An improved method for counting 6-cycles in low-density parity-check codes
Since their rediscovery in the early 1990s, low-density parity-check (LDPC) codes have become the most popular error-correcting codes owing to their excellent performance. An LDPC code is a linear block code that has a sparse parity-check matrix. Cycles in this matrix, particularly short cy...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Faculty of Technical Sciences in Cacak
2023-01-01
|
| Series: | Serbian Journal of Electrical Engineering |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/1451-4869/2023/1451-48692301083S.pdf |
| _version_ | 1811155192895242240 |
|---|---|
| author | Slimani Djamel Kaddai Abdellah |
| author_facet | Slimani Djamel Kaddai Abdellah |
| author_sort | Slimani Djamel |
| collection | DOAJ |
| description | Since their rediscovery in the early 1990s, low-density parity-check (LDPC)
codes have become the most popular error-correcting codes owing to their
excellent performance. An LDPC code is a linear block code that has a sparse
parity-check matrix. Cycles in this matrix, particularly short cycles,
degrade the performance of such a code. Hence, several methods for counting
short cycles in LDPC codes have been proposed, such as Fan’s method to
detect 4-cycles, 6- cycles, 8-cycles, and 10-cycles. Unfortunately, this
method fails to count all 6- cycles, i.e., ignores numerous 6-cycles, in
some given parity-check matrices. In this paper, an improvement of this
algorithm is presented that detects all 6-cycles in LDPC codes, as well as
in general bipartite graphs. Simulations confirm that the improved method
offers the exact number of 6-cycles, and it succeeds in detecting those
ignored by Fan’s method. |
| first_indexed | 2024-04-10T04:30:08Z |
| format | Article |
| id | doaj.art-f28bb450507a46e1977fc7676a01dd28 |
| institution | Directory Open Access Journal |
| issn | 1451-4869 2217-7183 |
| language | English |
| last_indexed | 2024-04-10T04:30:08Z |
| publishDate | 2023-01-01 |
| publisher | Faculty of Technical Sciences in Cacak |
| record_format | Article |
| series | Serbian Journal of Electrical Engineering |
| spelling | doaj.art-f28bb450507a46e1977fc7676a01dd282023-03-10T08:06:08ZengFaculty of Technical Sciences in CacakSerbian Journal of Electrical Engineering1451-48692217-71832023-01-01201839110.2298/SJEE2301083S1451-48692301083SAn improved method for counting 6-cycles in low-density parity-check codesSlimani Djamel0Kaddai Abdellah1Faculty of Electrical Engineering, University of Science and Technology of Oran (USTO), AlgeriaFaculty of Technology, University of Hassiba Benbouali Chlef (UHBC), AlgeriaSince their rediscovery in the early 1990s, low-density parity-check (LDPC) codes have become the most popular error-correcting codes owing to their excellent performance. An LDPC code is a linear block code that has a sparse parity-check matrix. Cycles in this matrix, particularly short cycles, degrade the performance of such a code. Hence, several methods for counting short cycles in LDPC codes have been proposed, such as Fan’s method to detect 4-cycles, 6- cycles, 8-cycles, and 10-cycles. Unfortunately, this method fails to count all 6- cycles, i.e., ignores numerous 6-cycles, in some given parity-check matrices. In this paper, an improvement of this algorithm is presented that detects all 6-cycles in LDPC codes, as well as in general bipartite graphs. Simulations confirm that the improved method offers the exact number of 6-cycles, and it succeeds in detecting those ignored by Fan’s method.http://www.doiserbia.nb.rs/img/doi/1451-4869/2023/1451-48692301083S.pdflow-density parity-check (ldpc) code6-cycleparity-check matrixtanner graph. |
| spellingShingle | Slimani Djamel Kaddai Abdellah An improved method for counting 6-cycles in low-density parity-check codes Serbian Journal of Electrical Engineering low-density parity-check (ldpc) code 6-cycle parity-check matrix tanner graph. |
| title | An improved method for counting 6-cycles in low-density parity-check codes |
| title_full | An improved method for counting 6-cycles in low-density parity-check codes |
| title_fullStr | An improved method for counting 6-cycles in low-density parity-check codes |
| title_full_unstemmed | An improved method for counting 6-cycles in low-density parity-check codes |
| title_short | An improved method for counting 6-cycles in low-density parity-check codes |
| title_sort | improved method for counting 6 cycles in low density parity check codes |
| topic | low-density parity-check (ldpc) code 6-cycle parity-check matrix tanner graph. |
| url | http://www.doiserbia.nb.rs/img/doi/1451-4869/2023/1451-48692301083S.pdf |
| work_keys_str_mv | AT slimanidjamel animprovedmethodforcounting6cyclesinlowdensityparitycheckcodes AT kaddaiabdellah animprovedmethodforcounting6cyclesinlowdensityparitycheckcodes AT slimanidjamel improvedmethodforcounting6cyclesinlowdensityparitycheckcodes AT kaddaiabdellah improvedmethodforcounting6cyclesinlowdensityparitycheckcodes |