CN102412848B - QC-LDPC (quasi cyclic-low density parity check) code construction method based on mode Golomb rulers - Google Patents

Abstract

The invention provides a QC-LDPC (quasi cyclic-low density parity check) code construction method based on mode Golomb rulers. The method comprises the following steps: I, setting a quaternary parameter group (N, J, L, g), wherein N=qL and N is the code length of LDPC codes, J and L are column weight and row weight of a check matrix H, g is target girth and q is the size of a submatrix in the check matrix; II, randomly generating a mode-q Golomb ruler A with J identifiers and a mode-q Golomb ruler B with L identifiers; III, constructing the check matrix H by utilizing the mode-q Golomb ruler A and the mode-q Golomb ruler B; IV, utilizing a computer to search the girth of H and judge whether the girth is greater than or equal to g, if not, repeating the steps II-III, and if so, executing a step V; and V, outputting the check matrix H, thus completing the construction of the LDPC codes. In the method, the LDPC codes with the quaternary parameter groups of (582,3,6,10), (1099,3,7,10), (2168,3,8,10) and (16926,2,26,12) are constructed. According to the method, two mode Golomb rulers are utilized to construct the LDPC codes which have the girth greater than or equal to 10 and the code length reaching the Gallager limit, so that the error correction performance is better and the search complexity is reduced.

Description

The building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler

(1) technical field

The present invention relates to the channel coding technology field of the communications industry, be specially a kind of building method of the Quasi-cyclic Low-density Parity-check Codes (Quasi Cyclic-Low Density Parity Check, QC-LDPC) based on Mo Geluomu (Golomb) ruler.

(2) background technology

Communication system is intended to information to be sent to efficiently, reliably the stay of two nights by information source.The noise of thanksing for your hospitality communication channel can produce and disturb the information of transmission, thereby may reduce the reliability of communication.So, a key issue of Communication System Design is the in the situation that of random noise disturbance, transmission information how effectively and reliably, its core is by increasing the mode of redundancy, for the information bit that will send provides immunocompetence with the impact of noise on information in opposing communication process, channel coding technology is exactly in order to guarantee communication reliability.

1948, the C.E.Shannon of U.S.'s Bell Laboratory has proposed famous channel coding theorem in the authoritative paper " a mathematical theory of communication " of its initiative, provided the channel capacity of so-called communication to represent the limit of transmission ability, this is Shannon limit.Under the guide of its channel coding theorem, people are devoted to find error correcting capability always and approach as far as possible the Shannon limit, and encoding and decoding complexity lower can practical application channel coding schemes.

Loe-density parity-check code (Low Density Parity Check, LDPC) code is that a class can approach channel capacity and have the linear block codes of practical decoding algorithm.LDPC code adds glug by Gallager(the earliest) in 1962 years, propose.Because LDPC coding techniques can utilize low complex degree iterative message pass-algorithm to reach, approach the error-correcting performance that Shannon capacity is limit, many-sided researchs such as the structure of LDPC code, coding, decoding and performance evaluation and practical application are become to the research emphasis of channel coding technology.

Numerous scholars have proposed various LDPC code constructing methods, mainly can be divided into two large classes, structured LDPC code and random LDPC code.

(1) structured constitution method: utilize algebraic method or combined method to construct needed check matrix, check matrix has certain architectural characteristic.Finite geometry LDPC code has obtained a lot of scholars' research and concern because of its excellent coding and decoding characteristic.The scholars such as Y.Kou utilize the point of finite geometry and line to construct finite geometry LDPC code, such LDPC code has that in good minimum range characteristic and corresponding Tanner figure, not comprise length be 4 ring, can be obtained and be approached the performance that Shannon limits by iterative decoding.Meanwhile, the isostructure finite geometry LDPC code of Y.Kou is cyclic code or quasi-cyclic code, can realize linear time code by linear shift register.The scholars such as Lin Shu have proposed the method based on finite field structure LDPC code, this class code is cyclic code or quasi-cyclic code, there is good minimum range, eliminated that Tanner(is smooth to be received) 4 rings in figure, when high code check, can also obtain good performance, and can realize linear time code with simple feedback shift register.The people such as Tanner and Fossorier has proposed the QC-LDPC code based on cyclic permutation matrices structure, and has derived and constructed the given sufficient and necessary condition that encloses long QC-LDPC code.This class code is easily eliminated little ring, and same suitablely with feedback shift register, realizes uniform enconding.On this basis, Tanner utilizes the circular matrix of QC-LDPC code to construct convolution LDPC code, and the Algebraic Structure of QC-LDPC code is also conducive to the realization of high speed lsi.In addition, also have some methods based on other mathematical tool structural textures LDPC code, comprise BIB DESIGN (Balanced Incomplete Block Design, BIBD), circulation difference set and binary sequence etc.

