Convolutional Coder The following rate $\frac{1}{2}$ convolutional coder is given.

Assume throughout that all registers of the encoder are initially set to zero. Further, zeros will be transmitted after the information sequence to ensure that all registers will contain zeros at the end of the encoding.

1. How would this encoder be tabulated in literature on convolutional coding?
2. Assume the following information sequence, including trailing zeros for resetting the encoder, is to be transmitted
   
   $$\underline{i} = \{1 0 1 1 0 0\}.$$
   
   
   Find the encoded bits $\underline{v}$.
   Hint: There should be 12 coded bits.
3. Now, assume the following sequence of bits is received
   
   $$\underline{v} = \{1 1 1 0 1 0 1 0 0 1 1 1\}.$$
   
   
   Find the most likely information sequence for this observation.
4. How many (uncoded) bit errors have occurred during transmission?
5. Illustrate your result in a suitably chosen trellis diagram.