other. This is shown in Figure 8.15(a). Then, we start by examining the top node at Chapter Eight r1 = (1.1,0.1) time O time 1 so=(1,0) S4=(-1,0) node under consideration = node O (time 1) Best: S.=(0,1) best parent node = node O (time 0) So=(0,-1) branch = top branch Lowest total = 0.02 Figure 8.15 Using the VA to move from time 0 to time 1 through trellis Trellis-Coded Modulation (TCM): The Wisdom of Modulator and Coder Togetherness time 1 Node 0 (time 0), top Node 3 (time 0), top 22 0.5 Node 1 (time 0), top Node 2 (time 0), top 22 0.02 Figure 8.15 (continued) Using the VA to move from time 0 to time 1 through trellis time 1, which you can see in Figure 8.15(b). For this node, there are two possible parent nodes, node 0 at time 0 and node 1 at time 0. Each node comes with two pos- sible branches, a top branch and a bottom branch. We are going to decide which is the best parent node and the best branch for node 0 (time 1), like this: 1. If we started at node 0 (time 0) and moved to node 0 (time 1) using the top branch, the first output symbol would be (1, 0). Comparing this to r where the first symbol is (1.1, 0.1), we say "d1 = (1.1-1 1)2 + (0.1-0)2 = 0.02 distance if parent is node 0 (time 0), top branch." We add this 0.02 to the 0 number that we gave node 0 (time 0) in Figure 8.15(a), for a grand total of 0.02. 2. If we started at node 0 (time 0) and moved to node 0 (time 1) using the bottom branch, the first output symbol S1 would be (-1, 0). Comparing this to r where the first symbol is (1.1, 0.1), we say "d2 = (1.1- (- 1))2 + (0.1-0)2 = 4.85 distance if parent is node 0 (time 0), bottom branch." We add this 4.85 to the 0 number that we gave node 0 (time 0) in Figure 8.15(a), for a grand total of 4.85. Chapter Eight 3. If we started at node 1 (time 0) and moved to node 0 (time 1) using the top branch, the first output symbol S1 would be (0, 1). Comparing this to r where the first output symbol is (1.1, 0.1), we say "d = (1.1 - 0)2 + (0.1 - 1)² = 2.02 distance parent is node 1 (time 0), top branch." We add t