Edge-cloud speculative decoding (SD) accelerates inference by having a cloud-based large language model (LLM) that verifies draft tokens generated by a resource-constrained small language model (SLM) at the edge. A central bottleneck is the limited bandwidth of the edge-cloud link, which necessitates efficient compression of draft token distributions. We first derive an information-theoretic bound that decomposes the token rejection rate into contributions from SLM-LLM distribution mismatch and from quantization distortion. Guided by this analysis, we propose the Sparse Quantize-and-Sample SD (SQS-SD) framework, which exploits distributional sparsity through structured sparsification and lattice-based quantization. Within this framework, K-SQS applies fixed top-K truncation, while C-SQS adaptively adjusts the retained token set via online conformal prediction to ensure bounded deviation from the dense distribution. Empirical results confirm that both approaches improve end-to-end latency and rejection rates in complimentary operating regimes.