  We propose a new family of polar coding which realizes high coding gain, low
complexity, and high throughput by introducing a protograph-based design. The
proposed technique called as quasi-cyclic (QC) polar codes can be highly
parallelized without sacrificing decoding complexity. We analyze short cycles
in the protograph polar codes and develop a design method to increase the
girth. Our approach can resolve the long-standing unsolved problem that belief
propagation (BP) decoding does not work well for polar codes due to the
inherently short cycles. We demonstrate that a high lifting factor of QC polar
codes can improve the performance and that QC polar codes with BP decoding can
outperform conventional polar codes with state-of-the-art list decoding.
Moreover, we show that a greedy pruning method can improve the
performance-complexity trade-off.
