Permutation-Based Trellis Optimization for a Large-Kernel Polar Code Decoding Algorithm

Compared to Arikan’s G2 kernel, large-kernel polar codes exhibit higher polarization rates and superior error correction performance. The critical steps of exact successive cancellation (SC) decoding for such codes can be implemented via trellis-based computations to reduce complexity. However, the complexity remains high for large kernels. This paper proposes a permutation-based trellis optimization scheme. The approach builds on the Massey minimal trellis and reorders its time axis to find a permutation that minimizes the number of trellis edges, thereby further reducing the exact SC decoding complexity. For smaller kernels (G3–G12), an exhaustive search is conducted to identify the optimal trellis. For larger kernels (G13–G16), where an exhaustive search becomes infeasible due to the factorial growth of the permutation space, an ant colony optimization (ACO)-based method is employed to find a near-optimal permutation. Simulation results show that the permutation-optimized trellis lowers the direct SC decoding complexity drastically. Furthermore, compared to the l-expression, the W-formula and original Massey trellis methods, it achieves multiplication operation reductions of up to 99.2%, 58.1%, and 56.5%, respectively. The improvement is particularly beneficial for large kernels, where traditional decoding methods become computationally prohibitive.