QC-LDPC codes from various Golomb Rulers

In this paper, we analyze the girth of QC-LDPC codes constructed using a special type of Golomb rulers called B
h
sequences and a well-known multiplication table method. We investigate the condition for the existence of 8-cycles and we are able to count the exact number of 8-cycles in the QC-LDPC codes using B
h
sequences. The analysis focuses on the case h =3. By computer simulation, we show that the resulting codes for h =3 have a better performance than those from general Golomb rulers (non-B
3
sequences) and have a comparable performance to the modified LDPC codes from basegraph2 in 5GNR spec. As h increases, the result could have higher girth but the performance improvement is only marginal.