3 - Block Codes

Abstract

This chapter focuses on block codes. Cyclic codes—an important class of codes—are used in many systems because they are easy to implement. Because a cyclic code is a linear code, it is decoded by making use of the syndrome. The syndrome polynomial is used for decoding cyclic codes instead of the syndrome vector. Bose, Chaudhuri and Hocquenghem (BCH) codes are one of the most important error-correcting codes. BCH codes are constructed on the basis of the BCH bound. Reed–Solomon codes are a special class of BCH codes. Some codes can be decoded using majority logic circuits, which are relatively easy to implement. The chapter describes the principle of majority logic decoding using an example. The number of parity check equations in the set is called—the orthogonalization number. Interleaving is a method for breaking up a burst into shorter ones and making detection or correction of the burst easier. The chapter describes codes suited to detection and correction of burst errors.