Iterative Viterbi decoding is an

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

that spots the subsequence ''S'' of an observation ''O'' = having the highest average probability (i.e., probability scaled by the length of ''S'') of being generated by a given

hidden Markov model A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process — call it X — with unobservable ("''hidden''") states. As part of the definition, HMM requires that there be an ob ...

''M'' with ''m'' states. The algorithm uses a modified

Viterbi algorithm The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events, especiall ...

as an internal step. The scaled probability measure was first proposed by John S. Bridle. An early algorithm to solve this problem,

sliding window A sliding window protocol is a feature of packet-based data transmission protocols. Sliding window protocols are used where reliable in-order delivery of packets is required, such as in the data link layer (OSI layer 2) as well as in the Transm ...

, was proposed by Jay G. Wilpon et al., 1989, with constant cost ''T'' = ''mn''²/2. A faster algorithm consists of an iteration of calls to the

, reestimating a filler score until convergence.

The algorithm

A basic (non-optimized) version, finding the sequence ''s'' with the smallest normalized distance from some subsequence of ''t'' is:

// input is placed in observation s ..n template t ..m
// and distance matrix 

In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. Depending upon the application involved, the ''dist ...
 d ..n,1..m// remaining elements in matrices are solely for internal computations
(int, int, int) AverageSubmatchDistance(char s ..(n+1) char t ..(m+1) int d ..n,0..(m+1)

The ViterbiDistance() procedure returns the tuple (''e'', ''B'', ''E''), i.e., the Viterbi score "''e''" for the match of ''t'' and the selected entry (''B'') and exit (''E'') points from it. "''B''" and "''E''" have to be recorded using a simple modification to Viterbi. A modification that can be applied to CYK tables, proposed by Antoine Rozenknop, consists in subtracting ''e'' from all elements of the initial matrix ''d''.

References

* Silaghi, M., "Spotting Subsequences matching a HMM using the Average Observation Probability Criteria with application to Keyword Spotting", AAAI, 2005. * Rozenknop, Antoine, and Silaghi, Marius; "Algorithme de décodage de treillis selon le critère de coût moyen pour la reconnaissance de la parole", TALN 2001.

The algorithm

References

Further reading