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=== Convolution Codes ===
Convolutional codes are used in voiceband modems (V.32, V.17, V.34) and in GSM mobile phones.
additionaly they have widespread use in satellite and military use.
Here the idea is to make every codeword symbol, be the weighted sum of the various, input message
symbols. This is like [[Convolution]] used in [[Linear Time Invariant | LTI]] systems to find
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of the input bit, against the states of the convolution encoder, registers.
Fundementally, convolutional codes do not offer more protection against noise than an
equivelent block code. In many cases, they generally offer greater simplicity of
implementation over a block code of equal power. The encoder is usually a simple
circuit which has state memory and some feedback logic, normally XOR gates. The decoder
The [[viterbi algorithm]] is used to decode convolutional codes.▼
can be implemented in software or firmware
▲The [[viterbi algorithm]] is the optimum algorithm used to decode convolutional codes.
There are simplifications to reduce the computational load. They rely on searching only
the most likely paths. Although not optimum, they have generally found to give good results
in the lower noise environments. Moderm microprocessors are capable of implementing these reduced
search algorithims at rate greater than 4000 codewords/s.
== Applications of Coding Theory ==
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