m of definite basic extension matrix _b+ Δ m) * (n _b+ Δ m), wherein, Δ m=Δ xm _b,

Expression rounds up, R ₀Be female sign indicating number matrix corresponding code rate, m _bAnd n _bBe respectively the line number and the columns of female sign indicating number matrix, R is a target bit rate; With basic extension matrix H ^ExtensionBe divided into six submatrixs, $H^{\mathrm{extension}}=\left[\begin{array}{ccc}{H}_b^{\mathrm{system}}& H_b^{\mathrm{parity}}& H^{\mathrm{upper}\_\mathrm{right}}\\ H^{\mathrm{lower}\_\mathrm{left}}& H^{\mathrm{lower}\_\mathrm{mid}}& H^{\mathrm{lower}\_\mathrm{right}}\end{array}\right],$ Wherein, H _b ^SystemBe the information submatrix of described female sign indicating number matrix, H _b ^ParityBe the syndrome matrix of described female sign indicating number matrix, H ^Upper_right, H ^Lower_left, H ^Lower_mid, H ^Lower_rightSize is respectively m _b* Δ m, Δ m * (n _b-m _b), Δ m * m _b, Δ m * Δ m; With submatrix H ^Upper_rightAll elements be set to-1; For submatrix H ^Lower_mid, all elements on the default diagonal is set to 0, and all the other elements are set to-1, and described default diagonal is for connecting the Row the 0th column element and nm _b-1 row

The diagonal of column element, and connect (n-1) m _bRow

Element and

Row m _bThe diagonal of-1 column element, wherein, n=1 ..., Δ x, and n is a positive integer; The constructor matrix H ^Lower_rightMask code matrix H _MASK ^Lower_rightFor possessing many cornerwise lower triangular matrixs, comprise mask code matrix H in described many diagonal _MASK ^Lower_rightLeading diagonal and Δ x bar counter-diagonal, wherein, described Δ x bar counter-diagonal is described matrix H ^Lower_midDescribed in default cornerwise extended line, all elements on described many diagonal is set to 1, all the other elements are set to 0; According to submatrix H _b ^System, H _b ^Parity, H ^Upper_right, H ^Lower_midWith submatrix H ^Lower_rightMask code matrix determine submatrix H ^Lower_leftMask code matrix H _MASK ^Lower_leftDegree distribute structure mask code matrix H _MASK ^Lower_leftWith mask code matrix H _MASK ^Lower_rightIn all values be that 0 element is at submatrix H ^Lower_rightMiddle corresponding element is set to " 1 ", with matrix H _MASK ^Lower_rightElement on the middle leading diagonal is at submatrix H ^Lower_rightMiddle corresponding element is set to " 0 ", with mask code matrix H _MASK ^Lower_leftIn all values be that 0 element is at submatrix H ^Lower_leftMiddle corresponding element is set to " 1 "; According to the long maximization of minimum ring criterion, be matrix H _MASK ^Lower_rightElement on the middle counter-diagonal is in matrix H ^Lower_rightMiddle corresponding element and matrix H _MASK ^Lower_leftThe element that middle value is " 1 " is at submatrix H ^Lower_leftMiddle corresponding element is provided with corresponding side-play amount; Six submatrixs determining are merged obtain described basic extension matrix;

The correcting process unit is used to utilize current spreading factor z that the basic extension matrix that described basic extension matrix determining unit obtains is carried out correcting process;

Expanding element is used for utilizing big or small replacement matrix P for z * z that the revised basic extension matrix that described correcting process unit obtains is expanded, and obtains check matrix, wherein,

Expression rounds up, and K is the information bit length of present encoding, k _b=n _b-m _b

Coding unit, the check matrix that is used to utilize described expanding element to obtain carries out the LDPC coding to data to be encoded.

Preferably, described basic extension matrix determining unit comprises determines subelement and storing sub-units,

Described definite subelement, be further used for according to the basic extension matrix under a plurality of optional target bit rate select target matrixes and definite each target bit rate, and each optional target bit rate is kept in the described storing sub-units with basic extension matrix is corresponding accordingly;

Described correcting process unit is further used for shifting to an earlier date the basic extension matrix corresponding with the current target code check in described storing sub-units.

As seen from the above technical solution, among the present invention, select female sign indicating number matrix, and the size of definite basic extension matrix; Basic extension matrix is divided into six submatrixs, $H^{\mathrm{extension}}=\left[\begin{array}{ccc}{H}_b^{\mathrm{system}}& H_b^{\mathrm{parity}}& H^{\mathrm{upper}\_\mathrm{right}}\\ H^{\mathrm{lower}\_\mathrm{left}}& H^{\mathrm{lower}\_\mathrm{mid}}& H^{\mathrm{lower}\_\mathrm{right}}\end{array}\right],$ According to the minimum ring maximization principle, determine the value of each submatrix respectively, again each submatrix is merged the formation base extended matrix; At last, utilize current spreading factor z that the basic extension matrix that obtains is revised, utilize big or small matrix P that revised basic extension matrix is expanded again, obtain check matrix for z * z; Utilize this check matrix that data to be encoded are carried out the LDPC coding.Through the LDPC sign indicating number that aforesaid way obtains, on the one hand, can realize rate-compatible, on the other hand, minimize the value that maximization principle is determined each submatrix in each basic extension matrix owing to adopt, therefore, LDPC sign indicating number with respect to hole knockout realization rate-compatible can improve decoding performance.

Description of drawings

Fig. 1 utilizes binary matrix to represent the schematic diagram of LDPC code check matrix.

Fig. 2 is the schematic diagram that utilizes Tanner figure expression LDPC code check matrix.

Fig. 3 is the flow chart of the check matrix acquisition methods of LDPC among the present invention.

Fig. 4 is the structural representation one of basic extension matrix among the present invention.

Fig. 5 is the structural representation two of basic check matrix among the present invention.