(2) random configuration method: go out needed check matrix by computer random search according to certain design criterion and the conditions such as length, degree distribution, the Stopping Sets of enclosing; Its check matrix does not have structural, square being directly proportional of LDPC code encoder complexity and code length generally, and the hardware store of its higher-dimension check matrix is also comparatively complicated, becomes a practical Main Bottleneck of LDPC code.

The random LDPC code constructing method that the people such as MacKay proposes can make in the corresponding Tanner figure of code number of rings order less, and code word has good error-correcting performance.The scholars such as Xiao-Yu Hu adopt progressively optimal idea to propose a kind of building method that progressive edge increases (Progressive Edge Growth, PEG) that is called.This algorithm can be constructed and enclose more greatly long LDPC code under given degree sequence condition.

For the code of random configuration, check matrix is random generation, and code length and code check are more flexible, better error-correcting performance, still, due to the randomness of check matrix, cannot realize simple code, and the storage complexity of check matrix is higher, and complexity has determined system configuration and design.The code of structured configurations, can overcome the generation of becate, has definite structure, and the LDPC code of generation is cyclic code or quasi-cyclic code, can realize linear time code, and can design and enclose long larger code.Structured LDPC code LDPC code of performance and random configuration when short-and-medium code length is suitable, but is slightly worse than the code of random configuration during long code.

In view of above analysis, need to design a kind of building method of new LDPC code, to obtain to have, enclose greatly the quasi-cyclic LDPC code of long short code (QC-LDPC code), its code performance is better than the code of PEG algorithm construction in random configuration strategy.

(3) summary of the invention

The object of the invention is to design a kind of Quasi-cyclic Low-density Parity-check Codes (Quasi Cyclic-Low Density Parity Check based on Mo Geluomu ruler, QC-LDPC) building method, to quote two Mo Geluomu rulers structure column weights be 2, enclose and be longly equal to or greater than 10 and code length reaches the Algebraic Construction of the QC-LDPC code of Gallager limit, reduce search complexity, also there is better error-correcting performance simultaneously.

Ge Luomu ruler is one group of sign in integer position, and the distance meeting between any two signs is not identical.Wherein, the number of sign is the rank of Ge Luomu ruler, and distance maximum between sign is ruler length.Its mathematical notation is:

A={a ₁,a ₂,...,a _i,...,a _j,...,a _l,...,a _m} a ₁<a ₂<..a _i<..a _j..<a _l..<a _m

$\&ForAll;i,j,k,l\&Element;\{\mathrm{1,2},....,m\},$ $a_i-a_j=a_k-a_l\&DoubleLeftRightArrow;i=k,j=l$ (1)

In formula, A represents Ge Luomu ruler;

A _i, a _j, a _k, a _l, a _mrepresent a certain scale in Ge Luomu ruler;

The rank of this Ge Luomu ruler are m, and its length is a _m-a ₁.

Mo Geluomu ruler is by k remainder a ₁, a ₂...., a _kform, and meet a _i-a _j(i ≠ j) is different under mould k.Mo Geluomu ruler has following character:

If q=p ^m, m is a positive integer, has so q+1 integer d ₀, d ₁..., d _q, and when considering with q ²when+q+1 is mould, all q ²+ q poor d _i-d _j(i ≠ j) is all different.

Code length is that the QC-LDPC code of qL is represented by following check matrix:

$H=\left[\begin{array}{cccc}{I}_{\left(p_{\mathrm{0,0}}\right)}& I_{\left(p_{\mathrm{0,1}}\right)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{\left(p_{0,L-1}\right)}\\ I_{\left({\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{1,0}}\right)}& I_{\left({\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{1,1}}\right)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{\left({\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{1,L-1}\right)}\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& I_{\left(p_{j,l}\right)}& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ I_{\left(p_{J-\mathrm{1,0}}\right)}& I_{\left(p_{J-\mathrm{1,1}}\right)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{\left(p_{J-1,L-1}\right)}\end{array}\right]---\left(2\right)$

Wherein, the subscript p of matrix element _j,lfor integer,

the cyclic permutation matrices that represents a q * q, by the unit matrix I of q * q _{q * q}every row is cyclic shift p to the right _j,lposition obtains.The full null matrix I of q * q _(∞)represent.

