Convolutional code: Difference between revisions

Revision as of 13:55, 30 April 2006

Revision as of 16:40, 30 April 2006

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A convolutional encoder is called so because it performs a ''convolution'' of the input stream with encoder's ''impulse responses'':

<center><math>y_i^j=\sum_{k=0}^{+\infty} h(k)x(^j_k x_{i-k).},</math></center>

where <math>x</math> is an input sequence, <math>y^j</math> is a sequence from output <math>j</math> and <math>h^j</math> is an impulse response for output <math>j</math>.

A convolutional encoder is a discrete [[LTI system|linear time-invariant system]]. Every output of an encoder can be described by its own [[transfer function]], which is closely related to a generator polynomial. An impulse response is connected with a transfer function through [[Z-transform]].