  A finite set system (FSS) is a pair (V; B) where V is a finite set whose
members are called points, equipped with a finite collection of its subsets B
whose members are called blocks. In this paper, finite set systems are used to
define a class of Quasi-cyclic low- density parity-check (LDPC) codes, called
FSS codes, such that the constructed codes possess large girth and arbitrary
column-weight distributions. Especially, the constructed column weight-2 FSS
codes have higher rates than the column weight-2 geometric and cylinder-type
codes with the same girths. To find the maximum girth of FSS codes based on (V;
B), inevitable walks are defined in B such that the maximum girth is determined
by the smallest length of the inevitable walks in B. Simulation results show
that the constructed FSS codes have very good performance over the AWGN channel
with iterative decoding and achieve significantly large coding gains compared
to the random-like LDPC codes of the same lengths and rates.