Suppose j ₁, j ₂∈ 1,2 ..., J-1}, j ₁≠ j ₂,

And $\{({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}),({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}),...,({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})\}$ It not the Ge Luomu ruler that has the mould q of L sign.To there be so two ordered pair (x ₁, x ₂) ≠ (x ₃, x ₄) meet

$({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})-({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})\&equiv;({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})-({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})\mathrm{mod}q$

Do not considering j ₁and j ₂displacement while being related to, will have following several situation:

a)(x ₁=l ₁,x ₂=l ₂)≠(x ₃=l ₂,x ₄=l ₁)

b)(x ₁=l ₁,x ₂=l ₂)≠(x ₃=l ₂,x ₄=l ₃)

c)(x ₁=l ₁,x ₂=l ₂)≠(x ₃=l ₃,x ₄=l ₄)

By the known length that certainly exists of the character of Mo Geluomu ruler, it is 8 ring.For enclosing long being more than or equal to for 10 code, by above-mentioned c) set that provides must be the Ge Luomu ruler that has L the mould q identifying.More than comprehensive, structure LDPC code encloses and is longly more than or equal to 10 and must meets:

$\{(a_{{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">j</figure-callout>}}_1,0}-a_{{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">j</figure-callout>}}_2,0}),(a_{{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">j</figure-callout>}}_1,1}-a_{{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">j</figure-callout>}}_2,1}),...,(a_{{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">j</figure-callout>}}_1,L-1}-a_{{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">j</figure-callout>}}_2,L-1})\},{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">j</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">j</figure-callout>}}_{2\&Element;\{\mathrm{1,2},...,J-1\},{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">j</figure-callout>}}_1\&NotEqual;j_2---\left(3\right)}$

Be one to have the Ge Luomu ruler of mould q of L sign; Simultaneously

$\{(a_{{0,l}_1}-a_{{0,l}_2}),(a_{{1,l}_1}-a_{{1,l}_2}),...,(a_{{J-1,l}_1}-a_{{J-1,l}_2})\},l_1,l_2\&Element;\{\mathrm{1,2},...,L-1\},l_1\&NotEqual;l_2---\left(4\right)$

Be one to have the Ge Luomu ruler of mould q of J sign.

The check matrix that can obtain thus QC-LDPC code meets in formula (3) or formula (4), and the length of enclosing of this yard is at least 6 so.

Suppose to exist 4 rings, have j ₁, j ₂, l ₁, l ₂, meet

$({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})-({\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})\&equiv;0\mathrm{mod}q$

Like this, for l ∈ 1,2 ..., L-1}; J ∈ 1,2 ..., J-1}, has

$({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})-({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})\&equiv;({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})-({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})\mathrm{mod}q$

$({\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="1"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})-(p_{j,l_1}-p_{j,l_2})\&equiv;({\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}}-{\mathrm{<figure-callout\; id="2"\; label="p\; j"\; filenames="HDA0000121131600000011.png"\; state="\{\{state\}\}">p</figure-callout>}}_{j_{}})-(p_{j,l_1}-p_{j,l_2})\mathrm{mod}q$

Clearly this and structure LDPC code enclose long 10 necessary condition formula (3), the formula (4) of being more than or equal to and run counter to, so hypothesis is false, thereby can this yard enclose is longly at least 6.

Because the length of enclosing of QC-LDPC code mostly is 12 most, when J=2, ring length can only be 4i, i=1, and 2 ..., n.Therefore can obtain:

The length of enclosing of QC-LDPC code during J=2 is that 12 sufficient and necessary condition is: { (p _1,0-p _0,0), (p _1,1-p _0,1) ..., (p _{1, L-1}-p _{0, L-1}) be one to be designated the Ge Luomu ruler of the mould q of L.

Enclose greatly after the problem of long code having solved structure, also wish that LDPC code length is short as much as possible.Gallager discloses the length of enclosing of given Tanner figure, column weight be J capable be heavily the lower limit of the code length N of the regular LDPC code of L.For enclosing long g=4p,

N≥L(L-1) ^(p-1)(J-1) ^(p-1)+....+L(L-1)(J-1)+L (5)

If g=4p+2, so

$N\&GreaterEqual;\frac{L^2{(L-1)}^{(P-1)}{(J-1)}^p+...+L^2(J-1)+L}{J}---\left(6\right)$

Especially, for a QC-LDPC code, as g=12 and during J=2, this limit becomes

q≥(L-1) ²+(L-1)+1 (7)

Here, q refers to the dimension of cyclic permutation in check matrix.

Based on above-mentioned analysis, the present invention proposes the Singh based on Singe() structural property that encloses greatly long QC-LDPC code check matrix H perfact difference set, that can reach Gallager code length limit.

Construct a check matrix

$H=\left[\begin{array}{cccc}{I}_{(a_0\&CenterDot;b_0)}& I_{(a_0\&CenterDot;b_1)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{(a_0\&CenterDot;b_{L-1})}\\ I_{(a_1\&CenterDot;b_0)}& I_{(a_1\&CenterDot;b_1)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{(a_1\&CenterDot;b_{L-1})}\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& I_{(a_j\&CenterDot;b_j)}& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ I_{(a_{J-1}\&CenterDot;b_0)}& I_{(a_{J-1}\&CenterDot;b_1)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{(a_{J-1}\&CenterDot;b_{L-1})}\end{array}\right]---\left(8\right)$

Here, A={a ₀, a ₁..., a _j-1be a Ge Luomu ruler that has the mould q of J sign, and same, B={b ₀, b ₁..., b _l-1it is a Ge Luomu ruler that has the mould q of L sign;

meaning and formula (2) in

the same.The length of enclosing of the quasi-cyclic LDPC code of (8) formula definition is at least 6 so.

