12.3 Find the integer metric table for the DMC of Figure 12.3 when c1 = 1 and c2 = 10. Use the Viterbi algorithm to decode the received sequence r of Example 12.1 with this integer metric table and the treilis diagram of Figure 12.1. Compare your answer with the result of Example 12.1. EXAMPLE 12.1 Output DMC The Viterbi Algorithm for a Binary-Input, Quaternary Consider the binary-input, quaternary-output (Q 4) DMC shown in Figure 12.3. Using logarithms to the base 10, we display the bit metrics for this channel in a metric table in Figure 12.4(a). Choosing cl = 1 and c2 = 17.3, we obtain the integer metric table shown in Figure 12.4(b). Now, assume that a codeword from the trellis 0.3 0.3 FIGURE 12.3: A binary-input, quaternary-output DMC. 0102 0.4-0.52-0.7 1.00.7 01 02 12 11 0 10850 05810 12 Ul ul 0 1.0 0.52-0.4 FIGURE 12.4: Metric tables for the channel of Figure 12.3. diagram of Figure 12.1 is transmitted over the DMC of Figure 12.3 and that the quaternary received sequence is given by diagram of Figure 12.1 is transmitted over the DMC of Figure 12.3 and that the quaternary received sequence is given by (12.7) The application of the Viterbi algorithm to this received sequence is shown in Figure 12.5. The numbers above each state represent the metric of the survivor for that state, and the paths eliminated at each state are shown crossed out on the trellis diagram. The final survivor, (111, 010, 110, 011, 000, 000, 000) (12.8) is shown as the highlighted path. This surviving path corresponds to the decoded information sequence (11000). Note that the final m2 branches in any trellis 9 3x so 3 36 5( S, 12.3 Find the integer metric table for the DMC of Figure 12.3 when c1 = 1 and c2 = 10. Use the Viterbi algorithm to decode the received sequence r of Example 12.1 with this integer metric table and the treilis diagram of Figure 12.1. Compare your answer with the result of Example 12.1. EXAMPLE 12.1 Output DMC The Viterbi Algorithm for a Binary-Input, Quaternary Consider the binary-input, quaternary-output (Q 4) DMC shown in Figure 12.3. Using logarithms to the base 10, we display the bit metrics for this channel in a metric table in Figure 12.4(a). Choosing cl = 1 and c2 = 17.3, we obtain the integer metric table shown in Figure 12.4(b). Now, assume that a codeword from the trellis 0.3 0.3 FIGURE 12.3: A binary-input, quaternary-output DMC. 0102 0.4-0.52-0.7 1.00.7 01 02 12 11 0 10850 05810 12 Ul ul 0 1.0 0.52-0.4 FIGURE 12.4: Metric tables for the channel of Figure 12.3. diagram of Figure 12.1 is transmitted over the DMC of Figure 12.3 and that the quaternary received sequence is given by diagram of Figure 12.1 is transmitted over the DMC of Figure 12.3 and that the quaternary received sequence is given by (12.7) The application of the Viterbi algorithm to this received sequence is shown in Figure 12.5. The numbers above each state represent the metric of the survivor for that state, and the paths eliminated at each state are shown crossed out on the trellis diagram. The final survivor, (111, 010, 110, 011, 000, 000, 000) (12.8) is shown as the highlighted path. This surviving path corresponds to the decoded information sequence (11000). Note that the final m2 branches in any trellis 9 3x so 3 36 5( S
