BEC信道下高维核矩阵极化码的精确设计

Exact Design on High-dimensional Kernel Matrix Polar Code Based on BEC Channel

针对高维核矩阵极化码的设计问题,将二进制擦除信道(BEC)下的2×2核矩阵极化码的设计方法推广至高维核矩阵极化码。基于l-公式证明了当原始信道为BEC信道时,单步位信道同样为BEC信道;获得了单步位信道的擦除概率多项式,从而可以递归计算位信道的擦除概率;依据最后一层位信道的擦除概率选择出信息位集合和冻结位集合(极化码)。仿真结果表明,基于BEC信道下设计高维核矩阵极化码的方法优于高斯近似方法设计的相对应的高维核矩阵极化码,并且优于同等码长和码率下的原2×2核矩阵极化码。

Aiming at the design of polar codes with high dimensional kernel matrix,the design method of 2×2 kernel matrix polar codes based on binary erasure channel (BEC) is extended to polar codes with high dimensional kernel matrix.Based on l -formula,it is proved that if the original channels are BEC channel,the single-step bit channel is also BEC channel.The erasure probability polynomial of single step bit channel is obtained,and the erasure probability of bit channel can be calculated recursively.Finally,according to the erasure probabilities of the last bit channels,the information bit set and the frozen bit set,namely the polarization code,are selected.The simulation results show that the proposed method is superior to the Gaussian approximation method and the original 2×2 kernel matrix polar codes with the same code length and code rate.