Improved Bit-Flipping Algorithm for Successive Cancellation Decoding of Polar Codes

TL;DR

This paper introduces the Thresholded SC-Flip (TSCF) decoding algorithm for polar codes, which improves error correction and reduces complexity compared to existing methods, making it more practical for 5G applications.

Contribution

The paper develops the TSCF algorithm that leverages average LLR values and a comparator to enhance performance and reduce complexity of polar code decoding.

Findings

TSCF achieves up to 0.45 dB performance gain over SC-Flip.

TSCF reduces computational complexity by up to 40%.

TSCF requires up to 5 times fewer maximum iterations.

Abstract

The interest in polar codes has been increasing significantly since their adoption for use in the 5$^{\rm th}$ generation wireless systems standard. Successive cancellation (SC) decoding algorithm has low implementation complexity, but yields mediocre error-correction performance at the code lengths of interest. SC-Flip algorithm improves the error-correction performance of SC by identifying possibly erroneous decisions made by SC and re-iterates after flipping one bit. It was recently shown that only a portion of bit-channels are most likely to be in error. In this work, we investigate the average log-likelihood ratio (LLR) values and their distribution related to the erroneous bit-channels, and develop the Thresholded SC-Flip (TSCF) decoding algorithm. We also replace the LLR selection and sorting of SC-Flip with a comparator to reduce the implementation complexity. Simulation results demonstrate that for practical code lengths and a wide range of rates, TSCF shows negligible loss compared to the error-correction performance obtained when all single-errors are corrected. At matching maximum iterations, TSCF has an error-correction performance gain of up to $0.45$ dB compared with SC-Flip decoding. At matching error-correction performance, the computational complexity of TSCF is reduced by up to $40\%$ on average, and requires up to $5\times$ lower maximum number of iterations.