9.1 Introduction

In the previous chapter we have seen how messages are computed in the decoding node in the factor graph of the distribution p( B, Y = y ) (see Fig. 9.1). Now we will deal with the second node, the demapping node, representing the distribution p( A C, ), where C is a sequence of N _c coded bits, and A is a sequence of N _s coded symbols, each belonging to some constellation ? (for instance, 16-QAM). By mapping the coded bits onto a signaling constellation, we can tune the spectral efficiency of the system: the more bits we map onto any constellation point, the fewer complex symbols we need to transmit.

Figure 9.1: A factor graph of p(Y = yB, ). The node is opened to reveal its structure. The node in bold is the topic of this chapter.

While there exists a wide variety of mapping schemes, we will focus on two popular instances: bit-interleaved coded modulation (BICM) and trellis-coded modulation (TCM). The former was first introduced by Zehavi [90] and later analyzed in detail by Caire et al. [91]. It was only with [92, 93, 94] that it was realized that employing BICM at the transmitter naturally leads to an iterative receiver. Trellis-coded modulation, on the other hand, was proposed by Ungerboeck in [95] as a way to combine (convolutional) coding and mapping to obtain a receiver that could...