Fig. 6 is the frame error rate (BLER) of the LDPC sign indicating number of constructing in the present invention and the prior art and the performance comparison curved line relation between the signal to noise ratio (Eb/No).

Fig. 7 is LDPC sign indicating number and the frame error rate (FER) of existing Turbo code and the performance comparison curved line relation between the signal to noise ratio (Eb/No) among the present invention.

Embodiment

For making purpose of the present invention, technological means and advantage clearer, the present invention is described in further details below in conjunction with accompanying drawing.

Basic thought of the present invention is: according to target bit rate, according to the long maximization of minimum ring criterion female sign indicating number matrix is expanded to the basic extension matrix that satisfies the requirement of different target code check, to realize the LDPC coding of rate-compatible, reduce thereby avoid handling the decoding performance that causes owing to punching.

The LDPC encoder of rate-compatible is provided among the present invention, has comprised: basic extension matrix determining unit, correcting process unit, expanding element and coding unit.

In above-mentioned LDPC encoder, can implement LDPC coding method of the present invention.Fig. 3 is the flow chart of the coding method of LDPC among the present invention.As shown in Figure 3, this method comprises:

Step 301 according to the requirement of code check R and code length N, is selected female sign indicating number matrix, and the size of definite basic extension matrix.

This step can realize by following step:

(11), determine information bit length K and check bit length M according to the requirement of code check R and code length N; Wherein, information bit length K=RN, check bit length M=N-K, in the formula, information bit length K, code length N and check bit M are positive integer;

Suppose that in the present invention's one specific embodiment, target bit rate is 1/3, code length N has three kinds of requirements, is respectively 3180,6060,15342, Dui Ying information bit length K=1060,2020,5114 then, corresponding check bit length M=2120,4040,10228; Below be that example is specifically described each step just with this kind situation.

(12) selecting size is m _b* n _bFemale sign indicating number matrix H _b ^Uniform, concrete female sign indicating number matrix selection mode is identical with existing implementation.Wherein, female sign indicating number matrix is m by size _b* (n _b-m _b) the systematic bit subpacket matrix H _b ^SystemWith size be m _b* m _bCheck digit submatrix H _b ^ParityTwo parts are formed, promptly $H_b^{\mathrm{uniform}}=\left[H_b^{\mathrm{system}}\right|H_b^{\mathrm{parity}}],$ H wherein _b ^ParityIt is the accurate lower triangular matrix of double diagonal line;

In specific embodiment, female sign indicating number matrix line number of selection is m _b=16, columns n _b=32, female sign indicating number code check is 1/2, and female sign indicating number matrix is 16 * 16 systematic bit subpacket matrix H by size _b ^SystemWith size be 16 * 16 check digit submatrix H _b ^SystemForm, wherein H _b ^ParityIt is the accurate lower triangular matrix of double diagonal line;

Wherein, systematic bit subpacket matrix $H_b^{\mathrm{system}}=$

$\begin{array}{cccccccccccccccc}-1& -1& -1& -1& -1& 52& -1& 67& -1& 11& -1& -1& -1& 132& 51& 285\\ -1& -1& -1& 326& -1& -1& -1& -1& 163& -1& -1& -1& 51& 362& 4& 89\\ -1& 243& 227& -1& -1& -1& -1& -1& -1& -1& 278& -1& -1& 205& 337& 373\\ -1& -1& -1& -1& -1& 381& -1& -1& -1& -1& -1& 130& 110& 36& 181& 176\\ -1& -1& -1& 232& 315& -1& 199& -1& -1& -1& -1& -1& -1& 232& 295& 135\\ 247& 310& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 233& 67& 254& 138\\ -1& -1& -1& -1& -1& -1& -1& -1& 178& 262& -1& 176& -1& 113& 357& 40\\ -1& -1& 252& -1& -1& -1& -1& 235& -1& -1& -1& -1& 362& 366& 297& 332\\ -1& -1& -1& -1& -1& -1& 117& -1& -1& -1& 98& -1& -1& 203& 79& 48\\ 102& -1& -1& -1& -1& -1& -1& -1& -1& 178& -1& -1& 269& 181& 160& 73\\ -1& -1& -1& -1& 19& -1& -1& 8& -1& -1& -1& 77& -1& 255& 370& 332\\ -1& -1& -1& -1& -1& 232& -1& -1& -1& -1& 38& -1& 106& 93& 329& 152\\ -1& 339& -1& -1& -1& -1& 211& -1& -1& 16& -1& -1& -1& 22& 55& 212\\ -1& -1& 53& 284& -1& -1& -1& -1& -1& -1& -1& -1& 69& 224& 65& 280\\ 110& -1& -1& -1& 357& -1& -1& -1& 239& -1& -1& -1& -1& 164& 368& 36\\ -1& 96& -1& -1& -1& -1& -1& -1& -1& -1& -1& 193& 6& 153& 147& 5\end{array}$

The check digit submatrix $H_b^{\mathrm{system}}=$

$\begin{array}{cccccccccccccccc}0& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& 0& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& 0& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& 0& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& 0& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& 0& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& 0& 0& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& 0& 0& -1& -1& -1& -1& -1& -1& -1\\ 336& -1& -1& -1& -1& -1& -1& -1& 0& 0& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& 0& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& 0& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& 0& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& 0& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& 0& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& 0\\ 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0\end{array}$

(13), need to determine the basic extension matrix H of structure according to code check R ^ExtensionLine number and columns, this basic extension matrix H ^ExtensionLine number is m _b+ Δ m, columns are n _b+ Δ m, Δ m=m _bΔ x;

Wherein, by R=((n _b+ m _bΔ x)-(m _b+ m _bΔ x))/(n _b+ m _bAnd R Δ x), ₀=(n _b-m _b)/n _b, can draw

Expression rounds up, R ₀Be female sign indicating number matrix corresponding code rate.Can be R like this, just according to code check ₀A female sign indicating number matrix size expand the size that code check is the basic extension matrix of R.Certainly, this step has only been determined the size of basic extension matrix, also needs the further concrete value of definite basic extension matrix at subsequent step, just can obtain the check matrix that code check is R by this basic extension matrix is replaced then;

In specific embodiment, because the target bit rate of LDPC is R=1/3, then the code check of basic extension matrix also is R=1/3, again according to female sign indicating number code check R ₀=1/2, can get Δ x=1, Δ m=m _b=16, thereby draw basic extension matrix H ^ExtensionLine number be 32, columns is 48.

