Question

Briefly explain the operation of the Viterbi algorithm for convolutional codes. What are the advantages and disadvantages of this method compared to the sequential decoding algorithm? Consider a convolutional encoder defined by the following generator polynomials: $g_1(D) = D \oplus D^2$, $g_2(D) = 1 \oplus D$, $g_3(D) = 1 \oplus D \oplus D^2$. (i) Draw the encoder, the state transition diagram and the trellis diagram to a branch depth of 6. (ii) Determine the output sequence for the input sequence 010110 and show this on the trellis diagram. (iii) Determine how many errors this code will correct. (iv) Apply the Viterbi decoding method to the codeword sequence 110001011. Write down the path metrics for each state. Explain which paths would be selected to be survivors.

          Briefly explain the operation of the Viterbi algorithm for convolutional
codes. What are the advantages and disadvantages of this method
compared to the sequential decoding algorithm?
Consider a convolutional encoder defined by the following generator
polynomials: $g_1(D) = D \oplus D^2$, $g_2(D) = 1 \oplus D$, $g_3(D) = 1 \oplus D \oplus D^2$.
(i) Draw the encoder, the state transition diagram and the trellis
diagram to a branch depth of 6.
(ii) Determine the output sequence for the input sequence 010110
and show this on the trellis diagram.
(iii) Determine how many errors this code will correct.
(iv) Apply the Viterbi decoding method to the codeword sequence
110001011. Write down the path metrics for each state. Explain
which paths would be selected to be survivors.

Briefly explain the operation of the Viterbi algorithm for convolutional
codes. What are the advantages and disadvantages of this method
compared to the sequential decoding algorithm?
Consider a convolutional encoder defined by the following generator
polynomials: g1(D) = D ⊕ D^2, g2(D) = 1 ⊕ D, g3(D) = 1 ⊕ D ⊕ D^2.
(i) Draw the encoder, the state transition diagram and the trellis
diagram to a branch depth of 6.
(ii) Determine the output sequence for the input sequence 010110
and show this on the trellis diagram.
(iii) Determine how many errors this code will correct.
(iv) Apply the Viterbi decoding method to the codeword sequence
110001011. Write down the path metrics for each state. Explain
which paths would be selected to be survivors.

Added by Alba G.

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