Prior-Assisted Hierarchical ADMM Decoding for Punctured Globally Coupled LDPC Codes.

Future wireless networks require channel coding schemes that can provide high reliability, low latency, and strong adaptability under finite-blocklength and structurally heterogeneous transmission scenarios. Globally coupled low-density parity-check (GC-LDPC) codes are promising for such systems because their coupled structure can enhance error-correction capability, but the additional global constraints also increase decoding complexity and make conventional fixed-parameter decoders less effective. This paper proposes a prior-assisted hierarchical alternating direction method of multipliers (ADMMs) decoding framework for GC-LDPC codes. The proposed decoder first partitions the GC-LDPC parity-check structure into two local subgraphs and performs tuned ADMM decoding on the local blocks in parallel. The local decoding outputs are then merged and verified by the full GC-LDPC parity-check matrix. If the merged local decision satisfies all global constraints, it is directly accepted, thereby avoiding unnecessary full-graph decoding. Otherwise, a global fallback ADMM decoder is activated. In this stage, the channel log-likelihood ratios are fused with soft priors extracted from the local ADMM outputs, where prior clipping and conflict scaling are introduced to control unreliable or contradictory local information. The resulting fused reliability information is used to guide full-matrix ADMM decoding. This local-to-global strategy reduces unnecessary global iterations while preserving the ability to enforce global consistency when local decoding is insufficient. Simulation-oriented metrics, including bit error rate, frame error rate, local pass rate, global fallback rate, global fallback success rate, and average iteration count, are used to evaluate reliability and decoding efficiency. The proposed framework provides an average-complexity-aware and reliability-aware decoding approach for advanced channel coding in future wireless networks.