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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). Trellises are used in encoders and ...
Convolutional code. In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'.
Small multiple. A small multiple (sometimes called trellis chart, lattice chart, grid chart, or panel chart) is a series of similar graphs or charts using the same scale and axes, allowing them to be easily compared. It uses multiple views to show different partitions of a dataset. The term was popularized by Edward Tufte. According to Tufte,
Viterbi decoder. 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 ...
In geomorphology, drainage systems, also known as river systems, are the patterns formed by the streams, rivers, and lakes in a particular drainage basin. They are governed by the topography of land, whether a particular region is dominated by hard or soft rocks, and the gradient of the land. Geomorphologists and hydrologists often view streams ...
e. 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 ...
Viterbi algorithm. The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path —that results in a sequence of observed events.
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.
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