Mo Geluomu chi A and B can be regarded as set 0,1 ..., two subsets of q-1}.Its character is:

If A={a ₀, a ₁..., a _j-1and B={b ₀, b ₁..., b _l-1be set 0,1 ..., two subsets of q-1}, to have the length of enclosing of the code of formula (2) form be that 10 necessary condition is that A and B are the Ge Luomu ruler of mould q to check matrix so.

If the length of enclosing of this yard is more than or equal to 10, so set { (a ₀-a ₁) b _l: 0≤l≤L-1} and set { (b ₀-b ₁) a _j: 0≤j≤J-1} must be the Ge Luomu ruler of mould q.Consider gcd ((a ₀-a ₁) ^-1, q)=1 and gcd ((b ₀-b ₁) ^-1, q)=1, wherein gcd represents greatest common factor (G.C.F.), by the character of Mo Geluomu ruler, knows that A and B are the Ge Luomu rulers of mould q.

For J=2, L-1 is a plain index, if q=(L-1) ²+ (L-1)+1, A={0,1} and B is a Singer perfact difference set that has L integer, can construct quasi-cyclic LDPC code by the given check matrix of formula (8) so, and it encloses and reaches 12.From formula (7), corresponding code length reaches Gallager lower limit.

As structurized building method, the QC-LDPC code constructing method that the present invention proposes makes can realize linear time code with simple feedback shift register in the process of coding.Meanwhile, the Algebraic Structure of QC-LDPC code is also conducive in the upper realization of high speed lsi (VLSI).

The building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler that the present invention proposes, comprises the following steps:

I, quaternary parameter group (N, J, L, g) is set, wherein N=qL represents the code length of Quasi-cyclic Low-density Parity-check Codes, i.e. QC-LDPC code length, J and L represent respectively the column weight of check matrix H and row heavy, g represents that target encloses length, and q is the size of submatrix in check matrix, and r is code check;

100＜N＜100000，

J and L are positive integer, 2≤J≤11, and r ≈ (L-J)/L, r >=0.1,

g≥10；

II, produce two Mo Geluomu ruler A and B, A={a at random ₀, a ₁..., a _j-1, be a Ge Luomu ruler that has the mould q of J sign; B={b ₀, b ₁..., b _l-1, be a Ge Luomu ruler that has the mould q of L sign;

III, utilize the Mo Geluomu ruler A that produces in step II and B structure check matrix H;

$H=\left[\begin{array}{cccc}{I}_{(a_0\&CenterDot;b_0)}& I_{(a_0\&CenterDot;b_1)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{(a_0\&CenterDot;b_{L-1})}\\ I_{(a_1\&CenterDot;b_0)}& I_{(a_1\&CenterDot;b_1)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{(a_1\&CenterDot;b_{L-1})}\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& I_{(a_j\&CenterDot;b_j)}& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ I_{(a_{J-1}\&CenterDot;b_0)}& I_{(a_{J-1}\&CenterDot;b_1)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{(a_{J-1}\&CenterDot;b_{L-1})}\end{array}\right]$

The element of described check matrix

the cyclic permutation matrices that represents a q * q, it is by the unit matrix I of q * q _{q * q}every row is cyclic shift a to the right _jb _lposition obtains;

IV, computer search, whether enclosing of the check matrix that step III produces is longly more than or equal to target and encloses long g,

If enclosing of the check matrix producing is longly less than target and encloses long g, repeating step II～III,

If enclosing of the check matrix producing is longly more than or equal to target and encloses long g, enter step V,

If can not produce, enclose the long check matrix that target is enclosed length 10 that is more than or equal to, return to step I, Reparametrization;

The check matrix H that V, output meet the demands, check matrix H represents that code length is the QC-LDPC code of N=qL.

In described step III, take the dimension of q cyclic permutation in Quasi-cyclic Low-density Parity-check Codes check matrix, as g=12 and during J=2, q>=(L-1) ²+ (L-1)+1.

The length of enclosing of described step V gained Quasi-cyclic Low-density Parity-check Codes is at least 6.

The Ge Luomu ruler A that described step II arranges be 0,1} and Ge Luomu ruler B is Singh's perfact difference set that has L integer, and the Quasi-cyclic Low-density Parity-check Codes that described step V gained check matrix H is constructed to enclose length be 12, and code length reaches and adds glug and limit.

The Ge Luomu ruler A of described step II setting and B be set 0,1 ...., two subsets of q-1}.