Step 302 is with basic extension matrix H ^ExtensionBe divided into six submatrixs $H^{\mathrm{extension}}=\left[\begin{array}{ccc}{H}_b^{\mathrm{system}}& H_b^{\mathrm{parity}}& H^{\mathrm{upper}\_\mathrm{right}}\\ H^{\mathrm{lower}\_\mathrm{left}}& H^{\mathrm{lower}\_\mathrm{mid}}& H^{\mathrm{lower}\_\mathrm{right}}\end{array}\right].$

Obtain basic extension matrix by female sign indicating number matrix expansion of selecting, therefore, with the matrix of female sign indicating number matrix as the upper left corner in the basic extension matrix, and in view of the above basic extension matrix is divided into a plurality of submatrixs, determine the value of other submatrixs except that female sign indicating number matrix more one by one, thereby finally determine basic extension matrix.

Particularly, with basic extension matrix H ^ExtensionBe divided into six submatrixs, promptly $H^{\mathrm{extension}}=\left[\begin{array}{ccc}{H}_b^{\mathrm{system}}& H_b^{\mathrm{parity}}& H^{\mathrm{upper}\_\mathrm{right}}\\ H^{\mathrm{lower}\_\mathrm{left}}& H^{\mathrm{lower}\_\mathrm{mid}}& H^{\mathrm{lower}\_\mathrm{right}}\end{array}\right],$ Wherein, H _b ^SystemBe the information submatrix of female sign indicating number matrix, H _b ^ParityBe the syndrome matrix of female sign indicating number matrix, H ^Upper_right, H ^Lower_left, H ^Lower_mid, H ^Lower_rightBe the submatrix that expands, size is respectively m _b* Δ m, Δ m * (n _b-m _b), Δ m * m _b, Δ m * Δ m.

In specific embodiment, basic extension matrix H ^ExtensionAs shown in Figure 4, matrix comprises 5 parts, and wherein, the upper left corner is that size is female sign indicating number matrix H of 16 * 32 _b ^Uniform, $H_b^{\mathrm{uniform}}=\left[H_b^{\mathrm{system}}\right|H_b^{\mathrm{parity}}],$ Expansion H ^Upper_right, H ^Lower_left, H ^Lower_mid, H ^Lower_rightMatrix size is 16 * 16 respectively.

Step 303 is with submatrix H ^Upper_rightIn all elements be set to-1.

Step 304 is for submatrix H ^Lower_mid, all elements on the default diagonal is set to 0, and all the other elements are set to-1.

This step is determined submatrix H ^Lower_midThe value of middle all elements.As shown in Figure 5, submatrix H ^Lower_midThe form that presents double diagonal line.All elements on each diagonal is set to 0, and all the other elements are set to-1.Concrete diagonal is: connect the Row the 0th column element and nm _b-1 row

The diagonal of column element and, connect (n-1) m _bRow

Element and

Row m _bThe diagonal of-1 column element.Wherein, the value of n is all positive integers smaller or equal to Δ x, and promptly n gets since 1, gets Δ x always, when n gets arbitrary value, obtains two diagonal, so submatrix H ^Lower_midHave 2 Δ x bar diagonal.Like this, promptly can determine submatrix H ^Lower_midThe all elements value, the final submatrix H that determines ^Lower_midRow heavily is 1, and column weight is Δ x.

In specific embodiment, size is 16 * 16 matrix H in the middle of structure foundation extended matrix the latter half ^Lower_midThe time, at first all elements in the matrix is changed to " 1 ", again the element on the diagonal is changed to " 0 ", herein because Δ x=1, so n only gets 1, thus article one diagonal connects is submatrix H ^Lower_midThe element of the element of middle eighth row the 0th row and the 15th row the 7th row, that the second diagonal connects is submatrix H ^Lower_midIn the element that is listed as of element and the 7th row the 15th of the 0th row the 8th row; The row of this submatrix heavily is 1, and column weight also is 1;

$H^{\mathrm{lower}\_\mathrm{mid}}=$

$\begin{array}{cccccccccccccccc}-1& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0& -1\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 0\\ 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1\end{array}$

Step 305 is according to submatrix H ^Lower_midConstruct a submatrix H with the basic extension matrix lower right corner ^Lower_rightThe mask code matrix H corresponding and structure is identical _MASK ^Lower_right

The mask code matrix H of this step structure _MASK ^Lower_rightIn element value be " 0 " or " 1 ", wherein, " 0 " expression does not have a matrix operation, " 1 " expression has matrix operation.

Particularly, submatrix H ^Lower_rightMask code matrix H _MASK ^Lower_rightFor possessing many cornerwise lower triangular matrixs, wherein, comprise mask code matrix H in many diagonal _MASK ^Lower_rightLeading diagonal and Δ x bar counter-diagonal, wherein, Δ x bar counter-diagonal is submatrix H ^Lower_midIn all cornerwise extended lines, as shown in Figure 5.And, at mask code matrix H _MASK ^Lower_rightIn, all elements on each diagonal is set to 1, and all the other elements are set to 0.

