# Polar Code Parameter Recognition Algorithm Based on Dual Space
###### Abstract  
To improve the performance of polar code parameter recognition in the fields of intelligent communication, communication detection, and network countermeasures, we propose a new recognition scheme for the additive white Gaussian noise (AWGN) channel. The scheme turns parameter recognition problems into hypothetical tests and is effective due to the check relationship between the received codeword and the dual space determined by the correct parameters. First, a sub-matrix is obtained by removing the frozen-bit-index rows of the polar code generator matrix, and then its dual matrix is calculated. To check the relationship of the dual matrix and codewords, the average likelihood ratio of codewords is introduced as a test statistic, and then the corresponding decision threshold is deduced. Next, the degree of conformity of polar code recognition is defined, and the minimum code length and code rate corresponding to the highest degree of conformity are chosen to calculate the index of information-bit positions by a Gaussian approximation (GA) construction algorithm. Finally, the chosen code length, code rate, and corresponding index are provided as the recognition results. Simulation results show that the algorithm can achieve effective parameter recognition in both high-signal-to-noise (SNR) and low-SNR environments, and that the algorithm's recognition performance increases with decreasing code rate and code length. The parameter recognition rate with a code length of 128 and code rate of 1/5 is close to 100% when the SNR is 4 dB, and the algorithm complexity increases almost linearly with the decreasing code rate and the increasing length of the intercepted data. channel coding; polar code; dual space; recognition 202211251111625112511251125112512511251125112511251125112511251125112511251125112511251125112511251125112511251251125125112511251125112512  
used in [6] to identify LDPC code parameters. On this basis, maximum likelihood based on comprehensive posterior probability was proposed in [7]. In addition, there are many other conventional parameter-recognition algorithms for BCH [8] and RSC [9] codes. With the development of computer vision, machine learning has received increasingly more attention. By applying machine learning to channel coding parameter recognition, scholars in the field of communication have already achieved rich results. Machine learning was used in [10; 11] to realize blind recognition of convolutional codes. An improved deep convolutional network was used in [12] to realize parameter recognition of convolutional codes and turbo codes, but the experimental setting parameters are relatively simple and complete parameter experiments were lacking. In [13], the test vector of the RS code was determined by equivalence of the binary field, and a parameter joint recognition model was established to avoid the calculation of high-order spectral components, which effectively improves the recognition performance of the RS code. However, machine-learning algorithms all face the test of robustness under different parameters and few studies exist on the recognition of polar code parameters. Polar code parameter recognition under erasure channel was studied in [14], in which a polar code supervision matrix was defined and the product of the supervision matrix and the hard-decision-codeword matrix used as the check standard to determine the coding parameters. Obviously, hard-decision codewords will lose a significant amount of useful information compared with the soft-decision sequence, and the recognition performance of the algorithm has substantial room for improvement. The open-set recognition problem of polar code coding under a Gaussian channel was studied in [15], in which the rows of the Kronecker power matrix were eliminated one by one to obtain its dual vector, and parameter recognition was carried out row by row using the test relationship between the dual vector and soft-decision codeword, which leads to a large amount of calculation. Ref.