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## The Viterbi algorithm (1973)

Venue: | Proceedings of the IEEE |

Citations: | 994 - 3 self |

### Citations

10901 |
The Mathematical Theory of Communication
- Shannon, Weaver
- 1963
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Citation Context ...es from the frequencies of (vf1)-letter combinations [(v+l)-grams]. While such models do not fully describe the generation of natural language (for examples of digram and trigram English, see Shannon =-=[45]-=-, [46]), they account for a large part of the statistical dependencies in the language and are easily handled. With such a model, English letters are viewed as the outinstant of time. The trellis begi... |

59 |
Viterbi decoding for satellite and space communication”,
- Heller, Jacobs
- 1971
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Citation Context ...(zk/ 4;c) is the only com- transistor logic circuits and that can operate at up to 2 ponent that depends on the data; again, it is typical that Mbits/s perhaps represents the current state of the art =-=[22]-=-. many fk lead to the same output yk, and hence the value Even a software decoder for a similar code can be run at a -In P(zk 1 yk) need be computed or looked up for all these .$x. rate the order of 1... |

38 | On the Viterbi Decoding Algorithm - Omura - 1969 |

30 |
Prediction and entropy of printed English,” Bell system technical journal
- Shannon
- 1951
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Citation Context ...m the frequencies of (vf1)-letter combinations [(v+l)-grams]. While such models do not fully describe the generation of natural language (for examples of digram and trigram English, see Shannon [45], =-=[46]-=-), they account for a large part of the statistical dependencies in the language and are easily handled. With such a model, English letters are viewed as the outinstant of time. The trellis begins and... |

22 |
Optimal Decoding of Convolutional Codes
- Odenwalder
- 1970
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Citation Context ...ystem of reference,” Phys. Reu., vol. 134, pp. A799A804, 1964. [9] T. C. Mo, “Theory of electrodynamics in media in noninertial frames and applications,” J. Math. Phys., vol. 11, pp. 2589-2610, 1970. =-=[lo]-=- R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetk Fields, Energy and Forces. New York: Wiley, 1960. pp. 407-416. [ll] L. Robin, Fonctions Sphiriques de Legendre et Fonctions Sphtroidulcs, vol. 3... |

17 |
A survey of coding schemes for transmission or recording of digital data
- Kobayashi
- 1971
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Citation Context ...uts of a finite-state machine and hence fall tribution Authorized P(zt licensed I&). use limited to: Universitatsbibliothek der TU Wien. Downloaded into on March our general 03,2010 at setup 07:23:58 =-=[49]-=-. EST from IEEE Xplore. Restrictions apply.270 PROCEEDINGS OF THE IEEE, MARCH 1973 JEi-J-E B. Intersymbol Interference In digital transmission through analog channels, we frequently encounter the fol... |

13 |
A variant on the shortest-route problem
- Minty
- 1958
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Citation Context ...most succinct solution was \Ye are accustomed to associating with a discrete-time given by Minty in a quarter-page correspondence in 1957 finite-state Markov process a state diagram of the type shown =-=[55]-=-, which we quote almost in its entirety: in Fig. 7(a), for a four-state shift-register process like that of Fig. 3 or Fig. 4 (in this case, a de Bruijn diagram [54]). Here The shortest-route problem .... |

13 | Optimal Receiver Design for Convolutional Codes and Channels with Memory via Control Theoretical Concepts - Omura - 1971 |

12 |
Coherent demodulation of frequency-shift keying with low deviation ratio
- Buda
- 1972
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Citation Context ...ibel of this bound [22]. Channels available for space communications are frequently accurately modeled as white Gaussian channels. The VA is attractive for such channels because it gives per* De Buda =-=[44]-=- actually proves that an optimum decision on the phase xt at time k can be made by examining the received waveform only at times k- 1 and k; Le., (zo.~-I, z~t-l), (ZU, w). The proof is that the log li... |

