CN105375933B - A kind of LDPC loops detection based on message transmission and ring enumeration - Google Patents
A kind of LDPC loops detection based on message transmission and ring enumeration Download PDFInfo
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Abstract
The LDPC loops detection and ring enumeration that the invention discloses a kind of based on message transmission, by setting check matrix, determine that Tanner schemes, information is transmitted using Message Passing Algorithm between variable node and check-node, the quantity of various designated length rings and its respective path under record, simultaneously in search process, the path for having emphasis or weight side is deleted in time, and save the path for constituting ring.The present invention can not only count ring, moreover it is possible to sufficiently grasp ring information, the length including location information, the construction of ring, ring.It is influenced due to encoding by figure dimension, after leaving out becate, becate is reduced, and is alleviated and is restricted by figure dimension, conducive to being used to improve code construction.
Description
Technical field
The invention belongs to the information coding techniques of non-cooperative communication, and in particular to a kind of LDPC ring based on message transmission is searched
Rope and ring enumeration.
Background technique
Iterative message pass-algorithm can obtain superior performance table in terms of LDPC code decoding with relatively low complexity
It is existing, and with the fast development of this iterative algorithm, the LDPC code of channel capacity can be approached again under many channel conditions
Become research hotspot.Tanner figure is widely used in the research of LDPC code, and the low complex degree of LDPC code iterative decoding is just
It is the sparsity due to its Tanner figure.Moreover, the dimension of Tanner figure also influences whether the performance of LDPC code.At present
Substantially think, more wants to obtain preferable coding efficiency, the appearance of becate should be more evaded in corresponding Tanner figure.
2013, scholar M.Karimi, A.H.Banihashemi, in " Message-passing algorithms for
Counting short cycles in a graph " (IEEE Trans.Commun, vol.61, no.2, Feb.2013.) is mentioned
Go out a kind of information pass-algorithm that becate number is counted in figure, but without being carried out at algorithm for duplicate node invalid loops
Reason, coding are limited by figure dimension, and the ring information in LDPC code figure is not utilized effectively, influence the becate of code construction according to
Right objective reality.So the algorithm more lays particular stress on theory deduction, and the important information for grasping improvement code construction is not made
Further work.
Summary of the invention
The LDPC loops detection and ring enumeration that the purpose of the present invention is to provide a kind of based on message transmission, improve it
The problem of being limited in iterative decoding process vulnerable to becate and trap collection.
The technical solution for realizing the aim of the invention is as follows: a kind of LDPC loops detection based on message transmission and ring enumerate calculation
Method, method and step are as follows:
Step 1, setting H-matrix, determine that Tanner schemes, and obtain total node number n and by node AiNumber consecutively, i are node
Sequence number, i=1,2,3 ..., n；Initialize i=1, AiFor start node, determine to include start node AiRing maximum length
For 2K, iteration total degree is K, is transferred to step 2.
Step 2, for start node Ai, the number of iterations k, k=1,2,3 ... ... K initialize k=1；
If k≤K, by start node AiInformation transmitting is carried out, in information exchanging process, if returning without residual paths
Step 1；Otherwise, it there are when residual paths, records and enters step 3；
If k > K, enables i=i+1, when i≤n, return step 1；As i > n, output token node and its corresponding path.
Step 3 counts the ring in information exchanging process, removes start node AiIn outer residual paths, find
Becate comprising duplicate node is sequentially output the data information of the duplicate node according to the minmal sequence number of node and position is believed
Breath, records and deletes endless path, be transferred to step 4.
Step 4, record storage are with node AiFor start node, and length is the quantity of the ring of 2k, and enables k=k+1, is transferred to
Step 2.
Further, in step 2, to start node AiInformation transmitting is carried out, information exchanging process is as follows: by start node
AiThe information itself contained passes to node adjacent thereto, the adjacent section as new external information plus external information
The information that point again has itself passes to the node adjacent with adjacent node plus new external information, complete with this iteration
It is transmitted at information, the node transmits the mutual transmitting between variable node and detection node.
Further, it in step 3, when being counted to ring, determines with AiFor start node, and length is the number of the ring of 2k
Amount, formula are as follows:
Wherein,Expression start node is AiAnd the number of the ring of a length of 2k.
Expression start node is Ai, starting path be ei, end path be ej, a length of 2k of ring ring number.
Expression start node is Ai, a length of 2k ring number, ulFor in ring at least through duplicate node twice,
As flag node determines its corresponding endless path；L represents its minmal sequence number, wherein l={ 1,2,3 ..., n }.
N represents the node total number of figure.
