Q7) A convolution encoder has a 2-stage shift register, three modulo-2 adders, and an output multiplexer. The generator sequences of the encoder are as follows:
$g^{(1)} = (1,0,1)$;
$g^{(2)} = (1,1,0)$;
$g^{(3)} = (1,1,1)$.
(a) Draw the block diagram of the encoder.
(4 marks)
(b) Obtain the state and trellis diagrams for the above convolution code
(10 marks)
(c) Consider a convolution encoder with the state table as shown on the next page.
Current Input Next Output
state state
$S_0$ (00) 0 $S_0$ 00
1 $S_2$ 11
$S_1$ (01) 0 $S_0$ 11
1 $S_2$ 00
$S_2$ (10) 0 $S_1$ 10
1 $S_3$ 01
$S_3$ (11) 0 $S_1$ 01
1 $S_3$ 10
Compute the code-word corresponding to the message sequence 101110111001.
