Noisy channel model

The noisy channel model is a framework used in spell checkers, question answering, speech recognition, and machine translation. In this model, the goal is to find the intended word given a word where the letters have been scrambled in some manner.

Given an alphabet ${\displaystyle \Sigma }$, let ${\displaystyle \Sigma ^{*}}$ be the set of all finite strings over ${\displaystyle \Sigma }$. Let the dictionary ${\displaystyle D}$ of valid words be some subset of ${\displaystyle \Sigma ^{*}}$, i.e., ${\displaystyle D\subseteq \Sigma ^{*}}$.

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