Speculative decoding accelerates large language model inference using a smaller draft model. In this paper, we establish a surprising connection between speculative sampling and the concept of channel simulation from information theory, which aims at simulating a noisy channel using as few bits as possible. This connection allows us to provide an information-theoretic analysis of the speed up that can be achieved by speculative sampling. Leveraging this link, we derive an explicit relation between generation speed-up and the number of tokens k generated by the draft model for large k, which serves as an upper bound for all k. We also propose a novel speculative sampling method via exponential races called ERSS that matches state-of-the-art performance.