Abstract: Aiming at the problem of high complexity in the polarization code constructed by the high-dimensional kernel matrix to improve the error correction performance, a construction scheme based on the 3×3 high-dimensional kernel matrix terminating the polarization code is proposed. Firstly, the kernel matrix G₅₃₁ with the highest polarization rate is selected to construct a termination polarization code, and it is theoretically proved on the binary erasure channel that the termination polarization code can reduce the computational complexity of encoding and decoding without affecting the error correction performance, and derive the upper and lower bounds of the complexity reduction ratio (CRC) of terminating polarization codes at the same time. Simulation shows that the complexity reduction ratio of the termination polarization code is related to the BEC (binary erasure channel) erasure probability. When the erasure probability is about 0.5, the complexity reduction ratio reaches the smallest, and the higher the target frame error rate (FER), the greater the complexity reduction ratio. When the FER is 10^-5, the highest complexity reduction rate of 71.43% can be achieved.

Key words: 3×3 kernel matrix, relaxed polar codes, full polar codes, target frame error rate, complexity reduction ratio (CRC)