In this paper, we propose new constructions for regular girth-8 quasi-cyclic low-density parity-check (QC-LDPC) codes based on circulant permutation matrices (CPM). The constructions assume symmetries in the structure of the parity-check matrix and employ a greedy exhaustive search algorithm to find the permutation shifts of the CPMs. As a result of symmetries, the new codes have a more compact representation compared with their counterparts. In majority of cases, also, they achieve the girth 8 at a shorter block length for the same degree distribution (code rate). Deterministic (explicit) constructions are also presented to expand the proposed parity-check matrices to larger block lengths and higher rates. The proposed long high-rate codes are often substantially shorter than regular girth-8 QC-LDPC codes of similar rate in the literature. Simulation results demonstrate that the proposed symmetric codes have competitive performance in comparison with similar existing QC-LDPC codes that lack symmetry.

Additional Metadata
Keywords girth, protograph-based LDPC codes, QC-LDPC code construction, QC-LDPC codes, QC-LDPC codes of girth 8, regular LDPC codes, symmetrical QC-LDPC codes
Persistent URL dx.doi.org/10.1109/TCOMM.2016.2617335
Journal IEEE Transactions on Communications
Citation
Tasdighi, A. (Alireza), Banihashemi, A, & Sadeghi, M.-R. (Mohammad-Reza). (2017). Symmetrical Constructions for Regular Girth-8 QC-LDPC Codes. IEEE Transactions on Communications, 65(1), 14–22. doi:10.1109/TCOMM.2016.2617335