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

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.