All possible transmitted data streams are fed into this distorted channel model.
In cases that are most computationally straightforward, root mean square deviation can be used as the decision criterion[1] for the lowest error probability.
That is, the estimate of {x(t)} is defined to be a sequence of values which maximize the functional where p(r | x) denotes the conditional joint probability density function of the observed series {r(t)} given that the underlying series has the values {x(t)}.
In this case the estimate of {x(t)} is defined to be a sequence of values which maximize the functional where p(x | r) denotes the conditional joint probability density function of the underlying series {x(t)} given that the observed series has taken the values {r(t)}.
Bayes' theorem implies that In cases where the contribution of random noise is additive and has a multivariate normal distribution, the problem of maximum likelihood sequence estimation can be reduced to that of a least squares minimization.