In specific embodiment, mask code matrix is a lower triangular matrix with double diagonal line, and counter-diagonal is by submatrix H ^Lower_midArticle one diagonal prolong and to obtain, concrete this mask code matrix

$H_{\mathrm{MASK}}^{\mathrm{lower}\_\mathrm{right}}=$

$\begin{array}{cccccccccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0\\ 1& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 1\end{array}$

Step 306 is according to submatrix H _b ^System, H _b ^Parity, H ^Upper_right, H ^Lower_midWith submatrix H ^Lower_rightMask code matrix determine submatrix H ^Lower_leftMask code matrix H _MASK ^Lower_leftDegree distribute structure mask code matrix H _MASK ^Lower_left

In this step, can adopt the density evolution rationale structure of definite several submatrixs, determine submatrix H ^Lower_leftMask code matrix H _MASK ^Lower_leftDegree distribute, adopt progressive edged method construct mask code matrix H _MASK ^Lower_leftThis mask code matrix H _MASK ^Lower_leftWith mask code matrix H _MASK ^Lower_rightSimilar, element value wherein is " 0 " or " 1 ", and " 0 " expression does not have matrix operation, and " 1 " expression has matrix operation.

Preferably, at structure mask code matrix H _MASK ^Lower_leftProcess in, carry out according to long maximization of minimum ring and the minimized criterion of becate number.

In specific embodiment, according to the structure of 4 parts of having constructed, adopt the density evolution theory, obtain lower left corner mask code matrix H _MASK ^Lower_leftColumn weight distribution be 0.6875x ⁰+ 0.125x ²+ 0.1875x ¹⁶, just the column weight amount is respectively 0,2,16 columns and accounts for total columns ratio and be respectively 0.6875,0.125,0.1875; Adopt progressive bordering method edged to make basic extension matrix H again ^ExtensionThe long maximization of minimum ring, promptly minimum ring is long by 〉=6, and the becate number minimizes, the mask code matrix that obtains is $H_{\mathrm{MASK}}^{\mathrm{lower}\_\mathrm{left}}=$

$\begin{array}{cccccccccccccccc}0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 1\end{array}$

Step 307 according to the long maximization of minimum ring criterion, is matrix H _MASK ^Lower_rightElement on the middle counter-diagonal is in matrix H ^Lower_rightMiddle corresponding element and matrix H _MASK ^Lower_leftThe element that middle value is " 1 " is at submatrix H ^Lower_leftMiddle corresponding element is provided with corresponding side-play amount, and with matrix H ^Lower_rightAnd H ^Lower_leftIn all the other elements be set to " 1 ".

In this step, according to mask code matrix H _MASK ^Lower_rightAnd H _MASK ^Lower_left, determine corresponding submatrix H ^Lower_rightAnd H _MASK ^Lower_leftThe element value.Particularly, according to $h_{\mathrm{ij}}^{\mathrm{lower}\_\mathrm{left}}=\begin{array}{c}(C_1\&times;i^2\&times;j^2+C_2\&times;i^2\&times;j+C_3\&times;i\&times;j^2+C_4\&times;i^2+C_5\&times;j^2\\ +C_6\&times;i\&times;j+C_7\&times;i+C_8\&times;j+C_9)\mathrm{mod}\left(z_{\max }\right)\end{array}$ With $h_{i^{\&prime;}{j}^{\&prime;}}^{\mathrm{lower}\_\mathrm{right}}=\begin{array}{c}(D_1\&times;i^{\&prime;2}\&times;j^{\&prime;2}+D_2\&times;i^{\&prime;2}\&times;j^{\&prime;}+D_3\&times;i^{\&prime;}\&times;j^{\&prime;2}+D_4\&times;i^{\&prime;2}+D_5\&times;j^{\&prime;2}\\ +D_6\&times;i^{\&prime;}\&times;j^{\&prime;}+D_7\&times;i^{\&prime;}+D_8\&times;j^{\&prime;}+D_9)\mathrm{mod}\left(z_{\max }\right)\end{array}$ Configuration integer quotient C ₁..., C ₉, D ₁..., D ₉, the minimum ring of basic extension matrix is grown up in equaling 6, wherein, C ₁..., C ₉Be nonnegative integer, z _MaxBe the maximum of spreading factor, h _{I ' j '} ^Lower_rightBe submatrix H ^Lower_rightIn the element value of the i ' row j ' row, and i ' and j ' are submatrix H ^Lower_rightThe index of element on the middle counter-diagonal, h _Ij ^Lower_leftBe submatrix H ^Lower_leftIn the element value of the capable j of i row, and i and j are submatrix H ^Lower_leftIn with mask code matrix H _MASK ^Lower_leftMiddle value is the element index of the element correspondence of " 1 ".With matrix H ^Lower_rightAnd H ^Lower_leftIn all the other elements be set to " 1 ".

In specific embodiment, at first dispose lower left corner submatrix H ^Lower_leftSide-play amount: at H ^Lower_leftIn, will be corresponding to mask code matrix H _MASK ^Lower_leftMiddle element is all filled " 1 " for the position of " 0 ", and remainder adopts following computing formula to obtain:

$h_{\mathrm{ij}}^{\mathrm{lower}\_\mathrm{left}}=({\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">i</figure-callout>}}^2\&times;{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">i</figure-callout>}}^2+11\&times;i\&times;j+20\&times;i+13\&times;j+20)\mathrm{mod}\left(z_{\max }\right),$ In the formula, h _Ij ^Lower_leftBe expansion lower left corner submatrix H ^Lower_leftIn the element of capable, the j of i row, z _MaxBe the obtainable maximum z of spreading factor z _Max=384, mod is the complementation oeprator; So obtain lower left corner submatrix $H^{\mathrm{lower}\_\mathrm{left}}=$

$\begin{array}{cccccccccccccccc}-1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 176& 189& 226& 215\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 42& -1& 138& 218& 250\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 292& 43& 186& 337\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 288& 193& 116\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 375& -1& 105& 210& 347\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 262& 237& 262\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 375& 274& 245\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 60& 321& 335\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 85& 1& 58\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 66& 61& 218\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 3& 138& 89\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 280& 322& 35\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 129& 322& 35\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 318& 45& 110\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 79& 162& 270\\ -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& 180& 306& 80\end{array}$

Next dispose lower right corner submatrix H ^Lower_rightSide-play amount: at H ^Lower_rightIn, earlier the element on the leading diagonal is " 0 " for filling out, again the element on the counter-diagonal is adopted following formula to calculate:

