For the 2 1 2 convolutional code shown in the below figure a

For the (2, 1, 2) convolutional code shown in the below figure: (a) What are the code rate and constraint length of the code? (b) What are the generator polynomials of the code?. (c) Design the state diagram of the code. (d) Sketch the trellis diagram of the code for the input sequence 11011001 and zero initial conditions. (e) Find the output of the encoder for the input sequence 11011001 and zero initial conditions.

Solution

Ans: here we are dicussing about convolutional code.

covolutional code:

a) constraint lenth of the code:

n=# of ouput bits

k=# of input bits

m=# of memory registers

constrain length = k(m-1)

for e.g (2,1,4) memory register=4, constrain length 1(4-1)=3. That means # of state required for output is 2cap 3=8. for the all other examples listed in this file, constraint length works out as described by k(m-1).

b) polynomial code:

Definition:

c) state diagram:

d) Trellis code:

e) initial condition: