ASWE: Adaptive Small-World Encoder for Efficient Channel Coding

Neural channel encoders must efficiently spread information across message dimensions to ensure robustness under noise, especially for large symbol alphabets. We propose an encoder architecture inspired by small-world networks, combining local and global mixing within a compact residual design. Each message is mapped to a power-constrained codeword using residual blocks composed of (i) adaptive multi-dilation circular depthwise convolutions and (ii) sparse long-range links grouped by hop distance with shared parameters. The resulting Adaptive Small-World Encoder (ASWE) maintains low parameter and compute cost while enabling efficient information propagation. We evaluate several ASWE variants, including ones with annealed rewiring and increased link density. Experiments across symbol sizes M = 64,256,1024 show that ASWE consistently outperforms low-rank and fixed-kernel baselines, and rivals dense encoders despite using significantly fewer parameters and lower or matched compute. Gains are most pronounced at moderate and large M, where structured long-range links enhance mixing. These results highlight the utility of small-world connectivity in designing efficient neural encoders.