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Viterbi path and Viterbi algorithm have become standard terms for the application of dynamic programming algorithms to maximization problems involving probabilities. [3] For example, in statistical parsing a dynamic programming algorithm can be used to discover the single most likely context-free derivation (parse) of a string, which is ...
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 Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has been encoded using a convolutional code or trellis code. There are other algorithms for decoding a convolutionally encoded stream (for example, the Fano algorithm). The Viterbi algorithm is the most resource-consuming, but it does the maximum likelihood decoding. It ...
Furthermore, a variant of the Baum–Welch algorithm, which is used for training HMMs, can be used to estimate parameters when training data has incomplete or missing labels. [2] The optimal state sequence , …, can be found using a very similar Viterbi algorithm to the one used for HMMs. The dynamic program uses the forward probability:
The maximum likelihood decoding problem can also be modeled as an integer programming problem. [ 1 ] The maximum likelihood decoding algorithm is an instance of the "marginalize a product function" problem which is solved by applying the generalized distributive law .
In contrast, convolutional codes are typically decoded using soft-decision algorithms like the Viterbi, MAP or BCJR algorithms, which process (discretized) analog signals, and which allow for much higher error-correction performance than hard-decision decoding. Nearly all classical block codes apply the algebraic properties of finite fields ...
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
To convolutionally encode data, start with k memory registers, each holding one input bit.Unless otherwise specified, all memory registers start with a value of 0. The encoder has n modulo-2 adders (a modulo 2 adder can be implemented with a single Boolean XOR gate, where the logic is: 0+0 = 0, 0+1 = 1, 1+0 = 1, 1+1 = 0), and n generator polynomials — one for each adder (see figure below).