-PSK constellation Chapter Eight Next, separate these points, by putting half on the left and half on the right- making sure you separate them SO that every point has a new neighbor, and SO that each point in a new set of points is as far away as possible from its new neighbors. You can see this in the second drawing of Figure 8.7. Then, take these points and split them again, just as you split the first set. You can see this in the third drawing of Figure 8.7. Do this again, and again, until all that's left is a set of single points, just as on the bottom picture of Figure 8.7. At this point you might think that Ungerboeck had given up engineering alto- gether and taken an unusual interest in modern art, but fear not, he had good engineering intentions. Next, he said, you build a modulator with this cool-looking picture, where at the bottom of the picture are single points (representing output modulation signals). You match the bits coming into the modulator to the output modulation signals shown at the bottom of the picture in Figure 8.7, using the trellis diagram. Ungerboeck came up with just two rules: (1) All parallel transitions (transitions that start and end at the same node) are separated by the maximum possible distance; and (2) All transitions diverging from or merging to a single node are assigned the next maximum distance. It's hard to explain these time O time 1 rules in general, SO let's go to our example, where they will make sense. Take a look at Figure 8.8. Look first at the top branches. There are two branches starting at node 0 and ending at node 0- these are called parallel branches. Ungerboeck said in rule (1) that these branches should be as- signed points that are as far apart as possible. Looking at Figure 8.7, I will assign one branch point 4 and the other branch point 0. You can see this in Figure 8.8, marked (a). You can also see that our selection tells us that modulator input bits (000) are mapped by the modulator to point 0, and (1 0 0) is mapped by the modulator to Figure 8.8 Assig