Explicit Construction of QC-LDPC Codes Without Short Cycles via Shifting Dual Increasing Sequences

Abstract

Explicit construction methods for Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes offer greater descriptive simplicity and stronger applicability than search-based methods. A column weight that is either too large or too small makes it difficult to simultaneously balance the waterfall and error floor regions of the decoding performance curve. Therefore, this paper proposes an explicit construction method for QC-LDPC codes with a column weight approximately equal to 4 via shifting dual increasing sequences. For any given row weight L, this method can directly construct a $4 \times L$ exponent matrix, where evenindexed rows are defined by deterministic mathematical formulas to form dual increasing sequences, and odd-indexed rows are generated by applying cyclic right-shift operations to the corresponding even-indexed rows. Theoretical analysis proves that when the circulant size $\boldsymbol{P}$ is not less than a specific lower bound, the proposed codes achieve a girth of 8. Simulation results demonstrate that the proposed codes outperform benchmark codes constructed using the horizontal symmetrical, column multipliers, and decrease-increase methods, while remaining comparable to product-like counterparts. Furthermore, when combined with the masking operation, their decoding performance is significantly improved compared to the original codes; when combined with the splitting and concatenation operation, the proposed codes outperform the 5G-NR code based on BG2 in the high signal-to-noise regime.