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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Faculty of Technical Sciences in Cacak
2023-01-01
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| Series: | Serbian Journal of Electrical Engineering |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/1451-4869/2023/1451-48692301083S.pdf |
| Summary: | 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. |
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| ISSN: | 1451-4869 2217-7183 |