CN1614896A - Channel coding method for low-density checking code - Google Patents
Channel coding method for low-density checking code Download PDFInfo
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- CN1614896A CN1614896A CN 200410084554 CN200410084554A CN1614896A CN 1614896 A CN1614896 A CN 1614896A CN 200410084554 CN200410084554 CN 200410084554 CN 200410084554 A CN200410084554 A CN 200410084554A CN 1614896 A CN1614896 A CN 1614896A
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Abstract
The method includes following steps: the check matrix of low density check code is mapped into a geometrical body; the check matrix is built into four layers by using different threading method; each layer relates to a threading method in geometrical body; the check matrix built with four layer structure is converted into generator matrix by using Gaussian elimination method or triangularization method; the generator matrix is used in generating code word of code device. The check matrix is used in decode procedure of decoder.
Description
Technical field
The present invention relates to a kind of channel coding method, relate in particular to a kind of channel coding method of the loe-density parity-check code based on how much thoughts.Be used for digital signal transmission field.
Background technology
Loe-density parity-check code (being called for short the LDPC sign indicating number) is compared with traditional chnnel coding has superior performance.In the communication system of an employing LDPC sign indicating number, available generator matrix of LDPC sign indicating number and check matrix are described.At make a start (encoder) of system, generator matrix is used for the generation of code word, and check matrix has determined the generation of generator matrix; Simultaneously check matrix also is directly used in the decoding of receiving terminal (decoder), and therefore a kind of LDPC sign indicating number can be fully determined that by its check matrix the performance quality of LDPC sign indicating number also depends on the structure of check matrix.The check matrix of LDPC sign indicating number is a sparse matrix, and " 1 " number is much smaller than the number of " 0 " in the matrix.Check matrix is made of binary digit " 0 " and " 1 ", and size has N row K capable for the matrix of N*K, the corresponding information bit of each row, check equations of each row definition.Classify " 1 " as the capable n of k in the matrix, mean that n bit in the code word participated in k check equations.Each row of LDPC code check matrix for rule comprise λ " 1 ", each row comprises ρ " 1 ", but the check matrix of LDPC sign indicating number does not also require that each is listed as " 1 " that each row comprises similar number respectively, therefore λ and ρ are variable when structure LDPC code check matrix, can represent with function lambda (n), the ρ (k) of n and k accordingly.How constructing the check matrix with bigger minimum ring length when given λ (n), ρ (k) is one of key that improves LDPC chnnel coding performance.The building method of LDPC sign indicating number mainly is divided into random device and certainty ground method at present, and random device can obtain relative error-correcting performance preferably and can construct the numeral of random length arbitrary bit rate, but the numeral hardware of its generation realizes all comparing difficulty.The LDPC sign indicating number of deterministic method construct has stronger rule, helps the realization of hardware.But the numeral of its performance and random configuration still has bigger difference when code length is longer.The more important thing is that utilize the LDPC sign indicating number of deterministic method construct, its code length and code check relative fixed, this point have seriously limited the application in practice of certainty LDPC sign indicating number.Present certainty building method is coming with some shortcomings in various degree all.
Find through literature search prior art, people such as Y.Kou are at " IEEE Trans.Inform.Theory " vol.47, pp2711-2736 Nov 2001 delivers " Low-density parity-checkcodes based on finite geometries:A rediscovery and new results ", (IEEE information theory journal November calendar year 2001, the 47th volume, 2711 to 2736 pages, low density parity check code based on finite geometry: some new discoveries and new result) proposes to utilize the notion of finite geometry to produce check matrix in this article by generator polynomial, though it is the appearance of 4 ring that this method has been avoided length fully, be that minimum ring length is 6 (ring length must be even number), but there are three problems in this method: (1) minimum ring length is 6, it is long further to improve minimum ring, for example can't construct minimum ring length and be 8 check matrix.(2) number of " 1 " is many in the check matrix, causes the ldpc decoder hardware complexity higher.(3) code length and code check relative fixed have seriously limited its application in actual conditions.And some other certainty building method also all in various degree have the problems referred to above.
