CN102843145A - Construction method of low bit-rate quasi-cyclic accumulative repeat accumulate codes - Google Patents
Construction method of low bit-rate quasi-cyclic accumulative repeat accumulate codes Download PDFInfo
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Abstract
The invention provides a construction method of low bit-rate quasi-cyclic accumulative repeat accumulate codes, wherein an accumulative repeat accumulate code protograph, a check node expanding by a linear block code check matrix, a basic check matrix corresponding to a basic bipartite graph and a cyclic offset searching method of quasi-cyclic approximate cycle extrinsic message degree are comprised. The construction method comprises the following steps of: constructing a basic accumulative repeat accumulate code protograph; expanding the check node of the accumulative repeat accumulate code protograph by using the linear block code check matrix; carrying out copying and repeating processing for eliminating multiple edges to obtain the basic bipartite graph; converting the basic bipartite graph into a matrix, and carrying out square matrix expansion on data in the matrix to obtain a quasi-cyclic matrix; and carrying out optimized searching on cyclic offset of a non-zero cyclic square matrix by using a quasi-cyclic approximate cycle extrinsic message degree method and finishing encoding. The low bit-rate quasi-cyclic accumulative repeat accumulate codes constructed by the construction method disclosed by the invention have the advantages of high performance, moderate complexity, simple encoding and decoding structure and the like and can be applied to a channel encoding occasion in the digital communication field.
Description
Technical field
The present invention relates to digital communication technology field, the accurate circulative accumulation of particularly a kind of low code check structuring repeats to accumulate the building method of sign indicating number.
Background technology
The wireless communication transmissions channel mainly contains channels such as white Gaussian noise channel, Rayleigh channel.Transmission information in these channels needs to adopt chnnel coding to realize the higher quality of reception.The class Turbo code of at present, encoding and mainly containing turbine (Turbo) sign indicating number, low density parity check code (LDPC) sign indicating number and combine the two characteristic near the modern high performance of shannon limit.
Turbo code is the channel code near shannon limit.It mainly constructs thinking is how to optimize interleaver parameter and component code, to obtain the flat decoding scheme with low complex degree of low bit error.Wherein, the flat finger of error code is in the channel code ber curve, and the error rate increases the phenomenon that descends slowly or do not descend with signal to noise ratio.But, this coding mainly exist decoding complexity higher with problems such as error code is flat, the method for simplifying that can only adopt poor-performing perhaps adopts the outer sign indicating number of cascade to overcome the scheme of the flat grade of error code to reduce complexity.The LDPC code performance also can be near shannon limit, and its decoding is fast, is prone to realize and has advantages such as low bit error is flat.This sign indicating number adopts iterative manner decoding, and all available bipartite graph of coding and decoding process is represented and analyzed.Aspect the LDPC code construction,,, will cause the self feed back of iteration information and influence decoding performance as in its bipartite graph, having becate because of it adopts iterative decoding.To this principle, industry adopts heuristic increase limit to construct bipartite graph and reduces progressive edge-growth (PEG) method of becate, carries out the optimization structure of such code check matrix.In addition, the decoding performance of this yard is also with to stop collection (describe ring distribute) characteristics etc. relevant in its bipartite graph.So through outer message degree (ACE) method of the approximate ring that improves ring distribution character in the bipartite graph, can't avoid under the situation about encircling, can optimize its check matrix of structure.But the LDPC encoder complexity is higher usually, is difficult to Project Realization.
The full complexity of LDPC sign indicating number at random that performance is good becomes quadratic relation with code length.Long code length will cause that coding is too complicated and be difficult to realize.Solution is exactly to adopt the class Turbo code that has low encoder complexity of Turbo code and the low decoding complexity of LDPC sign indicating number concurrently.This type sign indicating number mainly contains irregular accumulation (ARA) sign indicating number and the accurate circulation QC-LDPC sign indicating number etc. of repeating.In addition, also has one type of structuring generalized L DPC sign indicating number through method constructs such as expansion linear block codess.This sign indicating number also has design and easy analysis, the characteristics of excellent performance, and in the structured LDPC code construction, obtained extensive use.On ARA sign indicating number basis, one type of low complex degree and the flat AR4JA sign indicating number of low bit error have also been developed based on the protograph structure.This yard adopts protograph to construct the framework of check matrix, and expanded this framework, constructs whole check matrix with the structuring square matrix of several A RA sign indicating number.Wherein, protograph is basic bipartite graph prototype.It can obtain the corresponding bipartite graph of yard matrix through expansion.In addition, on ARA sign indicating number basis, also can be through the permutatation of different accumulative frequencies and the verification and the order that adds up, construct the good comprehensive properties structuring accumulation sign indicating number that repeats to interweave.This series class Turbo code better performances, implementation complexity is moderate, but only limits to design high code check sign indicating number, is difficult to construct high performance low code check sign indicating number, so can not adapt to the application scenario demand of low signal-to-noise ratio communications such as space, satellite communication.