It is 2 that the advantage of building method that the present invention is based on the Quasi-cyclic Low-density Parity-check Codes of Mo Geluomu ruler is to utilize two Mo Geluomu rulers structure column weights, enclose and reach 12 and code length reaches the Algebraic Construction of the QC-LDPC code of Gallager limit, greatly reduces search complexity; 2, the QC-LDPC of this law structure has improved the length of enclosing of code, and the error correcting capability of lift structure LDPC code is compared with the code based on PEG algorithm construction, and performance is more excellent, and search complexity is lower.

(4) accompanying drawing explanation

Fig. 1 is three kinds of QC-LDPC codes (582,3,6,10), (1099 of the building method embodiment structure of this Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler, 3,7,10), (2168,3,8,10) with the error-correcting performance comparison of the corresponding code of EPG structure.

Fig. 2 is the error-correcting performance comparison of QC-LDPC code (16926,2,26,12) with the corresponding code of EPG structure of institute of the present invention extracting method structure.

(5) embodiment

The embodiment 1 of the building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler

The concrete implementation step of this example is as follows:

I, quaternary parameter group (N, J, L, g) is set, wherein N=qL represents the code length of Quasi-cyclic Low-density Parity-check Codes, i.e. QC-LDPC code length; J and L represent respectively the column weight of check matrix H and row heavy, g represents that target encloses length; Q is the size of submatrix in check matrix,

This routine designing requirement N > 500, r > 0.4, g=10, gets J=3,

(L-J)/L > 0.4 so, 0.6L > 3, and L > 5, this example is got L=6;

N=qL, this routine N=6q > 500, q >=84;

So first with J=3, L=6, g=10, q=84, N=qL=504 continues following steps;

II, produce two Mo Geluomu ruler A and B at random, A={12,31,69}, is a Ge Luomu ruler that has the mould q=84 of J=3 sign; B={13,17,35,36,59,76}, is a Ge Luomu ruler that has the mould q=84 of L=6 sign;

III, utilize the Mo Geluomu ruler A that produces in step II and B structure check matrix H;

$H=\left[\begin{array}{cccccc}{I}_{\left(72\right)}& I_{\left(36\right)}& I_{\left(0\right)}& I_{\left(12\right)}& I_{\left(36\right)}& I_{\left(72\right)}\\ I_{\left(67\right)}& I_{\left(23\right)}& I_{\left(77\right)}& I_{\left(24\right)}& I_{\left(65\right)}& I_{\left(4\right)}\\ I_{\left(57\right)}& I_{\left(81\right)}& I_{\left(63\right)}& I_{\left(48\right)}& I_{\left(39\right)}& I_{\left(36\right)}\end{array}\right]$

The element of described check matrix

represent the cyclic permutation matrices of 84 * 84, it is by 84 * 84 unit matrix I _{q * q}every row is cyclic shift p to the right _j,lposition obtains;

Take the dimension of q=84 cyclic permutation in Quasi-cyclic Low-density Parity-check Codes check matrix;

IV, computer search, whether enclosing of the check matrix that step III produces is longly more than or equal to target and encloses long g=10,

Repeating step II～III repeatedly, the long target that equals of enclosing of the check matrix that can not produce is enclosed longly by 10, returns to step I, Reparametrization;

Repeating step I～IV repeatedly,

When quaternary parameter group (N, J, L, g) is set, with J=3, L=6, g=10, q=85～96, N=qL=510～576, all fail to obtain check matrix enclose long equal target enclose long by 10, extremely

I, quaternary parameter group (N, J, L, g) is set,

J=3，L=6，g=10，q=97，N=qL=582，

II, produce two Mo Geluomu ruler A and B at random, A={35,41,57}, is a Ge Luomu ruler that has the mould q=97 of J=3 sign; B={1,23,44,58,67,95}, is a Ge Luomu ruler that has the mould q=97 of L=6 sign, q is 97;

III, utilize the Mo Geluomu ruler A that produces in step II and B structure check matrix H;

$H=\left[\begin{array}{cccccc}{I}_{\left(35\right)}& I_{\left(29\right)}& I_{\left(85\right)}& I_{\left(90\right)}& I_{\left(17\right)}& I_{\left(27\right)}\\ I_{\left(41\right)}& I_{\left(70\right)}& I_{\left(58\right)}& I_{\left(50\right)}& I_{\left(31\right)}& I_{\left(15\right)}\\ I_{\left(57\right)}& I_{\left(50\right)}& I_{\left(83\right)}& I_{\left(8\right)}& I_{\left(36\right)}& I_{\left(80\right)}\end{array}\right]$

The element of described check matrix

the cyclic permutation matrices that represents a q * q, it is by the unit matrix I of q * q _{q * q}every row is cyclic shift p to the right _j,lposition obtains;

Take the dimension of q=97 cyclic permutation in Quasi-cyclic Low-density Parity-check Codes check matrix;

IV, computer search, whether enclosing of the check matrix that step III produces is longly more than or equal to target and encloses long g=10,

If the long target that is less than of enclosing of the check matrix producing is enclosed length 10, repeating step II～III,

If the long target that is more than or equal to of enclosing of the check matrix producing is enclosed length 10, enter step V;

The check matrix H that V, output meet the demands, check matrix H represents that code length is the QC-LDPC code of qL=97 * 6=582.

