Low-density parity-check (LDPC) codes are part of many special codes, such as Gallager codes, IRA codes, Systematic codes, Turbo codes, Tornado codes, Online codes, Fountain codes, LT codes, and Raptor codes. The remaining part of the book is devoted to these codes and related topics. The following LDPC codes are discussed in this chapter:

(i) Gallager codes. They encompass all codes represented with Tanner graphs (with two types of nodes: c-nodes and p-nodes) and nonsymmetric codes, and require matrix operations for encoding and decoding.