The best introduction to HMMs and the Viterbi algorithm is the classical tutorial by Rabiner ( see e.g. https://www.cs.ubc.ca/~murphyk/Bayes/rabiner.pdf https:/

The best introduction to HMMs and the Viterbi algorithm is the classical tutorial by Rabiner ( see e.g. https://www.cs.ubc.ca/~murphyk/Bayes/rabiner.pdf https://www.cs.ubc.ca/~murphyk/Bayes/rabiner.pdf ). What is missing from Steve's clear explanation is (1) a graphic depiction of the central data structure called the "trellis" (Fig. 6 in the above paper) and (2) a citation to the original Viterbi paper [1]. For many years, HMMs - together with a Viterbi triphone decoder - defined the state of the art in ASR (automatic speech recognition), until eventually, neural networks took over. [1] A. J. Viterbi, “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm,” IEEE Trans. Inform. Theory, vol. IT-13, pp. 260-269, Apr. 1967.