Relation Between Parity-Check Matrixes and Cycles of Associated Tanner Graphs

Ru-wei, Chen; Huang, Huawei; Xiao, Gao

doi:10.1109/lcomm.2007.07613

Cited by 10 publications

(4 citation statements)

References 8 publications

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“…As another experiment, we randomly generate six parity-check matrices for each of the following three rate-1/2 LDPC code ensembles: (d u , d w ) = (3, 6), (4,8), (5,10). The lengths for each degree distribution are: n = 200, 500, 1000, 5000, 10, 000 and 20, 000.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The complexity of their method is O(m k+1 ) where m is the number of the check nodes in the graph. Their method quickly becomes prohibitively complex even for counting cycles as short as 6, particularly in graphs with large m. An algorithm with similar complexity was proposed in [4] for counting only the shortest cycles of a Tanner graph. Halford and Chugg [8] presented a method for counting short cycles of length g, g + 2 and g + 4 in bipartite graphs with girth g. The complexity of their method is O(gn 3 ), where n is the size of the larger set between the two node partitions.…”

Section: Introductionmentioning

confidence: 99%

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A message-passing algorithm for counting short cycles in a graph

Karimi

Banihashemi

2010

IEEE Information Theory Workshop 2010 (ITW 2010)

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A message-passing algorithm for counting short cycles in a graph is presented. For bipartite graphs, which are of particular interest in coding, the algorithm is capable of counting cycles of length g, g + 2, . . . , 2g − 2, where g is the girth of the graph. For a general (non-bipartite) graph, cycles of length g, g + 1, . . . , 2g − 1 can be counted.The algorithm is based on performing integer additions and subtractions in the nodes of the graph and passing extrinsic messages to adjacent nodes. The complexity of the proposed algorithm grows as O(g|E| 2 ), where |E| is the number of edges in the graph. For sparse graphs, the proposed algorithm significantly outperforms the existing algorithms in terms of computational complexity and memory requirements.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A message-passing algorithm for counting short cycles in a graph

Karimi

Banihashemi

2010

IEEE Information Theory Workshop 2010 (ITW 2010)

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“…For bipartite graphs with cycles, there is an interesting structure in the corresponding parity check matrix. The underlying structure of the matrix corresponding to cycle in Tanner graph can be summarized in the following way [12]. Definition 6.…”

Section: Consistency Of Structured Equations In Fqmentioning

confidence: 99%

On the Minimum Distance of Non Binary LDPC Codes

Pulikkoonattu

2009

Preprint

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Minimum distance is an important parameter of a linear error correcting code. For improved performance of binary Low Density Parity Check (LDPC) codes, we need to have the minimum distance grow fast with n, the codelength. However, the best we can hope for is a linear growth in d min with n. For binary LDPC codes, the necessary and sufficient conditions on the LDPC ensemble parameters, to ensure linear growth of minimum distance is well established. In the case of non-binary LDPC codes, the structure of logarithmic weight codewords is different from that of binary codes. We have carried out a preliminary study on the logarithmic bound on the the minimum distance of non-binary LDPC code ensembles. In particular, we have investigated certain configurations which would lead to low weight codewords. A set of simulations are performed to identify some of these configurations. Finally, we have provided a bound on the logarithmic minimum distance of nonbinary codes, using a strategy similar to the girth bound for binary codes. This bound has the same asymptotic behaviour as that of binary codes.

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“…In particular, we use G b and the set of cycles in G b of minimum length to create a three-partite graph G t . The algorithms given in [14][15][16] may be employed to determine the girth and number of minimum length cycles in G b . Let V be the set of all three element subsets of vertices in G t such that any element of V has a vertex in each part of G t that either forms a triangle in G t or no two elements of this set are adjacent in G t .…”

Section: Introductionmentioning

confidence: 99%