- In spelling correction, the first stage of the noisy channel algorithm proposes candidate corrections by finding words with a similar spelling to the input word.
- Spelling error data indicates that the majority of spelling errors consist of a single-letter change (insertion, deletion, substitution, or transposition), which often have an edit distance of 1 from the error word.
- To generate this candidate list, the algorithm uses an extended minimum edit distance algorithm, known as the Damerau-Levenshtein edit distance, which adds transpositions (swapping two adjacent letters) to the standard insertion, deletion, and substitution edits.

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- Is used for treating the misspelled word as if a correctly spelled word had been “distorted” by being passed through a noisy communication channel.
- Is a kind of Bayesian inference.

The Noisy Channel

- We use a confusion matrix that contains counts of errors
- A confusion matrix lists the number of times one thing was confused with another.
- we’ll use four confusion matrices.
  + del[x, y]: count(xy typed as x)
  + ins[x, y]: count(x typed as xy)
  + sub[x, y]: count(x typed as y)
  + trans[x, y]: count(xy typed as yx)

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