In a word, be that the channel code of representative has huge application potential with the class Turbo code.With respect to Turbo and LDPC sign indicating number, such yard has the decoding performance near shannon limit, and decoding speed is fast, be prone to realize and to have an extremely low error code flat, and also is up to now near one of channel code of shannon limit.Because above-mentioned advantage, they have been applied to fields such as radio communication (comprising terrestrial wireless, satellite communication etc.), WLAN and metropolitan area network, like DVB-S2, and standards such as IEEE802.11n and IEEE 802.16e.Renowned company also all begins one's study and develops this sign indicating number both at home and abroad, and produces related chip.But such code constructing method also needs further to improve, so that can construct the low code check sign indicating number of high-performance, and adapts to the application scenario of low signal-to-noise ratio communication.
Summary of the invention
The objective of the invention is to have low coding and decoding complexity and high bit error performance defect and deficiency simultaneously, provide the accurate circulative accumulation of a kind of low code check to repeat to accumulate code constructing method to existing low code check chnnel coding.
The objective of the invention is to realize by the following technical programs: the accurate circulative accumulation of a kind of low code check structuring repeats to accumulate the building method of sign indicating number, and this method may further comprise the steps realization:
(1) selects the long linear block codes of short code,, it is mapped as the bipartite graph structure of standard according to its check matrix; Mapping process is following: with the line label of check matrix, as the check-node in the bipartite graph; With the row label of check matrix, as the variable node in the bipartite graph; There are data 1 in crossover location like line label be expert in check matrix and row label place row, then line of increase between the corresponding check-node of line label and the corresponding variable node of row label; All be mapped as a line in the bipartite graph up to all data 1 of matrix;
(2) accumulation of structure high-performance repeats accumulation sign indicating number protograph, and with a check-node in this protograph, the compound check-node H that forms with all check-nodes of step 1 gained bipartite graph replaces, and obtains compound protograph G; Wherein, the fillet quantity of this compound check-node H and variable node is constant with relation, but the limit can be multiple limit, makes limit number between variable and check-node greater than 1; In addition, compound check-node H except with former figure in the limit annexation of variable node, also need increase the Partial Variable node, its quantity and relation with outer edge fit is remained unchanged;
(3) according to the tuple on different multiple limits among the compound protograph G of step 2 gained, calculate their least common multiple
k, and
kBe integer; Copy step 2 gained protographs
kIndividual, eliminate multiple limit through following method, obtain compound bipartite graph F: keep the numbering of two ends, limit institute connected node constant, but numbering can belong to the copy of a compound protograph G arbitrarily, make the multiple limit in the different protographs be able to eliminate;
(4) on the compound bipartite graph F basis of step 3 gained; Compound check-node H and annexation thereof are launched: with all check-nodes in the corresponding bipartite graph of step 1 neutral line block code; Be updated to the compound check-node H among the compound bipartite graph F: with the limit annexation of all verifications and variable node in the step 1 gained bipartite graph; Replace compound check-node H and the limit annexation of variable node among this compound bipartite graph F, obtain benchmark bipartite graph S;
(5) mapping relations of employing described matrix of step 1 and bipartite graph; According to the variable of the benchmark bipartite graph S of step 4 gained and the annexation between check-node; Be converted into basic matrix, and, be mapped as complete zero square matrix or the unit circulation square matrix of certain dimension respectively the data in this matrix 0 and 1; Obtain the check matrix that the final required accurate circulative accumulation of low code check structuring repeats to accumulate sign indicating number, accomplish code construction; Wherein, said unit circulation square matrix is 1 for diagonal data in this square matrix, and other data are 0 unit square formation, the matrix that behind the some positions of ring shift right, obtains, and the figure place of ring shift right is designated as the cycle offset parameter; Said ring shift right is: data line is kept the constant some position of moving to right of order, and will shift out the data of this row, add in some that this row Far Left is available because of moving to right by order.
