Some New Constructions of Girth-8 QC-LDPC Codes for Future GNSS

In this letter, we propose a new construction of girth-8 Quasi-Cyclic Low-Density Parity-Check codes (QC-LDPC) with various lengths for the global navigation satellite systems (GNSS). This scheme combines two steps. The first is the construction of a family of regular girth-8 QC-LDPC codes of various lengths and rates with two designed sequences. The second is the performance improvement of those from the first construction of half-rate cases using a proposed weight matrix so that the result becomes type-II QC-LDPC codes. This results in some final codes with short lengths of 600, 1200, and 1800, especially for future GNSS. We performed a simulation and confirmed that the proposed QC-LDPC codes of lengths 600 and 1200 have an additional coding gain about 0.3 dB at frame error rate 10-5 over the LDPC codes used in the Global Positioning System.