Given a sentence f in the source language, the goal of an SMT model is to produce a translation e in the target language. This is modeled using the noisy channel framework Equation (9).

This framework relies on a translation model p(f|e) and a language model p(e). In addition, a decoder is in charge of producing the most probable e given an f.

There are different approaches for implementing the translation model and the decoder. In practice, they all rely on a linear combination of these and additional features, which are directly optimized to maximize translation quality, rather than on the generative noisy channel model.