Reduce the Complexity of List Decoding of Polar Codes by Tree-Pruning

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 SCL/CA-SCL decoding algorithms is proposed in this letter. 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 how much pruning 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 as many as possible of the redundant candidate paths 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.