The invention has the beneficial effects as follows; The accurate circulative accumulation of using method construct of the present invention repeats accumulation sign indicating number moderate complexity, better performances; Coding and decoding postpones few, can be widely used in being fit to the digital communicating fields such as terrestrial wireless emergency communication, satellite and deep space communication of low signal-to-noise ratio transmission.
Description of drawings
Last additional content and the characteristics addressed of the present invention will become obviously, understand easily and implement in below in conjunction with the description of accompanying drawing to embodiment, wherein:
Fig. 1 repeats to accumulate the protograph of sign indicating number for the typical high-performance accumulation of the existing method construct of embodiment of the invention utilization;
Fig. 2 is the structure chart of embodiment of the invention Hamming code (7,3,4) matrix and corresponding bipartite graph;
Fig. 3 adopts the polygon structure chart of Hamming code (7,3,4) check matrix expansion among Fig. 2 embodiment for embodiment of the invention high-performance accumulation shown in Figure 1 repeats accumulation sign indicating number protograph;
Fig. 4 the present invention is directed to embodiment expansion protograph shown in Figure 2, in order to eliminate its multiple limit, and duplicates the structure chart with duplicate node and annexation thereof;
Fig. 5 is for the present invention is directed to embodiment structure chart shown in Figure 4, the expander graphs of gained after eliminating compound check-node, and the corresponding basic check matrix and the structure chart of accurate cyclic check matrix;
Fig. 6 is the flow chart of the cycle offset parameter optimization searching method of the outer message degree of the approximate ring of accurate circulation in the embodiment of the invention accurate cycle basis matrix shown in Figure 5.
Embodiment
The present invention proposes the building method that the accurate circulative accumulation of a kind of low code check structuring repeats to accumulate sign indicating number; Mainly comprise following process: utilize existing heuristic optimization method (method see " A. Abbasfar, K. Yao and D. Disvalar, " Accumulate repeat accumulate codes; " In Proc. IEEE Globalcom; Nov. 2004, pp. 509-513. "), construct basic high-performance accumulation and repeat accumulation (ARA) sign indicating number protograph; According to required code check; Some check nodes in this protograph are expanded with the long linear block codes of short code (like code length less than 15 Hamming code) check matrix, i.e. the expansion of this node adopts the restriction relation of different code length, code check linear block codes check matrix to realize; This expansion back protograph is eliminated duplicating of multiple limit and reprocessing, obtain basic bipartite graph, but the annexation of check-node and variable node remains unchanged all; To the protograph after this expansion; Convert the corresponding check matrix into; And these matrix equation data are carried out square matrix expansion, with 0,1 be mapped as certain dimension respectively complete zero or unit circulation square matrix (be the some positions of unit matrix ring shift right after matrix), obtain accurate circular matrix.At last, the cycle offset parameter in the expansion gained check matrix non-zero circulation square matrix with the outer message degree method of the approximate ring of accurate circulation, is optimized search, obtains the check matrix that the low accurate circulative accumulation of code check structuring repeats to accumulate sign indicating number, accomplishes coding.The present invention is through basic protograph design; Expansion is eliminated on expansion of protograph node and multiple limit; The accurate cyclic node mapping of expansion back protograph; The methods such as the outer message degree of the approximate ring of accurate circulation selection of cycle offset have been constructed the accurate circulative accumulation of low code check structuring that implementation complexity is low, error performance is higher and have been repeated the accumulation sign indicating number in the accurate circulation square matrix.
The present invention proposes the building method that the accurate circulative accumulation of a kind of low code check structuring repeats to accumulate sign indicating number, this method specifically may further comprise the steps:
1, selects the long linear block codes (code length is less than 15) of short code,, it is mapped as the bipartite graph structure of standard according to its check matrix; Mapping process is following: with the line label of check matrix, as the check-node in the bipartite graph; With the row label of check matrix, as the variable node in the bipartite graph; There are data 1 in crossover location like line label be expert in check matrix and row label place row, then line of increase between the corresponding check-node of line label and the corresponding variable node of row label; All be mapped as a line in the bipartite graph up to all data 1 of matrix.
2, use existing heuristic optimization method (method see " A. Abbasfar, K. Yao and D. Disvalar, " Accumulate repeat accumulate codes; " In Proc. IEEE Globalcom; Nov. 2004, pp. 509-513. ") construct the high-performance accumulation and repeat accumulation (ARA) sign indicating number protograph, with a check-node in this protograph; use the compound check-node H replacement of forming by all check-nodes of step 1 gained bipartite graph; obtain compound protograph G, and H, G is respectively compound check-node and compound protograph label.Wherein, the fillet quantity of this compound check-node H and variable node is constant with relation.But the limit can be multiple limit, makes limit number between variable and check-node greater than 1.In addition, compound check-node H except with former figure in the limit annexation of variable node, also need increase the Partial Variable node, its quantity and relation with outer edge fit is remained unchanged.