Compared with prior art, the present invention its remarkable advantage is: (1) can not only be counted to ring, moreover it is possible to sufficiently
Grasp ring information, the length including location information, the construction of ring, ring.
(2) it is influenced due to encoding by figure dimension, after leaving out becate, becate is reduced, and is alleviated and is restricted by figure dimension, is conducive to
For improving code construction.
(3) algorithm can be generalized in general bipartite graph.
Detailed description of the invention
Fig. 1 is the flow chart of the LDPC loops detection of the invention based on message transmission and ring enumeration.
Fig. 2 is the analogous diagram of the LDPC loops detection of the invention based on message transmission and ring enumeration, wherein (a) is code
Word A:252.252.3.252 variable node dimension figure；It (b) is code word B:504.504.3.504 variable node dimension figure；(c) it is
Code word C:PEGReg252x504 variable node dimension figure；It (d) is code word D:PEGReg504x1008 variable node dimension figure.
Fig. 3 is the non-simple ring schematic diagram of the present invention, and (a) is the first；(b) it is second；It (c) is the third；It (d) is the
Four kinds.
Fig. 4 is U and W according to Message Passing Algorithm transmitting information schematic diagram.
Specific embodiment
Present invention is further described in detail with reference to the accompanying drawing.
In order to which better by hardware realization LDPC code, general iterative decoding using based on message passing mechanism etc. is quasi- most
Maximum-likelihood algorithm is decoded.Tanner figure is determined according to check matrix, using disappearing between variable node and check-node
It ceases pass-algorithm and transmits information.But since the presence of ring especially becate can seriously affect algorithm performance, so we are calculating
In the implementation procedure of method, can note down down various designated length rings quantity and its respective path.Simultaneously in search process, and
When delete have emphasis or weight side path, and save constitute ring path.And it is proposed that algorithm searched unlike other algorithms
The limitation of rope object self structure, can search for the ring for being arbitrarily designated length.Executing the ring information that this algorithm obtains can be used in
Change code construction, to promote error-correcting performance or reduce error floor.And algorithm has generality, can be used for not including certainly
Ring and weight side bipartite graph, or even common figure.
In conjunction with Fig. 1, a kind of LDPC loops detection based on message transmission and ring enumeration, method and step are as follows:
Step 1, H-matrix is set, determines that Tanner schemes, obtains total node number n and by node AiNumber consecutively, i are node
Sequence number, i=1,2,3 ..., n；Initialize i=1, AiFor start node, determine to include start node AiRing maximum length
For 2K, iteration total degree is K.
Step 2, for start node Ai, the number of iterations k, k=1,2,3 ... ... K initialize k=1:
If k≤K, by start node AiInformation transmitting is carried out, in information exchanging process, if returning without residual paths
Step 1；Otherwise, it there are when residual paths, records and enters step 3.
If k > K, enables i=i+1, when i≤n, return step 1；As i > n, output token node and its corresponding path.
In bipartite graph, define LDPC coding information code and detection code be corresponding information node and detection node, two
Component indicates are as follows:
G=(V, E) (1)
Wherein, bipartite graph G is defined as the node collection of information node U and detection node W, and
With a path set E, wherein represent the path between u and W, and { (u, w) | u ∈ U, w ∈ W }.Take i=0, i=i+1.
Message Passing Algorithm indicates are as follows:
U and W transmits information, such as Fig. 4 according to Message Passing Algorithm.
In information exchanging process, example is done by three-phase neighbors of X, Y, Z, the information transmitting between X and Y can indicate
For following formula: IX→ Y=∑z∈N(X)IZ→X-IY→X+IX=∑z∈N(X)-{Y}IZ→X+IX.That is:
In Tanner figure, the information that the variable node (detection node) of LDPC coding contains oneself itself is plus outside
Information passes to its adjacent detection node (variable node) as new external information, what which had with subset itself again
Information passes to next adjacent node plus new external information again, with this iteration, completes information transmitting.Start node sequence
Number i < n, start node traverse whole nodes.
The information of transmitting is only and the self-information of the node is related with the external information that adjacent node transmits.But Message Passing Algorithm
When encountering the structures such as ring etc. is special, the independence such as transmitted message just be cannot be guaranteed.That is the presence of ring, especially
Becate can seriously affect the performance of iterative decoding.It is therefore desirable to be scanned for algorithm rapidly and efficiently to ring, this is to detection
The error-correcting performance of existing LDPC code, the error correcting capability for further increasing existing LDPC code and design have more preferable error-correcting performance
LDPC code has a very important significance.
