Ordered Statistic Decoding for Short Polar Codes

In this letter, the ordered statistic decoding (OSD) is considered to decode short polar codes. Since the number of tested codewords is high in the original OSD, a threshold-based OSD is proposed to reduce the complexity. The analysis shows that the threshold affects the OSD in two ways. One is the error floor in high signal-to-noise ratio (SNR) region while the other is the reduction of the number of tested codewords. The estimation on the BLER performance in high SNR region and the average number of tested codewords are discussed. After that, CRC-aided OSD is proposed to further improve the performance of polar codes. Simulation results show that a well-designed threshold-based OSD can reduce the complexity without significant performance loss. And a higher order OSD decoder is needed if OSD is used to decoding moderate or long polar codes. It is also illustrated that the CRC-aided OSD outperforms the CRC-aided list decoding when the code rate is high. When code rate is low, the result inverses.