Iterative Viterbi Decoding
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Iterative Viterbi Decoding
Iterative Viterbi decoding is an algorithm 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 ''M'' with ''m'' states. The algorithm uses a modified Viterbi algorithm as an internal step. The scaled probability measure was first proposed by John S. Bridle. An early algorithm to solve this problem, sliding window, 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 Viterbi algorithm, 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 squar ...
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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 specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ...
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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 observable process Y whose outcomes are "influenced" by the outcomes of X in a known way. Since X cannot be observed directly, the goal is to learn about X by observing Y. HMM has an additional requirement that the outcome of Y at time t=t_0 must be "influenced" exclusively by the outcome of X at t=t_0 and that the outcomes of X and Y at t handwriting recognition, handwriting, gesture recognition, part-of-speech tagging, musical score following, partial discharges and bioinformatics. Definition Let X_n and Y_n be discrete-time stochastic processes and n\geq 1. The pair (X_n,Y_n) is a ''hidden Markov model'' if * X_n is a Markov process whose behavior is not directly observable ("hidden"); * \operatorname\bigl(Y_n \i ...
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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, especially in the context of Markov information sources and hidden Markov models (HMM). The algorithm has found universal application in decoding the convolutional codes used in both CDMA and GSM digital cellular, dial-up modems, satellite, deep-space communications, and 802.11 wireless LANs. It is now also commonly used in speech recognition, speech synthesis, diarization, keyword spotting, computational linguistics, and bioinformatics. For example, in speech-to-text (speech recognition), the acoustic signal is treated as the observed sequence of events, and a string of text is considered to be the "hidden cause" of the acoustic signal. The Viterbi algorithm finds the most likely string of text given the acoustic signal. History The Viterbi a ...
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John S
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope J ...
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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 Transmission Control Protocol (TCP). They are also used to improve efficiency when the channel may include high latency. Packet-based systems are based on the idea of sending a batch of data, the ''packet'', along with additional data that allows the receiver to ensure it was received correctly, perhaps a checksum. The paradigm is similar to a window sliding sideways to allow entry of fresh packets and reject the ones that have already been acknowledged. When the receiver verifies the data, it sends an acknowledgment signal, or "ACK", back to the sender to indicate it can send the next packet. In a simple automatic repeat request protocol (ARQ), the sender stops after every packet and waits for the receiver to ACK. This ensures packets arrive ...
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Jay G
A jay is a member of a number of species of medium-sized, usually colorful and noisy, passerine birds in the Crow family, Corvidae. The evolutionary relationships between the jays and the magpies are rather complex. For example, the Eurasian magpie seems more closely related to the Eurasian jay than to the East Asian blue and green magpies, whereas the blue jay is not closely related to either. Systematics and species Jays are not a monophyletic group. Anatomical and molecular evidence indicates they can be divided into an American and an Old World lineage (the latter including the ground jays and the piapiac), while the grey jays of the genus ''Perisoreus'' form a group of their own.http://www.nrm.se/download/18.4e32c81078a8d9249800021299/Corvidae%5B1%5D.pdf PDF fulltext The black magpies, formerly believed to be related to jays, are classified as treepies. Old World ("brown") jays Grey jays American jays In culture Slang The word ''jay'' has an archaic ...
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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 ''distance'' being used to define this matrix may or may not be a metric. If there are elements, this matrix will have size . In graph-theoretic applications the elements are more often referred to as points, nodes or vertices. Non-metric distance matrix In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes. This distance function, while well defined, is not a metric. There need be no restrictions on the weights other than the need to be able to combine and compare them, so negative weights are used in some appli ...
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Error Detection And Correction
In information theory and coding theory with applications in computer science and telecommunication, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Definitions ''Error detection'' is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. ''Error correction'' is the detection of errors and reconstruction of the original, error-free data. History In classical antiquity, copyists of the Hebrew Bible were paid for their work according to the number of stichs (lines of verse). As the prose books of the Bible were hardly ever ...
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