Stochastic Flipping Decoding for Short Polar Codes

Polar codes are considered a promising candidate for URLLC. Due to the inevitable decoding delay and error propagation brought by successive cancellation (SC) based decoders, the ordered statistic decoding (OSD) algorithm, which has a parallel structure, raises much attention in polar decoding, especially for the short codelength cases. However, the OSD algorithm contains many unnecessary attempts for different error patterns (EPs), increasing the complexity and decoding delay. To address this issue, we propose a novel stochastic flipping decoding (SFD) algorithm. Instead of processing all EPs in the search space, each time, the proposed SFD decoder only processes a small set of EPs generated by stochastic flipping and then chooses the one that has the best distance to get the new reference codeword. The flipping probability vector depends on how the flip of each bit potentially affects the overall distance, and it is updated progressively towards all-zero. The complexity of the algorithm can be further reduced by eliminating all the duplicated EPs. Numerical results show that improved SFD with adequately selected parameters outperforms OSD while the search space of these two algorithms is close.