A Design Method of Large Girth Type II Quasi-Cyclic LDPC Codes Based on Sidon Sequence

An LDPC code and quasi-cyclic technology, which is applied in the design field of large girth II type quasi-cyclic LDPC codes, can solve the problems of inflexible code rate, inability to meet the coding requirements of various code rates, and inability to guarantee the girth length, etc., so as to improve flexibility sexual effect

Active Publication Date: 2022-05-24
XIAN INSTITUE OF SPACE RADIO TECH
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  • Abstract
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  • Claims
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Problems solved by technology

As for the Type II QC-LDPC code with a girth of 8, it is still in the research stage. Because the scheme proposed at this stage ignores the 6-ring mode, it cannot guarantee a girth of 8, and it can only be achieved when the code rate is fixed at 0.5. Obtain a larger minimum distance, resulting in inflexible code rate, which cannot meet the coding requirements of multiple code rates in practical applications

Method used

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  • A Design Method of Large Girth Type II Quasi-Cyclic LDPC Codes Based on Sidon Sequence
  • A Design Method of Large Girth Type II Quasi-Cyclic LDPC Codes Based on Sidon Sequence
  • A Design Method of Large Girth Type II Quasi-Cyclic LDPC Codes Based on Sidon Sequence

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Experimental program
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Embodiment 1

[0080] The code rate of II type QC-LDPC code in embodiment 1 and embodiment 2 is 1 / 2, and the method that adopts computer detection shows figure 2The 6-ring shown in (j) does not exist. The code rate of Type II QC-LDPC codes in Embodiments 3 and 4 is 2 / 3, which is directly eliminated without computer detection. figure 2 The 6-ring shown in (j).

[0081] Example 1:

[0082] It is assumed that a type II QC-LDPC code with a code length of 1680 and a code rate R of 1 / 2 needs to be designed. Since R=(L-1) / L in the present invention, L=2 is taken. Since the code length in the present invention is NLP, NP is 1680 / L=840. N cannot be too large, otherwise P will be small, which will result in no Sidon sequence with many elements. Might as well take N=5, then P=840 / N=168.

[0083] (Step 1) Build a weight matrix. in satisfying a 0 ≠a 1 and mod(a 0 +a 1 , N)≠0, select the (a) that maximizes the upper bound of the minimum distance 0 ,a 1 ). (a 0 ,a 1 ) = (1, 2), it can be ...

Embodiment 2

[0090] It is assumed that a type II QC-LDPC code with a code length of 3456 and a code rate R of 1 / 2 needs to be designed. Since R=(L-1) / L in the present invention, L=2 is taken. Since the code length in the present invention is NLP, NP is 3456 / L=1728. Might as well take N=6, then P=1728 / N=288.

[0091] (Step 1) Select the weight matrix. in satisfying a 0 ≠a 1 and mod(a 0 +a 1 , N)≠0, select the (a) that maximizes the upper bound of the minimum distance 0 ,a 1 ). (a 0 ,a 1 )=(1,4), it can be known that the upper bound of the minimum distance is 66 by the S-V method. Actually 66 is the maximum value of the upper bound on the minimum distance that can be reached by any two blocks (either circular or acyclic) for N=6. by (a 0 ,a 1 ) to get the weight matrix, such as Figure 4 shown.

[0092] (Step 2) Assign parity pairs to each element 2 in the weight matrix. For P=288, use the Bose construction method to obtain a Sidon sequence, and divide the sequence into pari...

Embodiment 3

[0098] It is assumed that a type II QC-LDPC code with a code length of 3600 and a code rate R of 2 / 3 needs to be designed. Since R=(L-1) / L in the present invention, L=3 is taken. Since the code length in the present invention is NLP, NP is 3600 / L=1200. Might as well take N=10, then P=1200 / N=120.

[0099] (Step 1) Select the weight matrix. In satisfying mod(a i +a j ,N)≠0(0≤i,j≤L-1) and mod(a 0 +a 1 +a 2 , N)≠0, choose (a 0 ,a 1 ,a 2 ). Since it is very difficult to use the S-V method to calculate the upper bound of the minimum distance when N = 10, we choose the local optimal value and determine (a 0 ,a 1 ,a 2 )=(1, 4, 7), the weight matrix is ​​obtained.

[0100] (Step 2) Assign parity pairs to each element 2 in the weight matrix. For P=120, use the Bose construction method to obtain a Sidon sequence, and divide the sequence into parity to obtain S=S 1 ∪S 2 , where S 1 ={0,54,64,68,70,98}, S 2 ={29,37,55,75,117}. use S 1 All 6 even numbers and S in 2 All...

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Abstract

The invention discloses a method for designing a large girth type II quasi-cyclic LDPC code based on a Sidon sequence. The method first uses the S-V method to establish a weight matrix; then uses the Sidon sequence to assign index values ​​to the elements in the weight matrix to generate an index matrix; finally generates a parity check matrix based on the index matrix to complete the construction of type II quasi-cyclic LDPC codes. The present invention has been innovated when establishing the weight matrix and the index matrix, thereby ensuring that the present invention can construct a Type II (3,3L) QC-LDPC code with a girth of 8, a flexible code rate, and a relatively large minimum distance.

Description

technical field [0001] The invention relates to a design method for a large girth type II quasi-cyclic LDPC code based on a Sidon sequence, and belongs to the field of channel coding in a digital communication system. Background technique [0002] Low Density Check Code (LDPC) is the null space of Sparse Check Matrix (PCM). Quasi-cyclic (QC-) LDPC codes are a special kind of LDPC codes, which have received extensive attention due to their relatively low coding and decoding complexity. [0003] The PCM of the QC-LDPC code is an N*M array composed of P*P cyclic matrices. The cyclic matrix can be a zero matrix (ZM), a cyclic permutation matrix (CPM) or a superposition of k different CPMs (2≤k≤P). The weights of these three types of circulant matrices are 0, 1 and k, respectively. If all cyclic matrices in the PCM are CPM, the corresponding code is called a typical QC-LDPC code; if the PCM is composed of CPM and ZM, the corresponding code is called a Type I QC-LDPC code; if t...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H03M13/11
CPCH03M13/116
Inventor 张国华王菊花谢天娇袁瑞佳张建华
Owner XIAN INSTITUE OF SPACE RADIO TECH
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