CN103236861B - A kind of method of trigonometric ratio under class of galois field LDPC check matrix - Google Patents
A kind of method of trigonometric ratio under class of galois field LDPC check matrix Download PDFInfo
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Abstract
The present invention relates to LDPC code coding techniques field, specifically refer to and the LPDC code check matrix of a non-square matrix is farthest converted into class lower triangular structure, strengthen the anti-noise ability of LDPC code.The algorithm based on trigonometric ratio process under the LDPC check matrix class of galois field that the present invention proposes, comprises the following steps: a, check matrix is converted into stepped matrix; B, stepped matrix is converted into the matrix of class lower triangular structure; The object of the invention is to overcome above-mentioned deficiency existing in prior art, under guarantee does not change the openness prerequisite of LDPC check matrix, by basic elementary transformation, check matrix is converted into as much as possible the form of class lower triangular structure, to improve LDPC coding efficiency.
Description
Technical field
The present invention relates to LDPC code coding techniques field, specifically refer to and the LPDC code check matrix of a non-square matrix is farthest converted into class lower triangular structure, strengthen the anti-noise ability of LDPC code.
Background technology
In field of channel coding, LDPC code is the linear block codes that a class has sparse check matrix, not only have the superperformance of approaching Shannon limit, and decoding complexity is low, flexible structure, becomes the study hotspot of field of channel coding in recent years.
Mainly utilize Gaussian elimination by trigonometric ratio under check matrix or trigonometric ratio matrix class will be verified by elementary transformation (row-column transform) under in the method for LDPC code coding field process check matrix.Although Gaussian elimination method is simple, to sacrifice LDPC code performance for cost.And trigonometric ratio check matrix only carries out elementary transformation to check matrix under class, openness (in matrix, non-zero ∈ GF (q) element accounts for the ratio of matrix all elements) of not influence matrix, in LDPC coding, the openness of check matrix is one of most critical factor affecting encoder complexity and coding efficiency.
In the LDPC code coding of lower triangular form check matrix, the LDPC code noiseproof feature after the coding that under the class of check matrix, trigonometric ratio degree directly determines.Comparatively general is the Greedy_A algorithm proposed by ThomasJ.Richardson and RudigerL.Urbanke by the algorithm of trigonometric ratio under verification matrix class at present.
The drawback algorithm of trigonometric ratio under matrix class being eliminated Greedy_A algorithm and exist in this paper.By partitioning of matrix process, while guarantee check matrix is openness, obtain the higher check matrix of relative Greedy_A algorithm diagonalization degree.
Summary of the invention
The object of the invention is to overcome above-mentioned deficiency existing in prior art, under guarantee does not change the openness prerequisite of LDPC check matrix, by basic elementary transformation, check matrix is converted into as much as possible the form of class lower triangular structure, to improve LDPC coding efficiency.
In order to realize foregoing invention object, the invention provides following technical scheme:
The core concept of technical scheme of the present invention carries out piecemeal process to check matrix exactly, 0 ∈ GF (q) in matrix is moved to the upper right side of matrix as much as possible, to be converted into stepped matrix, the basis of echelon matrix is carried out trigonometric ratio process under class.
Being achieved through the following technical solutions of this algorithm:
A method for trigonometric ratio under the class of the LDPC check matrix of galois field, under matrix class, trigonometric ratio process comprises following two processes:
A, check matrix is converted into stepped matrix.
B, stepped matrix is converted into the matrix of class lower triangular structure.
Wherein step a is the committed step of this algorithm, embodies the core technology scheme of this calculation, is the process of the different piece of matrix being carried out repeatedly to same operation, and defining these same operation is repeatedly pulling operation.
Pulling operation is carried out to the check matrix H (m × n) of a non-square matrix, two matrixes can be obtained.Be through respectively the new matrix H after row-column transform ' and the sub-matrix M of H'.The Main Function of pulling operation is exactly that verification matrixing is become preliminary stepped-style.