3, according to the tuple on different multiple limits among the compound protograph G of step 2 gained (as
NHeavy limit, then tuple does
N), calculate their least common multiple
k, and
kBe integer; Copy step 2 gained protographs
kIndividual; Eliminate multiple limit through following method; Obtain compound bipartite graph F (F is compound bipartite graph label): keep the numbering of two ends, limit institute connected node constant, but numbering can belong to the copy of a compound protograph G arbitrarily, make the multiple limit in the different protographs be able to eliminate.For example, protograph G comprises the double limit of variable node A and check-node B, and A and B are nodal scheme.Copy G through protograph G
1With G
2Exchange double limit wherein makes G
1In limit and the G of node A
2Middle Node B links to each other, and G
2In limit and the G of node A
1Middle Node B links to each other, and G
1And G
2Label for figure.So can eliminate this multiple limit keeping two ends, limit node serial number to concern on the basis of invariable.
4, on the compound bipartite graph F basis of step 3 gained, compound check-node H and annexation thereof are launched:, be updated to the compound check-node H among the compound bipartite graph F all check-nodes in the corresponding bipartite graph of step 1 neutral line block code; With the limit annexation of all verifications and variable node in the step 1 gained bipartite graph, replace compound check-node H and the limit annexation of variable node among this compound bipartite graph F, obtain benchmark bipartite graph S, and S is the label of benchmark bipartite graph.
5, adopt the mapping relations of described matrix of step 1 and bipartite graph; According to the variable of the benchmark bipartite graph S of step 4 gained and the annexation between check-node; Be converted into basic matrix; And with the data in this matrix 0 and 1, complete zero square matrix or the unit circulation square matrix that are mapped as certain dimension respectively are (promptly
t*
tThe dimension matrix,
tBe integer, and
t>1), obtains the check matrix that the final required accurate circulative accumulation of low code check structuring repeats to accumulate sign indicating number, accomplish code construction.Wherein, said " unit circulation square matrix " is 1 for diagonal data in this square matrix, and other data are 0 unit square formation, the matrix that behind the some positions of ring shift right (being designated as the cycle offset parameter), obtains; Said " ring shift right " is: data line is kept the constant some position of moving to right of order, and will shift out the data of this row, add in some that this row Far Left is available because of moving to right by order.
In the said step 5, the cycle offset parameter that unit circulation square matrix moves to right, through the outer message degree method of the approximate ring of accurate circulation, adopt following steps to realize:
5.1, the initialization of parameter: preset all variable and check-nodes are live-vertex; The every capable square matrix number of blocks that the low accurate circulative accumulation of code check structuring repeats to accumulate the check matrix of sign indicating number does
m, every row square matrix number of blocks does
n, and
mWith
nBe natural number; In outer message degree (ACE) parameter of the progressive ring of coding, the girth of maximum loop does
d ACE , the long ACE value of minimum ring does
η ACE , and
d ACE With
η ACE Be natural number, establish
iBe the parameter of cycle count,
i=
n-1, and be integer;
5.2, establish
jBe the parameter of cycle count,
j=0, and be integer;
5.3, carry out following steps successively: non-0
iRow, the
jFirst row of the square matrix data block of row produces variable node at random
v i , and
v i Be label, be no more than the one dimension dimension in the square matrix; Calculate variable node
v i ACEValue:
ACE(
v i )=(
d i -2); Wherein,
d i Be variable node
v i Degree, be integer; Check-node
ACEValue is 0, and the ACE of certain ring or a limit institute pie graph is expressed as: ∑
i (
d i -2), and
d i Be all variable nodes in ring or the limit
v i Degree; For all variablees and check-node
μ t , initial setting up:
p(
μ t (∞ can use bigger number to)=∞, as 10
4, replace).Wherein,
μ t Label for variable or check-node; For variable node
v i , initial setting up:
p(
v i )=
ACE(
v i ).
