Protograph-Based Design for QC Polar Codes

We propose a new family of polar codes to realize high coding gain, low complexity, and high throughput by introducing a protograph-based design. Our proposed technique, called 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.