2020/08/04 by Farzane Amirzade, Amirzade, Farzane, Mohammad‐Reza Sadeghi +3
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Cooperative Communication and Network Coding #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2008.01322
openalex publication_date 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Controlling small size trapping sets and short cycles can result in LDPC codes with large minimum distance dmin. We prove that short cycles with a chord are the root of several trapping sets and eliminating these cycles increases dmin. We show that the lower bounds on dmin of an LDPC code with chordless short cycles, girths 6 (and 8), and column weights γ (and 3), respectively, are 2γ (and 10), which is a significant improvement compared to the existing bounds γ+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.