FlexH: Conditional Structural Capacity for Compact Transformer Decoding

Transformer-based decoders have achieved strong error-correction performance, but their feed-forward networks (FFNs) remain a major parameter bottleneck. In this paper, we propose FlexH, a plug-in structural preprocessor that addresses this bottleneck by adapting the parity-check representation to each received word. Using channel reliabilities, FlexH prioritizes unreliable positions when selecting linearly independent columns and turns the selected columns into an identity block. This preserves the code and syndrome constraints and provides conditional structural capacity without additional trainable parameters. This allows the FFN expansion factor to be reduced from four to two within otherwise unchanged Transformer decoders. Experiments across three Transformer decoders on BCH, Polar, and punctured Reed–Muller (PRM) codes show average reductions of roughly two orders of magnitude in both bit error rate (BER) and block error rate (BLER) at 6 dB. At the same time, parameters and FLOPs decrease by about one third, with lower peak GPU memory. FlexH–EfficientMPT also surpasses Chase-II in nearly all matched BCH comparisons, with BLER approaching available maximum-likelihood (ML) references on BCH and Polar. Ablation studies further support reliability-guided structural adaptation as a practical way to improve decoding performance with smaller FFNs.