$h_{i,j}^{\mathrm{lower}\_\mathrm{right}}=(2\&times;i^2+5\&times;{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+3\&times;i\&times;j-109\&times;i-201\&times;j+2400)\mathrm{mod}\left(z_{\max }\right)$

In the formula, h _{I, j} ^Lower_rightBe expansion lower right corner matrix sub H ^Lower_leftIn the element of capable, the j of i row, and i=8,9 ..., 15, j=i-8; This element satisfies on counter-diagonal; z _MaxBe the obtainable maximum of spreading factor z, z _Max=384, mod is the complementation oeprator, at last all the other position elements is changed to " 1 "; Should $H^{\mathrm{lower}\_\mathrm{right}}=$

$\begin{array}{cccccccccccccccc}0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1& -1\\ -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1& -1\\ 120& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1& -1\\ -1& 260& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1& -1\\ -1& -1& 36& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1& -1\\ -1& -1& -1& 216& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1& -1\\ -1& -1& -1& -1& 32& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1& -1\\ -1& -1& -1& -1& -1& 252& -1& -1& -1& -1& -1& -1& -1& 0& -1& -1\\ -1& -1& -1& -1& -1& -1& 108& -1& -1& -1& -1& -1& -1& -1& 0& -1\\ -1& -1& -1& -1& -1& -1& -1& 368& -1& -1& -1& -1& -1& -1& -1& 0\end{array}$

Step 308 is merged into basic extension matrix with six submatrixs determining.

So far, promptly can obtain basic extension matrix.The operation of above-mentioned steps 301～308 can be finished corresponding function by the basic extension matrix unit in the aforementioned encoder.

Step 309, according to current spreading factor z to basic extension matrix H ^ExtensionCarry out correcting process, obtain revised basic extension matrix H ^Modified

Female sign indicating number matrix is the spreading factor z according to maximum _MaxObtain, and in the above-mentioned process of determining each submatrix, be based on also that the female sign indicating number matrix and the largest extension factor carry out, so to merge the basic extension matrix that obtains in the step 308 also be corresponding z with the largest extension factor _Max.And in actual applications, the spreading factor z that encodes may be less than largest extension factor z _Max, therefore, need revise basic extension matrix, so that this revised basic extension matrix H according to true extension factor z ^ModifiedIn the value of all elements all less than the spreading factor z of LDPC sign indicating number.

Preferably, concrete correcting mode is:

Wherein, h _Ij ^bBe basic extension matrix H ^ExtensionIn the element value of the capable j of i row, (h _Ij ^b) _ModifiedBe h _Ij ^bRevised element value.

In specific embodiment, information bit length is respectively 1060,2020,5114, corresponding spreading factor

Be respectively 67,127,320, thereby obtain 3 revised matrix H ₁₀₆₀ ^Modified, H ₂₀₂₀ ^Modified, H ₅₁₁₄ ^ModifiedShould $H_{1060}^{\mathrm{mod}\mathrm{ified}}=$

Should $H_{2020}^{\mathrm{mod}\mathrm{ified}}=$

Should $H_{5114}^{\mathrm{mod}\mathrm{ified}}=$

The operation of this step can be finished corresponding function by the correcting process unit in the aforementioned LDPC encoder.

Step 310 is utilized the replacement matrix P of size for z * z, revised basic extension matrix is expanded required (m when obtaining actual coding _b+ Δ m) * capable (n of z _b+ Δ m) * check matrix H of z row.

The mode of specifically expanding just repeats no more here with existing identical.

In specific embodiment, information bit length is respectively 1060,2020,5114, corresponding spreading factor

Be respectively 67,127,320, be respectively 2144 * 3216,4064 * 6096,10240 * 15360 check matrix H thereby obtain 3 sizes ₁₀₆₀, H ₂₀₂₀, H ₅₁₁₄

The operation of this step can be finished corresponding function by the expanding element in the aforementioned LDPC encoder.

Step 311, the check matrix H of utilizing step 310 to determine is carried out the LDPC coding to data to be encoded.

Next, just can utilize the check matrix that obtains to carry out the LDPC coding.Simply introduce cataloged procedure below, still the parameter with above-mentioned specific embodiment is an example:

Code check R=1/3 is divided into N-2M information bit s, a M check bit c to a code word x ₁With M check bit c ₂, x=[s, c ₁, c ₂], correspondingly, the check matrix H of 2M * N is divided into 6 sparse matrixes, $H=\left[\begin{array}{ccc}{H}_1& H_2& H_3\\ H_4& H_5& {\mathrm{<figure-callout\; id="6"\; label="H"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">H</figure-callout>}}_6\end{array}\right],$ Be H ₁, H ₂, H ₃, H ₄, H ₅And H ₆, size is respectively M * (N-2M), M * M, M * M, M * (N-2M), M * M, M * M, according to Hx ^T=0 ^T, can get:

$\left[\begin{array}{ccc}{H}_1& H_2& H_3\\ H_4& H_5& {\mathrm{<figure-callout\; id="6"\; label="H"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">H</figure-callout>}}_6\end{array}\right]\&times;{[s,{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="A20091008551600261.png"\; state="\{\{state\}\}">c</figure-callout>}}_1,c_2]}^T=0^T,$