5.4, establish
kBe the parameter of cycle count,
k=1, and be integer;
5.5, for (
k-1) any live-vertex of layer
w s , search this node adjacency subclass
Ch(
w s ); Wherein, the notion of layer is: with node
w s Be root node, node that in bipartite graph, obtains after the tree-like expansion and root node
w s Between the number on limit;
Ch(
w s ) be and root node
w s The set of all nodes that link to each other; In addition, the tree-like term that expands into graph theory is the figure that a plurality of annexations is arranged to; Launch successively by node, promptly choose wherein some nodes, node that the limit is connected is arranged as its child node with this node as the 1st layer tree root; Enumerate at the 2nd layer, then at the 3rd layer, except the joint of in tree graph, having enumerated; With the 2nd layer of node that all nodes link to each other as the 3rd layer, and the like enumerate until whole nodes and finish; For any child node
μ t ∈
Ch(
w s ), operation below carrying out: calculate
p Temp =
p(
w s )+
ACE(
μ t ); Wherein,
p(
μ t ) function definition is: root node and aleatory variable or check-node
μ t Between the summation of all node ACE values; Step 5.3 is seen in the calculating of ACE value;
p Temp Be temporary variable, be real number; Judge inequality:
p Temp +
p(
μ t )-
ACE(
v i )-
ACE(
μ t )<
η ACE Set up like the result, then forward step 5.1 to, otherwise forward step 5.6 to.
5.6, judge inequality:
p Temp >=
p(
μ t ); Set up like the result, then at current parent's node
w s kIn the layer, revise child node
μ t Be non-live-vertex, otherwise calculate
p(
μ t )=
p Temp
5.7, determining step 5.5 described child nodes
μ t ∈
Ch(
w s ), whether all calculated.As calculated, forward step 5.8 to, otherwise, forward step 5.5 to, to the child node of not calculating, continue to calculate.
5.8, the parameter of minute book second son circular matrix side-play amount.
5.9, judge inequality: for length≤2
d ACE Ring, its
ACEValue<
η ACE If set up, forward step 5.3 to, otherwise calculate
k=
k + 1.
5.10, judge inequality:
k≤
d ACE As setting up, forward step 5.5 to, otherwise: calculate
j=
j + 1.
5.11, judge inequality:
j≤
m-1; If set up, forward step 5.2 to, otherwise calculate
i=
i-1.
5.12, judge inequality:
i>=0.If set up, forward step 5.2 to, otherwise search for the process success of all cycle offsets, the parameter of all circular matrix side-play amounts of record is the required offset parameter of whole matrix.
Below through specific embodiment and combine accompanying drawing that the present invention is described in further detail
The building method that the accurate circulative accumulation of low code check structuring provided by the present invention repeats to accumulate sign indicating number can be applicable to the design and construction of the low code check structured low density parity check code of high-performance, is not limited to the field that following examples specify.Embodiment of the present invention can specify through following legend successively.
As shown in Figure 1; For adopt in the embodiment of the invention existing method (method see " A. Abbasfar, K. Yao and D. Disvalar, " Accumulate repeat accumulate codes; " In Proc. IEEE Globalcom; Nov. 2004, pp. 509-513. "), the basic high-performance accumulation of being constructed repeats to accumulate the representative instance of yard protograph.The essence of this method is to adopt heuristic receipts Suo Fangfa, utilizes the means of modern analysis decoding thresholds such as Gaussian approximation, and the protograph of being searched for is carried out the prediction of decoding threshold, can obtain the notional result very approaching with actual performance, conveniently further expands.Wherein, comprise the circle expression variable node of equal sign, and circumference be solid line be variable or the check bit that needs transmission, and circumference be dotted line be non-transmission deletion of node; The box indicating check-node that comprises plus sige.
As shown in Figure 2, be Hamming code in the embodiment of the invention (7,3,4) pairing check matrix and bipartite graph.Wherein, check-node is shown in the variable node in the line display bipartite graph of check matrix, tabulation.There is annexation with the 1 expression row corresponding variable node at place, row crosspoint in row with the corresponding check-node of row in the check matrix, promptly has a corresponding fillet of numbering.Specifically, can from figure, the annexation shown in left side row matrix column number and the right bipartite graph find out its corresponding relation.
As shown in Figure 3, be the representative instance of in the embodiment of the invention some check nodes in the protograph shown in Figure 1 being expanded with the corresponding check matrix of common efficient linear block code.Wherein, the high-performance linear block codes can adopt linear block codess such as Hamming code.In the present embodiment, with the typical linear block code---Hamming code shown in Figure 2 (7,3,4) is an instance, carries out the protograph expansion.In expansion process, need to satisfy the relation of the variable check-node wiring quantity that increases Hamming code newly.Because by shown in Figure 2, Hamming code (7,3; 4) all check-nodes link to each other with 7 variable nodes altogether, so the Hamming code (7,3 after the expansion; 4) annexation of compound check-node H and variable node also need comprise 7 limits, specifically comprises the variable node p of new expansion
2~ p
54 limits, with deletion of node s
012 heavy limit, and with former variable node p
01 limit.Wherein, p
2~ p
5, s
0, H is a label.
