一种基于网格的大核极化码低复杂度译码算法

A Trellis-Based Algorithm for Low-Complexity Decoding of Large-Kernel Polar Codes

在同等码长的情况下,大核极化码有着更优的译码性能。但是,大核极化码连续消去(Successive Cancellation,SC)译码的复杂度随着核的增大呈指数级增长。为降低大核极化码SC译码复杂度过高的问题,提出一种基于Forney网格的极化码译码方案,用于任意维大核矩阵极化码SC译码中核内部的计算。该方案中,核内部计算由核矩阵生成码的网格结构进行计算。首先,基于Forney网格构造法,构造出了相应的网格,降低了核内部运算的计算量;其次,通过网格时间轴的重新排列简化了网格结构,进一步降低了核内部运算的计算量。仿真结果表明,对于长度为125、码率为1/2的G_5~(?3)极化码,与SC译码相比,在译码性能不变的情况下可以降低62.9%的计算量。

Under the same code length,large-kernel polar codes exhibit superior decoding performance.However,the complexity of SC(Successive Cancellation)decoding for large-kernel polar codes increases exponentially with the size of the kernel.To address the issue of excessive SC decoding complexity in largekernel polar codes,this paper proposes a Forney trellis-based decoding scheme for polar codes,which is used to carry out the internal computations of the kernel in SC decoding of polar codes with arbitrarydimensional large kernel matrices.In this scheme,the internal computations of the kernel are carried out using the trellis structure generated by the kernel matrix.First,based on the Forney trellis construction method,the corresponding trellis is constructed,reducing the computational load of the internal kernel operations.Then,by rearranging the time axis of the trellis,the trellis structure is further simplified,which further reduces the computational load of the internal kernel operations.Simulation results indicate that for a 35 G⊗polar code with a length of 125 and a code rate of 1/2,the computational load can be reduced by 62.9%compared to SC decoding while maintaining the same decoding performance.