The embodiment 2 of the building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler

Comprise the following steps:

I, quaternary parameter group (N, J, L, g) is set, each meaning of parameters is identical with embodiment 1, this routine designing requirement N > 1000, and r > 0.57, g=10, gets J=3,

(L-J)/L > 0.57 so, 0.43L > 3, and L > 6.98, this example is got L=7;

N=qL, this routine N=7q > 1000, q >=142.9;

So, with J=3, L=6, g=10, q=143～156, N=qL=1001～1092, repeating step I～IV repeatedly, all fail to obtain check matrix enclose long equal target enclose long by 10, to J=3, L=6, g=10, q=157, N=7*157=1099;

II, produce two Mo Geluomu ruler A and B at random, A={33,66,108}, is a Ge Luomu ruler that has the mould q=157 of J=3 sign; B={7,33,66,98,118,119,155}, is a Ge Luomu ruler that has the mould q=157 of L=7 sign, q is 157;

III, utilize the Mo Geluomu ruler A that produces in step II and B structure check matrix H;

$H=\left[\begin{array}{ccccccc}{I}_{\left(74\right)}& I_{\left(147\right)}& I_{\left(137\right)}& I_{\left(94\right)}& I_{\left(126\right)}& I_{\left(2\right)}& I_{\left(91\right)}\\ I_{\left(148\right)}& I_{\left(137\right)}& I_{\left(117\right)}& I_{\left(31\right)}& I_{\left(95\right)}& I_{\left(4\right)}& I_{\left(25\right)}\\ I_{\left(128\right)}& I_{\left(110\right)}& I_{\left(63\right)}& I_{\left(65\right)}& I_{\left(27\right)}& I_{\left(135\right)}& I_{\left(98\right)}\end{array}\right]$

The element of described check matrix

the cyclic permutation matrices that represents a q * q, it is by the unit matrix I of q * q _{q * q}every row is cyclic shift p to the right _j,lposition obtains;

Take the dimension of q=157 cyclic permutation in Quasi-cyclic Low-density Parity-check Codes check matrix;

IV, computer search, whether enclosing of the check matrix that step III produces is longly more than or equal to target and encloses long g=10,

If the long target that is less than of enclosing of the check matrix producing is enclosed length 10, repeating step II～III,

If the long target that is more than or equal to of enclosing of the check matrix producing is enclosed length 10, enter step V;

The check matrix H that V, output meet the demands, check matrix H represents that code length is the QC-LDPC code of qL=157 * 7=1099.

The embodiment 3 of the building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler

Comprise the following steps:

I, quaternary parameter group (N, J, L, g) is set, each meaning of parameters is identical with embodiment 1, this routine designing requirement N > 2000, and r > 0.625, g=10, gets J=3,

(L-J)/L > 0.625 so, 0.375L > 3, and L >=8, this example is got L=8;

N=qL, this routine N=8q > 2000, q >=250;

So, with J=3, L=8, g=10, q=250～270, N=qL=2000～2160, repeating step I～IV repeatedly, all fail to obtain check matrix enclose long equal target enclose long by 10,

To J=3, L=8, g=10, q=271, N=8*2712168;

II, produce two Mo Geluomu ruler A and B at random, A={64,125,207}, is a Ge Luomu ruler that has the mould q=271 of J=3 sign; B={45,64,79,116,140,191,229,230}, is a Ge Luomu ruler that has the mould q=271 of L=8 sign, q is 271;

III, utilize the Mo Geluomu ruler A that produces in step II and B structure check matrix H;

$H=\left[\begin{array}{cccccccc}{I}_{\left(170\right)}& I_{\left(31\right)}& I_{\left(178\right)}& I_{\left(107\right)}& I_{\left(17\right)}& I_{\left(29\right)}& I_{\left(22\right)}& I_{\left(86\right)}\\ I_{\left(205\right)}& I_{\left(141\right)}& I_{\left(119\right)}& I_{7\left(137\right)}& I_{\left(156\right)}& I_{\left(27\right)}& I_{\left(170\right)}& I_{\left(24\right)}\\ I_{\left(101\right)}& I_{\left(240\right)}& I_{\left(93\right)}& I_{\left(164\right)}& I_{\left(254\right)}& I_{\left(242\right)}& I_{\left(249\right)}& I_{\left(185\right)}\end{array}\right]$

