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The Viterbi algorithm is named after Andrew Viterbi, who proposed it in 1967 as a decoding algorithm for convolutional codes over noisy digital communication links. [2] It has, however, a history of multiple invention, with at least seven independent discoveries, including those by Viterbi, Needleman and Wunsch, and Wagner and Fischer. [3]
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 ...
Iterative Viterbi decoding is an algorithm that spots the subsequence S of an observation O = {o 1, ..., o n} 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 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 .
The code rate of a convolutional code is commonly modified via symbol puncturing. For example, a convolutional code with a 'mother' code rate / = / may be punctured to a higher rate of, for example, / simply by not transmitting a portion of code symbols. The performance of a punctured convolutional code generally scales well with the amount of ...
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 ...
This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are thousands of such problems known, this list is in no way comprehensive. Many problems of this type can be found in Garey & Johnson (1979).