Basic Coding Definitions and Some Block Codes
摘要
The chapter introduces basic Channel Coding definitions and properties first limiting the treatment to binary linear block codes. They are defined by the Parity-Check and Generator matrices. These matrices are shown for the single parity check code, the repetition code, the Hamming code, Reed-Muller codes and the binary Golay code. Duality is defined and the Standard Array outlines decoding alternatives either toward the center of a decoding sphere or the coset leader, i.e., the error pattern. As coding bounds, the Singleton and the Hamming (Sphere-Packing) bounds are provided.