Decoding for channels with insertions, deletions, and substitutions with applications to speech recognition

A model for channels in which an input sequence can produce output sequences of varying length is described. An efficient computational procedure for calculating Pr
\{Y\mid X\}
is devised, where
X = x_1,x_2,\cdots,x_M
and
Y = y_1,y_2,\cdots,y_N
are the input and output of the channel. A stack decoding algorithm for decoding on such channels is presented. The appropriate likelihood function is derived. Channels with memory are considered. Some applications to speech and character recognition are discussed.