6 |
Convolutional Codes 11: Maximum Likelihood Decoding
- Forney
- 1973
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Citation Context ...n. Phys., vol. 6, no. 8, pp. 246-252, 1951. [6] H. Epheser and T. Schlomka, “Flachengrossen und elektrodynamische Grenzbedingungen bei bewegten Korpern,” Ann. Phys., vol. 6, no. 8, pp. 211-220, 1951. =-=[7]-=- J. L. Anderson and J. W. .Ryon, “Electromagnetic radiation in accelerated systems,” Phys. Rev., vol. 181, pp. 1765-1775, 1969. [8] C. V. Heer, “Resonant frequencies of an electromagnetic cavity in an... |

6 |
Solutions of the shortest-route problem-A review
- Pollack, Wiebenson
- 1960
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Citation Context ... well adapted to modern methods of machine computation, nor are assistants as pliable as formerly. It therefore becomes necessary to move on to the VA, which is also well known in operations research =-=[56]-=-. It requires one additional observation. We denote by xok a segment (xo, xl, . , xk) consisting of the states to time k of the state sequence x = (xo, x1, * , xk). In the trellis xok corresponds to a... |

5 |
An approach to artificial nonsymbolic cognition
- Preparata, Ray
- 1972
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Citation Context ...VA to digital magnetic recording systems. Timor [SI] has applied the algorithm to a sequential ranging system. Use of the algorithm in source coding has been proposed [52]. Finally, Preparata and Ray =-=[53]-=- have suggested using the algorithm to search ‘‘semantic maps” in syntactic pattern recognition. These exhaust the applications known to the author. 01 IO 11 Fig. 7. 2K:::w (b) (a) State diagram of a ... |

2 |
Coding systems study for high data rate telemetry links
- Corp
- 1970
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Citation Context ...the algorithm's firm decision; in this case, truncation costs nothing. In the rare cases when survivors disagree, any reasonable strategy for determining the algorithm's time-(k-6) decision will work =-=[20]-=-, [21]: choose an arbitrary time-(k-6) node, or the node associated with the shortest survivor, or a node chosen by majority vote, Authorized licensed use limited to: Universitatsbibliothek der TU Wie... |

2 |
Implementation of maximum likelihood decoders for convolutional codes
- Clark
- 1971
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Citation Context ...gorithm's firm decision; in this case, truncation costs nothing. In the rare cases when survivors disagree, any reasonable strategy for determining the algorithm's time-(k-6) decision will work [20], =-=[21]-=-: choose an arbitrary time-(k-6) node, or the node associated with the shortest survivor, or a node chosen by majority vote, Authorized licensed use limited to: Universitatsbibliothek der TU Wien. Dow... |

2 |
Two recent applications of errorcorrection coding to communications system design
- Clark, Davis
- 1971
(Show Context)
Citation Context ...s proportional simply to (zk-yk)*.) Finally, all of this can be signal-processing systems. done outside the central recursion (“pipelined”). Hence the For further details of implementation, see [22], =-=[23]-=-, and complexity of this computation tends not to be significant. the references therein. Furthermore, note that once the X&) are computed, the observation Zk need not be stored further, an attractive... |

2 | Configuring a TDMA satellite communication system with coding - Jacobs, Sims - 1972 |

2 |
Hybrid coding system study,” Final Rep. on Contract NAS2-6722, NASA Ames
- Corp
- 1972
(Show Context)
Citation Context ...ed as elements in It was for convolutional codes that the algorithm was first very-high-performance concatenated coding schemes [lo]developed, and naturally it has had its greatest impact here. [12], =-=[27]-=- and in decoding of convolutional codes in the The principal theoretical result is contained in Viterbi’s presence of intersymbol interference [35], [6O]. original paper [l]; see also [SI-[7]. It show... |

2 |
Error bounds for convolutional codes and an asympdigital sequences in the presence of intersynlbol interference,” IEEE totically optimum decoding algorithm
- Viterbi
- 1972
(Show Context)
Citation Context ...eatest impact here. [12], [27] and in decoding of convolutional codes in the The principal theoretical result is contained in Viterbi’s presence of intersymbol interference [35], [6O]. original paper =-=[l]-=-; see also [SI-[7]. It shows that for a suitably defined ensemble of random trellis codes and MAP decod- B. Intersymbol Interference ing, the error probability can be made to decrease exponen- Applica... |

