Improved Successive Cancellation Flip Decoding of Polar Codes Based on Error Distribution

TL;DR

This paper introduces two techniques to enhance SC-Flip decoding of polar codes, reducing implementation complexity and improving error correction by leveraging error distribution insights, suitable for 5G standards.

Contribution

The paper proposes fixed index selection and enhanced index selection methods to improve SC-Flip decoding efficiency and performance based on error distribution analysis.

Findings

24.6% reduction in logic implementation cost

Up to 0.42 dB error correction performance improvement

Effective for low-rate polar codes in 5G applications

Abstract

Polar codes are a class of linear block codes that provably achieves channel capacity, and have been selected as a coding scheme for $5^{\rm th}$ generation wireless communication standards. Successive-cancellation (SC) decoding of polar codes has mediocre error-correction performance on short to moderate codeword lengths: the SC-Flip decoding algorithm is one of the solutions that have been proposed to overcome this issue. On the other hand, SC-Flip has a higher implementation complexity compared to SC due to the required log-likelihood ratio (LLR) selection and sorting process. Moreover, it requires a high number of iterations to reach good error-correction performance. In this work, we propose two techniques to improve the SC-Flip decoding algorithm for low-rate codes, based on the observation of channel-induced error distributions. The first one is a fixed index selection (FIS) scheme to avoid the substantial implementation cost of LLR selection and sorting with no cost on error-correction performance. The second is an enhanced index selection (EIS) criterion to improve the error-correction performance of SC-Flip decoding. A reduction of $24.6\%$ in the implementation cost of logic elements is estimated with the FIS approach, while simulation results show that EIS leads to an improvement on error-correction performance improvement up to $0.42$ dB at a target FER of $10^{-4}$.