  Quasi-cyclic low-density parity-check (QC-LDPC) codes based on protographs
are of great interest to code designers because analysis and implementation are
facilitated by the protograph structure and the use of circulant permutation
matrices for protograph lifting. However, these restrictions impose undesirable
fixed upper limits on important code parameters, such as minimum distance and
girth. In this paper, we consider an approach to constructing QC-LDPC codes
that uses a two-step lifting procedure based on a protograph, and, by following
this method instead of the usual one-step procedure, we obtain improved minimum
distance and girth properties. We also present two new design rules for
constructing good QC-LDPC codes using this two-step lifting procedure, and in
each case we obtain a significant increase in minimum distance and achieve a
certain guaranteed girth compared to one-step circulant-based liftings. The
expected performance improvement is verified by simulation results.
