Lower Bounds on the Lifting Degree of QC-LDPC Codes by Difference Matrices
In this paper, we define two “difference matrices” which correspond to an exponent matrix. We present necessary and sufficient conditions for these difference matrices to have quasi-cyclic low-density parity-check codes (QC-LDPC) codes with a certain girth. We achieve all non-i...
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doaj-f94c5342467b477c8cf5e4625f4b4bc72021-03-29T20:44:05ZengIEEEIEEE Access2169-35362018-01-016236882370010.1109/ACCESS.2018.28304068350277Lower Bounds on the Lifting Degree of QC-LDPC Codes by Difference MatricesFarzane Amirzade0Mohammad-Reza Sadeghi1https://orcid.org/0000-0002-7676-4168School of Mathematical Sciences, Shahrood University of Technology, Shahrud, IranDepartment of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, IranIn this paper, we define two “difference matrices” which correspond to an exponent matrix. We present necessary and sufficient conditions for these difference matrices to have quasi-cyclic low-density parity-check codes (QC-LDPC) codes with a certain girth. We achieve all non-isomorphic QC-LDPC codes with the shortest length, girth 6, the column weight, m = 4, and the row weight, 5 ≤ n ≤ 11. Moreover, a method to obtain an exponent matrix with girth 10 is presented which reduces the complexity of the search algorithm. If the first row and the first column of the exponent matrix are all-zero, then by applying our method we do not need to test Fossorier's lemma to avoid 6-cycles and 8-cycles. For girth 10, we also provide a lower bound on the lifting degree which is tighter than the existing bound. For girth 12, a new lower bound on the lifting degree is achieved.https://ieeexplore.ieee.org/document/8350277/QC-LDPC codesprotographsgirthdifference matriceslifting degree |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Farzane Amirzade Mohammad-Reza Sadeghi |
spellingShingle |
Farzane Amirzade Mohammad-Reza Sadeghi Lower Bounds on the Lifting Degree of QC-LDPC Codes by Difference Matrices IEEE Access QC-LDPC codes protographs girth difference matrices lifting degree |
author_facet |
Farzane Amirzade Mohammad-Reza Sadeghi |
author_sort |
Farzane Amirzade |
title |
Lower Bounds on the Lifting Degree of QC-LDPC Codes by Difference Matrices |
title_short |
Lower Bounds on the Lifting Degree of QC-LDPC Codes by Difference Matrices |
title_full |
Lower Bounds on the Lifting Degree of QC-LDPC Codes by Difference Matrices |
title_fullStr |
Lower Bounds on the Lifting Degree of QC-LDPC Codes by Difference Matrices |
title_full_unstemmed |
Lower Bounds on the Lifting Degree of QC-LDPC Codes by Difference Matrices |
title_sort |
lower bounds on the lifting degree of qc-ldpc codes by difference matrices |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2018-01-01 |
description |
In this paper, we define two “difference matrices” which correspond to an exponent matrix. We present necessary and sufficient conditions for these difference matrices to have quasi-cyclic low-density parity-check codes (QC-LDPC) codes with a certain girth. We achieve all non-isomorphic QC-LDPC codes with the shortest length, girth 6, the column weight, m = 4, and the row weight, 5 ≤ n ≤ 11. Moreover, a method to obtain an exponent matrix with girth 10 is presented which reduces the complexity of the search algorithm. If the first row and the first column of the exponent matrix are all-zero, then by applying our method we do not need to test Fossorier's lemma to avoid 6-cycles and 8-cycles. For girth 10, we also provide a lower bound on the lifting degree which is tighter than the existing bound. For girth 12, a new lower bound on the lifting degree is achieved. |
topic |
QC-LDPC codes protographs girth difference matrices lifting degree |
url |
https://ieeexplore.ieee.org/document/8350277/ |
work_keys_str_mv |
AT farzaneamirzade lowerboundsontheliftingdegreeofqcldpccodesbydifferencematrices AT mohammadrezasadeghi lowerboundsontheliftingdegreeofqcldpccodesbydifferencematrices |
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