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The vector representation of a convolutional code is g1=[1 1]and g2=[1 0]. If the received sequence is 11 11 01 10, please use Viterbi Algorithm to decode it. Please show the full trellis diagram, including the updated trellis state metrics?
Ron don
The vector representation of a convolutional code is g1=[1 1] and g2=[1 0]. If the received sequence is 11 11 01 10, we can use Viterbi Algorithm to decode it. The full trellis diagram, including the updated trellis state metrics, is shown below:
Time t1:
State 0 (00): Metric = 0
State 1 (10): Metric = 0
Time t2:
State 0 (00): Metric = 0 + (1-1)^2 + (1-1)^2 = 0
State 1 (10): Metric = 0 + (1-1)^2 + (1-0)^2 = 1
Time t3:
State 0 (00): Metric = 0 + (1-1)^2 + (1-1)^2 = 0
State 1 (10): Metric = 1 + (1-1)^2 + (1-0)^2 = 2
State 0 (01): Metric = 0 + (1-1)^2 + (0-1)^2 = 1
State 1 (11): Metric = 0 + (1-1)^2 + (0-0)^2 = 0
Time t4:
State 0 (00): Metric = 0 + (1-1)^2 + (1-1)^2 = 0
State 1 (10): Metric = 2 + (1-1)^2 + (1-0)^2 = 3
State 0 (01): Metric = 1 + (1-1)^2 + (0-1)^2 = 2
State 1 (11): Metric = 0 + (1-1)^2 + (0-0)^2 = 0
Therefore, the decoded sequence is 11 11 01 10.
David Denton
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