Tanner-graph-assisted successive cancellation decoding for large kernel polar codes

Large kernel polar codes demonstrate exceptional error-correction capabilities in finite-length coding, making them promising candidates for enabling 6G'sultra-high reliability and ultra-low latency communication (URLLC) requirements. However, the decoding complexity exhibits exponential growth relative to the kernel dimension. In this paper, we study Tanner-graph-assisted (TGA) serial decoding to further reduce complexity without sacrificing error-correction performance. We first establish the standard for the Tanner graph to satisfy serial decoding and give rigorous proof. In particular, a gamified worm search scheme is designed, which makes the proposed standard practical for screening Tanner graphs by accurately tracking the worm's running trajectory in the node matrix. Then, we construct a low-complexity serial TGA successive cancellation (TGA-SC) decoder. The decoder takes the kernel matrix that satisfies both the standard and the optimal polarization exponent as the Tanner graph. Moreover, the serial decoding equations for arbitrary dimensional linear binary kernels are derived. Numerical results demonstrate that our scheme achieves significant error-correction improvement compared to classic polar codes while maintaining similar complexity.