CN102386933B - Construction method for quasi-cyclic low density parity check (LDPC) code check matrix - Google Patents

Abstract

The invention relates to a construction method for a quasi-cyclic low density parity check (LDPC) code check matrix. The construction method for the quasi-cyclic LDPC code check matrix comprises the following steps of: determining a line parameter J and a column parameter L of a basis matrix of the check matrix to be designed; after the line and column parameters are determined, traversing all columns by the line, and for the given position of the jth line and the lth column of the basis matrix, sequentially obtaining terms of each Hanoi tower array according to the definitions of the Hanoi tower array that f(1)=1 if n is 1 and that f(n+1)=s*f(n)+1 if n is more than 1; obtaining a circulant permutation matrix offset value pj,l according to a formula pj,l=f(j+1)+j, adding a digital value jof a corresponding line to each f(j+1) value obtained by the second step to obtain a circulant permutation matrix offset value pi,j and arranging the pi,j at the position of the jth line and the lth column of the basis matrix to be constructed; and constructing the basis matrix to be designed by using all the pj,l values. By the method, the performance of a quasi-cyclic LDPC code is improved, and simultaneously storage complexity is decreased.

Description

A kind of building method of quasi-cyclic LDPC code check matrix

Technical field

The invention belongs to communication technical field, particularly relate to a kind of building method of quasi-cyclic LDPC code check matrix.

Background technology

The LDPC code is low density parity check code (Low Density Parity Check Code, LDPC), is the linear block codes that is had sparse check matrix by the class that RobertG.Gallager proposes.By people such as MacKay and Neal the LDPC code is re-started research, proposed the feasibility decoding algorithm for the LDPC code, thereby further found the superperformance that the LDPC code has.

At present, the LDPC code has been widely used in the fields such as deep space communication, optical fiber communication, satellite digital video and audio broadcasting.The LDPC code has become the 4th strong competitor of generation communication system (4G), and is adopted by satellite digital video broadcast standard DVB-S2 of future generation based on the encoding scheme of LDPC code.

Random LDPC code is because its performance near shannon limit is paid close attention to research widely.The high implementation complexity of random LDPC code check matrix becomes an obstacle that hinders its practical application.Subsequently, people study the check matrix of finding quasi-cyclic can obtain a well compromise between complexity and performance, therefore, the check matrix of quasi-cyclic LDPC code be configured to an important research direction for LDPC code structure.

The structure thinking of quasi-cyclic LDPC code is the basic matrix B that at first constructs check matrix H, then with the unit matrix I (0) and the p thereof that are of a size of p * p _{J, l}Inferior ring shift right matrix I (p _{J, l}) fill basic matrix formation check matrix, in the formula: 0≤j≤J-1; 0≤l≤L-1.Each position of basic matrix has provided the ring shift right number of times of cyclic permutation matrices corresponding to this position.Check matrix H and basic matrix B are defined as respectively:

Quasi-cyclic LDPC code based on array structure has provided a kind of thinking of constructing basic matrix.For the basic matrix that is of a size of J * L, the building method of taking is that 1 to JL integer is carried out random interleaving, and the parameter that interweaves is the capable L row of J, and the matrix that obtains is the basic matrix of forming array LDPC code just in time.

Analyze and find, its check matrix storage complexity is JL, is random configuration LDPC code

Still have very high storage complexity, simultaneously, this scheme do not have fine embodiment LDPC code near the shannon limit performance, main cause is that not have effective is the control of 4 becate to length.

Summary of the invention

Technical problem to be solved by this invention provides a kind of building method of quasi-cyclic LDPC code check matrix, effectively reduces the storage complexity in the LDPC code construction process.

The technical solution adopted for the present invention to solve the technical problems is: a kind of building method of quasi-cyclic LDPC code check matrix is provided, comprises the following steps:

(1) determines line parameter J and the row parameter L of the basic matrix of check matrix to be designed;

(2) after definite ranks parameter, by all row of row traversal; For the position of the capable l row of the j of given basic matrix, by the Han Nuota ordered series of numbers definition: when n is 1, f (1)=1, when n greater than 1 the time, f (n+1)=2 * f (n)+1 obtains the item of each Han Nuota ordered series of numbers successively;

(3) by formula p _{J, l}=f (j+l)+j obtains the cyclic permutation matrices deviant p of this position _{J, l}Each f (j+l) value that step (2) is obtained adds that the corresponding numerical value j that is expert at obtains cyclic permutation matrices deviant p _{I, j}, be placed on the position of the capable l row of the j of basic matrix of structure;

(4) by above-mentioned all p _{J, l}The basic matrix of Construction designing.

Described step (1) if in J=3, L=6, so the structure basic matrix be designated as B (3,6)

Described step (3) is calculated f (j+l) needs an adder, calculates p _{J, l}=f (j+l)+j needs an adder, whole deviant p _{J, l}Calculating need two adders.

