I-FGMP: Factorized Gated Message Passing for Efficient LDPC Decoding

Decoding low-density parity-check (LDPC) codes is a fundamental task in modern communication systems. Recent neural LDPC decoders have achieved strong decoding performance, but often require relatively large models and costly inference. In particular, diffusion- and score-based decoders can improve with additional inference steps, yet this test-time scaling incurs substantial computational cost. In this work, we propose Iterative Factorized Gated Message Passing (I-FGMP), which combines neural adaptability with two established principles of conventional message-passing decoding: sparse graph-local message exchange and reuse of a common update rule across iterations. Its core FGMP operator decomposes adaptive message exchange into source-side emission modulation, graph-structured aggregation, and destination-side acceptance gating. This design provides state-dependent message control without computationally expensive pairwise interaction modeling, while repeated application of the shared operator keeps the parameter count independent of inference depth. We train I-FGMP by finite-depth weight-tied unrolling, with supervision applied to the output state after each iteration. Experiments focused primarily on short codes show that I-FGMP trained for 12 iterations outperforms recent Transformer-based decoders with less than 1/10 the parameters and at most 4/5 the floating-point operations (FLOPs) of all baselines. When trained for 30 iterations, I-FGMP continues to improve with additional test-time iterations beyond its training depth, achieving performance comparable to the best diffusion- and score-based decoders while requiring less than 1/10 the parameters and roughly 1/3 the maximum allowable test-time FLOPs of the most competitive baseline.