Topic
Forward algorithm
About: Forward algorithm is a research topic. Over the lifetime, 1782 publications have been published within this topic receiving 76186 citations.
Papers published on a yearly basis
Papers
1 Feb 1989
TL;DR: In this paper, the authors provide an overview of the basic theory of hidden Markov models (HMMs) as originated by L.E. Baum and T. Petrie (1966) and give practical details on methods of implementation of the theory along with a description of selected applications of HMMs to distinct problems in speech recognition.
Abstract: This tutorial provides an overview of the basic theory of hidden Markov models (HMMs) as originated by L.E. Baum and T. Petrie (1966) and gives practical details on methods of implementation of the theory along with a description of selected applications of the theory to distinct problems in speech recognition. Results from a number of original sources are combined to provide a single source of acquiring the background required to pursue further this area of research. The author first reviews the theory of discrete Markov chains and shows how the concept of hidden states, where the observation is a probabilistic function of the state, can be used effectively. The theory is illustrated with two simple examples, namely coin-tossing, and the classic balls-in-urns system. Three fundamental problems of HMMs are noted and several practical techniques for solving these problems are given. The various types of HMMs that have been studied, including ergodic as well as left-right models, are described. >
24,315 citations
TL;DR: A generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph, that computes-either exactly or approximately-various marginal functions derived from the global function.
Abstract: Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms.
7,567 citations
1 Mar 1973
TL;DR: This paper gives a tutorial exposition of the Viterbi algorithm and of how it is implemented and analyzed, and increasing use of the algorithm in a widening variety of areas is foreseen.
Abstract: 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.
6,503 citations
TL;DR: An adaptive Metropolis (AM) algorithm, where the Gaussian proposal distribution is updated along the process using the full information cumulated so far, which establishes here that it has the correct ergodic properties.
Abstract: A proper choice of a proposal distribution for Markov chain Monte Carlo methods, for example for the Metropolis-Hastings algorithm, is well known to be a crucial factor for the convergence of the algorithm. In this paper we introduce an adaptive Metropolis (AM) algorithm, where the Gaussian proposal distribution is updated along the process using the full information cumulated so far. Due to the adaptive nature of the process, the AM algorithm is non-Markovian, but we establish here that it has the correct ergodic properties. We also include the results of our numerical tests, which indicate that the AM algorithm competes well with traditional Metropolis-Hastings algorithms, and demonstrate that the AM algorithm is easy to use in practical computation.
3,097 citations
27 Nov 1989
TL;DR: The Viterbi algorithm is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value, with the aim of producing soft decisions to be used in the decoding of outer codes.
Abstract: The Viterbi algorithm (VA) is modified to deliver the most likely path sequence in a finite-state Markov chain, as well as either the a posteriori probability for each bit or a reliability value. With this reliability indicator the modified VA produces soft decisions to be used in the decoding of outer codes. The inner software output Viterbi algorithm (SOVA) accepts and delivers soft sample values and can be regraded as a device for improving the signal-to-noise ratio, similar to an FM demodulator. Several applications are investigated to show the gain over the conventional hard-deciding VA, including concatenated convolutional codes, concatenation of trellis-coded modulation with convolutional FEC (forward error correcting) codes, and coded Viterbi equalization. For these applications additional gains of 1-4 dB as compared to the classical hard-deciding algorithms were found. For comparison, the more complex symbol-to-symbol MAP, whose optimal a posteriori probabilities can be transformed into soft outputs, was investigated. >
1,915 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 4 |
| 2023 | 8 |
| 2022 | 25 |
| 2021 | 15 |
| 2020 | 20 |