In this chapter we cover some of the more common applications of LDPC codes. The breadth and depth of work reported in the literature on the application of LDPC codes to data transmission and storage would fill many volumes. Thus, this chapter has the modest goal of introducing selected applications. These applications include coded modulation, turbo equalization and code design for intersymbol-interference channels, estimation of the level LDPC error floors, and decoder design for low error floors. We also provide in this chapter a brief introduction to LDPC convolutional codes. Because of their importance, we also include a section on so-called digital fountain codes, which have application to file transfer over networks and closely resemble LDPC codes.

LDPC-Coded Modulation

Trellis-coded modulation, multilevel coding, and bit-interleaved coded modulation (BICM), are all well-known bandwidth- and power-efficient coded-modulation schemes. More recently, turbo and LDPC codes have been combined with higher-order modulation schemes. For example, LDPC codes have been designed for multilevel coding in [6] and for MIMO channels in [7]. Near-capacity performance has been demonstrated in these higher-order signaling systems. The system under study is shown in Figure 15.1. We do not consider the multilevel coding format because it is shown in [8] and elsewhere that the single-code format of Figure 15.1 is superior for LDPC codes. Although this is a BICM-like system, because an LDPC encoder is employed, a bit interleaver is not necessary here. An interleaver would be equivalent to permuting the columns in the code's parity-check matrix.