The element of described check matrix

the cyclic permutation matrices that represents a q * q, it is by the unit matrix I of q * q _{q * q}every row is cyclic shift p to the right _j,lposition obtains;

Take the dimension of q=271 cyclic permutation in Quasi-cyclic Low-density Parity-check Codes check matrix;

IV, computer search, whether enclosing of the check matrix that step III produces is longly more than or equal to target and encloses long g=10,

If the long target that is less than of enclosing of the check matrix producing is enclosed length 10, repeating step II～III,

If the long target that is more than or equal to of enclosing of the check matrix producing is enclosed length 10, enter step V;

The check matrix H that V, output meet the demands, check matrix H represents that code length is the QC-LDPC code of qL=271 * 8=2168.

The embodiment 4 of the building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler

Comprise the following steps:

I, quaternary parameter group (N, J, L, g) is set, the implication of each parameter is identical with embodiment 1,

This routine designing requirement N > 16000, r > 0.923, g=12, gets J=2,

(L-J)/L > 0.923 so, 0.077L > 2, and L > 25.97, this example is got L=26;

q≥(L-1) ²+(L-1)+1≥651

So, this routine J=2, L=26, g=12, q=651, N=qL=651 * 26=16926;

II, produce two Mo Geluomu ruler A and B at random, A={0,1}, is a Ge Luomu ruler that has the mould q=651 of J=2 sign; B={0,1,33,83,104,110,124,163,185,200,203,249,251,258,314,318,343,356,386,430,440,456,464,475,487,492}, is a Ge Luomu ruler that has the mould q=651 of L=26 sign, q is 651;

III, utilize the Mo Geluomu ruler A that produces in step II and B structure check matrix H;

$H=\left[\begin{array}{cccccc}{I}_{\left(0\right)}& I_{\left(0\right)}& I_{\left(0\right)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{\left(0\right)}& I_{\left(0\right)}\\ I_{\left(0\right)}& I_{\left(1\right)}& I_{\left(33\right)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{\left(487\right)}& I_{\left(492\right)}\end{array}\right]$

The element of described check matrix

the cyclic permutation matrices that represents a q * q, it is by the unit matrix I of q * q _{q * q}every row is cyclic shift p to the right _j,lposition obtains;

Take the dimension of q=651 cyclic permutation in Quasi-cyclic Low-density Parity-check Codes check matrix; This routine g=12, J=2, q=651=(26-1) ²+ (26-1)+1=625+25+1;

IV, computer search, whether enclosing of the check matrix that step III produces is longly more than or equal to target and encloses long g=12,

If the long target that is less than of enclosing of the check matrix producing is enclosed length 12, repeating step II～III,

If the long target that is more than or equal to of enclosing of the check matrix producing is enclosed length 12, enter step V;

The check matrix H that V, output meet the demands, check matrix H represents that code length is the QC-LDPC code of N=qL=651 * 26=16926.

In above four embodiment, select four groups of different parameters, by the step of above-mentioned this method, obtained four kinds of QC-LDPC codes.Design parameter is as shown in table 1.

Table 1 this method embodiment parameter list

For clearer displaying superiority of the present invention, the resulting QC-LDPC code of this building method embodiment is carried out to computing power emulation.The QC-LDPC code adopting in emulation comprises the QC-LDPC code of the gained of above-mentioned four examples, and the quaternary parameter group of four examples (N, L, J, g) is respectively (582,3,6,10), (1099,3,7,10), (2168,3,8,10) and (16926,2,26,12).

Simulated environment parameter is set to: modulation adopts BPSK, and channel model is additive white Gaussian noise channel, QC-LDPC decoding algorithm for and amass decoding algorithm, maximum iterations is 50.The decoding performance curve of QC-LDPC code and the performance curve of the LDPC code with similar parameters of being constructed based on PEG algorithm as a comparison of example 1,2 and 3 in Fig. 1, with bit error probability standard, have been provided.In Fig. 1 ▲ the quaternary parameter group of wire list example 1 be the QC-LDPC code of (582,3,6,10), the line of △ represents the PEG code that quaternary parameter group is (582,3,6,8); The quaternary parameter group of the wire list example 2 of ■ is the QC-LDPC code of (1099,3,7,10), and the line of represents the PEG code that quaternary parameter group is (1099,3,7,8); ● the quaternary parameter group of wire list example 3 be the QC-LDPC code of (2168,3,8,10), zero line represents the PEG code that quaternary parameter group is (2168,3,8,8).

The decoding performance curve of QC-LDPC code and the performance curve of the LDPC code with similar parameters of being constructed based on PEG algorithm as a comparison of example 4 in Fig. 2, with bit error probability standard, have been provided.● the quaternary parameter group of wire list example 4 be the QC-LDPC code of (10926,2,26,12), zero line represents the PEG code that quaternary parameter group is (16926,2,26,10).

