  We propose a technique to design finite-length irregular low-density
parity-check (LDPC) codes over the binary-input additive white Gaussian noise
(AWGN) channel with good performance in both the waterfall and the error floor
region. The design process starts from a protograph which embodies a desirable
degree distribution. This protograph is then lifted cyclically to a certain
block length of interest. The lift is designed carefully to satisfy a certain
approximate cycle extrinsic message degree (ACE) spectrum. The target ACE
spectrum is one with extremal properties, implying a good error floor
performance for the designed code. The proposed construction results in
quasi-cyclic codes which are attractive in practice due to simple encoder and
decoder implementation. Simulation results are provided to demonstrate the
effectiveness of the proposed construction in comparison with similar existing
constructions.
