BP-LCGCD: A Gaussian-Elimination-Free and High-Performance Decoder for Surface Codes

Belief propagation (BP) combined with ordered statistics decoding (OSD) can achieve near-optimal logical error rates for surface codes. However, OSD requires high-latency and unstable-complexity Gaussian elimination (GE), limiting its practicality. In this paper, we propose BP-LCGCD, a GE-free and high-performance decoder that replaces the GE-based OSD with the GE-free LC-GCD. Moreover, in contrast to the original BP-OSD, which adopts a single fixed normalization factor α, we further propose a list-parameterized variant, BP-LCGCD+ α, which performs multiple BP decodings with different α to generate diverse posterior LLRs. We present complexity analysis, demonstrating that at low physical error rates, the average decoding complexity of the proposed algorithm approaches that of standard BP. Simulation results demonstrate that BP-LCGCD achieves logical error rates close to BP-OSD, while BP-LCGCD+α nearly matches the performance of the BP-OSD. They also show that both proposed decoders significantly outperform standard BP and minimum-weight perfect matching (MWPM) in terms of logical error rate and threshold.