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Based on complete cyclic difference sets LDPC codes
Author: SongDeYin
Tutor: TangYuanSheng
School: Yangzhou University
Course: Basic mathematics
Keywords: Lowdensity paritycheck code Cyclic difference sets Iterative Decoding
CLC: O157.4
Type: Master's thesis
Year: 2007
Downloads: 73
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Abstract
1962 Ge Lage (Gallager) first proposed LDPC code, several types of low density parity check code has been constructed, and the plot through iterative decoding algorithm simulation code to get the performance we can see that they are close to Shannon limit yards . In the past few years, the study group objective is to construct a pseudorandom lowdensity parity check code, making it both good error performance, but also close to the Shannon limit. Although some of the known pseudorandom lowdensity parity check code has excellent error correction performance, but the complexity of the problem of the code structure and the quality of design also plays a decisive role. Pseudorandom LDPC code having a high complexity is an important reason for this is not a code generation matrix corresponds to a sparse matrix. Lowdensity paritycheck code pseudorandom This problem can be constructed with a certain structure to solve the low density parity check code. There are several categories have a certain structure low density parity check codes are constructed, which compares well with the design based on a combination of lowdensity parity check codes constructed based on finite geometries and low density parity check codes based on orthogonal Latin The low density parity check matrix code structure. These low density parity check code has the structure has the quasicyclic nature and quasicyclic LDPC encoding superior to the pseudorandom lowdensity parity check code, they can use a simple linear feedback shift encoded register, the most important is its complexity and a linear relationship between the code length. In the iterative decoding conditions, the performance of lowdensity paritycheck code has a number of indicators of the decision of this code. These indicators is an important code girth, which is defined as the code corresponding to the two graph shortest loop length. One yard good performance in iterative decoding, it corresponds to two images can not contain too much of the short length of 4 rings, so the code must be constructed to prevent the loop length of 4 appears. The results of many experiments show that: under the iterative decoding low density parity check code error code basin effect largely dependent minimum Hamming distance, while the nonformal errors LDPC effects depend on it two basins Figure variable nodes and check nodes of degree distribution. Based on Combinatorial Mathematics complete cyclic difference sets made two lowdensity parity check code constructor. One is through the decomposition of the cyclic difference set complete correlation matrix Q to construct the lowdensity paritycheck code of the parity check matrix H (t), this decomposition method can reduce the parity check matrix of the density of nonzero components, which can greatly reducing the impact of the performance of LDPC short loop count. Another lowdensity parity check code and we know the matrix code (Array codes), as the parity check matrix is ??a cyclic permutation matrix of small components, and covers a large class of different bit rates and different column weight low density parity code. According to such structure, the use of large scale integrated circuit design of the parallel decoder is extremely effective. Since two types of codes corresponding to Figure girth (girth) of at least 6, thus greatly reducing the outer iteration graph the correlation between the information, thereby improving the decoding performance. According to the bit error rate and frame error rate standards in the additive white Gaussian noise channel, and a plot with iterative decoding algorithm for decoding simulation performed well, and the constructed codes have quasicyclic structure, so they can use a simple linear shift register within linear time encoding. It is worth noting that this advantage is not generally other random shared by lowdensity paritycheck code.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Coding theory ( on behalf of the digital theory )
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