In binary modulation all the bits receive the same “treatment” when transmitted over the channel, i.e., the L-values have the same conditional probability density function (PDF). The error probability is also the same for all bits, i.e., each bit is equally “protected” against errors. High-order modulations, on the other hand, introduce unequal error protection (UEP). This is an inherent property of bit-interleaved coded modulation (BICM) and depends on the labeling and the form of the constellation. While previously we considered the use of quasi-random interleavers (which average out the UEP), in this chapter we want to take advantage of the UEP. To this end, we propose to design interleavers for BICM, which requires the analytical tools developed in the previous chapters to be refined.
This chapter is organized as follows. In Section 8.1 we introduce the idea of UEP and study a particular interleaver that takes into account the presence of the UEP: the so-called multiple-input interleaver (M-interleaver). In Section 8.1.1 we study the performance of BICM with M-interleavers generalizing the results from Chapter 6. In Section 8.1.1 we also study the problem of a joint interleaver and code design for such BICM transceivers.
8.1 UEP in BICM and M-interleavers
UEP may be easily explained using the communication-theoretic tools of Chapter 6 or the information-theoretic tools of Chapter 4. Let us revisit these concepts through a simple example.