Critical-Set-Aided Simplified Blind SCL Recognition of Polar Codes

2026-07-19

AI Summary

This work addresses the high computational complexity of blind polar code identification in non-cooperative scenarios by proposing a key-set-aided simplified blind successive cancellation list (SCL) method. The approach performs dual-hypothesis path expansion only at critical bit positions, while employing low-complexity blind successive cancellation (SC) decoding elsewhere. It innovatively links error-prone bit locations to dominant terms in performance upper bounds and introduces a key-set mechanism guided by density evolution to construct tight analytical bounds, thereby enhancing selection reliability and performance estimation accuracy. Leveraging density evolution-derived LLR distributions, the method optimizes Chernoff bounds and overlap coefficients to inform key-set selection. Experimental results demonstrate that the proposed scheme achieves identification success rates comparable to those of blind SCL (BSCL) while significantly reducing complexity; moreover, the key-set size rapidly diminishes with increasing SNR, and the gap between the derived bounds remains below 1 dB at a misidentification rate of $10^{-2}$.

Abstract

Blind recognition of polar codes from noisy observations is a key problem in non-cooperative signal processing. Although existing blind successive cancellation list (BSCL) recognition exploits channel soft information, it performs two-hypothesis path expansion at every source-bit position, resulting in high complexity. In this paper, we first analyze the first recognition-error positions in the blind successive cancellation (BSC) recognition and observe that they are closely related to the corresponding contribution terms in the existing Bhattacharyya-parameter-based upper bounds. Based on this observation, a critical-set-aided simplified blind successive cancellation list (SBSCL) recognition method is proposed. SBSCL performs two-hypothesis path expansion only at the selected critical-set positions and keeps BSC recognition at the remaining positions, thereby reducing complexity. To improve the reliability of critical-set selection and refine the performance analysis, density-evolution (DE)-based bounds are further developed. Under the ideal SC-consistent condition, the synthetic log-likelihood-ratio (LLR) distributions obtained from density evolution are used to compute the optimized Chernoff coefficient for the upper bound and the overlap coefficient for the lower bound. Simulation results show that the DE-based bounds are tighter than the Bhattacharyya-parameter-based bounds. In the considered settings, the gap between the DE upper and lower bounds is within $1$ dB around a recognition-error probability of $10^{-2}$. Furthermore, SBSCL achieves nearly the same recognition success rate as BSCL, and the size of critical set decreases rapidly as the signal-to-noise ratio (SNR) increases.

Problem

• polar codes
• blind recognition
• successive cancellation list
• computational complexity
• non-cooperative signal processing

Innovation

• critical set
• blind recognition
• polar codes
• density evolution
• successive cancellation list