Chapter 4Information-Theoretic Elements

Information theory provides us with fundamental limits on the transmission rates supported by a channel. In this chapter, we analyze these limits for the coded modulation (CM) schemes presented in Chapter 2, paying special attention to bit-interleaved coded modulation (BICM).

This chapter is structured as follows. In Section 4.1, we introduce the concepts of mutual information (MI) and channel capacity; in Section 4.2, we study the maximum transmission rates for general CM systems; and in Section 4.3, for BICM systems. We review their relation and we analyze how they are affected by the choice of the (discrete) constellation. We pay special attention to the selection of the binary labeling and use of probabilistic shaping in BICM. We conclude the chapter by showing in Section 4.5 ready-to-use numerical quadrature formulas to efficiently compute MIs.

4.1 Mutual Information and Channel Capacity

We analyze the transmission model defined by (2.27), i.e., c04-math-0001, where c04-math-0002 is an c04-math-0003-dimensional zero-mean Gaussian vector with covariance matrix c04-math-0004. In this chapter, ...

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