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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).
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.
Trellis coded modulation (TCM) is a modulation scheme that transmits information with high efficiency over band-limited channels such as telephone lines. Gottfried Ungerboeck invented trellis modulation while working for IBM in the 1970s, and first described it in a conference paper in 1976. It went largely unnoticed, however, until he ...
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 ...
The random variable x(t) is the hidden state at time t (with the model from the above diagram, x(t) ∈ { x 1, x 2, x 3}). The random variable y(t) is the observation at time t (with y(t) ∈ { y 1, y 2, y 3, y 4}). The arrows in the diagram (often called a trellis diagram) denote conditional dependencies.
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.
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