Bit-Interleaved Coded Modulation: Fundamentals, Analysis and Design

Chapter 3Decoding

As explained in Chapter 2, the information bits that were mapped onto the codewords need to be correctly recovered at the receiver. This is the very essence of data transmission, where the role of the receiver is to “decode” the information bits contained in the received signals.

This chapter studies different decoding strategies and is organized as follows. The optimal maximum a posteriori (MAP) and maximum likelihood (ML) decoding strategies are introduced in Section 3.1 where we also introduce the L-values which become a key element used throughout this book. The bit-interleaved coded modulation (BICM) decoder is defined in Section 3.2. In Section 3.3, some important properties of L-values are discussed and we conclude with a discussion about hard-decision decoding in Section 3.4.

3.1 Optimal Decoding

In this section, we review well-known decoding rules. They will be compared in Section 3.2 to the BICM decoding rule, which will be based on the L-values which we will define shortly.

Definition 3.1 (MAP Decoding)

The MAP decoding rule is defined as

3.1

3.2

where is the set of symbol sequences (codewords) defined in Section 2.2.

The logarithm is used in ...