Beneficial effect

The present invention can generate the basic matrix of corresponding check matrix by simple algebraic operation, and do not need to the LDPC code based on array structure such, the cyclic shift number of times of each position of storage basic matrix.The present invention when promoting the quasi-cyclic LDPC code performance, the reduction that has brought storage complexity.

Embodiment

Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiment only to be used for explanation the present invention and be not used in and limit the scope of the invention.Should be understood that in addition those skilled in the art can make various changes or modifications the present invention after the content of having read the present invention's instruction, these equivalent form of values fall within the application's appended claims limited range equally.

The present invention is by structure ten thousand methods of the following examples explanation LDPC code check matrix, and it has reduced the storage complexity in the LDPC code construction process effectively.

Definition 1: for an ordered series of numbers f (n), n is nonnegative integer, if when n is 1, f (1)=1, when n greater than 1 the time, f (n+1)=2 * f (n)+1, the ordered series of numbers that then satisfies this recurrence relation is called the Han Nuota ordered series of numbers, and its item just is called Han Nuota ordered series of numbers number.A typical Han Nuota ordered series of numbers is as follows: 1,3,7,15,31,63,127,255,511 ....

Character 1: for a Han Nuota ordered series of numbers, if n＞m and n, m, k ∈ Z ⁺, then have

f(n+k)-f(n)＞f(m+k)-f(m)。

Proof: adopt mathematical induction to prove.

According to the definition of Han Nuota ordered series of numbers as can be known, the Han Nuota ordered series of numbers is a monotonic increase ordered series of numbers, that is, and and for n＞m,

F (n)＞f (m) is arranged.

When k=1, f (n+k)-f (n)=f (n+1)-f (n)=f (n)+1,

f(m+k)-f(m)＝f(m+1)-f(m)＝f(m)+1，

Because f (n)＞f (m),

So f (n+k)-f (n)＞f (m+k)-f (m);

f(n+k)-f(n)＝f(n+2)-f(n)＝f(n+2)-f(n+1)+f(n+1)-f(n)

When k=2,

＝f(n+1)+1+f(n)+1＝f(n+1)+f(n)+2’

f(m+k)-f(m)＝f(m+2)-f(m)＝f(m+2)-f(m+1)+f(m+1)-f(m)，

＝f(m+1)+1+f(m)+1＝f(m+1)+f(m)+2

Because f (n)＞f (m), f (n+1)＞f (m+1),

So f (n+k)-f (n)＞f (m+k)-f (m);

By that analogy,

$f(n+k)-f\left(n\right)$

$=f(n+k)-f(n+k-1)+f(n+k-1)-f(n+k-2)+f(n+k-2)-\·\·\·+f(n+1)-f\left(n\right),$

$=k+\underset{i=1}{\overset{k}{\mathrm{\Σ}}}f(n+k-i)$

$f(m+k)-f\left(m\right)$

$=k+\underset{i=1}{\overset{k}{\mathrm{\Σ}}}f(m+k-i)$

f(n)＞f(m)，f(n+1)＞f(m+1)，…，f(n+k-1)＞f(m+k-1)

So f (n+k)-f (n)＞f (m+k)-f (m).

So far, proposition f (n+k)-f (n)＞f (m+k)-f (m) must demonstrate,prove.

An implication of above-mentioned character 1 statement be exactly the new sequence that becomes of the poor equal Han Nuota ordered series of numbers array of Han Nuota ordered series of numbers middle term sequence number be monotonically increasing.

The ring length of LDPC code is defined as the length of the contained becate of its check matrix.Wherein, length is 4 ring having the greatest impact to the LDPC code performance.When shorter ring can cause deciphering, iterative information is cross-correlation after 2 iteration, the convergence of impact decoding.Therefore, the LDPC code that design performance is good will be eliminated the Fourth Ring at least.It is that 4 ring can be expressed as (j that the H matrix comprises length ₀, l ₀), (j ₀, l ₁), (j ₁, l ₁), (j ₁, l ₀), do not contain the necessary and sufficient condition at Fourth Ring according to check matrix, to (j arbitrarily ₀, l ₀) and (j ₁, l ₁), $(p_{j_0,l_0}-p_{j_0,l_1})+(p_{j_1,l_1}-p_{j_1,l_0})\≠0\mathrm{mod}p.$

Making the deviant of the cyclic permutation matrices of the capable l row of j among the basic matrix B of check matrix H is p _{J, l}=f (j+l)+j.P gets arbitrarily than the large value of numerical value maximum among the basic matrix B.Be without loss of generality, make j ₀＜j ₁, l ₀＜l ₁Then:

$(p_{j_0,l_1}-p_{j_0,l_0})=[f(j_0+l_1)+j_0]-[f(j_0+l_0)+j_0]=f(j_0+l_1)-f(j_0+l_0),$

$(p_{j_1,l_1}-p_{j_1,l_0})=[f(j_1+l_1)+j_1]-[f(j_1+l_0)+j_1]=f(j_1+l_1)-f(j_1+l_0).$

Utilize the character of above-mentioned Han Nuota ordered series of numbers as can be known:

[f(j ₁+l ₁)-f(j ₁+l ₀)]＞[f(j ₀+l ₁)-f(j ₀+l ₀)]，

Further can get:

$(p_{j_1,l_1}-p_{j_1,l_0})>(p_{j_0,l_1}-p_{j_0,l_0}),$

Namely

$(p_{j_1,l_1}-p_{j_1,l_0})+(p_{j_0,l_0}-p_{j_0,l_1})>0,$

Satisfy check matrix and do not contain the condition that length is 4 ring.Therefore, the ring length of the check matrix of design is at least 6.

