Enhancing Belief Propagation Decoders for Correlated Errors Using Cycle Error Characterization

Realistic error processes are often poorly modeled by independent Pauli errors typically assumed by many decoders. We study how spatially correlated errors impact the performance of Belief Propagation (BP) decoders for LDPC codes and propose a modification that adds virtual checks imposing soft constraints favoring correlated error patterns. The relative weights of these constraints, compared to standard parity checks, are tuned using error characterization data from Cycle Error Reconstruction (CER). Our approach achieves up to a threefold improvement in logical performance over standard BP across diverse error regimes. Ongoing work explores neural network–based methods to mitigate the adverse effects of short cycles in BP.