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?

Answer 1

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.