The particular content of explained later pulling operation:
The first step: all row first calculating described check matrix weigh (
) and all column weights (
).By matrix
row press
ascending order rearrange, by matrix
row press
descending rearrange.
Second step: according to
find out the row set of all column weight least members:
.
3rd step: to row set
in each row, look for all non-of these row
the row at element place, calculates the heavy sum of row of these row:
.
4th step: look for and arrange set
in,
these row are moved to matrix by minimum wherein row
last row.
5th step: by matrix
last row in all non-
the row at element place moves to matrix bottom.
So just, obtain new matrix H ' and his a sub-matrix M, M is the submatrix that H' removes all row of comprising non-zero ∈ GF (q) in last row and last row and obtains.
Through pulling operation check matrix change into new matrix H only containing a ladder ', and ensure that non-zero ∈ GF (q) element in H' tries one's best below matrix and left move.For class diagonalization process below provides favourable condition.
The detailed process of step a exactly to check matrix H carry out pulling operation obtain matrix H ' again pulling operation is carried out to the submatrix M of H', so repeat until cannot pulling operation position be carried out.By elementary transformation, former check matrix H will be converted into an echelon matrix.
The specific implementation process of step b is as described below:
The first step: last row finding out echelon matrix, that selects in these row is first non-
element is as starting point, and defining this element is
;
Second step: from
beginning travels through successively to matrix upper left side (
), judge that whether current element is
if fruit is, perform behaviour institute Y, otherwise executable operations N;
Wherein operate Y to be defined as:
The first non-of the element left side will be traveled through
element column exchanges with when prostatitis does to arrange.
Operation N is defined as:
Check in traversal element column, more than this element whether there is non-element, if existed, these are non-
element is expert at and is moved to matrix bottom, otherwise does not do any operation.
compared with prior art, beneficial effect of the present invention
One, the algorithm that the present invention announces exchanges only for exchanging with row and arrange all operations of matrix, can not affect the openness of LDPC coding checkout matrix.Use the LDPC coding checkout matrix after this algorithm process to carry out LDPC coding, the noiseproof feature of information sequence can be made to obtain and promote by a relatively large margin.
Two, this algorithm principle easy to understand, implementation procedure is simple.Because he only carries out basic ranks swap operation to check matrix.No matter be software emulation or hardware implementing, be all easy to realize.
Three, compared with comparatively general with current use Greedy_A algorithm, this algorithm eliminates the leak that Greedy_A algorithm exists, and performance is better than Greedy_A algorithm completely.
Four, this algorithm has certain versatility, binary system galois field and multi-system galois field all applicable.
Accompanying drawing explanation
Fig. 1 is the pulling operation schematic diagram of this algorithm steps a.
Fig. 2 is the performing step figure of this algorithm steps a.
Fig. 3 is this algorithm flow chart.
Fig. 4 is pulling operation flow chart.
Fig. 5 is this algorithm steps a flow chart.
Fig. 6 is this algorithm steps b flow chart.
Fig. 7 is Greedy_A algorithm schematic diagram in background technology.
Fig. 8 is for weighing check matrix class diagonalization degree g definition.
Fig. 9 is Greedy_A algorithm g mean value compare in this algorithm and background technology.
Figure 10 is Greedy_A algorithm g variance contrast in this algorithm and background technology.
Embodiment
Below in conjunction with test example and embodiment, the present invention is described in further detail.But this should be interpreted as that the scope of the above-mentioned theme of the present invention is only limitted to following embodiment, all technology realized based on content of the present invention all belong to scope of the present invention.
As shown in Figure 3, a kind of method of trigonometric ratio under class of LDPC check matrix of galois field, under matrix class, trigonometric ratio process comprises following two processes:
A, check matrix is converted into stepped matrix.
B, stepped matrix is converted into the matrix of class lower triangular structure.
