# An Improved SCFlip Decoder for Polar Codes

## TL;DR

This paper enhances the SCFlip decoder for polar codes by introducing an optimized metric for flip position selection and generalizing it to multiple nested flips, significantly improving decoding performance with manageable complexity.

## Contribution

It proposes an optimized metric for flip position selection and extends SCFlip to multiple nested flips, advancing polar code decoding methods.

## Key findings

- SCFlip-2 achieves performance comparable to CRC-aided SC-List with L=4
- Optimized metric closely approaches ideal SCFlip performance
- Decoding complexity remains similar to standard SC at high SNR

## Abstract

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 $\omega$ nested flips, denoted by SCFlip-$\omega$, 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.