When applying the noisy channel algorithm to real-word spelling correction, a simple approach to estimate the channel probability is to assume that the probability of the user writing the intended word correctly is $$ \alpha $$. The remaining probability mass, $$ 1 - \alpha $$, is then distributed evenly over all other candidate corrections $$ C(x) $$:

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The algorithm takes the input sentence $$X=\{x_{1}, x_{2},..., x_{k},..., x_{n}\}$$ and generates a set of candidate words $$C(x_{i})$$ for each word $$x_{i}$$. The candidates include every word with a small edit distance from $$x_{i}$$. Then we pick the sentence with the highest language model probability. Each sentence is scored by the noisy channel model as follows:

Noisy channel algorithm for real-word correction

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