A Hypothesis-Testing Analysis of Blind Recognition for Polar Codes

2026-06-16

AI Summary

This study addresses the blind identification of frozen and information bit positions in polar codes under non-cooperative scenarios. Assuming known code length, the problem is rigorously formulated for the first time as a binary hypothesis test based on a successive cancellation (SC) consistency model, and tight upper and lower bounds on the identification error probability are derived. The key contribution lies in establishing the equivalence between soft identification metrics and log-likelihood ratios, and in revealing an interpretable relationship between identification difficulty and Bhattacharyya parameters. The theoretical bounds precisely characterize the fundamental performance limits under an ideal SC consistency model. Simulations confirm that these bounds effectively capture the impacts of code length, number of observations, and signal-to-noise ratio, and further demonstrate a high degree of sequence-level consistency between the SC consistency recursion and the actual SC decoding process.

Abstract

Blind recognition of polar-coded transmissions is an important task in non-cooperative wireless forensics and security-oriented signal analysis. When the code length is known or has been estimated, recovering the frozen/information bit-position pattern is a key step in identifying the underlying polar-code structure and enabling subsequent information recovery from intercepted observations. In this paper, blind recognition of polar codes is investigated from a hypothesis-testing perspective under the successive cancellation (SC)-based synthetic bit-channel representation. First, under an ideal SC-consistent condition, we formulate position-wise recognition as a binary hypothesis test between frozen-position and information-position models, which provides a theoretical benchmark for analyzing their intrinsic distinguishability. Second, we show that the adopted soft recognition metric admits an exact shifted log-likelihood-ratio interpretation. This justifies ln 2 as the neutral threshold under equal priors and costs, while unequal priors or costs lead to the corresponding Bayesian threshold shift. Third, under the ideal SC-consistent model and this neutral setting, we derive upper and lower bounds on the position-wise and sequence-level recognition error probabilities with multiple independent observations. The resulting overlap coefficient is further related to the classical Bhattacharyya parameter, establishing an interpretable link between blind-recognition difficulty and polar synthetic-channel reliability. Simulation results show that the derived bounds characterize the recognition performance under the ideal SC-consistent model and capture the effects of code length, the number of intercepted observations, and SNR. Further paired comparisons in the tested settings indicate that the SC-consistent recursion provides a good sequence-level match to the realistic SC-recursive procedure.

Problem

• blind recognition
• polar codes
• frozen bit pattern
• hypothesis testing
• code structure identification

Innovation

• hypothesis testing
• polar codes
• blind recognition
• successive cancellation
• Bhattacharyya parameter