As shown in Figure 2, wherein step a is the committed step of this algorithm, embodies the core technology scheme of this calculation, is the process of the different piece of matrix being carried out repeatedly to same operation, and defining these same operation is repeatedly pulling operation.
Pulling operation is carried out to the check matrix H (m × n) of a non-square matrix, two matrixes can be obtained.Be through respectively the new matrix H after row-column transform ' and the sub-matrix M of H'.The Main Function of pulling operation is exactly that verification matrixing is become preliminary stepped-style.
As Figure 1 and Figure 4, the particular content of explained later pulling operation:
The first step: all row first calculating described check matrix weigh (
) and all column weights (
).By matrix
row press
ascending order rearrange, by matrix
row press
descending rearrange.
Second step: according to
find out the row set of all column weight least members:
.
3rd step: to row set
in each row, look for all non-of these row
the row at element place, calculates the heavy sum of row of these row:
.
4th step: look for and arrange set
in,
these row are moved to matrix by minimum wherein row
last row.
5th step: by matrix
last row in all non-
the row at element place moves to matrix bottom.
So just, obtain new matrix H ' and his a sub-matrix M, M is the submatrix that H' removes all row of comprising non-zero ∈ GF (q) in last row and last row and obtains.
Through pulling operation check matrix change into new matrix H only containing a ladder ', and ensure that non-zero ∈ GF (q) element in H' tries one's best below matrix and left move.For class diagonalization process below provides favourable condition.
As shown in Figure 5, the detailed process of step a exactly to check matrix H carry out pulling operation obtain matrix H ' again pulling operation is carried out to the submatrix M of H', so repeat until cannot pulling operation position be carried out.By elementary transformation, former check matrix H will be converted into an echelon matrix.
As shown in Figure 6, the specific implementation process of step b is as described below:
The first step: last row finding out echelon matrix, that selects in these row is first non-
element is as starting point, and defining this element is
;
Second step: from
beginning travels through successively to matrix upper left side (
), judge that whether current element is
if fruit is, perform behaviour institute Y, otherwise executable operations N;
Wherein operate Y to be defined as:
The first non-of the element left side will be traveled through
element column exchanges with when prostatitis does to arrange.
Operation N is defined as:
Check in traversal element column, more than this element whether there is non-element, if existed, these are non-
element is expert at and is moved to matrix bottom, otherwise does not do any operation.
The present invention no matter from theoretical level analysis or from actual performance two aspect the performance of relatively this algorithm and Greedy_A algorithm.The conclusion that this algorithm is better than Greedy_A algorithm can be obtained.
First sketch the thought of Greedy_A algorithm, as shown in Figure 7, mainly comprise three steps:
(1) for a check matrix A, following process is done to often row wherein: be declared as pivot column with the probability of 1 α (α ∈ (0,1)) independently, otherwise, be declared as delete columns, deleted.Order=A.
(2) judge whether to terminate.If both not pivot column in A, do not have yet weight be 1 row, current matrix is exported, terminates.Otherwise, perform diagonal angle and extend step.
(3) pivot column is announced.By in 1 in the row that are connected of row be declared as pivot column.Return the 2nd step.
Diagonal angle extends the core that step is Greedy_A algorithm.Suppose there is now a matrix A, and some row wherein are declared as pivot column.Our interested situation is nothing more than two kinds: otherwise these in pivot column neither one be with weight be 1 row be connected; These pivot column be all with weight be 1 row be connected.Here, r is capable to be connected with c row, refers to A
rc=1.Consider the previous case (this is also often situation when just starting), make row and exchange, make all pivot columns become the prostatitis of A.Then delete these row, using remaining matrix as.Consider latter event, if c
1..., c
kpivot column, r
1..., r
k1 heavy row, and c
iand c
iconnected.Rearrange these row and columns and make c
1..., c
kand r
1..., r
kthe front k row and the front k that become A are capable.Now, in A, k × k submatrix in the upper left corner is unit matrix, and the capable every provisional capital of front k only has a nonzero element.
