Convolutional
Code
A
convolutional code is generated by passing the information sequence to be
transmitted through the linear finite–state shift register . in general , the
shift register consist of K (k
bit) stage and n linear algebraic function generator as shown figure 2 . the
input data to the encoder which is assumed to be binary , is shifted into and along the shift register k bits at a time. The number of
output bits for each k-bit input sequence is n bits. Consequently , the code
rate is defined as Rc = k\n,
consistent with the definition of the code rate for a block code . the
parameter K is called the Constraint length of the convolutional code
One method for describing a convolutional code is to give its generator
matrix, just as we did for block code. In general , the generator matrix for a
convulsional code is semi-infinite since the input sequence is semi-infinite in
length . As alternative to specifying the generator matrix , we shall use a
functionality equivalent representation in which we specify a set of n vectors. One vector for each of the n modulo-2 adders. Each vector has ( K*k ) dimensions and
contains the connections of the encoder to that modulo-2 adder. A 1 in the
ith position of the vector indicate
that the corresponding stage in the
shift register is connected to the
modulo-2 adder and a 0in a given position indicates that no connection exists
between that stage and the modulo-2 adder