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This work has been released into the public domain by its author, Qef.This applies worldwide. In some countries this may not be legally possible; if so: Qef grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Convolutional code trellis diagram. A trellis is a graph whose nodes are ordered into vertical slices (time) with every node at almost every time connected to at least one node at an earlier and at least one node at a later time. The earliest and latest times in the trellis have only one node (hence the "almost" in the preceding sentence).
The commonly used rule of thumb of a truncation depth of five times the memory (constraint length K-1) of a convolutional code is accurate only for rate 1/2 codes. For an arbitrary rate, an accurate rule of thumb is 2.5(K - 1)/(1−r) where r is the code rate. [1]
Img.6. A trellis diagram for the encoder on Img.1. A path through the trellis is shown as a red line. The solid lines indicate transitions where a "0" is input and the dashed lines where a "1" is input. An actual encoded sequence can be represented as a path on this graph. One valid path is shown in red as an example.
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]
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The name trellis derives from the fact that a state diagram of the technique closely resembles a trellis lattice. The scheme is basically a convolutional code of rates ( r , r +1). Ungerboeck's unique contribution is to apply the parity check for each symbol , instead of the older technique of applying it to the bit stream then modulating the bits.