Iterative and Adjustable Soft List Decoding for Polar Codes

List decoding of polar codes is an outstanding decoding method, in which a fixed-size list is applied to retain the most probable paths. In general, it is preferable to use a large-size list in the decoding to achieve excellent error-control performance, but this can lead to high complexity. Moreover, the list decoding is still a one-time-pass algorithm with hard-decision outputs, which is not well suited for advanced concatenated coding systems. In this paper, a novel adjustable list decoding is proposed, in which the list size can be adjusted appropriately. Based on the reliability analyses of the decoding list, dynamic thresholds are designed to precisely guide the adjustments. The adjustable list decoding can also achieve excellent error-control performance, but the complexity is significantly reduced. Moreover, we propose an iterative adjustable list decoding scheme with soft-decision outputs for concatenated polar-coding systems, in which a log-likelihood-ratio update strategy is elaborately designed. It can achieve much better error-control performance compared with the existing iterative decoding schemes, such as the belief propagation (BP) decoding, and soft cancellation (SCAN) decoding. As the number of iterations increases, the decoding performance gradually improves, but the complexity increases little due to efficient complexity control designs.