Identifying wireless modulation schemes is essential for cognitive radio, but standard supervised models often degrade under distribution shift, and training domain-specific wireless foundation models from scratch is computationally prohibitive. Large Language Models (LLMs) offer a promising training-free alternative via in-context learning, yet feeding raw floating-point signal statistics into LLMs overwhelms models with numerical noise and exhausts token budgets. We introduce DiSC-AMC, a framework that reformulates Automatic Modulation Classification (AMC) as an LLM reasoning task by combining aggressive feature discretization with nearest-neighbor retrieval over self-supervised embeddings. By mapping continuous features to coarse symbolic tokens, DiSC-AMC aligns abstract signal patterns with LLM reasoning capabilities and reduces prompt length by over $50$\%. Simultaneously, utilizing a DINOv2 visual encoder to retrieve the $k_\text{NN}$ most similar labeled exemplars provides highly relevant, query-specific context rather than generic class averages. On a 10-class benchmark, a fine-tuned 7B-parameter LLM using DiSC-AMC achieves $83.0$\% in-distribution accuracy ($-10$\,to\,$+10$\,dB) and $82.50$\% out-of-distribution (OOD) accuracy ($-11$\,to\,$-15$\,dB), outperforming supervised baselines. Comprehensive ablations on vanilla LLMs demonstrate the token efficiency of DiSC-AMC. A training-free $7$B LLM achieves $71$\% accuracy using only $0.5$\,K-token prompt,surpassing a $200$B-parameter baseline that relies on a $2.9$K-token prompt. Furthermore, similarity-based exemplar retrieval outperforms naive class-average selection by over $20$\%. Finally, we identify a fundamental limitation of this pipeline. At extreme OOD noise levels ($-30$\,dB), the underlying self-supervised representations collapse, degrading retrieval quality and reducing classification to random chance.

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