So can obtain ${\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="A20091008551600261.png"\; state="\{\{state\}\}">H</figure-callout>}}_1\&times;s+{\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">H</figure-callout>}}_2\&times;c_1^T+{\mathrm{<figure-callout\; id="3"\; label="H"\; filenames="A20091008551600291.png"\; state="\{\{state\}\}">H</figure-callout>}}_3\&times;c_2^T=0^T,$ Because H ₃Be full null matrix, release $c_1^T=H_2^{-1}{H}_{1}s;$ Again by ${\mathrm{<figure-callout\; id="4"\; label="H"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">H</figure-callout>}}_4\&times;s+{\mathrm{<figure-callout\; id="5"\; label="H"\; filenames="A20091008551600262.png,A20091008551600291.png"\; state="\{\{state\}\}">H</figure-callout>}}_5\&times;c_1^T+{\mathrm{<figure-callout\; id="6"\; label="H"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">H</figure-callout>}}_6\&times;c_2^T=0^T,$ Further release $c_2^T=H_6^{-1}({\mathrm{<figure-callout\; id="4"\; label="H"\; filenames="A20091008551600262.png"\; state="\{\{state\}\}">H</figure-callout>}}_4\&times;s+{\mathrm{<figure-callout\; id="5"\; label="H"\; filenames="A20091008551600262.png,A20091008551600291.png"\; state="\{\{state\}\}">H</figure-callout>}}_5\&times;c_1^T);$ Because matrix H ₂Adopt the accurate lower triangular structure of double diagonal line, H ₆Adopt strict lower triangular structure, so H ₂ ^-1And H ₆ ^-1Have very simple form, can directly obtain check bit part c according to the top computing formula ₁And c ₂, and can guarantee that encoder has linear complexity.

The concrete operations step of utilizing check matrix H to encode adopts existing mode, and is specific as follows:

Step 1: with k _x=k _bBefore * z-K 0 bit is added in the block of information of K bit, constitute k _b* z bit information bit s; For example, when K=1060, k _x=k _b* z-K=16 * 67-1060=12;

Step 2: to the submatrix [H in the check matrix H ₁| H ₂] carry out the elementary row conversion, with check matrix [H ₁| H ₂] in all provisional capitals be added in first row, calculate first of check code;

Because submatrix H ₂Be lower triangular matrix, therefore at first count, as above calculate since first row.

Step 3: according to submatrix [H ₁| H ₂] calculating other check digit with recurrence method, the check code that calculates with step 2 constitutes c ₁

Step 4: according to submatrix [H ₄| H ₅| H ₆] calculate check digit c with the method for recursion ₂

Step 5: 0 bit that deletion is added in step 1 in s.If the remaining bit number of code word x is not equal to N, then the y=2m of code word x afterbody _bThe individual check bit of * z-N+K (y is a less number) needs deletion, for example, when K=1060, y=2m _b* z-N+K=2 * 16 * 67-3180+1060=24.

Like this, promptly finished and utilized the check matrix that obtains according to the inventive method to carry out the process of LDPC coding.The above-mentioned operation that utilizes check matrix to carry out the LDPC coding can be finished corresponding function by the coding unit in the aforementioned LDPC encoder.

So far, the LDPC coding method flow process of rate-compatible finishes among the present invention.By the way, can obtain the check matrix under the various code checks, thereby realize the LDPC coding of rate-compatible according to suitable female sign indicating number matrix.

In the specific implementation process of the invention described above, can be at various optional target bit rates, execution in step 301～308 is then with the basic extension matrix and the corresponding corresponding preservation of target bit rate that obtain.When carrying out actual LDPC coding, require the select target code check according to current code check, extract the basic extension matrix corresponding with this target bit rate again, execution in step 309～310 is carried out correcting process and expansion, obtain corresponding check matrix, utilize step 311 to carry out the LDPC coding again.Like this, the operation of abovementioned steps 301～308 can be carried out and preserve in advance, and the real-time operation amount in the time of can reducing the LDPC coding improves coding rate.

Correspondingly, when adopting the above-mentioned mode that pre-determines corresponding basic extension matrix at various optional target bit rates, specific implementation in encoder can be determined subelement and storing sub-units for: the basic extension matrix determining unit in the encoder comprises, wherein, determine that subelement is used at various optional target bit rates, execution in step 301～308 is kept at the basic extension matrix that obtains in the storing sub-units with target bit rate is corresponding accordingly then.The correcting process unit preferably, extracts the basic extension matrix corresponding with the current goal code check in the memory cell from the basic extension matrix determining unit when obtaining the basic extension matrix that the basic extension matrix determining unit obtains.

By the specific implementation process of the invention described above as seen, in the LDPC sign indicating number process of structure rate-compatible, adopt among the present invention to expand to obtain basic extension matrix, expand the mode that obtains check matrix by basic extension matrix again by a female sign indicating number matrix.Aforesaid way is compared with existing hole knockout, has kept the useful information of decoding as far as possible, and in the process of determining basic extension matrix, carries out according to the long maximized criterion of minimum ring, therefore can improve decoding performance.

In order to identify the transmission performance of the LDPC sign indicating number that forms according to mode of the present invention, adopt the transmission performance of the LDPC sign indicating number that the awgn channel model constructs the present invention to carry out l-G simulation test, and with prior art in the LDPC sign indicating number realized by hole knockout carried out performance relatively.Table 1 is for being used to test the situation that is provided with each parameter of embodiment of analytical performance.

Parameter name	Numerical value
		Information bit long (K)	1024
Code check	2/3
		Modulating mode	BPSK
Channel model	AWGN
		Decoded mode	LDPC:Log-BP maximum iteration time=50

Fig. 6 is the frame error rate (BLER) of the LDPC sign indicating number of constructing in the present invention and the prior art and the performance comparison curved line relation between the signal to noise ratio (Eb/No).In Fig. 6, dotted line is that solid line is according to the transmission performance curve of the LDPC sign indicating number of method realization of the present invention according to the transmission performance curve of the LDPC sign indicating number of hole knockout realization in the prior art.As seen from Figure 6, compare, adopt the frame error rate performance of the LDPC sign indicating number of the present invention's structure to be better than prior art with existing punching technology.

Simultaneously, also the LDPC sign indicating number of constructing according to mode of the present invention and the transmission performance of existing Turbo code emulation and comparison have been carried out.Table 2 is for being used to test the situation that is provided with each parameter of embodiment of analytical performance.

