基于3×3高维核矩阵的终止极化码研究

针对高维核矩阵构造的极化码中为提升纠错性能而造成的复杂度增加的问题,提出了基于3×3高维核矩阵终止极化码的构造方案。首先筛选出极化率最高的核矩阵G₅₃₁构造终止极化码,并在二进制擦除信道上证明了在不影响纠错性能的前提下终止极化码能够降低编译码计算复杂度,同时推导出终止极化码的复杂度降低比的上下界。仿真表明,终止极化码复杂度降低比与二进制擦除信道(binary erasure channel,BEC)的擦除概率有关,在擦除概率为0.5左右时,复杂度降低比最小,且目标误帧率(frame error rate,FER)越高,复杂度降低比越大,在目标误帧率为10^-5时,最高可实现71.43%的复杂度降低比。

Research on Relaxed Polar Code Based on 3×3 High Dimensional Kernel Matrix

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.