3×3核矩阵极化码的BP译码算法

BP Decoding Algorithm for 3×3 Kernel Matrix Polar Codes

相比于2×2核极化码,3×3核极化码的码长更加丰富以及有着更高的极化速率。同时,极化码的置信传播(Belief Propagation, BP)算法相比于传统串行消去(Successive Cancellation, SC)译码算法具有更低的延时。将2×2核极化码的BP译码算法推广至3×3核。获得了3×3核内部最小计算单元的信息更新公式;基于信息更新公式,给出了3×3核的BP译码算法。仿真结果表明,对于3×3核极化码,BP译码算法相比于SC译码算法,在中低信噪比下性能要优于SC译码算法。在译码性能相当的条件下,BP译码算法有着更低的译码延时。

Compared with 2×2 kernel polar codes,3×3 kernel polar codes have richer code lengths and higher polarization rates.At the same time,Belief Propagation(BP)algorithm for polar codes,as opposed to the traditional Successive Cancellation(SC)decoding algorithm,demonstrates lower latency.In this paper,the BP decoding algorithm of 2×2 kernel polar codes is extended to 3×3 kernel polar codes.Firstly,the information update formula for the minimal computing unit within the 3×3 kernel is derived.Then,based on the information update formula,a 3×3 kernel BP decoding algorithm is given.Subsequently,based on this update formula,the BP decoding algorithm for the 3×3 kernel is presented.Simulation results indicate that,for 3×3 kernel polar codes,the BP decoding algorithm outperforms the SC decoding algorithm at medium to low signal-to-noise ratios.Moreover,under comparable decoding performance conditions,the BP decoding algorithm exhibits lower decoding latency.