Low-Complexity Sphere Decoding of Polar Codes based on Optimum Path Metric

TL;DR

This paper introduces a low-complexity sphere decoding algorithm for polar codes using an innovative path metric, significantly reducing computational effort while maintaining near-optimal error performance.

Contribution

It proposes a novel stack sphere decoding algorithm with an exact ML-based path metric and a simple high-SNR approximation, greatly lowering complexity for polar code decoding.

Findings

Complexity reduced by up to 100 times compared to conventional SD.

The proposed metrics effectively narrow the search range.

Simulation results confirm near-ML performance with lower complexity.

Abstract

Sphere decoding (SD) of polar codes is an efficient method to achieve the error performance of maximum likelihood (ML) decoding. But the complexity of the conventional sphere decoder is still high, where the candidates in a target sphere are enumerated and the radius is decreased gradually until no available candidate is in the sphere. In order to reduce the complexity of SD, a stack SD (SSD) algorithm with an efficient enumeration is proposed in this paper. Based on a novel path metric, SSD can effectively narrow the search range when enumerating the candidates within a sphere. The proposed metric follows an exact ML rule and takes the full usage of the whole received sequence. Furthermore, another very simple metric is provided as an approximation of the ML metric in the high signal-to-noise ratio regime. For short polar codes, simulation results over the additive white Gaussian noise channels show that the complexity of SSD based on the proposed metrics is up to 100 times lower than that of the conventional SD.