CN110350924B - Construction of (72,36,14) linear quasi-cyclic code - Google Patents
Construction of (72,36,14) linear quasi-cyclic code Download PDFInfo
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/13—Linear codes
- H03M13/15—Cyclic codes, i.e. cyclic shifts of codewords produce other codewords, e.g. codes defined by a generator polynomial, Bose-Chaudhuri-Hocquenghem [BCH] codes
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Abstract
The invention discloses a new structure of (72,36,14) linear quasi-cyclic code, which relates to the communication field, and is characterized in that a linear block code array of (72,36) is used for coding an input information sequence, and a coding sequence with the length of 72 is output, wherein when the input information bit length is 36, the minimum code distance of the output coding sequence is 14.
Description
Technical Field
The invention relates to the technical field of communication, in particular to a (72,36,14) linear quasi-cyclic code structure.
Background
Currently, human beings have stepped into the information society, and communication is indispensable. A communication system is required to transmit messages reliably and quickly, however, the requirement for high speed inevitably results in a short time occupied by each code element, a narrow waveform and reduced energy, which increases the possibility of generating errors after interference and reduces the reliability of the messages. In modern communication systems, linear block codes are mostly used to encode control information of short length. For a linear block code with a short code length, the size of the minimum code distance directly affects the error correction performance. The larger the minimum distance of the code groups is, the larger the minimum difference between the code words is, and the stronger the anti-interference capability is. Therefore, when designing linear block codes, people generally try to make the minimum code distance of the linear block codes reach the theoretical maximum value, and the performance of the linear block codes is optimal at the moment. However, the equivalent classes of the 100 classes of 36-order Hadamard matrices known in the prior art only construct self-dual [72,36,8], [72,36,12] error correction codes, so that the performance of the system is not optimal.
Disclosure of Invention
In view of the deficiencies of the prior art, the present invention provides a construction of a (72,36,14) linear quasi-cyclic code that solves the problems set forth in the background above.
The invention provides the following technical scheme: a construction of a (72,36,14) linear quasi-cyclic code for encoding an input information sequence using a linear block code matrix of (72,36), outputting a code sequence of length 72, wherein, when the input information bit length is 36, the minimum code distance of the output code sequence is made 14;
constructing a matrix of G ═ (I | a), where I is a 36 × 36 identity matrix;
and a is a 36 × 36 circulant matrix:
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
| 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
the minimum code distance obtained according to the matrix G is 14; the circulant matrix only needs to know that the matrix is in the first row, other rows can be obtained by circularly shifting the first row, and the first row of the matrix can be regarded as a 36-bit binary number and converted into an integer in decimal, and later, the matrix A is represented by a large integer, and the A matrix can be written as the integer 60327799.
Most preferably, the minimum distance to find the (72,36) code closer to the theoretical code distance is 14.
Most preferably, from G ═ (I | a), the a matrix is a code weight distribution constructed from integers 60327799 of
0:{1}
14:{9036}
16:{121716}
18:{1212396}
20:{9058338}
22:{52125372}
24:{231411882}
26:{803179548}
28:{2198817432}
30:{4781527704}
32:{8301694689}
34:{11541552984}
36:{12878054540}
38:{11541552984}
40:{8301694689}
42:{4781527704}
44:{2198817432}
46:{803179548}