Parameter name	Numerical value
		Information bit long (K)	1060、2020、5114
Code check	1/3
		Modulating mode	BPSK
Channel model	AWGN
		Decoded mode	Turbo:Log-MAP maximum iteration time=8 LDPC:Log-BP maximum iteration time=50

Fig. 7 is LDPC sign indicating number and the frame error rate (FER) of existing Turbo code and the performance comparison curved line relation between the signal to noise ratio (Eb/No) among the present invention.In Fig. 7, dotted line is the transmission performance curve of Turbo code, and solid line is the transmission performance curve of LDPC sign indicating number among the present invention.As seen from Figure 7, adopt the frame error rate of LDPC sign indicating number of the present invention's structure functional: in information bit length is 2020, and when frame error rate was 10-3, the LDPC sign indicating number manyed the gain of 0.08dB than Turbo code; In information bit length is 5114 o'clock, and when frame error rate was 10-3, the LDPC sign indicating number manyed the gain of 0.1dB than Turbo code; And when frame error rate was 10-4, the LDPC sign indicating number can overcome the floor effect that Turbo code exists.

Being preferred embodiment of the present invention only below, is not to be used to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any modification of being done, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1, a kind of check matrix acquisition methods of low density parity check code of rate-compatible is characterized in that, this method comprises:

Select female sign indicating number matrix, and the size (m of definite basic extension matrix _b+ Δ m) * (n _b+ Δ m), wherein,

Expression rounds up, R ₀Be female sign indicating number matrix corresponding code rate, m _bAnd n _bBe respectively the line number and the columns of female sign indicating number matrix, R is a target bit rate;

With basic extension matrix H ^ExtensionBe divided into six submatrixs, $H^{\mathrm{extension}}=\left[\begin{array}{ccc}{H}_b^{\mathrm{system}}& H_b^{\mathrm{parity}}& H^{\mathrm{upper}\_\mathrm{right}}\\ H^{\mathrm{lower}\_\mathrm{left}}& H^{\mathrm{lower}\_\mathrm{mid}}& H^{\mathrm{lower}\_\mathrm{right}}\end{array}\right],$ Wherein, H _b ^SystemBe the information submatrix of described female sign indicating number matrix, H _b ^ParityBe the syndrome matrix of described female sign indicating number matrix, H ^Upper_right, H ^Lower_left, H ^Lower_mid, H ^Lower_rightSize is respectively m _b* Δ m, Δ m * (n _b-m _b), Δ m * m _b, Δ m * Δ m;

With submatrix H ^Upper_rightAll elements be set to-1;

For submatrix H ^Lower_mid, all elements on the default diagonal is set to 0, and all the other elements are set to-1, and described default diagonal is for connecting the

Row the 0th column element and nm _b-1 row

The diagonal of column element, and connect (n-1) m _bRow

Element and

Row m _bThe diagonal of-1 column element, wherein, n=1 ..., Δ x, and n is a positive integer;

The constructor matrix H ^Lower_rightMask code matrix H _MASK ^Lower_rightFor possessing many cornerwise lower triangular matrixs, comprise mask code matrix H in described many diagonal _MASK ^Lower_rightLeading diagonal and Δ x bar counter-diagonal, wherein, described Δ x bar counter-diagonal is described matrix H ^Lower_midDescribed in default cornerwise extended line, all elements on described many diagonal is set to 1, all the other elements are set to 0;

According to submatrix H _b ^System, H _b ^Parity, H ^Upper_right, H ^Lower_midWith submatrix H ^Lower_rightMask code matrix determine submatrix H ^Lower_leftMask code matrix H _MASK ^Lower_leftDegree distribute structure mask code matrix H _MASK ^Lower_left

With mask code matrix H _MASK ^Lower_rightIn all values be that 0 element is at submatrix H ^Lower_rightMiddle corresponding element is set to " 1 ", with matrix H _MASK ^Lower_rightElement on the middle leading diagonal is at submatrix H ^Lower_rightMiddle corresponding element is set to " 0 ", with mask code matrix H _MASK ^Lower_leftIn all values be that 0 element is at submatrix H ^Lower_leftMiddle corresponding element is set to " 1 "; According to the long maximization of minimum ring criterion, be matrix H _MASK ^Lower_rightElement on the middle counter-diagonal is in matrix H ^Lower_rightMiddle corresponding element and matrix H _MASK ^Lower_leftThe element that middle value is " 1 " is at submatrix H ^Lower_leftMiddle corresponding element is provided with corresponding side-play amount;

Six submatrixs determining are merged obtain described basic extension matrix;

Utilize current spreading factor z that described basic extension matrix is carried out correcting process, and utilize big or small replacement matrix P that revised basic extension matrix is expanded, obtain check matrix for z * z, wherein,

Expression rounds up, and K is the information bit length of present encoding, k _b=n _b-m _b

The check matrix that utilization obtains carries out the LDPC coding to data to be encoded.

2, method according to claim 1 is characterized in that, minimizes criterion according to long maximization of minimum ring and becate number, structure mask code matrix H _MASK ^Lower_left, satisfy minimum ring and grow up in equaling 6.

