Blind Recognition of Polar Code Parameters Based on Log-Likelihood Ratio

The syndrome a posteriori probability of the log-likelihood ratio of intercepted codewords is used to develop an algorithm that recognizes the polar code length and generator matrix of the underlying polar code. Based on the encoding structure, three theorems are proved, two related to the relationship between the length and rate of the polar code, and one related to the relationship between frozen-bit positions, information-bit positions, and codewords. With these three theorems, polar codes can be quickly reconstruced. In addition, to detect the dual vectors of codewords, the statistical characteristics of the log-likelihood ratio are analyzed, and then the information- and frozen-bit positions are distinguished based on the minimum-error decision criterion. The bit rate is obtained. The correctness of the theorems and effectiveness of the proposed algorithm are validated through simulations. The proposed algorithm exhibits robustness to noise and a reasonable computational complexity.