48:{231411882}
50:{52125372}
52:{9058338}
54:{1212396}
56:{121716}
58:{9036}
72:{1}
Wherein the previous number represents the weight, and the number in { } represents the number of codewords, e.g., 14: {9036} represents that the number of codewords with the weight of 14 is 9036;
the generator matrix G ═ (I | a) with the same code weight distribution as above, where a can also be represented by the following integer:
62620775，200163635，214443901，613261187，813591625，1320494245，1385322169，1420920235，1760106775，1792067221，1951157131。
the A matrix is a code weight distribution constructed from integer 82472243 as
0:{1}
14:{9036}
16:{121959}
18:{1209468}
20:{9073620}
22:{52081740}
24:{231479265}
26:{803146716}
28:{2198758896}
30:{4781573208}
32:{8301956535}
34:{11540800440}
36:{12879054968}
38:{11540800440}
40:{8301956535}
42:{4781573208}
44:{2198758896}
46:{803146716}
48:{231479265}
50:{52081740}
52:{9073620}
54:{1209468}
56:{121959}
58:{9036}
72:{1}
The generator matrix G ═ (I | a) with the same code weight distribution as above, where a can also be represented by the following integer:
107328185，608050009，649469705，1270107181，1483223735，1483225939，1511593705，1521555139，1639204525，2323059865，2569596497。
the A matrix is a code weight distribution constructed from integer 83137423 as
0:{1}
14:{9036}
16:{122121}
18:{1207540}
20:{9083376}
22:{52056324}
24:{231504603}
26:{803198268}
28:{2198514240}
30:{4782049080}
32:{8301367323}
34:{11541348936}
36:{12878555040}
38:{11541348936}
40:{8301367323}
42:{4782049080}
44:{2198514240}
46:{803198268}
48:{231504603}
50:{52056324}
52:{9083376}
54:{1207540}
56:{122121}
58:{9036}
72:{1}
The generator matrix G ═ (I | a) with the same code weight distribution as above, where a can also be represented by the following integer:
126765433，1120907413，1126976411，1152680863，1184547251，1263043559，1418131873，1723968689，1827215969，2317628909，2437164523。
the A matrix is a code weight distribution constructed from integer 75310053 as
0:{1}
14:{9360}
16:{120114}
18:{1210564}
20:{9088542}
22:{52042212}
24:{231485136}
26:{803276640}
28:{2198499048}
30:{4781863536}
32:{8301570813}
34:{11541466872}
36:{12878211060}
38:{11541466872}
40:{8301570813}
42:{4781863536}
44:{2198499048}
46:{803276640}
48:{231485136}
50:{52042212}
52:{9088542}
54:{1210564}
56:{120114}
58:{9360}
72:{1}
The generator matrix G ═ (I | a) with the same code weight distribution as above, where a can also be represented by the following integer:
87959025，104519835，113826531，296168775，351309525，359539173，475438257，1457041677，1481018805，2611110789，2714125785。
the A matrix is a code weight distribution constructed from integer 77932509 as
0:{1}
14:{9360}
16:{119583}
18:{1216872}
20:{9056772}
22:{52123752}
24:{231411513}
26:{803072304}
28:{2199399984}
30:{4780089216}
32:{8303869863}
34:{11539163376}
36:{12880411544}
38:{11539163376}
40:{8303869863}
42:{4780089216}
44:{2199399984}
46:{803072304}
48:{231411513}
50:{52123752}
52:{9056772}
54:{1216872}
56:{119583}
58:{9360}
72:{1}
The generator matrix G ═ (I | a) with the same code weight distribution as above, where a can also be represented by the following integer:
98510121，620662923，711182547，782287347，851767701，870367581，876765129，1379436021，1473285669，4601829069，4671228489，4909788369，6020179089。
the invention has the following beneficial effects: the generator matrix has a quasi-cyclic structure G ═ (I | a), the transpose of a equals a; the minimum code distance of the (72,36) code is 14 by adding 2 bits on the basis of the original minimum code distance 12 of the (72,36) code. This shows that its interference immunity is enhanced, and a code having a cyclic structure that can correct 6 bit errors. Therefore, the error rate in a digital communication system and a computer storage and operation system is reduced, the reliability of digital communication is improved, and the system performance is enhanced. The service quality and the operation speed of the communication network are obviously improved.
Drawings
FIG. 1 is a diagram of a linear block code submatrix A of the present invention (72,36, 14).
