This paper proposes a generalization of the recently introduced successive cancellation flip (SCFlip) decoding of polar codes, characterized by a number of extra decoding attempts, where one or several positions are flipped from the standard SC decoding. To make such an approach effective, we first introduce the concept of higher order bit flips and propose a new metric to determine the bit flips that are more likely to correct the trajectory of the SC decoding. We then propose a generalized SCFlip decoding algorithm, referred to as dynamic-SCFlip (D-SCFlip), which dynamically builds a list of candidate bit flips, while guaranteeing that the next attempt has the highest probability of success among the remaining ones. Simulation results show that D-SCFlip is an effective alternative to SC-list decoding of polar codes, by providing very good error correcting performance, with an average computation complexity close to the one of the SC decoder.

This paper focuses on the recently introduced Successive Cancellation Flip (SCFlip) decoder of polar codes. Our contribution is twofold. First, we propose the use of an optimized metric to determine the flipping positions within the SCFlip decoder, which improves its ability to find the first error that occurred during the initial SC decoding attempt. We also show that the proposed metric allows closely approaching the performance of an ideal SCFlip decoder. Second, we introduce a generalisation of the SCFlip decoder to a number of ω nested flips, denoted by SCFlip-ω, using a similar optimized metric to determine the positions of the nested flips. We show that the SCFlip-2 decoder yields significant gains in terms of decoding performance and competes with the performance of the CRC-aided SC-List decoder with list size L=4, while having an average decoding complexity similar to that of the standard SC decoding, at medium to high signal to noise ratio.