As shown in Figure 4, in the embodiment of the invention to the protograph after the expansion shown in Figure 3, eliminate duplicating and duplicate node and annexation of multiple limit, obtain the typical structure of basic bipartite graph.The specific descriptions of this process are following: because in this basic protograph, the number of repetition on maximum multiple limit is 2.So, at first will this basic protograph, duplicate 2 times, and in different copy backups,, name by sequence number respectively part of the variable node in the protograph and check-node part.Then; With the annexation on original multiple limit,, break up multiple limit by identical sequence number contrast relationship; Make multiple limit respectively in two protograph copies; Interconnection obtains common bipartite graph (being that the Tanner schemes) annexation that variable and check-node link to each other one by one, thereby eliminates multiple limit.
As shown in Figure 5, in the embodiment of the invention to bipartite graph shown in Figure 4, its composite node is carried out the expansion of check-node, the common LDPC sign indicating number bipartite graph structure of being shone upon one by one, and convert the representative instance of check matrix one to one into.Wherein, the corresponding check equations (row in the matrix) of check-node, variable node corresponding bit node (row in the matrix), and verification and variable node have the correspondence position of line, places data 1, otherwise placement data 0.In addition; Also to shown in data in the basic check equations carry out the square matrix expansion; Promptly be mapped as certain dimension complete zero or unit circulation square matrix with 0,1 respectively and (be about to that the data in the diagonal are 1 in the matrix; And the circular matrix that obtains behind other data some positions that are 0 unit square formation ring shift right), required to the end accumulation repeats to accumulate the accurate cyclic check matrix of sign indicating number, accomplish cataloged procedure.Wherein, 0 draw in the matrix of the lower right corner
IBe respectively complete 0 square matrix and circulation square matrix, and the circulation square matrix
IBe the matrix behind the some positions of unit matrix ring shift right, and the offset parameter of institute's ring shift right, adopt method shown in Figure 6 to obtain.
As shown in Figure 6, in the embodiment of the invention cycle offset of non-zero circulation square matrix in the accurate circular matrix shown in Figure 5 being optimized the representative instance flow chart of search.This optimization searching method is following:
1) term definition of method and explanation:
(1) father node and child node: in figure, represent that respectively the node of current layer reaches the node of the following one deck that links to each other with this node with tree-shaped arrangement.In this method is described, do as describing father node
w s , then its corresponding child node set does
Ch(
w s );
(2) node
v i Be the variable node in the LDPC sign indicating number; Node
μ t Be the check-node in the LDPC sign indicating number;
(3) degree of variable node definition: be the number of the check-node that links to each other with certain variable node; The degree of check-node is defined as: the number of the variable node that links to each other with certain check-node;
(4) each LDPC basic parameter that sign indicating number has (
d ACE ,
η ACE ), represent in the graph structure of this LDPC sign indicating number, as the girth with maximum loop does
d ACE , the long ACE value of circlet then must be arranged
η ACE
(5)
p(
μ t ) function definition is: root node and aleatory variable or check-node
μ t Between the summation of all node ACE values;
(6) in the corresponding self-loopa matrix of LDPC sign indicating number, laterally non-zero matrix-block maximum number does
n, vertically the maximum number of non-zero matrix-block does
m
(7) in this method is described,
d ACE ,,
η ACE ,
i,
n,
m,
j,
d i ,
kBe integer,
v i ,
μ t ,
w s Be identifier,
p Temp Be real number, " label redo " changes the used label of control for method.In addition, descriptive statements such as " for ", " if-else if-else " are accomplished the function that circulation and condition are selected respectively; " begin-end " pseudo-code descriptive statement is supporting sub-function module, promptly does as a whole in structured statements such as circulation, being able to and handles.
