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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 ...
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 ...
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.
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.
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%.
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
For example, for each bit, the front end of a traditional wireless-receiver has to decide if an internal analog voltage is above or below a given threshold voltage level. For a turbo code decoder, the front end would provide an integer measure of how far the internal voltage is from the given threshold.