  Polar codes has been selected as the channel coding scheme for 5G new radio
(NR) control channel. Specifically, a special type of parity-check polar
(PC-Polar) codes was adopted in uplink control information (UCI). In this
paper, we propose a parity-check soft-cancellation (PC-SCAN) algorithm and its
simplified version to decode PC-Polar codes. The potential benefits are
two-fold. First, PC-SCAN can provide soft output for PC-Polar codes, which is
essential for advanced turbo receivers. Second, the decoding performance is
better than that of successive cancellation (SC). This is due to the fact that
parity-check constraints can be exploited by PC-SCAN to enhance the reliability
of other information bits over the iterations. Moreover, we describe a
cyclic-shift-register (CSR) based implementation "CSR-SCAN" to reduce both
hardware cost and latency with minimum performance loss.
