LLM-Assisted LDPC Decoding via Syndrome-Verified Semantic Priors

Semantic communication exploits the meaning of the payload, which bit-level processing discards. When channel decoding fails on a natural language payload, the errors appear as corrupted characters in the recovered text. A large language model (LLM) infers the intended characters from the semantic context, but it can also produce incorrect corrections. Applying them directly introduces new bit errors when the LLM modifies characters incorrectly. In this paper, we propose an LLM-assisted decoding framework for low-density parity-check (LDPC) codes. Rather than trusting LLM predictions, the decoder evaluates the modified characters jointly against the parity-check constraints and admits only the accepted corrections as verified semantic priors. These priors are injected as soft updates to the channel log-likelihood ratios, preserving the original channel evidence without modifying the decoder. A subsequent belief propagation pass distributes the injected evidence across the check nodes, recovering not only the injected bits but also the residual errors that the LLM fails to correct. Simulations demonstrate a 73% bit error rate reduction over a conventional decoder at 2.0 dB, whereas doubling its iterations to the same budget yields only 21%. The verification maintains an injection precision above 0.88 despite inaccurate LLM predictions, demonstrating that semantic knowledge can be reliably translated into physical-layer reliability gains.