Multi-Bit-Flipping Decoding of Polar Codes Based on Medium-Level Bit-Channels Sets

For short to moderate finite block-lengths, due to incompletely polarized bit-channels, polar codes fail to deliver competitive performance under successive cancellation (SC) decoding. In this paper, we first define $\omega$-order medium-level bit-channels (MBC) sets, which are used to quantitatively identify the incompletely polarized bit-channels of polar codes. And then, using the reliability ordering of bit-channels, which is calculated and used for encoding and decoding of polar codes, an algorithm for finding the MBC sets is given. Finally, we propose a multi-bit-flipping SC decoding algorithm, which builds a list of candidate bit-flips with 1 up to $\omega$ flipping positions within the $\omega$-order MBC sets. The iteration trajectory of bit-flipping positions is a fixed subsequence of reliability ordering, which avoids the sorting operation of log likelihood rates in each codeword frame. Simulation results show that, with a code rate 0.5, the search scope and decoding latency of the proposed algorithm can be reduced about 1/3 to 1/6 without loss of performance compared with the standard SCFlip decoding.