CR-CCM: Coset-Reduced Concatenated-Code Modeling for Neural Decoding

Transformer-based neural decoders have achieved strong empirical performance under a unified formulation: binary linear codes are represented by parity-check matrices, and decoding is treated as bit-level noise prediction. This unified formulation is convenient, but it treats different code families in much the same way and can hide their structural advantages. For concatenated codes, the full-binary representation likewise obscures the distinct roles of the inner and outer codes. We propose Coset-Reduced Concatenated-Code Modeling (CR-CCM), a neural decoding framework tailored to algebraic concatenated codes. CR-CCM reformulates full-binary neural decoding as residual prediction on the binary-expanded outer graph. A coset-coordinate reduction removes repeated inner-code constraints from the neural task. A local soft interface provides tentative outer symbols and bitwise reliability, and the neural decoder predicts the remaining errors in these symbols. Relative to EfficientMPT, CR-CCM-EfficientMPT generally maintains or improves BER while substantially reducing computational cost. Average and maximum reductions are 81.0% and 94.9% in FLOPs, and 49.8% and 73.8% in peak training memory. At $\mathrm{SNR}=6\mathrm{dB}$, BER is reduced by $2.37\times$ on average and up to approximately $72\times$.