# Viterbi Algorithm

@inproceedings{Forney2010ViterbiA, title={Viterbi Algorithm}, author={Jr. G. Forney}, booktitle={Encyclopedia of Machine Learning}, year={2010} }

The Viterbi algorithm (VA) is a recursive optimal solution to the problem of estimating the state sequence of a discrete-time finite-state Markov process observed in memoryless noise. Many problems in areas such as digital communications can be cast in this form. This paper gives a tutorial exposition of the algorithm and of how it is implemented and analyzed. Applications to date are reviewed. Increasing use of the algorithm in a widening variety of areas is foreseen.

## 3,077 Citations

### Extended Viterbi Algorithm for Hidden Markov Process: A Transient/Steady Probabilities Approach

- Mathematics
- 2012

An extended Viterbi algorithm is presented for first-order hidden Markov processes, with the help of a dummy combined state sequence, and also picks up the state switching earlier, which is particularly important for the out of sample applications.

### Large Deviation Bounds for Functionals of Viterbi Paths

- MathematicsIEEE Transactions on Information Theory
- 2011

The aim of this paper is to provide the corresponding large deviation estimates of the maximum a posteriori estimator based on a finite number of observations of the hidden Markov model through available observations.

### The Viterbi Algorithm

- Computer ScienceEncyclopedia of Biometrics
- 2009

A proposal for further research into the use of the Viterbi Algorithm in Signature Verification is presented, and is the area of present research at the moment.

### The Viterbi Algorithm 1 1 The Viterbi Algorithm .

- Computer Science
- 2009

A proposal for further research into the use of the Viterbi Algorithm in Signature Verification is presented, and is the area of present research at the moment.

### Parameters Identiication of a Time-varying Stochastic Dynamic Systems Using Viterbi Algorithm

- Computer Science, Mathematics

A new algorithm based on the Viterbi algorithm developped for decoding convolutional codes is presented that applies the dynamic programming principle to the detection of discrete-time nite state Markov processes with noisy observation.

### The Viterbi Algorithm for Subset Selection

- Computer ScienceIEEE Signal Processing Letters
- 2015

A new method based on the computationally efficient Viterbi algorithm is proposed which is shown to achieve better performance than competing algorithms such as Orthogonal Matching Pursuit (OMP), orthogonal Least-Squares (OLS), Multi-Branch Matching pursuit (MBMP), Iterative Hard Thresholding (IHT), and l1 minimization.

### Constrained multiple model maximum a posteriori estimation using list Viterbi algorithm

- Computer Science2017 20th International Conference on Information Fusion (Fusion)
- 2017

A new approach for constrained multiple model (MM) maximum a posteriori (MAP) estimation through the expectation-maximization (EM) method by using the previously developed constrained sequential list Viterbi algorithm (CSLVA).

### ViterbiNet: Symbol Detection Using a Deep Learning Based Viterbi Algorithm

- Computer Science2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)
- 2019

ViterbiNet is a data-driven symbol detector obtained by converting the Viterbi algorithm into a system utilizing deep neural networks (DNNs), which operates without CSI and demonstrates the conceptual benefit of designing DNN-based communication systems to implement established algorithms.

### Analysis of the Viterbi Algorithm Using Tropical Algebra and Geometry

- Computer Science2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)
- 2018

This work analyzes the Viterbi algorithm in the field of tropical (min-plus) algebra, and utilizes its pruning variant in order to define a polytope, and interprets certain faces of the polytopes as the most probable states of the algorithm.

### Equivalence of ML decoding to a continuous optimization problem

- Computer Science, Mathematics2020 IEEE International Symposium on Information Theory (ISIT)
- 2020

This work proves that the ML estimation of a discrete input sequence (with no assumptions on the encoder/channel used) is equivalent to the solution of a continuous non-convex optimization problem, and that this formulation is closely related to the computation of symbolwise MAP estimates.

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The problems of reducing the Viterbi algorithm to hardware, the various tradeoffs and compromises that must be made, and the short cuts that are available are described.

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