ABSTRACT The sphere decoding (SD) algorithm for polar codes can achieve maximum likelihood decoding performance, but suffers from high computational complexity. Based on the polar codes with symmetrical structure, the complexity of the SD algorithm can be reduced at the expense of a slight performance loss. To further improve the performance of the SD algorithm for symmetric polar codes, an improved flip SD algorithm is proposed in this paper. When the estimated codeword fails the cyclic redundancy check (CRC), the proposed algorithm flips an unreliable combined value and re‐performs the decoding process. Specifically, using the structure of symmetric polar codes, a flipping set is first constructed to incorporate unreliable combined values. The combined values in the flipping set are sorted according to their reliability. Then, a new flipping operation is developed for the flipped values to further improve performance. Simulation results show that, compared to the symmetric SD algorithms, the proposed algorithm can achieve a performance gain of up to 1.6 dB for the polar code of length 64 with different rates at the frame error rate (FER) of , with a slightly higher computational complexity; when compared to the original SD algorithm, the proposed algorithm can achieve a maximum of 1.58 dB performance gain at FER = but with a lower computational complexity.
Li et al. (Thu,) studied this question.