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Sphere decoding (SD) of polar codes is an efficient method to achieve theerror performance of maximum likelihood (ML) decoding. But the complexity ofthe conventional sphere decoder is still high, where the candidates in a targetsphere are enumerated and the radius is decreased gradually until no availablecandidate 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. Basedon a novel path metric, SSD can effectively narrow the search range whenenumerating the candidates within a sphere. The proposed metric follows anexact ML rule and takes the full usage of the whole received sequence.Furthermore, another very simple metric is provided as an approximation of theML metric in the high signal-to-noise ratio regime. For short polar codes,simulation results over the additive white Gaussian noise channels show thatthe complexity of SSD based on the proposed metrics is up to 100 times lowerthan that of the conventional SD.

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