Error Control Coding

Abstract

In this chapter, we discuss a number of codes for error control. Only block codes are treated here. Discussion on convolutional codes will be deferred until next chapter. After reviewing some information theoretic foundations of coding in the first section, linear block codes are treated in Section 3.2. The concepts of parity-check and generator matrices to represent linear block codes are discussed. Several examples of block codes are given, including the important class of Hamming codes. Principles behind syndrome decoding and decoding using a standard array are treated in Section 3.3. Section 3.4 provides some useful bounds on coding and introduces the concept of coding gain. Section 3.5 discusses the principles behind cyclic codes. Some important decoding techniques for these codes are treated in Section 3.6. These include the Meggitt and error-trapping decoders. After introducing some algebra in Section 3.7, in the next three sections that follow, we treat the most important and practical of all cyclic codes, the Bose-Chaudhuri-Hocquenghem (BCH) codes and Reed-Solomon codes. The treatment includes the MasseyBerlekamp algorithm for decoding these codes. In Section 3.11, we turn to coding for burst error control, which has been successfully applied to storage media such as magnetic tapes and compact disc. Automatic-repeat-request (ARQ) schemes find wide applicability in computer networks and these schemes are treated in the last section.