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, (1) a linear block code may be constructed (72,36,14) according to the following a matrix available in fig. 1, where the generator matrix G ═ (I | a);
(2) because the generation matrix is in a systematic form, the check matrix H of the code is easily obtained as (a | I);
(3) according to the information m with the length of 36 to be transmitted, the length of the code word c obtained by the generating matrix G is 72, and c is m × G;
(4) the code word c is transmitted through a channel and received by a vector r, and a syndrome s is calculated according to a check matrix, wherein the syndrome s is r multiplied by HT
HT denotes the transpose of the check matrix H;
(5) constructing an error pattern table capable of correcting code words according to the check matrix, wherein t is 6 in the error correction capability of the code, and the error pattern table comprises
A correctable error pattern;
(6) an error pattern e is found for syndrome s in the table, and r is translated as c ═ r + e.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (1)
1. A construction of a (72,36,14) linear quasi-cyclic code, characterized by encoding an input information sequence using a linear block code matrix of (72,36), outputting a code sequence of length 72, wherein, when the input information bit length is 36, the minimum code distance of the output code sequence is 14;
constructing a matrix of G ═ (I | a), where I is a 36 × 36 identity matrix;
and a is a 36 × 36 circulant matrix:
the minimum code distance obtained according to the matrix G is 14; the circulant matrix only needs to know that the matrix is in the first row, other rows can be obtained by circularly shifting the first row, the first row of the matrix can be regarded as a binary number with 36 bits, the binary number is converted into an integer with decimal, the matrix A is represented by a large integer, and the matrix A can be written as the integer 60327799 as above;
the minimum distance to find the (72,36) code closer to the theoretical code distance is 14;
from G ═ I | a, the a matrix is a code weight distribution constructed from integers 60327799 as
0:{1}
14:{9036}
16:{121716}
18:{1212396}
20:{9058338}
22:{52125372}
24:{231411882}
26:{803179548}
28:{2198817432}
30:{4781527704}
32:{8301694689}
34:{11541552984}
36:{12878054540}
38:{11541552984}
40:{8301694689}
42:{4781527704}
44:{2198817432}
46:{803179548}
48:{231411882}
50:{52125372}
52:{9058338}
54:{1212396}
56:{121716}
58:{9036}
72:{1}
Wherein the former number represents weight, the number in { } represents the number of code words, for example, 14: {9036} represents the number of code words with weight of 14 as 9036;
the generator matrix G ═ I | a with the same code weight distribution as above, where a is represented by the following integer:
62620775，200163635，214443901，613261187，813591625，1320494245，1385322169，1420920235，1760106775，1792067221，1951157131；
the A matrix is a code weight distribution constructed from integers 82472243 as
0:{1}
14:{9036}
16:{121959}
18:{1209468}
20:{9073620}
22:{52081740}
24:{231479265}
26:{803146716}
28:{2198758896}
30:{4781573208}
32:{8301956535}
34:{11540800440}
36:{12879054968}
38:{11540800440}
40:{8301956535}
42:{4781573208}
44:{2198758896}
46:{803146716}
48:{231479265}
50:{52081740}
52:{9073620}
54:{1209468}
56:{121959}
58:{9036}
72:{1}
The generator matrix G ═ I | a with the same code weight distribution as above, where a is represented by the following integer:
107328185，608050009，649469705，1270107181，1483223735，1483225939，1511593705，1521555139，1639204525，2323059865，2569596497；
the A matrix is a code weight distribution constructed from integer 83137423 as
0:{1}
14:{9036}
16:{122121}
18:{1207540}
20:{9083376}
22:{52056324}
24:{231504603}
26:{803198268}
28:{2198514240}
30:{4782049080}
32:{8301367323}
34:{11541348936}
36:{12878555040}
38:{11541348936}
40:{8301367323}
42:{4782049080}
44:{2198514240}
46:{803198268}
48:{231504603}