2) method is described:
for(
i=
n-1;
?i>=0;?
i--)
begin
for(
j=0;?
j≤
m-1;?
j++)
begin
Label redo:
According to the distribution of accurate circulation square matrix, first row in this non-zero square matrix produces variable node at random
v i , promptly select the side-play amount of place line data 1 at random; Preset all nodes are live-vertex;
Calculate variable node
v i ACE, be designated as
ACE(
v i ), be expressed as:
ACE(
v i )=(
d i -2).Wherein,
d i Be variable node
v i Degree, check-node
ACEValue is 0, and the ACE of certain ring or a limit institute pie graph is expressed as: ∑
i (
d i -2), and
d i Be all variable nodes in ring or the limit
v i Degree;
For all variablees and check-node
μ t , be provided with:
p(
μ t ) ← infinitely great ∞;
For variable node
v i , be provided with:
p(
v i ) ←
ACE(
v i );
for?(
k?=1;?
k≤
d ACE ;?
k++)
begin
For (
k-1) any live-vertex of layer
w s
begin
Search this node adjacency subclass
Ch(
w s );
For any child node
μ t ∈
Ch(
w s );
begin
p temp ?←?
p(
w s )?+?
ACE(
μ t )；
if p temp +
p(
μ t )-
ACE(
v i )-
?ACE(
μ t )<
η ACE
This searches for inefficacy, forwards this method section start again to and carries out search;
elseif
p temp ≥?
p(
μ t )
At current parent's node
w s kIn the layer, revise child node
μ t Be non-live-vertex;
else
p(
μ t )←
p temp ；
end；
end；
end；
This is searched for successfully, recording parameters;
IfFor length≤2
d ACE Ring, its
ACEValue<
η ACE
Forward to: label
Redo
end；
end。
Although described embodiments of the invention; But to those skilled in the art; Can under the situation that does not break away from the inventive method principle and thought, carry out multiple variation, modification, replacement and distortion to these embodiment, scope of the present invention is accompanying claims and be equal to and limit.Promptly through changing the linear block codes word of basic protograph in the method for the invention, expansion check-node, the dimension of basic square matrix, the parameters such as variation of cycle offset numerical value still belong to the category of the method for the invention, still receive this patent protection.
Claims (2)
1. one kind low accurate circulative accumulation of code check structuring repeats to accumulate the building method of sign indicating number, it is characterized in that this method may further comprise the steps realization:
(1) selects the long linear block codes of short code,, it is mapped as the bipartite graph structure of standard according to its check matrix; Mapping process is following: with the line label of check matrix, as the check-node in the bipartite graph; With the row label of check matrix, as the variable node in the bipartite graph; There are data 1 in crossover location like line label be expert in check matrix and row label place row, then line of increase between the corresponding check-node of line label and the corresponding variable node of row label; All be mapped as a line in the bipartite graph up to all data 1 of matrix;
(2) accumulation of structure high-performance repeats accumulation sign indicating number protograph, and with a check-node in this protograph, the compound check-node H that forms with all check-nodes of step 1 gained bipartite graph replaces, and obtains compound protograph G; Wherein, the fillet quantity of this compound check-node H and variable node is constant with relation, but the limit can be multiple limit, makes limit number between variable and check-node greater than 1; In addition, compound check-node H except with former figure in the limit annexation of variable node, also need increase the Partial Variable node, its quantity and relation with outer edge fit is remained unchanged;
(3) according to the tuple on different multiple limits among the compound protograph G of step 2 gained, calculate their least common multiple
k, and
kBe integer; Copy step 2 gained protographs
kIndividual, eliminate multiple limit through following method, obtain compound bipartite graph F: keep the numbering of two ends, limit institute connected node constant, but numbering can belong to the copy of a compound protograph G arbitrarily, make the multiple limit in the different protographs be able to eliminate;
(4) on the compound bipartite graph F basis of step 3 gained; Compound check-node H and annexation thereof are launched: with all check-nodes in the corresponding bipartite graph of step 1 neutral line block code; Be updated to the compound check-node H among the compound bipartite graph F: with the limit annexation of all verifications and variable node in the step 1 gained bipartite graph; Replace compound check-node H and the limit annexation of variable node among this compound bipartite graph F, obtain benchmark bipartite graph S;
(5) mapping relations of employing described matrix of step 1 and bipartite graph; According to the variable of the benchmark bipartite graph S of step 4 gained and the annexation between check-node; Be converted into basic matrix, and, be mapped as complete zero square matrix or the unit circulation square matrix of certain dimension respectively the data in this matrix 0 and 1; Obtain the check matrix that the final required accurate circulative accumulation of low code check structuring repeats to accumulate sign indicating number, accomplish code construction; Wherein, said unit circulation square matrix is 1 for diagonal data in this square matrix, and other data are 0 unit square formation, the matrix that behind the some positions of ring shift right, obtains, and the figure place of ring shift right is designated as the cycle offset parameter; Said ring shift right is: data line is kept the constant some position of moving to right of order, and will shift out the data of this row, add in some that this row Far Left is available because of moving to right by order.