Summary of the invention
The objective of the invention is to overcome deficiency of the prior art, propose a kind of channel coding method of loe-density parity-check code, make its decoding performance more excellent, have stronger error-correcting performance, the hardware of codec is realized easily.
The present invention is achieved by the following technical solutions, the present invention is mapped to a solid with the low-density check code check matrix of core and is divided into four layers of structure respectively, point is wherein represented the row of check matrix, line is wherein represented the row of check matrix, a kind of threading mode in the equal corresponding solid of each layer, select the threading mode to generate check matrix line by line, be converted into corresponding generator matrix by Gaussian elimination method or last trigonometric ratio again by the check matrix that is built into, the code word that generator matrix is used for encoder generates, and check matrix is used for the decode procedure of decoder.The present invention has the long check matrix of big minimum ring by choosing the threading mode, can constructing, and makes loe-density parity-check code have stronger error-correcting performance.
Below the present invention is further illustrated, concrete steps are as follows:
1) according to required code length N, code check Rate selects appropriate parameter k, L.In order to guarantee the error-correcting performance of numeral, make K and L all more than or equal to 4 and generally speaking L greater than k.Make the low-density check code check matrix column count N=k
2* L, line number M=4*k*L, code check
Because generally speaking the check matrix of LDPC sign indicating number of structure all can comprise redundant row (being not full rank of matrix), therefore generally need make a try k and the integer smaller slightly than k are in the hope of finding out the design parameter of approaching required code check.Each row of the matrix that obtains at last comprises k " 1 ", and each row comprises 4 " 1 ".This check matrix constitutes by four layers, each layer ρ
2Row N row.
2) at a coordinate be (x, y, cuboid of structure in three-dimensional system of coordinate z), the axial length of side of its x is L, the axial length of side of y axle and z is k and is each node serial number according to 1 to N order.
3) carry out threading according to the direction of y axle, every line comprises k node, total k*L bar straight line.The delegation of the corresponding check matrix of each bar straight line is arranged to 1 with the node that each the row line correspondence in the check matrix passes, and remaining node remains 0.The ground floor of structure check matrix.
4) in like manner, on the direction of z axle, carry out threading, the second layer of structure check matrix according to the mode of step 3).
5) on the face that x and y direction constitute, carry out threading according to the mode of step 3) in 45 degree diagonals, the 3rd layer of structure check matrix.Here the ranks coordinate that it should be noted that the hypothesis node is for (x y), when x＞L, gets x=x mod L, when y＞k, gets y=y mod k simultaneously.Just can guarantee that so each node is all got once, guarantee that simultaneously minimum ring length is 8.
6) in like manner, on the face of x and z direction formation, construct according to the mode of step 5).
7) get k=k-1 respectively, k=k-2, and repeat step 1)-6), select an immediate numeral of code check at last.
8) the above-mentioned four-layer structure that obtains is built into check matrix H, again it is converted into corresponding generator matrix G by Gaussian elimination method (or method of last trigonometric ratio), generator matrix G can be used for the making a start code word of (LDPC encoder) generates, check matrix H is used for the decode procedure of receiving end (ldpc decoder), has realized the chnnel coding of loe-density parity-check code like this.
The very approaching code check that will design of code check that the present invention obtains by above method.Accurate if desired code check then can further be revised the check matrix that obtains by splitting capable mode.The geometric meaning of this mode correspondence is equivalent to a line segment that passes k node is divided into several sections, and it is long therefore can not to influence minimum ring, also can not influence column weight.And this method mainly divides redundant row, and as far as possible little adjustment matrix, therefore can not produce significantly influence to the performance of matrix.
The inventive method utilizes solid character that the low-density check code check matrix is divided into four layers of structure respectively, can guarantee that by this layered structure the minimum ring length of check matrix is 8, makes decoding performance more excellent.And on certain degree, overcome the shortcoming that traditional certainty LDPC building method code length and code check interfix, the peculiar character of this matrix can reduce the hardware complexity of loe-density parity-check code codec greatly simultaneously, and the hardware that therefore is specially adapted to digital data transmission (storage) system high-speed codec is realized.
