The decoders, which improve the error-correction performance by finding and correcting the error bits caused by channel noise, are a hotspot for polar codes. In this paper, we present a threshold based D-SCFlip (TD-SCFlip) decoder with two improvements based on the D-SCFlip decoder. First, we propose the LLR fidelity criterion to define the LLR threshold and investigate confidence probability to calculate the LLR threshold indirectly. The information bits whose LLR values are smaller than the LLR threshold will be excluded from the range of candidate bits, which reduces the complexity of constructing the flip-bits list without the loss of error-correction performance. Second, we improve the calculation method for flip-bits metric with two perturbation parameters, which locates the channel-induced error bits faster, thus improving the error-correction performance. Then, TD-SCFlip-ω decoder is also proposed, which is limited to correcting up to ω bits in each extra decoding attempt. Simulation results show that the TD-SCFlip decoding is slightly better than the D-SCFlip decoding in terms of error-correction performance and decoding complexity, while the error-correction performance of TD-SCFlip-ω decoding is comparable to that of D-SCFlip-ω decoding but with lower decoding complexity.

This paper presents a successive cancellation (SC) decoding of polar codes modified for insertion/deletion/substitution (IDS) error channels, in which insertions and deletions are described by drift values. The recursive calculation of the original SC decoding is modified to include the drift values as stochastic variables. The computational complexity of the modified SC decoding is O (D3) with respect to the maximum drift value D, and O (N log N) with respect to the code length N. The symmetric capacity of polar bit channel is estimated by computer simulations, and frozen bits are determined according to the estimated symmetric capacity. Simulation results show that the decoded error rate of polar code with the modified SC list decoding is lower than that of existing IDS error correction codes, such as marker-based code and spatially-coupled code.