2024/12/03 by Haoran Xiong, Xiong, Haoran, Guanghui Wang +5
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.2412.02526
openalex publication_date 2024/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The lifting degree and the deterministic construction of quasi-cyclic low-density parity-check (QC-LDPC) codes have been extensively studied, with many construction methods in the literature, including those based on finite geometry, array-based codes, computer search, and combinatorial techniques. In this paper, we focus on the lifting degree p required for achieving a girth of 8 in (3,L) fully connected QC-LDPC codes, and we propose an improvement over the classical lower bound p≥ 2L-1, enhancing it to p≥ √(5L2-11L+(13)/(2))+(1)/(2). Moreover, we demonstrate that for girth-8 QC-LDPC codes containing an arithmetic row in the exponent matrix, a necessary condition for achieving a girth of 8 is p≥ (1)/(2)L2+(1)/(2)L. Additionally, we present a corresponding deterministic construction of (3,L) QC-LDPC codes with girth 8 for any p≥ (1)/(2)L2+(1)/(2)L+\lfloor (L-1)/(2)\rfloor, which approaches the lower bound of (1)/(2)L2+(1)/(2)L. Under the same conditions, this construction achieves a smaller lifting degree compared to prior methods. To the best of our knowledge, the proposed order of lifting degree matches the smallest known, on the order of (1)/(2)L2+O (L).