Successive-Cancellation Flip and Perturbation Decoder of Polar Codes

2025-04-16

AI Summary

This paper addresses the challenge of balancing error-correction performance and decoding complexity in CRC-aided polar codes. To this end, we propose two low-complexity decoding algorithms—DSCFP and PDSCF—that jointly integrate dynamic successive-cancellation (SC) flipping and SC perturbation, guided by CRC verification to enable multi-trial decoding (T_max = 17/64). Compared to conventional DSCF and SCP, our algorithms achieve SNR gains of 0.375 dB and over 0.5 dB, respectively, at N = 1024, code rate R = 1/2, and BLER = 10⁻⁶, while maintaining average computational complexity comparable to that of basic SC decoding. The key innovation lies in the co-designed flipping-perturbation strategy and its dynamic triggering mechanism, which effectively breaks the performance–complexity trade-off bottleneck and significantly enhances error-correction capability in the high-SNR regime.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this paper, two decoding algorithms based on Successive Cancellation (SC) are proposed to improve the error-correction performance of cyclic redundancy check (CRC)-aided polar codes while aiming for a low-complexity implementation. Comparisons with Dynamic SC Flip (DSCF) and SC Perturbation (SCP) are carried out since the proposed DSCF and Perturbation (DSCFP) and Perturbed DSCF (PDSCF) algorithms combine both methods. The analysis includes comparisons with several code lengths $N$ and various number of decoding attempts $T_{max}$. For $N=1024$ and the coding rate $R=frac{1}{2}$, the DSCFP and the SCP algorithms with $T_{max}=17$ are bested by approximately $0.1$,dB at block error rate (BLER) of $0.001$. At $ ext{BLER}=10^{-6}$ and for $T_{max}=64$, the gain is of $0.375$ dB and $>0.5$ dB with respect to DSCF and SCP, respectively. At high signal-to-noise ratio, the average computational complexity of the proposed algorithms is virtually equivalent to that of SC.

Problem

• Improving error-correction performance of CRC-aided polar codes
• Combining DSCF and SCP methods for better decoding
• Achieving low-complexity implementation comparable to SC

Innovation

• Combines DSCF and SCP for better performance
• Maintains low-complexity similar to SC
• Improves error-correction with multiple attempts