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

TL;DR

This paper introduces a tree-pruning scheme for polar code decoding that significantly reduces computational complexity while maintaining near-original error performance, especially effective at low SNR levels.

Contribution

A novel tree-pruning method using upper bounds and dynamic thresholds to efficiently reduce decoding complexity of polar codes without degrading FER performance.

Findings

Complexity reduced to about 40% of standard CA-SCL decoding at low SNR.

Negligible FER performance loss with the proposed pruning scheme.

Approaches the complexity of SC decoding in moderate/high SNR regions.

Abstract

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.