Editing Coding theory (section)

====Convolutional codes====
{{Main|Convolutional code}}

The idea behind a convolutional code 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 the output of a system, when you know the input and impulse response.

So we generally find the output of the system convolutional encoder, which is the convolution of the input bit, against the states of the convolution encoder, registers.

Fundamentally, convolutional codes do not offer more protection against noise than an equivalent 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 gate]]s. The [[Decoding methods|decoder]] 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 been found to give good results in low noise environments.

Convolutional codes are used in voiceband modems (V.32, V.17, V.34) and in GSM mobile phones, as well as satellite and military communication devices.