Low‐Density Parity‐Check Codes: Design and Decoding

In this chapter, we treat code design and decoding for a family of error correction codes known as low-density parity-check (LDPC) codes. The chapter begins with an introduction to error correction in telecommunications with the focus on parity-check equations and codes defined by their parity-check matrices. To introduce the concepts behind iterative decoding, a hard-decision iterative algorithm is discussed before the soft-decision sum-product decoding algorithm is presented. Following sections focus on the relationship of graph-based representations of codes to the development of both the theoretical understanding and implementation of iterative decoders, and current methods for design of LDPC codes. The chapter concludes with the connections of LDPC codes and their decoding to other topics and likely future directions in the area. Keywords: low-density parity-check codes; error correction; iterative decoding; sum-product algorithm; min-sum algorithm; a posteriori decoding; Tanner graph; factor graph; graphical models; soft-decision decoding; message-passing decoders

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