2. repeat to accumulate the building method of sign indicating number according to the accurate circulative accumulation of the said low code check structuring of claim 1; It is characterized in that, in the said step 5, the cycle offset parameter that unit circulation square matrix moves to right; Through the outer message degree method of the approximate ring of accurate circulation, adopt following substep to realize:
(5.1) initialization of parameter: preset all variable and check-nodes are live-vertex; The every capable square matrix number of blocks that the low accurate circulative accumulation of code check structuring repeats to accumulate the check matrix of sign indicating number does
m, every row square matrix number of blocks does
n, and
mWith
nBe natural number; In outer message degree (ACE) parameter of the progressive ring of coding, the girth of maximum loop does
d ACE , the long ACE value of minimum ring does
η ACE , and
d ACE With
η ACE Be natural number, establish
iBe the parameter of cycle count,
i=
n-1, and be integer;
(5.2) establish
jBe the parameter of cycle count,
j=0, and be integer;
(5.3) carry out following steps successively: non-0
iRow, the
jFirst row of the square matrix data block of row produces variable node at random
v i , and
v i Be label, be no more than the one dimension dimension in the square matrix; Calculate variable node
v i ACEValue:
ACE(
v i )=(
d i -2); Wherein,
d i Be variable node
v i Degree, be integer; Check-node
ACEValue is 0, and the ACE of certain ring or a limit institute pie graph is expressed as: ∑
i (
d i -2), and
d i Be all variable nodes in ring or the limit
v i Degree; For all variablees and check-node
μ t , initial setting up:
p(
μ t )=10
4Wherein,
μ t Label for variable or check-node; For variable node
v i , initial setting up:
p(
v i )=
ACE(
v i );
(5.4) establish
kBe the parameter of cycle count,
k=1, and be integer;
(5.5) for (
k-1) any live-vertex of layer
w s , search this node adjacency subclass
Ch(
w s ); Wherein, the notion of layer is: with node
w s Be root node, node that in bipartite graph, obtains after the tree-like expansion and root node
w s Between the number on limit;
Ch(
w s ) be and root node
w s The set of all nodes that link to each other; In addition, the tree-like term that expands into graph theory is the figure that a plurality of annexations is arranged to; Launch successively by node, promptly choose wherein some nodes, node that the limit is connected is arranged as its child node with this node as the 1st layer tree root; Enumerate at the 2nd layer, then at the 3rd layer, except the joint of in tree graph, having enumerated; With the 2nd layer of node that all nodes link to each other as the 3rd layer, and the like enumerate until whole nodes and finish; For any child node
μ t ∈
Ch(
w s ), operation below carrying out: calculate
p Temp =
p(
w s )+
ACE(
μ t ); Wherein,
p(
μ t ) function definition is: root node and aleatory variable or check-node
μ t Between the summation of all node ACE values; Step 5.3 is seen in the calculating of ACE value;
p Temp Be temporary variable, be real number; Judge inequality:
p Temp +
p(
μ t )-
ACE(
v i )-
ACE(
μ t )<
η ACE Set up like the result, then forward step 5.1 to, otherwise forward step 5.6 to;
(5.6) judge inequality:
p Temp >=
p(
μ t ); Set up like the result, then at current parent's node
w s kIn the layer, revise child node
μ t Be non-live-vertex, otherwise calculate
p(
μ t )=
p Temp
(5.7) determining step 5.5 described child nodes
μ t ∈
Ch(
w s ), whether all calculated; As calculated, forward step 5.8 to, otherwise, forward step 5.5 to, to the child node of not calculating, continue to calculate;
(5.8) parameter of minute book second son circular matrix side-play amount;
(5.9) judge inequality: for length≤2
d ACE Ring, its
ACEValue<
η ACE If set up, forward step 5.3 to, otherwise calculate
k=
k+ 1;
(5.10) judge inequality:
k≤
d ACE As setting up, forward step 5.5 to, otherwise: calculate
j=
j+ 1;
(5.11) judge inequality:
j≤
m-1; If set up, forward step 5.2 to, otherwise calculate
i=
i-1;
(5.12) judge inequality:
i>=0; If set up, forward step 5.2 to, otherwise search for the process success of all cycle offsets, the cycle offset parameter of all square matrixes of record is the required cycle offset parameter of whole matrix.
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