It needs to illustrate to being, in the case that the present invention considers simple ring；
If other nodes are different in ring other than two terminal nodes, in other words, the ring that a length is k can
With a series of corresponding unduplicated path { e1, e2, L, ekIndicate, then it is defined as a simple ring, is accordingly, there are non-
Simple ring, such as Fig. 3.
Step 3, the ring in information exchanging process is counted, is removing start node AiIn outer residual paths, seek
The becate comprising duplicate node is looked for, data information and the position of the duplicate node are sequentially output according to the minmal sequence number of node
Information records and deletes endless path, is transferred to step 4.
When being counted to ring, determine with node AiFor start node, and length is the quantity of the ring of 2k, and formula is as follows:
Wherein,Expression start node is AiAnd the number of the ring of a length of 2k；
Expression start node is Ai, starting path be ei, end path be ej, a length of 2k of ring ring number；
Expression start node is Ai, a length of 2k ring number, uiFor in ring at least through duplicate node twice,
As flag node determines its corresponding endless path.L represents its minmal sequence number, wherein l={ 1,2,3 ..., n }；
N represents the node total number of figure.
Step 4, record storage is with node AiFor start node, and length is the quantity of the ring of 2k, and enables k=k+1, is transferred to
Step 2.Until all node traverses finish, terminate.
Embodiment 1
A kind of LDPC loops detection based on message transmission and ring enumeration, method and step are as follows:
Step 1, it is downloaded by http://www.inference.phy.cam.ac.uk/mackay/codes/data.html
Code word A:252.252.3.252, B:504.504.3.504, C:PEGReg252x504 and D:PEGReg504x1008 is right respectively
Answer check matrix HA(252,504), HB(504,1008), HC(252,504), HD(504,1008), encoding rate are 0.5, A and B
Code line weight is 3, C and D row weight is 4, determines that Tanner schemes.By node AiNumber consecutively, i are the sequence number of node, i=
1,2,3 ..., n；Initialize i=1, AiFor start node, determine to include start node AiRing maximum length be 2K, iteration is always secondary
Number is K；We have done K=3,4,5,6,7, the results are shown in Table 1 in Matlab respectively.
The number of rings mesh that 1 four kinds of code word ring lengths of table are 6 to 14
| Encode A | Encode B | Encode C | Encoding D | |
| N6 | 169 | 165 | 0 | 0 |
| N8 | 1312 | 1258 | 802 | 2 |
| N10 | 10052 | 10169 | 11279 | 11238 |
| N12 | 83007 | 83489 | 86791 | 91101 |
| N14 | 699526 | 707468 | 723426 | 748343 |
Step 2, for start node Ai, the number of iterations k, k=1,2,3 ... ... K initialize k=1:
If k≤K, by start node AiInformation transmitting is carried out, in information exchanging process, if returning without residual paths
Step 1；Otherwise, it there are when residual paths, records and enters step 3.
If k > K, enables i=i+1, when i≤n, return step 1；As i > n, output token node and its corresponding path.
In bipartite graph, define LDPC coding information code and detection code be corresponding information node and detection node, two
Component indicates are as follows:
G=(V, E) (1)
Wherein, bipartite graph G is defined as the node collection of information node U and detection node W, and
With a path set E, wherein represent the path between u and w, and { (u, w) | u ∈ U, w ∈ W }.Take i=0, i=i+1.
Message Passing Algorithm indicates are as follows:
U and W transmits information (as shown in Figure 4) according to Message Passing Algorithm.
In information exchanging process, example is done by three-phase neighbors of X, Y, Z, the information transmitting between X and Y can indicate
For following formula: IX→Y=∑z∈N(X)IZ→X-IY→X+IX=∑z∈N(X)-{Y}IZ→X+IX.That is:
In Tanner figure, the information that the variable node (detection node) of LDPC coding contains oneself itself is plus outside
Information passes to its adjacent detection node (variable node) as new external information, what which had with subset itself again
Information passes to next adjacent node plus new external information again, with this iteration, completes information transmitting.Start node sequence
Number i < n, start node traverse whole nodes.
It needs to illustrate to being, in the case that the present invention considers simple ring.
If other nodes are different in ring other than two terminal nodes, in other words, the ring that a length is k can
With a series of corresponding unduplicated path { e1, e2, L, ekIndicate, then it is defined as a simple ring, is accordingly, there are non-
Simple ring, such as Fig. 3.