2 | bounds on error probability in the presence of large 121 - “Lower - 1970 |

2 | of random tree codes,” NASA Ames - “Review - 1967 |

2 |
Correlative level coding and maximum-likelihood report on convolution coding research,” Advanced System Operadecoding
- Clark, Davis, et al.
- 1969
(Show Context)
Citation Context ...koryofRelatioity. London, England: Oxford Univ. Press, 1952, pp. 274-276, 302-309. [3] E. J. Post, Formal Structure of Elecfromagnetics. Amsterdam, The Netherlands: North-Holland, 1962, chs. 3, 6, 7. =-=[4]-=- A. Sommerfeld, Elektrodynamik. Wiesbaden, Germany: Dieterich’sche Verlag, 1948, pp. 281-289. [SI T. Schlomka, “Das Ohmsche Gesetz bei bewegten Korpern,” Ann. Phys., vol. 6, no. 8, pp. 246-252, 1951. ... |

2 | Convolutional codes and their performance in comsequence estimation for digital signaling in the presence of intersymmunicationsystems - Viterbi - 1971 |

2 | Statistical detection for communiCambridge - Abend, Fritchman - 1970 |

2 |
Coupled decoding of block-convolutional concatenated 58
- Zeoli
- 1970
(Show Context)
Citation Context ...etk Fields, Energy and Forces. New York: Wiley, 1960. pp. 407-416. [ll] L. Robin, Fonctions Sphiriques de Legendre et Fonctions Sphtroidulcs, vol. 3. Paris, France: Gauthier-Villars, 1959, pp. 94-10. =-=[12]-=- W. R. Symthe, Static and Dynamic Elec#ricity. New York: McGraw-Hill, 1950, p. 208. [13] M. Faraday, Experimental Researches in Electricity, vol. 3. New York: Dover, 1965, pp. 362-368. [14] E. G. Cull... |

2 | Optimal decoding of [43 - Bahl, Cocke, et al. - 1971 |

2 | Sequential ranging with the Viterbi algorithm,” Jet Propulsion - Tirnor - 1971 |

2 |
On the Viterbi algorithm for source coding
- Omura
- 1972
(Show Context)
Citation Context ...i [SO] has proposed applying the VA to digital magnetic recording systems. Timor [SI] has applied the algorithm to a sequential ranging system. Use of the algorithm in source coding has been proposed =-=[52]-=-. Finally, Preparata and Ray [53] have suggested using the algorithm to search ‘‘semantic maps” in syntactic pattern recognition. These exhaust the applications known to the author. 01 IO 11 Fig. 7. 2... |

2 |
Shift Regisln Sequcrrccs
- Golomb
- 1967
(Show Context)
Citation Context ...s a state diagram of the type shown [55], which we quote almost in its entirety: in Fig. 7(a), for a four-state shift-register process like that of Fig. 3 or Fig. 4 (in this case, a de Bruijn diagram =-=[54]-=-). Here The shortest-route problem . . . can be solved very simply . . . as follows: Build a string model of the travel network, ~K~des represent states, branches represent transitions, and where knot... |

2 |
Finite Graphs and Networks: An Zntroduction with Applications
- Busacker, Saaty
- 1965
(Show Context)
Citation Context ...ng time-(kfl) survivor. Recursion proceeds indefinitely without the number of survivors ever exceeding M. Many readers will recognize this algorithm as a simple version of forward dynamic programming =-=[57]-=-, [%I. By this \ r3 or any other name, the algorithm is elementary once the problem has been cast in the shortest route form. k= 5 We illustrate the algorithm for a simple four-state trellis covering ... |

2 |
Principres of Cmnunicaliorr Engineering
- Wozencraft, Jacobs
- 1965
(Show Context)
Citation Context ...r than {cos w(O)t, cos w(0)t 1, or in our coordinate notation that { (0, l), (0, - 1) ] is chosen over { (1, 0), (1, 0) 1. This is a two-hypothesis decision problem in a four-dimensional signal space =-=[59]-=-. In Gaussian noise of variance u* per dimension, only the Euclidean distance d between the two signals matters; in this cased = 43, and therefore the probability of this particular error event is Q(d... |