50:{52056324}
52:{9083376}
54:{1207540}
56:{122121}
58:{9036}
72:{1}
The generator matrix G ═ I | a with the same code weight distribution as above, where a is represented by the following integer:
126765433，1120907413，1126976411，1152680863，1184547251，1263043559，1418131873，1723968689，1827215969，2317628909，2437164523；
the A matrix is a code weight distribution constructed from integers 75310053 as
0:{1}
14:{9360}
16:{120114}
18:{1210564}
20:{9088542}
22:{52042212}
24:{231485136}
26:{803276640}
28:{2198499048}
30:{4781863536}
32:{8301570813}
34:{11541466872}
36:{12878211060}
38:{11541466872}
40:{8301570813}
42:{4781863536}
44:{2198499048}
46:{803276640}
48:{231485136}
50:{52042212}
52:{9088542}
54:{1210564}
56:{120114}
58:{9360}
72:{1}
The generator matrix G ═ I | a with the same code weight distribution as above, where a is represented by the following integer:
87959025，104519835，113826531，296168775，351309525，359539173，475438257，1457041677，1481018805，2611110789，2714125785；
the A matrix is a code weight distribution constructed from integer 77932509 as
0:{1}
14:{9360}
16:{119583}
18:{1216872}
20:{9056772}
22:{52123752}
24:{231411513}
26:{803072304}
28:{2199399984}
30:{4780089216}
32:{8303869863}
34:{11539163376}
36:{12880411544}
38:{11539163376}
40:{8303869863}
42:{4780089216}
44:{2199399984}
46:{803072304}
48:{231411513}
50:{52123752}
52:{9056772}
54:{1216872}
56:{119583}
58:{9360}
72:{1}
The generator matrix G ═ I | a with the same code weight distribution as above, where a is represented by the following integer:
98510121，620662923，711182547，782287347，851767701，870367581，876765129，1379436021，1473285669，4601829069，4671228489，4909788369，6020179089。
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6745362B1 (en) * | 1998-07-31 | 2004-06-01 | France Telecom | Method and device for error correction coding and corresponding decoding method and device |
| CN101868920A (en) * | 2007-12-24 | 2010-10-20 | Lg电子株式会社 | Channel coding method of variable length information using block code |
| CN102077470A (en) * | 2009-05-25 | 2011-05-25 | 华为技术有限公司 | Method and device for encoding by linear block code, and method and device for generating linear block code |
| CN102077469B (en) * | 2009-03-19 | 2013-09-11 | 华为技术有限公司 | Method and device for linear block code coding |
| CN103346803A (en) * | 2013-07-26 | 2013-10-09 | 中国科学院微电子研究所 | Channel coding method used in wireless communication system |
| CN109756234A (en) * | 2019-01-15 | 2019-05-14 | 江西理工大学 | Long code constructing method in a kind of LDPC of the high code rate based on matroid theory |
-
2019
- 2019-08-06 CN CN201910721919.2A patent/CN110350924B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US6745362B1 (en) * | 1998-07-31 | 2004-06-01 | France Telecom | Method and device for error correction coding and corresponding decoding method and device |
| CN101868920A (en) * | 2007-12-24 | 2010-10-20 | Lg电子株式会社 | Channel coding method of variable length information using block code |
| CN102077469B (en) * | 2009-03-19 | 2013-09-11 | 华为技术有限公司 | Method and device for linear block code coding |
| CN102077470A (en) * | 2009-05-25 | 2011-05-25 | 华为技术有限公司 | Method and device for encoding by linear block code, and method and device for generating linear block code |
| CN103346803A (en) * | 2013-07-26 | 2013-10-09 | 中国科学院微电子研究所 | Channel coding method used in wireless communication system |
| CN109756234A (en) * | 2019-01-15 | 2019-05-14 | 江西理工大学 | Long code constructing method in a kind of LDPC of the high code rate based on matroid theory |
Non-Patent Citations (4)
| Title |
|---|
| "Weight Distribution of Low-Density Parity-Check Codes";C. Di等;《IEEE Transactions on Information Theory》;20061023;第52卷(第11期);4839-4855 * |
| "一种短小的高码率LDPC码设计";巫光福 等;《应用科学学报》;20131130;第31卷(第6期);559-563 * |
| "基于可变拟阵搜索算法构造码率为1/p的二进制系统准循环码";张水平 等;《电子与信息学报》;20161130;第38卷(第11期);2916-2921 * |
| "深空通信中多进制LDPC码构造方法研究";李勇;《中国优秀博硕士学位论文全文数据库(硕士) 信息科技辑》;20170315;I136-488 * |
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