Low-Density Parity-Check Codes

Low-density parity-check (LDPC) codes can rightfully take their stand next to turbo codes as the most powerful and most popular error control codes known. They offer a performance spectacularly close to theoretical limits when decoded using iterative soft decision algorithms. This chapter explores the properties and structure of low-density parity-check codes. It begins with the fundamental construction of regular LDPC codes and their representation as bipartite graphs. The graphical representation of LDPC codes then leads to the notion of irregular LDPC codes, which have been used to improve performance, and to the density evolution analysis technique, which predicts the performance of these codes.