Description of drawings
Fig. 1 constitutes schematic diagram for layering LDPC code check matrix ground floor structure of the present invention.
Fig. 2 is based on the corresponding cube of LDPC sign indicating number and the threading mode schematic diagram of how much thoughts.
Fig. 3 is based on how much thought schematic diagrames of LDPC sign indicating number code check method of adjustment of how much thoughts.
Fig. 4 is a kind of code check 0.5, the LDPC code check matrix ground floor structure chart of code length 1029.
Fig. 5 is a kind of code check 0.5, the LDPC code check matrix second layer structure chart of code length 1029.
Fig. 6 is a kind of code check 0.5, the LDPC code check matrix three-layered node composition of code length 1029.
Fig. 7 is a kind of code check 0.5, the LDPC code check matrix four-layer structure figure of code length 1029.
Fig. 8 is a kind of code check 0.5, the LDPC code check matrix structure chart of code length 1029.
In the matrix, " 1 " represents that with point " 0 " does not mark shown in Fig. 4 to 8.
Embodiment
Technical scheme for a better understanding of the present invention provides a specific embodiment based on the LDPC code constructing method of how much thoughts below in conjunction with accompanying drawing:
The LDPC sign indicating number that needs is a code check 0.5, code length 1000, and concrete step is as follows:
1) according to designing requirement, select parameter to select k=7, L=21 makes the low-density check code check matrix column count N=1029, line number K=588, each row comprises 7 " 1 ", and each row comprises 4 " 1 ".This check matrix constitutes by four layers, each layer 147 row 1029 row.
2) at a coordinate be (x, y, cuboid of structure in three-dimensional system of coordinate z), the axial length of side of its x is L, the axial length of side of y axle and z is k and is each node serial number according to 1 to N order.
3) carry out the ground floor that threading is constructed the LDPC code check matrix according to the direction of y axle.
4) carry out the second layer that threading is constructed the LDPC code check matrix according to the direction of z axle.
5) on the face of x and y direction formation, carry out threading according to 45 degree diagonals, every line comprises k node, total k*L bar straight line.Each bar straight line is the delegation of corresponding check matrix also, and the node that each the row line correspondence in the check matrix passes is arranged to 1, and remaining node remains 0.Here the coordinate that it should be noted that node is for (x y), when x＞L, gets x=x mod L, when y＞k, gets y=y mod k simultaneously.
6) on the face of x and z direction formation, also carry out threading according to 45 degree diagonals, every line comprises k node, total k*L bar straight line.Each bar straight line is the delegation of corresponding check matrix also, and the node that each the row line correspondence in the check matrix passes is arranged to 1, and remaining node remains 0.In like manner, the coordinate of supposing node is for (x z), when x＞L, gets x=x mod L, when z＞k, gets z=z mod k simultaneously.This moment, code check was 0.52.
7), from redundant row, select 21 row, in 1 element mean allocation to two row of each row in order further to approach the design code check.Therefore last check matrix is 609 row altogether, 1029 row.Code check 0.5.
8), as shown in Figure 8, again it is converted into corresponding generator matrix G by Gaussian elimination method with the resulting check matrix H of said method.Generator matrix G be used to the to make a start code word of (LDPC encoder) generates, and check matrix H is used for the decode procedure of receiving end (ldpc decoder).
The loe-density parity-check code based on how much thoughts by said method is determined for the hardware of its coder is realized conveniently, can carry out the exchange of row or column to the check matrix of said method structure, and this exchange does not influence the low-density check code performance.
Claims (3)
1, a kind of channel coding method of loe-density parity-check code, it is characterized in that, the low-density check code check matrix is mapped to a solid, divide four layers of structure check matrix by different threading modes, point is wherein represented the row of check matrix, line is wherein represented the row of check matrix, a kind of threading mode in the equal corresponding solid of each layer, select the threading mode to generate check matrix line by line, be converted into corresponding generator matrix by Gaussian elimination method or last trigonometric ratio again by the check matrix that is built into, the code word that generator matrix is used for encoder generates, and check matrix is used for the decode procedure of decoder.