Although matrix can be changed near lower triangular form by Greedy_A algorithm.But there is a very large leak.
Be exactly when second step is adjudicated, if there is no pivot column, and can not find the row that row is heavily 1, then directly export current matrix and terminate algorithm.But this does not represent matrix can not continue diagonalization, waste very large diagonalizable space.Lift this algorithm leak of counter-example proof:
Such as matrix
Clearly this matrix is can be diagonalizable.If but according to the flow process of Greedy_A algorithm.Obtain matrix through second step, due to he not row be heavily the row of 1, the 3rd step announce known row time would not announce to there is pivot column.Both do not have pivot column when so returning second step judgement, also row is not heavily the row of 1.He will directly export, and can not continue diagonalization.So just having wasted 4 row can diagonalizable resource.
But according to the design philosophy of this algorithm, perform in strict accordance with algorithm flow.This special matrix can continue diagonalization and operates and obtain final class lower triangular structure matrix:
Weigh the standard of LDPC check matrix class diagonalization degree mainly to the T dimension of inferior triangular flap after check matrix piecemeal.Under we g weighs check matrix class, triangle talks about degree, and the dimension dimension that g is defined as check matrix line number and T is poor, sees accompanying drawing 8.Obvious g is less, and under check matrix class, trigonometric ratio degree is better.
For relatively this algorithm and Greedy_A performance gap.Simulating, verifying is carried out under MATLAB7.10.0 (R2010a) platform.Choosing code check is 0.5, and code length is by 200 to 2000 changes.Increase by 200 code lengths successively.Often kind of code length emulates 100 frames, the equal stochastic generation of check matrix of every frame.With two kinds of algorithms, class diagonalization process is carried out to check matrix.Average and variance process are done to g after the check matrix class diagonalization of often kind of code length.Relatively connect distribution performance difference.The results are shown in following table and accompanying drawing 9, accompanying drawing 10.
By table 1 and accompanying drawing 9, accompanying drawing 10 can be found out.Along with the increase of matrix dimension, under class, the g of trigonometric ratio matrix progressively rises.Relatively this algorithm and Greedy_A algorithm, the g average under this class of algorithms after trigonometric ratio matrix is significantly less than Greedy_A algorithm.In addition the g variance of this algorithm is also less than Greedy_A algorithm.Illustrate this algorithm not only performance be better than Greedy_A algorithm.And stability is also higher than Greedy_A algorithm.
Claims (1)
1. a method for trigonometric ratio under the class of the LDPC check matrix of galois field, is characterized in that, comprise the following steps:
A, check matrix is converted into stepped matrix;
B, stepped matrix is converted into the matrix of class lower triangular structure;
Described step a is specially: carry out repeatedly identical operating process to the different piece of described check matrix, and described operating process is pulling operation process
;
The process of pulling operation described in step a is specially:
The first step: all row first calculating described check matrix weigh (
) and all column weights (
);
By matrix
row press
ascending order rearrange, by matrix
row press
descending rearrange;
Second step: according to
find out the row set of all column weight least members:
;
3rd step: to row set
in each row, find out all non-of these row
the row at element place, calculates the heavy sum of row of these row:
;
4th step: find out row set
in,
these row are moved to matrix by minimum wherein row
last row;
5th step: by matrix
last row in all non-
the row at element place moves to matrix bottom
;
Described step b is specially:
The first step: last row finding out stepped matrix, that selects in these row is first non-
element is as starting point, and defining this element is
;
Second step: from
start to travel through successively to matrix upper left side
, judge that whether current element is
, if so, will the first non-of the element left side be traveled through
element column exchanges with when prostatitis does to arrange; If not, check in traversal element column, more than this element whether exist non-
element, if existed, these are non-
element is expert at and is moved to matrix bottom, otherwise does not do any operation.
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