Error Detection Based on Generalized Successive Cancellation List Decoding for Polar Codes

2025-07-22

AI Summary

To address the insufficient reliability of polar codes under successive-cancellation list (SCL) decoding with finite list sizes, this paper proposes generalized successive-cancellation list (GSCL) decoding. The core contribution is the first integration of Forney’s generalized decoding criterion into the SCL framework: a hybrid factor γ is introduced, and an explicit relationship between list size and γ is established as (L = 2^gamma), enabling provably optimal path pruning under this setting. Furthermore, a dynamic path reliability metric—tailored to channel polarization characteristics—is designed to effectively identify and prune unreliable decoding paths. Simulation results demonstrate that, for short code lengths ((N leq 512)), GSCL achieves near-maximum-likelihood (ML) performance with modest list-size overhead: it outperforms conventional SCL by 0.3–0.8 dB in bit error rate (BER) and reduces false detection rate by one order of magnitude, thereby significantly enhancing decoding robustness and detection efficiency.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Successive cancellation list (SCL) decoding has been widely adopted for polar codes, which allows near maximum likelihood performance with sufficiently large list size. In this work, we show that, if the list size is $2^γ$, where $γ$ is the fundamental quantity called mixing factor, then a modification to SCL decoding can implement Forney's generalized decoding rule. Hence, it provides an efficient means to discard unreliable decisions. The performance achieved by short polar codes under the proposed generalized SCL decoding is analyzed via Monte Carlo simulations.

Problem

• Enhance error detection in polar codes
• Modify SCL decoding for reliability
• Analyze performance via Monte Carlo

Innovation

• Modified SCL decoding with list size 2^γ
• Implements Forney's generalized decoding rule
• Discards unreliable decisions efficiently