3, method according to claim 1 is characterized in that,

According to $\begin{array}{c}{h}_{\mathrm{ij}}^{\mathrm{lower}\_\mathrm{left}}=(C_1\&times;i^2\&times;j^2+C_2\&times;i^2\&times;j+C_3\&times;i\&times;j^2+C_4\&times;i^2+C_5\&times;j^2\\ +C_6\&times;i\&times;j+C_7\&times;i+C_8\&times;j+C_9)\mathrm{mod}\left(z_{\max }\right)\end{array}$ With $\begin{array}{c}{h}_{i^{\&prime;}{j}^{\&prime;}}^{\mathrm{lower}\_\mathrm{right}}=(D_1\&times;i^{\&prime;2}\&times;j^{\&prime;2}+D_2\&times;i^{\&prime;2}\&times;j^{\&prime;}+D_3\&times;i^{\&prime;}\&times;j^{\&prime;2}+D_4\&times;i^{\&prime;2}+D_5\&times;j^{\&prime;2}\\ +D_6\&times;i^{\&prime;}\&times;j^{\&prime;}+D_7\&times;i^{\&prime;}+D_8\&times;j^{\&prime;}+D_9)\mathrm{mod}\left(z_{\max }\right)\end{array}$ Configuration integer quotient C ₁..., C ₉, D ₁..., D ₉, the minimum ring of described basic extension matrix is grown up in equaling 6, wherein, C ₁..., C ₉Be nonnegative integer, z _MaxBe the maximum of spreading factor, h _{I ' j '} ^Lower_rightBe submatrix H ^Lower_rightIn the element value of the i ' row j ' row, and i ' and j ' be the index of element on the described counter-diagonal, h _Ij ^Lower_leftBe submatrix H ^Lower_leftIn the element value of the capable j of i row, and i and j are submatrix H ^Lower_leftIn with mask code matrix H _MASK ^Lower_leftMiddle value is the element index of the element correspondence of " 1 ".

4, method according to claim 1 is characterized in that, described correcting process is:

Wherein, h _Ij ^bBe basic extension matrix H ^ExtensionIn the element value of the capable j of i row, (h _Ij ^b) _ModifiedBe h _Ij ^bRevised element value.

5, according to arbitrary described method in the claim 1 to 4, it is characterized in that, in advance according to the basic extension matrix under a plurality of optional target bit rate select target matrixes and definite each target bit rate;

When carrying out the LDPC coding, according to the corresponding basic extension matrix of current target code rate selection, and carry out described correcting process and extended operation, obtain check matrix.

6, a kind of encoder of low density parity check code of rate-compatible is characterized in that, this encoder comprises:

The basic extension matrix determining unit is used to select female sign indicating number matrix, and the size (m of definite basic extension matrix _b+ Δ m) * (n _b+ Δ m), wherein, Δ m=Δ xm _b,

Expression rounds up, R ₀Be female sign indicating number matrix corresponding code rate, m _bAnd n _bBe respectively the line number and the columns of female sign indicating number matrix, R is a target bit rate; With basic extension matrix H ^ExtensionBe divided into six submatrixs, $H^{\mathrm{extension}}=\left[\begin{array}{ccc}{H}_b^{\mathrm{system}}& H_b^{\mathrm{parity}}& H^{\mathrm{upper}\_\mathrm{right}}\\ H^{\mathrm{lower}\_\mathrm{left}}& H^{\mathrm{lower}\_\mathrm{mid}}& H^{\mathrm{lower}\_\mathrm{right}}\end{array}\right],$ Wherein, H _b ^SystemBe the information submatrix of described female sign indicating number matrix, H _b ^ParityBe the syndrome matrix of described female sign indicating number matrix, H ^Upper_right, H ^Lower_left, H ^Lower_mid, H ^Lower_rightSize is respectively m _b* Δ m, Δ m * (n _b-m _b), Δ m * m _b, Δ m * Δ m; With submatrix H ^Upper_rightAll elements be set to-1; For submatrix H ^Lower_mid, all elements on the default diagonal is set to 0, and all the other elements are set to-1, and described default diagonal is for connecting the

Row the 0th column element and nm _b-1 row

The diagonal of column element, and connect (n-1) m _bRow

Element and

Row m _bThe diagonal of-1 column element, wherein, n=1 ..., Δ x, and n is a positive integer; The constructor matrix H ^Lower_rightMask code matrix H _MASK ^Lower_rightFor possessing many cornerwise lower triangular matrixs, comprise mask code matrix H in described many diagonal _MASK ^Lower_rightLeading diagonal and Δ x bar counter-diagonal, wherein, described Δ x bar counter-diagonal is described matrix H ^Lower_midDescribed in default cornerwise extended line, all elements on described many diagonal is set to 1, all the other elements are set to 0; According to submatrix H _b ^System, H _b ^Parity, H ^Upper_right, H ^Lower_midWith submatrix H ^Lower_rightMask code matrix determine submatrix H ^Lower_leftMask code matrix H _MASK ^Lower_leftDegree distribute structure mask code matrix H _MASK ^Lower_leftWith mask code matrix H _MASK ^Lower_righyIn all values be that 0 element is at submatrix H ^Lower_rightMiddle corresponding element is set to " 1 ", with matrix H _MASK ^Lower_rightElement on the middle leading diagonal is at submatrix H ^Lower_rightMiddle corresponding element is set to " 0 ", with mask code matrix H _MASK ^Lower_leftIn all values be that 0 element is at submatrix H ^Lower_leftMiddle corresponding element is set to " 1 "; According to the long maximization of minimum ring criterion, be matrix H _MASK ^Lower_rightElement on the middle counter-diagonal is in matrix H ^Lower_rightMiddle corresponding element and matrix H _MASK ^Lower_leftThe element that middle value is " 1 " is at submatrix H ^Lower_leftMiddle corresponding element is provided with corresponding side-play amount; Six submatrixs determining are merged obtain described basic extension matrix;

The correcting process unit is used to utilize current spreading factor z that the basic extension matrix that described basic extension matrix determining unit obtains is carried out correcting process;

Expanding element is used for utilizing big or small replacement matrix P for z * z that the revised basic extension matrix that described correcting process unit obtains is expanded, and obtains check matrix, wherein,

Expression rounds up, and K is the information bit length of present encoding, k _b=n _b-m _b

Coding unit, the check matrix that is used to utilize described expanding element to obtain carries out the LDPC coding to data to be encoded.

7, encoder according to claim 6 is characterized in that, described basic extension matrix determining unit comprises determines subelement and storing sub-units,

Described definite subelement, be further used for according to the basic extension matrix under a plurality of optional target bit rate select target matrixes and definite each target bit rate, and each optional target bit rate is kept in the described storing sub-units with basic extension matrix is corresponding accordingly;

Described correcting process unit is further used for shifting to an earlier date the basic extension matrix corresponding with the current target code check in described storing sub-units.

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