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.