ommunication system with all the parts that we have drawn for it SO far. The source coder turns the information to bits; the channel coder adds extra (redundant) bits to help the receiver correct bit errors; and the modulator turns bits into signals ready to be sent over the channel. After traveling the length of the channel, a noisy signal arrives at the demodulator. The demodulator returns the signal to bits, the channel decoder corrects the bit errors, and the source decoder returns the bits to the original analog information. In trellis-coded modulation, or TCM for short, the idea is to consider some things together. Specifically, at the transmitter side, there is a thoughtful matching of the modulator to the channel coder. At the receiver side, the operation of the modulator and the channel decoder are actually combined. Let's look at why this is done and then at how it all works. Source coder Channel coder Modulator Information signal TCM considers this together channel r(t) = s(t) + n(t) Source decoder Channel decoder Demodulator TCM combines this Figure 8.1 The digital communication system (showing where TCM comes in) Chapter Eight 8.1 The Idea Consider the transmitter side of a communication system, which consists of a source coder, a channel coder, and a modulator. First, imagine that the channel coder is gone, and we have the transmitter shown in Figure 8.2(a). We have a source coder output- ting bits with a bit duration of T (a bit rate of R = 1/T), and a BPSK modulator which, for each bit (0 or 1) that comes in, outputs a signal as shown in Figure 8.2(a). Figure 8.2(a) also shows the signals output by the modulator in the frequency domain. From this figure, we can see that the output signals have a bandwidth (null-to-null) of BW = 2/T. Now, let's consider the transmission system with the channel coder back in place, as shown in Figure 8.2(b). Here, the source coder maps the information into bits duration T. The convolutional channel coder takes these bits, and for each bit that comes in it puts out t