wo bits. To operate in real time, the two bits that come out must Source coder Modulator Information signal s(t)= -Acos(wit) +Acos(wt -Acos(wt) s(t) = -Acos((ccc))r(t) + Acos (Wct)r(t-T)-Acos(Wct)r(t-2T) f--(1/T) +(1/T) BW = 2/T Figure 8.2(a) System without channel coder Trellis-Coded Modulation (TCM): The Wisdom of Modulator and Coder Togetherness fit (in time) into the same amount of time that the incoming one bit fits into-so each bit output from the channel coder is of width T/2. See Figure 8.2(b) to get a clearer picture of this. Finally, the bits that leave the convolutional coder are passed through the modulator, and each 0 and 1 are mapped to the signal as shown by the BPSK modulator of Figure 8.2(b). This figure also shows the output of the BPSK modulator in the frequency do- main. As you can see, this signal has a bandwidth (null-to-null bandwidth) of BW = 4/T. If we briefly compare the case of a system with a channel coder and the case of a system without one-Figure 8.2(b) VS. Figure 8.2(a)-you can see one clear differ- ence: you benefit from a channel coder because it corrects errors, but when you use channel coder you pay the price of sending signals that require a larger bandwidth. One day, a fellow named Ungerboeck said to himself, "There must be some way to get the benefit of a channel coder without the cost of increased bandwidth." He Convolutional Source coder Channel Modulator Coder Informational signal s(t)= -Acos(wt) -Acos(wit) -Acos(wt) Acos(wit) f--(2/T) f fc+(2/T) BW = 4/T Figure 8.2(b) System with channel coder Chapter Eight came up with the idea shown in Figure 8.3. First, comparing Figure 8.3 to Figure 8.2(b) shows us that these two figures are very closely related. In fact, the only differ- ence is that the system of Figure 8.3 uses a QPSK modulator, while the system of Figure 8.2(b) uses BPSK. Let's see what difference this makes. First, the transmitter uses the same source coder to map the information to bits of duration T. Then, a channel coder is used, which for every one bit that 