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The code rate of a convolutional code is commonly modified via symbol puncturing. For example, a convolutional code with a 'mother' code rate / = / may be punctured to a higher rate of, for example, / simply by not transmitting a portion of code symbols. The performance of a punctured convolutional code generally scales well with the amount of ...
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 is most often used for decoding convolutional codes with constraint lengths k≤3, but values up to k=15 are used in practice.
An example of a convolutional interleaver An example of a deinterleaver Efficiency of cross interleaver ( γ {\displaystyle \gamma } ): It is found by taking the ratio of burst length where decoder may fail to the interleaver memory.
Linear block codes; Convolutional codes; It analyzes the following three properties of a code – mainly: [citation needed] Code word length; Total number of valid code words; The minimum distance between two valid code words, using mainly the Hamming distance, sometimes also other distances like the Lee distance
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]
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.
Turbo codes, as described first in 1993, implemented a parallel concatenation of two convolutional codes, with an interleaver between the two codes and an iterative decoder that passes information forth and back between the codes. [6] This design has a better performance than any previously conceived concatenated codes.
A convolutional code that is terminated is also a 'block code' in that it encodes a block of input data, but the block size of a convolutional code is generally arbitrary, while block codes have a fixed size dictated by their algebraic characteristics. Types of termination for convolutional codes include "tail-biting" and "bit-flushing".