  Polar codes under cyclic redundancy check aided successive cancellation list
(CA-SCL) decoding can outperform the turbo codes and the LDPC codes when code
lengths are configured to be several kilobits. In order to reduce the decoding
complexity, a novel tree-pruning scheme for the \mbox{SCL/CA-SCL} decoding
algorithms is proposed in this paper. In each step of the decoding procedure,
the candidate paths with metrics less than a threshold are dropped directly to
avoid the unnecessary computations for the path searching on the descendant
branches of them. Given a candidate path, an upper bound of the path metric of
its descendants is proposed to determined whether the pruning of this candidate
path would affect frame error rate (FER) performance. By utilizing this upper
bounding technique and introducing a dynamic threshold, the proposed scheme
deletes the redundant candidate paths as many as possible while keeping the
performance deterioration in a tolerant region, thus it is much more efficient
than the existing pruning scheme. With only a negligible loss of FER
performance, the computational complexity of the proposed pruned decoding
scheme is only about $40\%$ of the standard algorithm in the low
signal-to-noise ratio (SNR) region (where the FER under CA-SCL decoding is
about $0.1 \sim 0.001$), and it can be very close to that of the successive
cancellation (SC) decoder in the moderate and high SNR regions.