Step 3, the ring in information exchanging process is counted, is removing start node AiIn outer residual paths, seek
The becate comprising duplicate node is looked for, data information and the position of the duplicate node are sequentially output according to the minmal sequence number of node
Information records and deletes endless path, is transferred to step 4；
When being counted to ring, determine with node AiFor start node, and length is the quantity of the ring of 2k, and formula is as follows:
Wherein,Expression start node is AiAnd the number of the ring of a length of 2k；
Expression start node is Ai, starting path be ei, end path be ej, a length of 2k of ring ring number；
Expression start node is Ai, a length of 2k ring number, ulFor in ring at least through duplicate node twice,
As flag node determines its corresponding endless path.L represents its minmal sequence number, wherein l={ 1,2,3 ..., n }.
N represents the node total number of figure.
Step 4, record storage is with node AiFor start node, and length is the quantity of the ring of 2k, and enables k=k+1, is transferred to
Step 2.Until all node traverses finish, terminate.
It is as follows by Matlab simulation result, the dimension histogram (as shown in Figure 2) of four kinds of code words.
By analogous diagram, we can be visually seen the corresponding dimension figure of four kinds of code words, corresponding becate number,
Sufficiently to grasp the ring information in LDPC coding, for improving code construction.Using our this algorithms rapidly and efficiently to ring
It scans for, this has the error-correcting performance of LDPC code to detection, further increases the error correcting capability and design of existing LDPC code
LDPC code with more preferable error-correcting performance has a very important significance.
Claims (1)
1. a kind of LDPC loops detection based on message transmission and ring enumeration, which is characterized in that method and step is as follows:
Step 1, setting H-matrix, determine that Tanner schemes, and obtain total node number n and by node AiNumber consecutively, i are the sequence of node
Number, i=1,2,3 ..., n；Initialize i=1, AiFor start node, determine to include start node AiRing maximum length be 2K,
Iteration total degree is K, is transferred to step 2；
Step 2, for start node Ai, the number of iterations k, k=1,2,3 ... ... K initialize k=1；
If k≤K, by start node AiInformation transmitting is carried out, in information exchanging process, if without residual paths, return step 1；
Otherwise, it there are when residual paths, records and enters step 3；
If k > K enables i=i+1, when i≤n, return step 1；As i > n, output token node and its corresponding path；
In step 2, start node AiFor variable node, to start node AiInformation transmitting is carried out, information exchanging process is as follows: will
Start node AiThe information itself contained passes to node adjacent thereto as new external information plus external information；It is described
The information that adjacent node again has itself passes to node adjacent thereto plus new external information, complete with this iteration
It is transmitted at information, the node transmits the mutual transmitting between variable node and detection node；
Step 3 counts the ring in information exchanging process, removes start node AiIn outer residual paths, find comprising weight
The becate of knot cluster point is marked if including multiple duplicate nodes in ring using the smallest duplicate node of sequence number, successively defeated
The data information and location information of the duplicate node out, records and deletes endless path, be transferred to step 4；
In step 3, when being counted to ring, determine with AiFor start node, and length is the quantity of the ring of 2k, and formula is as follows:
Wherein,Expression start node is AiAnd the number of the ring of a length of 2k；
Expression start node is Ai, starting path be ei, end path be ej, a length of 2k of ring ring number；
Expression start node is Ai, have emphasis ul, the number of the ring of a length of 2k；If having multiple emphasis in a ring track,
It is marked with the smallest emphasis of sequence number, to avoid computing repeatedly；
N represents the node total number of figure；
Step 4, record storage are with node AiFor start node, and length is the quantity of the ring of 2k, and enables k=k+1, is transferred to step
2。
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| CN103944585A (en) * | 2013-09-02 | 2014-07-23 | 中山大学 | Cycle-entropy-based nonbinary quasi-cyclic low density parity check code construction method |
| CN105071818A (en) * | 2015-08-31 | 2015-11-18 | 四川特伦特科技股份有限公司 | Low-complexity LDPC code coding method |
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| CN103944585A (en) * | 2013-09-02 | 2014-07-23 | 中山大学 | Cycle-entropy-based nonbinary quasi-cyclic low density parity check code construction method |
| CN105071818A (en) * | 2015-08-31 | 2015-11-18 | 四川特伦特科技股份有限公司 | Low-complexity LDPC code coding method |
Non-Patent Citations (3)
| Title |
|---|
| Message-Passing Algorithms for Counting Short Cycles in a Graph;Mehdi Karimi and Amir H.Banihashemi;《IEEE TRANSACTIONS ON COMMUNICATIONS》;20130228;正文第IV章 |
| On the Girth of Quasi-Cyclic Protograph LDPC Codes;Mehdi Karimi and Amir H.Banihashemi;《IEEE TRANSACTIONS ON INFORMATION THEORY》;20130731;全文 |
| 优化循环转移矩阵偏移量的QC-LDPC码构造;郑健 等;《北京邮电大学学报》;20140228;全文 |
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