Construction of protograph-based LDPC codes with chordless short cycles
Abstract
Controlling small size trapping sets and short cycles can result in LDPC codes with large minimum distance $d_{\min}$. We prove that short cycles with a chord are the root of several trapping sets and eliminating these cycles increases $d_{\min}$. We show that the lower bounds on $d_{\min}$ of an LDPC code with chordless short cycles, girths 6 (and 8), and column weights $\gamma$ (and 3), respectively, are $2\gamma$ (and 10), which is a significant improvement compared to the existing bounds $\gamma+1$ (and 6). Necessary and sufficient conditions for exponent matrices of protograph-based LDPC codes with chordless short cycles are proposed for any type of protographs, single-edge and multiple-edge, regular and irregular. The application of our method to girth-6 QC-LDPC codes shows that the removal of those cycles improves previous results in the literature.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2020
- DOI:
- 10.48550/arXiv.2008.01322
- arXiv:
- arXiv:2008.01322
- Bibcode:
- 2020arXiv200801322A
- Keywords:
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- Computer Science - Information Theory