  To address the challenge of constructing short girth-8 quasi-cyclic (QC)
low-density parity-check (LDPC) codes, a novel construction framework based on
vertical symmetry (VS) is proposed. Basic properties of the VS structure are
presented. With the aid of these properties, existing explicit constructions
for column weights from three to five which can be transformed into the VS
structure are sorted out. Then two novel explicit constructions with the VS
structure which guarantee short codes are presented for column weights of three
and six. Moreover, an efficient search-based method is also proposed to find
short codes with the VS structure. Compared with the state-of-the-art
benchmarks, both the explicit constructions and the search-based method
presented in this paper can provide shorter codes for most cases. Simulation
results show that the new shorter codes can perform almost the same as or
better than the longer existing counterparts. Thus, the new shorter codes can
fit better with the low-latency requirement for modern communication systems.
