We use the noisy-channel theory of human sentence comprehension to develop an incremental processing cost model that unifies and extends key features of expectation-based and memory-based models. In this model, which we call noisy-context surprisal, the processing cost of a word is the surprisal of the word given a noisy representation of the preceding context. We show that this model accounts for an outstanding puzzle in sentence comprehension, language-dependent structural forgetting effects (Gibson and Thomas, 1999;Vasishth et al., 2010;Frank et al., 2016), which are previously not well modeled by either expectation-based or memory-based approaches. Additionally, we show that this model derives and generalizes locality effects (Gibson, 1998;Demberg and Keller, 2008), a signature prediction of memory-based models. We give corpusbased evidence for a key assumption in this derivation.