Concrete constitution step is as follows:

1) determines line parameter J and the row parameter L of the basic matrix of check matrix to be designed.Suppose J=3, L=6, the basic matrix of structure is designated as B (3,6) so.

2) after definite ranks parameter, by all row of row traversal.For the position of the capable l row of the j of given basic matrix, by the Han Nuota ordered series of numbers definition: when n is 1, f (1)=1, when n greater than 1 the time, f (n+1)=2 * f (n)+1 obtains the item of each Han Nuota ordered series of numbers successively.For example: f (2)=2 * f (1)+1=3, f (3)=2 * f (2)+1=7 ....

3) by formula p _{J, l}=f (j+l)+j obtains the cyclic permutation matrices deviant p of this position _{J, l}Each f (j+l) value that (2) are obtained adds that the corresponding numerical value j that is expert at obtains cyclic permutation matrices deviant p _{I, j}, be placed on the position of the capable l row of the j of basic matrix of structure.For example, for the first row first row, p _1,1=f (2)+1=3+1=4; For the second row first row, p _2,1=f (3)+2=7+2=9; By that analogy, can obtain the p of the capable L row of all J _{J, l}Numerical value.

4) by above-mentioned all p _{J, l}The basic matrix of Construction designing.

1: one the basic matrix B (3,6) by the check matrix H (3,6) of said method structure is as follows for example.

$B\left(\mathrm{3,6}\right)=\left[\begin{array}{cccccc}4& 8& 16& 32& 64& 128\\ 9& 17& 33& 65& 129& 257\\ 18& 34& 66& 130& 258& 514\end{array}\right]$

Analyzing above-mentioned construction process can find, as long as system is the generator polynomial of storage Han Nuota ordered series of numbers and the general term formula of computation cycles permutation matrix deviant, when real system is used, can can generate by simple algebraic operation the basic matrix of corresponding check matrix, and do not need to the LDPC code based on array structure such, the cyclic shift number of times of each position of storage basic matrix.The following storage complexity difference of making a concrete analysis of the two.

Obviously, for the basic matrix that is of a size of J * L, be J * L=JL based on the storage complexity of the method for array structure.

Storage complexity based on the inventive method structure can be from formula p _{J, l}The computation complexity of=f (j+l)+j is considered.At first, calculating f (j+l) needs an adder, then, calculates p _{J, l}=f (j+l)+j needs an adder, therefore, and whole deviant p _{J, l}Calculating need two adders.Consider, the register number that needs is 2, and therefore, storage complexity of the present invention is 2.

The ratio of the complexity of two kinds of methods of contrast is

Therefore, along with the increase of basic matrix size, the reduced complexity effect that the present invention brings will increase gradually.

Simultaneously, simulation result shows, the quasi-cyclic LDPC code that the present invention constructs has performance boost about 3dB than array LDPC code.

Comprehensive above-mentioned conclusion shows, compares the code with array structure LDPC, the present invention when promoting the quasi-cyclic LDPC code performance, the reduction that has brought storage complexity.

Claims (3)

1. the building method of a quasi-cyclic LDPC code check matrix comprises the following steps:

(1) determines line parameter J and the row parameter L of the basic matrix of check matrix to be designed;

(2) after definite ranks parameter, by all row of row traversal; For the position of the capable l row of the j of given basic matrix, by the Han Nuota ordered series of numbers definition: when n is 1, f (1)=1, when n greater than 1 the time, f (n+1)=2 * f (n)+1 obtains the item of each Han Nuota ordered series of numbers successively;

(3) by formula p _{J, l}=f (j+l)+j obtains the cyclic permutation matrices deviant p of the capable l row of j _{J, l}, with the cyclic permutation matrices deviant p that obtains _{J, l}Be placed on the position of the capable l row of the j of basic matrix of structure;

(4) by above-mentioned all p _{J, l}The basic matrix of Construction designing.

2. the building method of a kind of quasi-cyclic LDPC code check matrix according to claim 1 is characterized in that: described step (1) if in J=3, L=6, the basic matrix of structure is designated as B (3,6) so

3. the building method of a kind of quasi-cyclic LDPC code check matrix according to claim 1 is characterized in that: adder of described step (3) calculating f (j+l) needs, calculating p _{J, l}=f (j+l)+j needs an adder, whole deviant p _{J, l}Calculating need two adders.