By Fig. 1 and 2, can know that the QC-LDPC code of seeing embodiment of the present invention structure is for enclosing greatly length code, its performance is better than the code of constructing based on PEG algorithm of similar parameters.

Adopt the QC-LDPC code of this method structure to be applied in Chinese Digital sound broadcast system, actual test shows that error-correcting performance is good, meets Chinese Digital sound radio needs.

Above-described embodiment, is only the specific case that object of the present invention, technical scheme and beneficial effect are further described, and the present invention is not defined in this.All any modifications of making, be equal to replacement, improvement etc., within being all included in protection scope of the present invention within scope of disclosure of the present invention.

Claims (6)

1. the building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler, is characterized in that comprising the following steps:

I, quaternary parameter group (N, J, L, g) is set, wherein N=qL represents the code length of Quasi-cyclic Low-density Parity-check Codes, J and L represent respectively the column weight of check matrix H and row heavy, g represents that target encloses length, q is the size of submatrix in check matrix, r is code check;

100＜N＜100000，

J and L are positive integer, 2≤J≤11,

and r>=0.1,

g≥10；

II, produce two Mo Geluomu ruler A and B, A={a at random ₀, a ₁..., a _j-1, be a Ge Luomu ruler that has the mould q of J sign; B={b ₀, b ₁..., b _l-1, be a Ge Luomu ruler that has the mould q of L sign;

III, utilize the Mo Geluomu ruler A={a producing in step II ₀, a ₁..., a _j-1and B={b ₀, b ₁..., b _l-1structure check matrix H element

obtain check matrix H;

$H=\left[\begin{array}{cccc}{I}_{(a_0\&CenterDot;b_0)}& I_{(a_0\&CenterDot;b_1)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{(a_0\&CenterDot;b_{L-1})}\\ I_{(a_1\&CenterDot;b_0)}& I_{(a_1\&CenterDot;b_1)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{(a_1\&CenterDot;b_{L-1})}\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& I_{(a_j\&CenterDot;b_j)}& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & \&CenterDot;\\ I_{(a_{J-1}\&CenterDot;b_0)}& I_{(a_{J-1}\&CenterDot;b_1)}& \&CenterDot;\&CenterDot;\&CenterDot;& I_{(a_{J-1}\&CenterDot;b_{L-1})}\end{array}\right]$

The element of described check matrix

the cyclic permutation matrices that represents a q * q, it is by the unit matrix I of q * q _{q * q}every row is cyclic shift a to the right _jb _lposition obtains;

IV, computer search, whether enclosing of the check matrix that step III produces is longly more than or equal to target and encloses long g,

If enclosing of the check matrix producing is longly less than target and encloses long g, repeating step II～III,

If enclosing of the check matrix producing is longly more than or equal to target and encloses long g, enter step V,

If can not produce to enclose to grow, be more than or equal to the check matrix that target is enclosed long g, return to step I;

The check matrix H that V, output meet the demands, check matrix H represents that code length is the Quasi-cyclic Low-density Parity-check Codes of qL.

2. the building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler according to claim 1, is characterized in that:

Described step III, take the dimension of q cyclic permutation in Quasi-cyclic Low-density Parity-check Codes check matrix, as g=12 and during J=2, and q>=(L-1) ²+ (L-1)+1.

3. the building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler according to claim 1, is characterized in that:

The length of enclosing of described step V gained Quasi-cyclic Low-density Parity-check Codes is at least 6.

4. the building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler according to claim 1, is characterized in that:

The Ge Luomu ruler A that described step II produces be 0,1} and Ge Luomu ruler B is Singh's perfact difference set that has L integer, and the Quasi-cyclic Low-density Parity-check Codes that described step V gained check matrix H is constructed to enclose length be 12, and code length reaches and adds glug and limit.

5. the building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler according to claim 1, is characterized in that:

The Ge Luomu ruler A that described step II produces and B be set 0,1 ...., two subsets of q-1}.

6. the building method of the Quasi-cyclic Low-density Parity-check Codes based on Mo Geluomu ruler according to claim 1, is characterized in that:

The Quasi-cyclic Low-density Parity-check Codes of constructing is that quaternary parameter group (N, L, J, g) is (582,3,6,10) Quasi-cyclic Low-density Parity-check Codes, or quaternary parameter group (N, L, J, g) be the Quasi-cyclic Low-density Parity-check Codes of (1099,3,7,10), or quaternary parameter group (N, L, J, g) be (2168,3,8,10) Quasi-cyclic Low-density Parity-check Codes, or quaternary parameter group (N, L, J, g) be the Quasi-cyclic Low-density Parity-check Codes of (16926,2,26,12).

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