2, the channel coding method of loe-density parity-check code according to claim 1 is characterized in that, further limits by following step:
1) according to required code length N, code check Rate selects parameter k, L, make k and L all more than or equal to 4 and L greater than k, make the low-density check code check matrix column count N=k
2* L, line number M=4*k*L, code check
Each row of the matrix that obtains at last comprises k " 1 ", and each row comprises 4 " 1 ", and this check matrix constitutes by four layers, each layer ρ
2Row N row;
2) row of structure in three-dimensional system of coordinate, row, the face length of side is respectively the cuboid of L, k, k, and is each node serial number according to 1 to N order;
3) carry out threading according to the direction of row, every line comprises k node, total k*L bar straight line, the delegation of the corresponding check matrix of each bar straight line, the node that each row line correspondence in the check matrix passes is arranged to 1, and remaining node remains 0, the ground floor of structure check matrix;
4) mode in like manner, set by step 3) is carried out threading in the direction of face, the second layer of structure check matrix;
5) be expert on the face that column direction constitutes, carry out threading according to the mode of step 3) in 45 degree diagonals, the 3rd layer of structure check matrix it should be noted that, the ranks coordinate of supposing node is (x, y), when x＞L, get x=xmodL, simultaneously when y＞k, get y=ymodk, so just guarantee that each node is all got once, guarantee that simultaneously minimum ring length is 8;
6) in like manner, on the face that the face direction of being expert at constitutes, construct according to the mode of step 5);
7) get k=k-1 respectively, k=k-2, and repeat step 1)-6), select an immediate numeral of code check at last;
8) the above-mentioned four-layer structure that obtains is built into check matrix H, again its method by Gaussian elimination method or last trigonometric ratio is converted into corresponding generator matrix G, it is the code word generation of LDPC encoder-side that generator matrix G is used to make a start, check matrix H is used for the decode procedure that receiving end is the ldpc decoder end, has realized the chnnel coding of loe-density parity-check code like this.
According to the channel coding method of claim 1 or 2 described loe-density parity-check codes, it is characterized in that 3, accurate if desired code check is then further revised the check matrix that obtains by splitting capable mode.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2009049504A1 (en) * | 2007-10-19 | 2009-04-23 | Zte Corporation | Method and device for coding the low density generator matrix code |
| CN1983823B (en) * | 2005-12-15 | 2010-05-12 | 富士通株式会社 | Encoder, decoder, methods of encoding and decoding |
| CN101405943B (en) * | 2005-10-03 | 2012-03-14 | 摩托罗拉移动公司 | Method and apparatus for a low-density parity-check decoder |
| CN113364470A (en) * | 2021-05-30 | 2021-09-07 | 南京理工大学 | Improved LDPC code decoding method based on GE model for QKD |
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| EP1480346A4 (en) * | 2002-02-28 | 2006-05-10 | Mitsubishi Electric Corp | Ldpc code inspection matrix generation method and inspection matrix generation device |
| EP1525664B9 (en) * | 2002-07-03 | 2015-09-02 | Dtvg Licensing, Inc | Method and system for memory management in low density parity check (ldpc) decoders |
| JP4163023B2 (en) * | 2003-02-28 | 2008-10-08 | 三菱電機株式会社 | Parity check matrix generation method and parity check matrix generation apparatus |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101405943B (en) * | 2005-10-03 | 2012-03-14 | 摩托罗拉移动公司 | Method and apparatus for a low-density parity-check decoder |
| CN1983823B (en) * | 2005-12-15 | 2010-05-12 | 富士通株式会社 | Encoder, decoder, methods of encoding and decoding |
| WO2009049504A1 (en) * | 2007-10-19 | 2009-04-23 | Zte Corporation | Method and device for coding the low density generator matrix code |
| US8291288B2 (en) | 2007-10-19 | 2012-10-16 | Zte Corporation | Method and device for encoding the low density generator matrix code |
| CN113364470A (en) * | 2021-05-30 | 2021-09-07 | 南京理工大学 | Improved LDPC code decoding method based on GE model for QKD |
| CN113364470B (en) * | 2021-05-30 | 2022-10-28 | 南京理工大学 | GE model-based improved LDPC code decoding method for QKD |
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