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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 ...
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 ...
Both Viterbi and sequential decoding algorithms return hard decisions: the bits that form the most likely codeword. An approximate confidence measure can be added to each bit by use of the Soft output Viterbi algorithm. Maximum a posteriori (MAP) soft decisions for each bit can be obtained by use of the BCJR algorithm.
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.
The maximum likelihood decoding algorithm is an instance of the "marginalize a product function" problem which is solved by applying the generalized distributive law. [ 2 ] Minimum distance decoding
Here is an example of transmitted digital code. 1 0 1 0 1 The following, distorted signal is received. 1 1 0 1 0 The VBER is determined by dividing the number of incorrectly received digits, or bits, (in this case 4), by the total number of bits received. So, in this case, the VBER is equal to 4/5 which equals 0.8, or 80%.
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 ...
Complexity of Forward Algorithm is (), where is the number of hidden or latent variables, like weather in the example above, and is the length of the sequence of the observed variable. This is clear reduction from the adhoc method of exploring all the possible states with a complexity of Θ ( n m n ) {\displaystyle \Theta (nm^{n})} .