  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.
