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A convolutional encoder is a finite state machine. An encoder with n binary cells will have 2 n states. Imagine that the encoder (shown on Img.1, above) has '1' in the left memory cell (m 0), and '0' in the right one (m −1). (m 1 is not really a memory cell because it represents a current value). We will designate such a state as "10".
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 ...
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).
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.
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]
The example encoder is composed of a 16-state outer convolutional code and a 2-state inner convolutional code linked by an interleaver. The natural code rate of the configuration shown is 1/4, however, the inner and/or outer codes may be punctured to achieve higher code rates as needed.
Under this definition codes such as turbo codes, terminated convolutional codes and other iteratively decodable codes (turbo-like codes) would also be considered block codes. A non-terminated convolutional encoder would be an example of a non-block (unframed) code, which has memory and is instead classified as a tree code.
The computational complexity of NPDs is determined by the parameterization of the neural networks, unlike successive cancellation (SC) trellis decoders, [15] whose complexity is determined by the channel model and are typically used for finite-state channels (FSCs).